Transport Phenomena in Food Processing (Food Preservation Technology)

Author: Jorge Welti-Chanes | Jorge F. Velez-Ruiz

431 downloads 2100 Views 8MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!

Report copyright / DMCA form

DOWNLOAD PDF

Transport Phenomena in Food Processing

© 2003 by CRC Press LLC

Library of Congress Cataloging-in-Publication Data Transport phenomena in food processing / edited by Jorge Welti-Chanes, Jorge F. Vélez-Ruiz, Gustavo V. Barbosa-Cánovas p. cm.— (Food preservation technology series) Includes bibliographical references and index. ISBN 1-56676-993-0 (alk. paper) 1. Food—Effect of heat on. 2. Food industry and trade. I. Welti-Chanes, Jorge. II. VélezRuiz, Jorge F. III. Barbosa-Cánovas, Gustavo V. IV. Series. TP371.2.T73 2002 664—dc21

2002073736

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microﬁlming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of speciﬁc clients, may be granted by CRC Press LLC, provided that $.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA. The fee code for users of the Transactional Reporting Service is ISBN 0-8493-0458-0/02/$0.00+$1.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Speciﬁc permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identiﬁcation and explanation, without intent to infringe.

Visit the CRC Press Web site at www.crcpress.com © 2003 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-56676-993-0 Library of Congress Card Number 2002073736 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper

© 2003 by CRC Press LLC

Series Preface Transport phenomena is one of food process engineering’s most important pillars, and this new addition to the CRC Food Preservation Technology Series offers a sound combination of the fundamental and applied aspects of this classic engineering topic. Transport Phenomena in Food Processing plays an important role in the series because it offers the tools for quantifying many important operations, classic or novel, using state-of-the-art calculation approaches. I am particularly impressed with the analytical depth of the chapters and the wide spectrum of covered topics. For me, this is a very inspiring book that hopefully will become a key reference. This book is also important because it is the ﬁrst in the CRC series to cover fundamental aspects of food processing. In short, I anticipate that this book will be in good company with upcoming books in the series on other fundamental aspects of food preservation. Gustavo V. Barbosa-Cánovas

© 2003 by CRC Press LLC

Preface The latest applications of new and improved traditional food preservation processes have generated the need for increased knowledge of the phenomenological and engineering principles that are the basis of the correct application of factors that produce stability and maintain the quality of transformed and processed products. This need for knowledge has given the ﬁeld of food engineering a new identity at both the research and industrial levels. Understanding the transport phenomena that govern the engineering analysis and design of food preservation processes is a key element in improving processing conditions and the employment of energy resources, and to increasing the quality of the product. This book presents the state of the art in the transport phenomena area as applied to food preservation and transformation. It is divided into four sections containing a total of 33 chapters, each written by prestigious scientists from institutions and universities around the world. The ﬁrst section reviews the fundamental concepts of mass, heat, and momentum transfer, while the remaining three sections discuss speciﬁc applications for a large variety of processes and products where the predominant transfer phenomenon is mass or heat, or processes employing more than one transport mechanism. The mass transfer section focuses on phenomena controlling osmotic dehydration and hot-air drying processes. However, the themes related to water transfer in superﬁcial ﬁlms placed on foods, and pre-evaporation, ultrasound, and spinning cone columns are also included. The seven chapters that constitute the heat transfer section study the effects of product shape and process equipment on the phenomenon’s efﬁciency. The chapters in the last section deal with the study of the combination of two or three transfer phenomena in frying, sterilization, and drying processes. We trust this book on transport phenomena will make a meaningful contribution in facilitating the understanding, design, and implementation of food processing unit operations that will result in the production of safer, higher quality, and more convenient foods. Jorge Welti-Chanes Jorge Vélez-Ruiz Gustavo V. Barbosa-Cánovas

© 2003 by CRC Press LLC

About the Editors Jorge Welti-Chanes is a Professor in the Departments of Chemical and Food Engineering and of Chemistry and Biology at the Universidad de las Americas– Puebla in Mexico. He earned his B.S. degree in Biochemical Engineering and his M.S. in Food Engineering from the ITESM, Mexico and his Ph.D. from the Universidad de Valencia, Spain. Dr. Welti-Chanes was president of the International Association of Engineering and Food and is a member of the editorial boards of ﬁve international journals. He is the author and co-author of more than 80 scientiﬁc papers and the editor of ﬁve books with the food technology, water activity, drying, emerging technologies, and minimal processing areas. Dr. Jorge F. Vélez-Ruiz was born in Puebla City, Mexico. He received a B.S. in Biochemical Engineering in 1977 and an M.S. in Food Science in 1981, both from the Instituto Tecnológico y de Estudios Superiores de Monterrey (ITESM), Mexico, and a Ph.D. in Food Engineering from Washington State University, Pullman in 1993. He began his professional career working in the food industry and in 1979 joined the Food Science Department, ITESM. Since 1980, he has been with the Department of Chemical and Food Engineering, University of the Américas, Puebla (UDLA,P), serving as chairman from 1987 to 1990. In 1990, he was recognized as Food Engineering Researcher by the National System of Researchers in Mexico and in 1999 was named titular professor. Dr. Vélez-Ruiz’s research activities are focused on rheology of foods; dairy products and milk processing; evaporation and dehydration of ﬂuid foods; osmotic concentration of fruits; heat and mass transfer through the frying process; and physical properties of foods. He is the author of approximately 45 scientiﬁc publications in international journals, more than 90 presentations at national and international professional meetings, and three book chapters, and he is an editor of three food science and engineering journals. Gustavo V. Barbosa-Cánovas earned his B.S. in Mechanical Engineering at the University of Uruguay and his M.S. and Ph.D. in Food Engineering at the University of Massachusetts–Amherst. He then worked as an Assistant Professor at the University of Puerto Rico from 1985–1990. Next, he went to Washington State University (WSU), where he is now a Professor of Food Engineering and Director of the Center for Nonthermal Processing of Food (CNPF). His current research areas are nonthermal processing of foods, physical properties of foods, and food powder technology.

© 2003 by CRC Press LLC

Acknowledgments The editors would like to acknowledge each one of the researchers who kindly agreed to participate in this project with their contributions. The support of the Universidad de las Américas, Puebla, of Washington State University, and of Texas Christian University is also acknowledged. For the manuscript’s revision and correction process, the editors counted on the valuable work of M.S. Reyna León and M.S. Daniela Bermúdez, who were supported by Ing. Luz del Carmen López, to help the complete book. We express our gratitude to them.

© 2003 by CRC Press LLC

Contributors A.G. Abdul-Ghani Food Science and Process Engineering Group Department of Chemical and Materials Engineering The University of Auckland Auckland, New Zealand E.A.A. Adell Departamento de Engenharia Química e Alimentos Escola de Engenharia Mauá Instituto Mauá de Tecnologia — Praça Mauá São Paulo, Brazil S.M. Alzamora Departamento de Industrias Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Buenos Aires, Argentina A. Andrés Department of Food Technology Universidad Politécnica de Valencia Valencia, Spain A. Angersbach Department of Food Biotechnology and Food Process Engineering Berlin University of Technology Berlin, Germany J. Arul Department of Food Science and Nutrition and Horticulture Research Center Laval University Sainte-Foy, Quebec, Canada

© 2003 by CRC Press LLC

P.M. Azoubel Faculdade de Engenharia de Alimentos UNICAMP Campinas, São Paulo, Brazil E. Azuara-Nieto Instituto de Ciencias Básicas Universidad Veracruzana Xalapa, Veracruz, México M.O. Balaban Food Science and Human Nutrition University of Florida Gainesville, Florida J. Barat Department of Food Technology Universidad Politécnica de Valencia Valencia, Spain G.V. Barbosa-Cánovas Department of Biological Systems Engineering Washington State University Pullman, Washington A.F. Baroni Departamento de Engenharia Química e Alimentos Escola de Engenharia Mauá Instituto Mauá de Tecnologia — Praça Mauá São Paulo, Brazil F.H. Barron Department of Packaging Science Clemson University Clemson, South Carolina

J. Benedito Food Technology Department Universidad Politécnica de Valencia Valencia, Spain C.I. Beristain-Guevara Instituto de Ciencias Básicas Universidad Veracruzana Xalapa, Veracruz, México J.M. Bunn Department of Packaging Science Clemson University Clemson, South Carolina

M.S. Chinnan Center for Food Safety and Quality Enhancement Department of Food Science and Technology University of Georgia, Grifﬁn Campus Grifﬁn, Georgia A. Chiralt Department of Food Technology Universidad Politécnica de Valencia Valencia, Spain

J. Cárcel Department of Food Technology Universidad Politécnica de Valencia Valencia, Spain

P. Coronel Department of Food Science North Carolina State University Raleigh, North Carolina

F. Castaigne Department of Food Science and Nutrition and Horticulture Research Center Laval University Sainte-Foy, Quebec, Canada

J.G. Crespo Department of Chemistry Faculdade de Ciências e Tecnología Universidade Nova de Lisboa Caparica, Portugal

M.A. Castro Departamento de Ciencias Biológicas Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Buenos Aires, Argentina K.V. Chau Biological and Agricultural Engineering University of Florida Gainesville, Florida X.D. Chen Food Science and Process Engineering Group Department of Chemical and Materials Engineering The University of Auckland Auckland, New Zealand

© 2003 by CRC Press LLC

S.L. Cuppett Department of Food Science and Technology University of Nebraska-Lincoln Lincoln, Nebraska F. Erdoˇgdu Department of Food Engineering University of Mersin Ciftlikkoy, Mersin, Turkey M.M. Farid Food Science and Process Engineering Group Department of Chemical and Materials Engineering The University of Auckland Auckland, New Zealand

H. Feng Department of Biological Systems Engineering Washington State University Pullman, Washington P. Fito Department of Food Technology Universidad Politécnica de Valencia Valencia, Spain A.L. Gabas Departamento de Engenharia de Alimentos Universidade Estadual de Campinas Campinas, São Paulo, Brazil M.A. Garcia-Alvarado Departamento de Ingeniería Química y Bioquímica Instituto Tecnológico de Veracruz Veracruz, México C. González-Martínez Department of Food Technology Universidad Politécnica de Valencia Valencia, Spain S. Grabowski Food Research and Development Centre Agriculture and Agri-Food Canada St. Hyacinthe, Quebec, Canada G.F. Gutiérrez-López Departamento de Graduados e Investigación en Alimentos Escuela Nacional de Ciencias Biológicas — I.P.N. México, México F. Hamouz Department of Nutritional Science and Dietetics University of Nebraska-Lincoln Lincoln, Nebraska

© 2003 by CRC Press LLC

J.A. Hernández-Pérez Joint Research Unit Food Process Engineering Cemagref, ENSIA, INAPG, INRA Massy, France B. Heyd Joint Research Unit Food Process Engineering Cemagref, ENSIA, INAPG, INRA Massy, France M.V. Karwe Department of Food Science Rutgers University New Brunswick, New Jersey D. Knorr Department of Food Biotechnology and Food Process Engineering Berlin University of Technology Berlin, Germany H. Krishnamurthy Department of Food Science and Agricultural Chemistry McGill University, Macdonald Campus Ste. Anne de Bellevue, Quebec, Canada R. León-Cruz Departamento de Ingeniería Química y Alimentos Universidad de las Américas-Puebla Santa Catarina Mártir Cholula, Puebla, México M. Marcotte Food Research and Development Centre Agriculture and Agri-Food Canada St. Hyacinthe, Quebec, Canada

J. Martínez-Monzó Department of Food Technology Universidad Politécnica de Valencia Valencia, Spain

K. Niranjan School of Food Biosciences The University of Reading Reading, Berkshire, U.K.

F.C. Menegalli Departamento de Engenharia de Alimentos Universidade Estadual de Campinas Campinas, São Paulo, Brazil

N. Nitin Department of Food Science Rutgers University New Brunswick, New Jersey

M.R. Menezes Departamento de Engenharia de Alimentos Universidade Estadual de Campinas Campinas, São Paulo, Brazil F.J. Molina-Corral Graduate Program in Food Science and Technology University of Chihuahua Chihuahua, México H. Mújica-Paz Facultad de Ciencias Químicas Universidad Autónoma de Chihuahua Chihuahua, México A. Mulet Food Technology Department Universidad Politécnica de Valencia Valencia, Spain F.E.X. Murr Faculdade de Engenharia de AlimentosUNICAMP Campinas, São Paulo, Brazil A. Nieto Departamento de Industrias Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Buenos Aires, Argentina © 2003 by CRC Press LLC

R. Olivas-Vargas Advanced Materials Research Center Complejo Industrial Chihuahua Chihuahua, México E. Ortega-Rivas Graduate Program in Food Science and Technology University of Chihuahua Chihuahua, México K.S. Pannu Food Process Engineering Delta British Columbia, Canada A. Pérez-Hernández Advanced Materials Research Center Complejo Industrial Chihuahua Chihuahua, México D.L. Pyle School of Food Biosciences The University of Reading Reading, Berkshire, U.K. H.S. Ramaswamy Department of Food Science and Agricultural Chemistry McGill University, Macdonald Campus Ste. Anne de Bellevue, Quebec, Canada A.L. Raoult-Wack CIRAD, Agri-Food Program Montpellier, France

N.K. Rastogi Department of Food Engineering Central Food Technological Research Institute Mysore, India E.P. Ribeiro Departamento de Engenharia Química e Alimentos Escola de Engenharia Mauá Instituto Mauá de Tecnologia—Praça Mauá São Paulo, Brazil C. Rosselló Chemistry Department Universitat de les Illes Balears Palma de Mallorca, Spain S.S. Sablani Department of Bioresource and Agricultural Engineering Sultan Qaboos University Muscat Sultanate of Oman K.P. Sandeep Department of Food Science North Carolina State University Raleigh, North Carolina T. Schäfer Department of Chemistry-CQFB Faculdade de Ciências e Tecnología Universidade Nova de Lisboa Caparica, Portugal M. Schnepf Department of Nutritional Science and Dietetics University of Nebraska-Lincoln Lincoln, Nebraska D.R. Sepúlveda Department of Biological Systems Engineering Washington State University Pullman, Washington © 2003 by CRC Press LLC

S. Simal Chemistry Department Universitat de les Illes Balears Palma de Mallorca, Spain R.P. Singh Department of Biological and Agricultural Engineering University of California, Davis Davis, California M.E. Sosa-Morales Chemical Engineering and Food Engineering Department Universidad de las Américas-Puebla Santa Catarina Mártir, Cholula Puebla, México J. Tang Department of Biological Systems Engineering Washington State University Pullman, Washington J. Telis-Romero Departamento de Engenharia e Tecnologia de Alimentos Universidade Estadual Paulista São José do Rio Preto, São Paulo, Brazil R.F. Testin Department of Packaging Science Clemson University Clemson, South Carolina G. Trystram Joint Research Unit Food Process Engineering Cemagref, ENSIA, INAPG, INRA Massy, France A. Valdez-Fragoso Facultad de Ciencias Químicas Universidad Autónoma de Chihuahua Chihuahua, México

M.E. Vargas-Ugalde Departamento de Ingeniería y Tecnología Facultad de Estudios Superiores Cuautitlán Izcalli, Edo. de México, México School of Food Biosciences The University of Reading Reading, Berkshire, U.K. Departamento de Graduados e Investigación en Alimentos Escuela Nacional de Ciencias Biológicas - I.P.N. México, México J.F. Vélez-Ruiz Chemical Engineering and Food Engineering Department Universidad de las Américas-Puebla Santa Catarina Mártir, Cholula Puebla, México P.J. Vergano Department of Packaging Science Clemson University Clemson, South Carolina

J. Welti-Chanes Departamento de Ingeniería Química y Alimentos Universidad de las Américas-Puebla Santa Catarina Mártir, Cholula Puebla, México S. Wichchukit Department of Biological and Agricultural Engineering University of California, Davis Davis, California J.L. Wiles Department of Packaging Science Clemson University Clemson, South Carolina Y. Wu Department of Research and Development The Wright Group Crowley, Louisiana

O. Vitrac INRA - Food Packaging Unit Centre de Recherches Agronomiques Reims, France

M.R. Zareifard Department of Food Science and Agricultural Chemistry McGill University, Macdonald Campus Ste. Anne de Bellevue, Quebec, Canada

C.L. Weller Industrial Agricultural Products Center and Department of Biological/Systems Engineering University of Nebraska-Lincoln Lincoln, Nebraska

S.E. Zorrilla Instituto de Desarrollo Tecnológico para la Industria Química (INTEC) Consejo Nacional de Investigaciones Cientíﬁcas y Técnicas Universidad Nacional del Litoral Santa Fe, Argentina

© 2003 by CRC Press LLC

Table of Contents Part I 1 2 3

Fundamentals of Mass Transport J. Welti-Chanes, H. Mújica-Paz, A. Valdez-Fragoso, and R. León-Cruz Heat Transfer in Food Products D.R. Sepúlveda and G.V. Barbosa-Cánovas Introductory Aspects of Momentum Transfer Phenomena J.F. Vélez-Ruiz

Part II 4

5 6 7

8

9

10

11

12

Fundamental Concepts

Mass Transfer

Structural Effects of Blanching and Osmotic Dehydration Pretreatments on Air Drying Kinetics of Fruit Tissues S.M. Alzamora, A. Nieto, and M.A. Castro Pretreatment Efﬁciency in Osmotic Dehydration of Cranberries S. Grabowski and M. Marcotte Mass Transfer Description of the Osmodehydration of Apple Slabs E. Azuara-Nieto, G.F. Gutiérrez-López, and C.I. Beristain-Guevara Combined Effect of High Hydrostatic Pressure Pretreatment and Osmotic Stress on Mass Transfer during Osmotic Dehydration N.K. Rastogi, A. Angersbach, and D. Knorr Hydrodynamic Mechanisms in Plant Tissues during Mass Transport Operations P. Fito, A. Chiralt, J. Martínez-Monzó, and J. Barat Effect of Pretreatment on the Drying Kinetics of Cherry Tomato (Lycopersicon esculentum var. cerasiforme) P.M. Azoubel and F.E.X. Murr Determination of Concentration-Dependent Effective Moisture Diffusivity of Plums Based on Shrinkage Kinetics A.L. Gabas, F.C. Menegalli, and J. Telis-Romero Modeling Dehydration Kinetics and Reconstitution Properties of Dried Jalapeño Pepper R. Olivas-Vargas, F.J. Molina-Corral, A. Pérez-Hernández, and E. Ortega-Rivas Application of an Artiﬁcial Neural Network for Moisture Transfer Prediction Considering Shrinkage during Drying of Foodstuffs J.A. Hernández-Pérez, M.A. García-Alvarado, G. Trystram, and B. Heyd

© 2003 by CRC Press LLC

13

14

15

16

17

18 19

Modeling of Prato Cheese Salting: Fickian and Neural Network Approaches A.F. Baroni, M.R. Menezes, E.A.A. Adell, and E.P. Ribeiro Inﬂuence of Vacuum Pressure on Salt Transport during Brining of Pressed Curd A. Chiralt, P. Fito, C. González-Martínez, and A. Andrés Effects of Water Concentration and Water Vapor Pressure on the Water Vapor Permeability and Diffusion of Chitosan Films J.L. Wiles, P.J. Vergano, F.H. Barron, J.M. Bunn, and R.F. Testin Water Vapor Permeability, Water Solubility, and Microstructure of Emulsiﬁed Starch–Alginate–Fatty Acid Composite Films Y. Wu, C.L. Weller, F. Hamouz, S.L. Cuppett, and M. Schnepf Mass Transport Phenomena during the Recovery of Volatile Compounds by Pervaporation T. Schäfer and J.G. Crespo Ultrasonic Mass Transfer Enhancement in Food Processing A. Mulet, J. Cárcel, J. Benedito, C. Rosselló, and S. Simal Mass Transfer and Residence Time Studies in Spinning Cone Columns M.E. Vargas-Ugalde, K. Niranjan, D.L. Pyle, and G.F. Gutiérrez-López

Part III 20 21

22

23

24

25 26

Heat Transfer

Transport Phenomena during Double-Sided Cooking of Meat Patties S.E. Zorrilla, S. Wichchukit, and R.P. Singh Thermal Processing of Particulate Foods by Steam Injection. Part 1. Heating Rate Index for Diced Vegetables K.S. Pannu, F. Castaigne, and J. Arul Thermal Processing of Particulate Foods by Steam Injection. Part 2. Convective Surface Heat Transfer Coefﬁcient for Steam K.S. Pannu, F. Castaigne, and J. Arul Modeling of Heat Conduction in Elliptical Cross Sections (Oval Shapes) Using Numerical Finite Difference Models F. Erdog˘du, M.O. Balaban, and K.V. Chau Heat Transfer Coefﬁcient for Model Cookies in a Turbulent Multiple Jet Impingement System N. Nitin and M.V. Karwe Flow Dynamics and Heat Transfer in Helical Heat Exchangers P. Coronel and K.P. Sandeep Relating Food Frying to Daily Oil Abuse. Part 1. Determination of Surface Heat Transfer Coefﬁcients with Metal Balls K.S. Pannu and M.S. Chinnan

© 2003 by CRC Press LLC

Part IV 27

28 29

30

31

32

33

Combined Transfer Phenomena

Relating Food Frying to Daily Oil Abuse. Part 2. A Practical Approach for Evaluating Product Moisture Loss, Oil Uptake, and Heat Transfer K.S. Pannu and M.S. Chinnan Heat and Mass Transfer during the Frying Process of Donuts J.F. Vélez-Ruiz and M.E. Sosa-Morales Inﬂuence of Liquid Water Transport on Heat and Mass Transfer during Deep-Fat Frying O. Vitrac, A.L. Raoult-Wack, and G. Trystram Numerical Simulation of Transient Two-Dimensional Proﬁles of Temperature, Concentration, and Flow of Liquid Food in a Can during Sterilization A.G. Abdul-Ghani, M.M. Farid, and X.D. Chen Heating Behavior of Canned Liquid/Particle Mixtures during End-over-End Agitation Processing S.S. Sablani, H.S. Ramaswamy, and H. Krishnamurthy Dimensionless Correlations for Forced Convection Heat Transfer to Spherical Particles under Tube-Flow Heating Conditions H.S. Ramaswamy and M.R. Zareifard Heat and Mass Transfer Modeling in Microwave and Spouted Bed Combined Drying of Particulate Food Products H. Feng and J. Tang

© 2003 by CRC Press LLC

Part I Fundamental Concepts

© 2003 by CRC Press LLC

1

Fundamentals of Mass Transport J. Welti-Chanes, H. Mújica-Paz, A. Valdez-Fragoso, and R. León-Cruz

CONTENTS 1.1 1.2

Introduction Mass Transfer Variables 1.2.1 Concentration 1.2.2 Velocity 1.2.3 Flux 1.2.4 Flux Relations for Binary Systems 1.3 Mass Transfer by Diffusion 1.3.1 Steady State Diffusion 1.3.2 Molecular Diffusion in Gases, Liquids, and Solids 1.3.2.1 Molecular Diffusion in Gases 1.3.2.2 Molecular Diffusion in Liquids 1.3.2.3 Molecular Diffusion in Solids 1.3.3 Unsteady State Diffusion 1.3.3.1 Solutions of Fundamental Equations 1.4 Mass Transfer by Convection 1.4.1 Film Theory and Mass Transfer Coefﬁcient 1.4.2 Two-Film Theory and Mass Transfer Coefﬁcient 1.4.3 Dimensionless Numbers for Mass Transfer 1.4.4 Transport Analogies 1.4.5 Mass Transfer Coefﬁcients and Correlations 1.4.6 Mass Transfer Units Nomenclature References

1.1 INTRODUCTION Mass transfer can be deﬁned as the migration of a substance through a mixture under the inﬂuence of a concentration gradient in order to reach chemical equilibrium. Biochemical and chemical engineering operations, such as absorption, humidiﬁcation, distillation, crystallization, and aeration, involve mass transfer principles.

© 2003 by CRC Press LLC

In food processing, mass transfer phenomena are present in freeze-drying, osmotic dehydration, salting or desalting, curing and pickling, extraction, smoking, baking, frying, drying of foods, membrane separations, and the transmission of water vapor, gases, or contaminants across a packaging ﬁlm. Food stability and the preservation of food quality are also affected by mass transfer of environmental components that can affect the rate of reactions. Among the components involved in these mass transfer processes are water, sugars, salt, oils, proteins, acids, ﬂavor and aroma substances, oxygen, carbon dioxide, residual monomers or polymer additives, and toxins or carcinogens produced by microorganisms. Furthermore, mass transfer phenomena are important in the scale-up of processes to pilot- or commercial-scale plants and in the control and optimization of the processes. This chapter presents the basic principles of mass transfer. First, the variables that occur in mass transfer are reviewed. Then the mechanisms of mass transfer, diffusion and convection are discussed. Analogies among momentum, heat, and mass transfer are described; convective mass transfer coefﬁcients and correlations are derived by analogy with convective heat transfer. Finally, the concept of transfer units is presented.

1.2 MASS TRANSFER VARIABLES Mass transfer processes involve concentration, velocity, and ﬂux variables, which are deﬁned and related by a set of basic equations (White, 1988).

1.2.1 CONCENTRATION The concentration of a mixture and its components may be expressed in terms of 3 mass and mol. In terms of mass, the mass concentration of the mixture (ρ, kg/m ), 3 the mass concentration of a component i (ρi, kg/m ), and the mass fraction of component i (wi) are given by: ρ= m/V

(1.1)

ρi = m i / V

(1.2)

w i = m i / m = ρi / ρ

(1.3)

where m and mi are the mass ﬂux of the mixture and component i, respectively. 3 The bulk molar concentration (C, kg mol/m ), the molar concentration of com3 ponent i (Ci, kg mol/m ), and the mole fraction of component i (xi) are deﬁned by: C = n/V

(1.4)

Ci = n i / V

(1.5)

x i = n i / n = Ci / C

(1.6)

where n and ni are the mol of the mixture and component i, respectively.

© 2003 by CRC Press LLC

According to the previous deﬁnitions, it can be easily shown that: n

m=

∑

n

m i and ρ =

i =1

∑

∑C

i

(1.8)

i =1

n

∑

(1.7)

n

n i and C =

i =1

w=

i

i =1

n

n=

∑ρ

n

w i = 1 and x =

i =1

∑x =1 i

(1.9)

i =1

where xi is the mole fraction of component i, and ρi and Ci are related through the molecular weight of constituent i (Mi, kg/kg mol): ρi = M i C i

(1.10)

1.2.2 VELOCITY In mass transfer phenomena, the velocity of a bulk mixture and of its components can be measured with respect to ﬁxed coordinates. In addition, the velocity of the components can also be measured relative to the bulk velocity. Figure 1.1 illustrates these velocities in a binary system of components A and B in the z direction.

fixed coordinate

vB – v = diffusion velocity of B = UB

vB

v= wA vA + wB vB vA

z vA – v = diffusion velocity of A = UA FIGURE 1.1 Scheme of individual and bulk velocities of a binary mixture.

© 2003 by CRC Press LLC

The mass bulk velocity of the mixture (v, m/sec) relative to ﬁxed coordinates is deﬁned as: n

v=

∑

n

wi vi =

i =1

∑ i =1

mi v = m i

n

ρi

∑ ρv

(1.11)

i

i =1

where vi is the velocity of component i with respect to stationary coordinates. In a similar manner, a molar bulk velocity ( V, m/sec) measured relative to stationary coordinates can be deﬁned as: n

n

V=

∑x V = ∑ i

i =1

i

i =1

ni V = n i

n

∑ CV Ci

(1.12)

i

i =1

The velocity of the constituent i relative to the bulk velocity of the mixture is: u i = vi − v

(1.13)

Ui = Vi − V

(1.14)

where ui (m/sec) and Ui (m/sec) are the mass and molar diffusion velocities, respectively.

1.2.3 FLUX 2

2

The mass bulk ﬂux (n, kg/m sec) and the molar bulk ﬂux ( N , kg mol/m sec) of a mixture relative to ﬁxed coordinates are: n

n = ρv =

∑ρ v

(1.15)

i i

i =1 n

N = CV =

∑C V i

i

(1.16)

i =1

The ﬂux of the components of a mixture can also be expressed relative either to ﬁxed coordinates or to the bulk average velocity. The ﬂux of the component i relative to stationary coordinates is: n i = ρi v i

(1.17)

N i = Ci Vi

(1.18)

The diffusion ﬂuxes of the constituents i of the mixture with respect to the 2 2 average bulk velocity are ji (kg/m sec) for the mass ﬂux and Ji (kg mol/m sec) for the molar ﬂux.

© 2003 by CRC Press LLC

ji = ρi u i = ρi ( vi − v)

(1.19)

J i = C i U i = C i (V i − V)

(1.20)

The use of concentration, velocities, and ﬂuxes in mass or molar terms is subject to preferences and convenience. Nevertheless, concentration and ﬂux expressed in molar units and average molar velocity are preferred. In discussing the fundamentals of mass transfer, systems are frequently assumed as a two-component mixture to facilitate the understanding of multi-component systems found in engineering applications.

1.2.4 FLUX RELATIONS

FOR

BINARY SYSTEMS

For a binary mixture of components A and B, Equations (1.18) and (1.20) become: N A = CA VA

(1.21)

J A = C A U A = C A (V A − V)

(1.22)

Substituting V from Equation (1.12) into Equation (1.22), J A = CA V A − CA V = CA VA −

CA (C A V A + C B V B ) C

(1.23)

Since N A = C A V A and N B = C B V B , for component A, Equation (1.23) becomes: NA = JA +

CA (N A + N B ) C

(1.24)

A similar mathematical derivation gives for component B: NB = JB +

CB (N A + N B ) C

(1.25)

Equations (1.24) and (1.25) show that the absolute molar ﬂux (NΑ or NB) results from a concentration gradient contribution or a molar diffusion ﬂux (JA or JB) and a convective contribution ( C A V or C B V). The molar diffusion ﬂux is described by Fick’s law, which for component A is written as: J A = − D AB

dC A dz

(1.26)

where DAB is the diffusion coefﬁcient of A through B and dCA/dz is the change of the concentration A with respect to the position z. In terms of mass, the mass ﬂuxes for components A and B are, respectively:

© 2003 by CRC Press LLC

n A = jA +

ρA (nA + nB ) ρ˜

(1.27)

n B = jB +

nB (n + n B ) ρ˜ A

(1.28)

Two important simple cases can be considered in Equation (1.24): 1. Diffusion of A through stagnant B, NB = 0 NA =

JA D dC A = − AB 1 − xA 1 − x A dz

(1.29)

2. Equimolar counter-diffusion NA + NB = 0, N A = J A = − D AB

dC A dz

(1.30)

where xA is the mole fraction of component A in the case of dilute systems xA << 1, and Equations (1.29) and (1.30) become the same.

1.3 MASS TRANSFER BY DIFFUSION Mass transfer by diffusion is the transport of molecules caused by a random molecular motion in a region in which a composition gradient exists.

1.3.1 STEADY STATE DIFFUSION Steady state diffusion, in which the concentration does not change with time at any position, is described by Fick’s ﬁrst law. J i = − Dim

∂Ci ∂z

(1.31) 2

where Ji is the molar diffusion ﬂux of component i (kg mol/sec m ) in the z direction 3 (m), Ci is the concentration of component i (kg mol/m ), and Dim is the diffusion 2 coefﬁcient of i with respect to the mixture (m /sec). This equation is widely used in problems related to the processing and preservation of foods. The mass ﬂux (ji) of the component i is expressed as: ji = − Dim

∂ρi ∂z

(1.32) 2

3

2

where the units of ji, ρi, and Dim are, respectively, kg/sec m , kg/m , and m /sec.

1.3.2 MOLECULAR DIFFUSION

IN

GASES, LIQUIDS,

AND

SOLIDS

Theoretical and empirical correlations for estimating the binary diffusion coefﬁcient DAB in gases, liquids, and solids are described in this section.

© 2003 by CRC Press LLC

1.3.2.1 Molecular Diffusion in Gases The diffusion coefﬁcient of component A through B (DAB) may be estimated for pressures below 20 atm from the formula: D AB = 0.001858T 3/ 2

(1 / M A + 1 / M B )1/ 2 Pσ 2ABΩ D

(1.33)

where P is the absolute pressure (atm), T is the absolute temperature (K), σAB is the collision diameter (°A), ΩD is the collision integral for molecular diffusion, and MA and MB are the molecular weights of A and B, respectively (Sherwood et al., 1975). 1.3.2.2 Molecular Diffusion in Liquids The diffusivity of a solute A in a dilute solution B (DAB) can be predicted by the following equation (Treybal, 1981): D AB = 7.4 × 10 −8 (ϕ BM B )1/ 2

T µ BVA0.6

(1.34)

where ϕB, µB, and MB are an association parameter, the viscosity (centipoises), and the molecular weight of solvent B, respectively, T is the absolute temperature (K), 3 and VA is the molal volume of A (cm /g mol). 1.3.2.3 Molecular Diffusion in Solids The diffusion of gases and liquids through porous solid materials may occur by a combination of Fick diffusion and Knudsen diffusion. If the pores are large, the mass transfer within the gas or liquid contained in the pores will be by Fick diffusion. Nevertheless, the diffusivity in the solid is reduced below what it would be in a ﬂuid, due to the tortuous nature of the path that a molecule must travel to advance a given distance in the solid and to the restricted free cross-sectional area (Sherwood et al., 1975). In such a case, the ﬂux must be described in terms of an “effective” diffusion coefﬁcient, deﬁned as: Deff =

ε D τ AB

(1.35)

where DAB is the diffusion coefﬁcient in a binary system, τ is the tortuosity, and ε is the fractional void space. Values of ε, τ, and Deff must be determined experimentally. Therefore, when the system is a porous solid that has interconnected voids that affect the diffusion, for a binary system the molar ﬂow is: dC ε N A = − D AB A dz τ

© 2003 by CRC Press LLC

(1.36)

Knudsen diffusion occurs when the pores are small and their size approaches the mean free path of the gas molecule. A gas molecule now collides predominantly with the walls of the pores rather than with other molecules. The Knudsen diffusion coefﬁcient (DK), derived from the kinetic theory of gases (Welty et al., 1984), is given by the expression: DK =

19400ε 2 τS′ ρ

T M

(1.37)

where ρ is the density of the solid material, M is the molecular weight of the diffusing gas, and T is the temperature (K). The molar ﬂux for gas and liquids through a porous solid can be described in terms of DK by: N A = DK

(C A1 − C A 2 ) (p − pA2 ) = D K A1 z RTz

(1.38)

where CA1 and CA2 are the bulk concentrations in the gas and liquid phases, respectively, and pA1 and pA2 are the partial pressures of the gas and liquid phases, respectively. When Fick and Knudsen diffusions are important, the effective diffusion coefﬁcient is deﬁned by: 1 1 1 = + Deff D AB D K

(1.39)

which applies for equimolar counter-diffusion. Diffusion in liquids is important in separation operations such as liquid–liquid extraction and distillation. Typical examples of diffusion of ﬂuids through solids are water vapor transport in the drying of porous foods, the diffusion of a gas through a polymer ﬁlm used in the packaging of foods, and separation processes through a membrane, such as reverse osmosis and ultraﬁltration.

1.3.3 UNSTEADY STATE DIFFUSION The unsteady state diffusion, in which the local concentration change with time is described in one dimension for slab shape and constant DAB, is shown by Fick’s second law: ∂C A d 2CA = D AB ∂t dz 2

(1.40)

Analogous equations can be written for diffusion in spherical or cylindrical shapes and two or three dimensions. These equations are used to ﬁnd the concentration of a solute as a function of time and position and are mainly applicable to diffusion in solids and to limited situations in ﬂuids. The analysis of unsteady state systems, however, is frequently simpliﬁed to a one-directional ﬂow.

© 2003 by CRC Press LLC

1.3.3.1 Solutions of Fundamental Equations Solutions to unsteady state diffusion equations can be obtained by analytical, numerical, and graphical methods. Analytical solutions for one-dimensional diffusion in an inﬁnite slab, an inﬁnite cylinder, and a sphere have been found by assuming a constant diffusion coefﬁcient given appropriate boundary conditions (Crank, 1975): 1. Inﬁnite slab: C − C∞ 4 = C0 − C∞ π

n =∞

 D(2n + 1)2 π 2 t  )πx  exp −  4δ 2   

∑ 2n− + 1 cos  2n 2+δ1 ( 1)n

(

n=0

(1.41)

2. Inﬁnite cylinder: C − C∞ 2 = C0 − C∞ R

n =∞

∑ b J (b , r) exp(−Db t) n =1

J0 (bn , r) n 1

2 n

(1.42)

n

3. Sphere: C − C∞ 2R = C0 − C∞ π

n =∞

∑ n =1

(−1)n +1 1 sin nπr  exp Dn 2 π 2 t  n

r

 R 

 2  R

 

(1.43)

where Co and C are the molar concentration at time t = 0 and t = ∞, respectively. When properties become dependent upon position or concentration, the solutions become more complicated. In this case, numerical techniques can be used, since they are more appropriate for complex and real problems. Among the numerical methods are ﬁnite difference and ﬁnite element analysis. The ﬁnite difference method is based on the approximation of the difference of a derivative at a point. This analysis is often limited to cases where the body has a simple geometry. The ﬁnite element method of analysis overcomes this problem; its basic concept is that any continuous quantity, such as a concentration, can be approximated by a discrete model composed of a set of piecewise continuous functions deﬁned over a ﬁnite number of domains. For unsteady state heat conduction problems in solids, solutions have been presented for simple geometries subject to a given set of boundary and initial conditions. These solutions are presented in charts in terms of dimensionless ratios and can be translated directly to analogous problems of unsteady state diffusion, allowing the application of heat transfer results to solve mass diffusion problems. The ordinate of these charts represents the fraction of the unaccomplished change 2 [(c1 – c)/(c1 – c0)] and the abscissa the relative time [DABt /x1 ]. These charts and their physical signiﬁcance, use, and application are presented in several books (Welty et al., 1984; Geankoplis, 1993). Table 1.1 summarizes the correspondence between variables for unsteady heat and molecular diffusion.

© 2003 by CRC Press LLC

TABLE 1.1 Relation between Mass and Heat Transfer Variables for Unsteady State Mass Transfer Heat Transfer

K=1

K≠1

T1 − T T1 − T0

c1 − c c1 − c 0

(c1 / K ) − c (c1 / K ) − c 0

X, Relative time

αt x12

D AB t x12

D AB t x12

m, Relative resistance

k hx1

D AB k m x1

D AB Kk m x1

n, Relative position

x x1

x x1

x x1

Y, Unaccomplished change

Note: T0 and c0 = temperature and concentration at time t = 0, respectively; T1 and c1 = temperature and concentration at the position of interest; x 1 = distance from the midpoint to the position of interest; m = ratio of the convective mass transfer resistance to the internal molecular resistance to the mass transfer; K = cLi/ci, where cLi = bulk ﬂuid concentration and ci = concentration in the ﬂuid adjacent to the solid surface. Source: Adapted from Welty, J.R., Wicks, C.E., and Wilson, R.E., Momentum, Heat, and Mass Transfer, John Wiley & Sons, New York, 1984 and Geankoplis, C.J., Transport Processes and Unit Operations, 3rd ed., Prentice-Hall, London, 1993. With permission.

1.4 MASS TRANSFER BY CONVECTION Convective mass transport, which occurs in liquids and gases, results from bulk motion of the ﬂuid imposed by external forces (forced convection) or occurring naturally, due to the concentration difference or density variations (free convection). The free or forced character is determined by the nature of the motion of the ﬂuid, which may be either laminar or turbulent. In laminar ﬂow, the mechanism is the same as in a stationary medium, and the transfer occurs by diffusion. In turbulent ﬂow, mass transfer is affected by the irregular motion of small volumes of the ﬂuid.

1.4.1 FILM THEORY

AND

MASS TRANSFER COEFFICIENT

Convective mass transfer problems in turbulent ﬂow are not always amenable to analytical methods of solution. Consequently, they are usually approached with the aid of coefﬁcients and empirical relationships. Among several models proposed for a better understanding of mass transfer under turbulent regime, we ﬁnd the model built around the ﬁlm theory. In this theory the interfacial region is treated as a hypothetical stagnant ﬁlm of thickness x, called the boundary layer, and it is assumed that all the concentration changes occur in this layer (Figure 1.2) (Welty et al., 1984).

© 2003 by CRC Press LLC

stagnant film solid

CA1

bulk fluid CA2

FIGURE 1.2 Fluid-solid interfacial region: the ﬁlm theory.

x z

Thus, the molar ﬂux and the concentration proﬁle of species A (JA) are found from JA =

D AB (C A1 − C A 2 ) = − k m (C A1 − C A 2 ) x

(1.44)

where DAB/z is the mass transfer coefﬁcient, km, CA1, and CA2 are the bulk concentrations in the ﬂuid and solid phase, respectively, and C A = C A1 −

z(C A1 − C A 2 ) x

(1.45)

Similarly, the corresponding expression for mass ﬂux is: jA = k ρ (ρA1 − ρA 2 )

(1.46)

where CA is the concentration of the components A, and ρA1 and ρA2 are the mass concentration of the ﬂuid and solid, respectively. 2 The mass transfer coefﬁcient kC or kρ has units of velocity (m /sec). It can be determined either from experimental data and empirical formulas derived from them or with the aid of methods of similitude theory. A rough estimation of km can be attained by assuming km = D/x, provided the effective ﬁlm thickness and the diffusion coefﬁcient are known (Sherwood, 1974).

1.4.2 TWO-FILM THEORY

AND

MASS TRANSFER COEFFICIENT

Mass transfer from a gas and/or a liquid to another ﬂuid is a common engineering problem. For interphase transfer, it is convenient to use an overall mass transfer coefﬁcient, the interpretation of which is achieved with the aid of the two-ﬁlm theory. Figure 1.3 schematically shows the transfer of component A from the gas phase to

© 2003 by CRC Press LLC

gas phase

liquid phase interface

x1

x2

CA1 CA1i CA2i CA2 layer

layer

C*A1 =

C*A 2 = mCA1

CA 2 m

FIGURE 1.3 Mass transfer at a gas liquid interphase: the two-ﬁlm theory.

the liquid phase. The two-ﬁlm theory assumes that the resistance to mass transfer lies in each adjacent phase to the interphase and that no resistance is offered to the transfer of the solute across the interphase (Welty et al., 1984). At steady state, the ﬂuxes in gas and liquid (J1) phases must be equal: J1 = k mG (C A1 − C A1i ) = k mL − (C A 2 i − C A 2 )

(1.47)

where kmG and kmL are the mass transfer coefﬁcients in the gas and liquid phases, respectively, CA1i and CA2i are the concentrations of component A at the interface, and CA1 and CA2 are the bulk concentrations in the gas and liquid phases, respectively. Since the concentrations at the interphase are not easily measurable, it is convenient to calculate an overall mass transfer coefﬁcient based on an overall potential gradient between the bulk compositions. The overall driving force is not, however, CA1 – CA2, since at the interphase discontinuity of the concentrations exists, and the solubility in the liquid is not necessarily the same as in the gas. Moreover, the ﬁlm thickness x1 and x2 and the diffusivity of the solute may be different in the two phases. The solubility relationship that governs the equilibrium concentration between phases is of the form: CG = mC L

(1.48)

where m is the solubility constant between the two phases, and CG and CL are the concentrations of the gas and liquid, respectively.

© 2003 by CRC Press LLC

Thus, the ﬂux in terms of the total potential gradient in the gas phase is: C   J = K mG (C A1 − C*A1 ) = K mG C A1 − A 2  m 

(1.49)

*

where CA2/m = C A1, which is the concentration in the gas phase that would exist in equilibrium with CA2, the concentration of species A in the liquid. A similar equation can be obtained for the overall coefﬁcient if the driving force is based on the concentration in the liquid phase: J = K mL (C*A1 − C A 2 ) = K mL ( mC A1 − C A 2 )

(1.50)

where mCA1 is the concentration in the liquid that would exist in equilibrium with * C A1. KmG and KmL represent the overall mass transfer coefﬁcient based on the gas phase and the liquid concentration driving force. Coefﬁcients KmG and KmL are related to the individual mass transfer coefﬁcients and the equilibrium constant m of a gas–liquid (kmG) or vapor–liquid (kmL) system as follows: 1 1 m = + K mG k mG k mL

(1.51)

1 1 1 = + K mL mk mG k mL

(1.52)

These last two equations show the relationship among the coefﬁcients for the individual phases and the overall transfer coefﬁcients, expressed as a global resistance (1/KmG or 1/KmL) to the transfer of the diffusing component. In studying performance separation processes, it is important to determine which individual resistance is the limiting factor.

1.4.3 DIMENSIONLESS NUMBERS

FOR

MASS TRANSFER

Mass transfer coefﬁcients are expected to vary with hydrodynamic conditions and with geometrical and physical properties of the ﬂuid. These variables are collected into the so-called dimensionless numbers. Dimensionless numbers that arise in mass transfer modeling and scale-up studies are presented in Table 1.2. For mass transport, the Biot number is deﬁned by the equation Bi = kmd/D. The Biot number compares the resistance to mass transfer at the surface of a solid to the resistance inside the solid. High Biot numbers can be obtained by increasing the mass transfer coefﬁcient. For instance, in solids drying, the higher the value of Bi, the faster the drying proceeds; hence, the air humidity increases rapidly. 2 The Fick number, Fi = Dt/d , is a nondimensional time parameter. It is important in studying unsteady state diffusion mass transfer in several simple shapes with certain restrictive boundary conditions (Gekas, 1992).

© 2003 by CRC Press LLC

TABLE 1.2 Dimensionless Numbers Related to Mass Transfer Dimensionless Number

Equation

Biot

Bi =

Fick

Fi =

Graetz Grashof

k md D

Mass transfer across the boundary/mass transfer within the solid

Dt d2

Dimensionless time in the unsteady state regime

ReSc Gr =

Physical Meaning

Mass transfer in laminar ﬂow

gd 3β∆Tρ2 ν

Buoyancy forces/viscous forces

Lewis

Le =

α D

Heat diffusivity/mass diffusivity

Peclet

Pe =

vd D

Convection/diffusion

Reynolds

Re =

vd ν

Inertial force/viscous force

Schmidt

Sc =

ν D

Momentum diffusivity/mass diffusivity

Sh =

k md D

Measure of boundary layer thickness

St =

km v

Wall mass transfer/mass transfer by convection

Sherwood Stanton

The Graetz number is deﬁned as the product of the Reynolds and Schmidt numbers. It includes the effects of forced and free convection. The Grashof number is a measure of free convection, which will be enhanced by buoyancy forces (ρ) and decreased by viscous forces (ν). The Grashof number is found in correlations of free convection mass transfer. The Lewis number, Le = α/D, is the ratio of heat to mass diffusivity. It plays an important role in processes where simultaneous convective transfer of energy and mass occurs. The Peclet number, deﬁned as Pe = vd/D, is the ratio of bulk mass transport to diffusive mass transport. The Reynolds number, Re = vd/ν, characterizes the nature of the motion of a ﬂowing gas or liquid, and is interpreted as the ratio of inertial forces to the viscous forces in the ﬂow. When the Re value is below a certain critical value, the ﬂow is laminar; when it is larger, the ﬂow is turbulent. In the Schmidt number, Sc = ν/D, the two molecular transport coefﬁcients (ν and D) are the physical properties of the medium in which the transfer of mass takes place. The Schmidt number, which represents the ratio of momentum to mass diffusivities, is of great importance in convective mass transfer (Welty et al., 1984).

© 2003 by CRC Press LLC

The Sherwood number is deﬁned as Sh = kmd/D, where km is the mass transfer coefﬁcient, d is a characteristic length dimension, and D is the diffusion coefﬁcient. The Sherwood number is a convenient parameter for the analysis of transfer processes occurring in a stationary medium in laminar ﬂow. In the case of purely molecular transfer, the Sherwood number is highly dependent on the geometrical shape of the body. The Stanton number is interpreted as the ratio of the mass-transfer coefﬁcient (km) to the ﬂow velocity (v). It represents a measure of the mass ﬂux in the direction transverse to that of the mean ﬂow. The Stanton number is used more conveniently in turbulent ﬂow. The dimensionless numbers Sc, Sh, and Le will be encountered in the analysis of convective mass transfer correlations.

1.4.4 TRANSPORT ANALOGIES The basic laws governing the ﬂux of momentum, heat, and mass transport due to molecular motion or vibration have the form: τ= q=−

µ d d (ρv) = v (ρv) ρ dz dz

k d d (ρC p T) = −α (ρC p T) ρC p dz dz Ji = −D

dC dz

(1.53)

(1.54)

(1.55)

All three processes are quite different from one another at a molecular level. However, certain analogies exist among them. In effect, molecular diffusivities kinematic viscosity (ν), thermal diffusivity (α), and diffusion (D) have the same 2 dimensions (L /t). Also, in Fick’s law, the molar ﬂux varies with the gradient in mol per volume; in the rewritten Fourier’s law, the energy ﬂux is proportional to the gradient of energy per volume (ρCpT); and the momentum ﬂux, given by the rewritten Newton’s law, varies with the gradient of the momentum per volume (ρv) (Cussler, 1984). These analogies are shown in Table 1.3. The corresponding equations for momentum, heat and mass ﬂux in convective motion are: 1 fv τ = f  ρv2  =   (ρv − 0) 2   2 q = h∆T =

h ∆(ρC p T) ρC p

N i = k m ∆Ci

© 2003 by CRC Press LLC

(1.56)

(1.57) (1.58)

TABLE 1.3 Analogies among Momentum, Heat, and Mass Transfer Analogous Form

Variable Molecular diffusivity Transfer coefﬁcient

Momentum Transfer

Heat Transfer

Mass Transfer

ρv (momentum/volume) ν (kinematic viscosity) f (friction factor)

ρC p T (energy/volume) α (thermal diffusivity) h (heat transfer coefﬁcient)

C (mol/volume) D (diffusion coefﬁcient) km (mass transfer coefﬁcient)

Dimensionless number

Pr = St =

ν α h / ρC p v

Sc =

ν D

St =

km v

Le =

α D

where the transfer coefﬁcient fv/2 is like h/ρCp and k. Note that the driving forces in the momentum, heat, and mass ﬂux are volume concentrations: (ρv − 0) is expressed in momentum per volume, ∆(ρC p T) in energy per volume, and ∆Ci in mol per volume (Table 1.3). Since the molecular diffusivities have the same dimensions, a ratio of any of two of these leads to dimensionless numbers: Pr number for heat transfer, Sc and Le numbers for mass transfer. Likewise, the ratio transfer coefﬁcients to the ﬂow velocity lead to an [St] number for heat transfer and an [St] number for mass transfer (Tables 1.2 and 1.3). A useful and simple analogy relating all three types of transport simultaneously is the Chilton–Colburn analogy, which is written as k m 2/3 h / ρC p 2/3 f Sc = Pr = v v 2 The group k m 2/3 Sc v is called the jD factor for mass transfer, and h / ρC p v deﬁnes the jH factor for heat transfer.

© 2003 by CRC Press LLC

Pr 2 / 3 = St Pr 2 / 3

(1.59)

The Chilton–Colburn analogy agrees well with a wide range of experimental data for ﬂow and geometries of different types in forced convection systems. Therefore, when an engineer is concerned with the calculation of heat and mass transfer coefﬁcients, the analogies are of great utility. In this way, when heat transfer and mass transfer occur by the same mechanism, the results of experiments on heat transfer may be used to calculate diffusion processes, or vice versa. Also, information obtained from a small-scale model can be used to scale up the process, or information obtained with one substance can be extended to another substance. In very particular cases, Pr = Sc = 1, which means that ν = α = D, and heat and mass transfer measurements may be used to predict momentum transfer or vice versa (Sherwood et al., 1975; Treybal, 1981).

1.4.5 MASS TRANSFER COEFFICIENTS

AND

CORRELATIONS

Although the analogy concept is useful in predicting mass transfer coefﬁcients, in certain turbulent situations correlations based on experimental observations are required. A few typical correlations for mass transfer in a variety of geometries and ﬂow conditions are given in Table 1.4 (Treybal, 1981).

TABLE 1.4 Typical Mass Transfer Correlations Situation Round tubes

Equation Sh = 0.023 Re 0.83 Sc 0.44 d Sh = 1.67 Re Sc x 

Flat plates

Remarks Used for turbulent ﬂow

1/ 3

Used for laminar ﬂow in a circular pipe

Sh = 0.664 Re1/ 2 Sc1/ 3

Transfer begins at leading edge

Sh = 0.332 Re

Used for laminar ﬂow over a plate

1/ 2

1/ 3

Sc

Evaporation drops

Sh = 2 + 0.6Sc1/ 3 Re1/ 2

Stirred drops

 d 4 ( P / V)  Sh = 0.13  3  ρν 

Solid spheres

dv Sh = 2 + 0.6   ν

1/ 2

Used for evaporation drops in spray drying

1/ 4

ν  D 

ν  D 

 d 3 [ ∆ρ]g  Sh = 2 + 0.6   2  ρν 

1/ 3

Used in mixing liquid solutions; P/V is important in scale-up

1/ 3

1/ 4

Used for forced convection ν  D 

1/ 3

Used for natural convection

Sh = 2 + 0.31(Gr )1/ 3 (Sc)1/ 2

Used for rising bubbles, d > 2.5 mm

Sh = 0.42 + (Gr ) (Sc)

Used for rising bubbles, d < 2.5 mm

Membranes

k =1 dD

Used in actual or hypothetical membranes

Packed bed of pellets

jD = 1.17 Re −0.415

Re f (particle diameter and superﬁcial velocity in the bed)

Bubbles

1/ 3

© 2003 by CRC Press LLC

1/ 2

1.4.6 MASS TRANSFER UNITS The number of transfer units is another approach in the application of pilot plant results to the design of mass transfer equipment, such as cooling towers, packed columns, extractors, or driers. This method can be illustrated in the determination of the height of a drier (Z), which is obtained as the product: Z = HTU C NTU D

(1.60)

where HTUc is the height of a transfer unit and NTUD is the number of mass transfer units given by: C2

NTU D =

∫ C −C

C1

dC

i

(1.61) b

Subscripts 1 and 2 refer to inlet and outlet values. The integral is evaluated from considerations of bulk (b) and interphase (i) conditions at any cross-section of the drier, absorption tower, etc., the former being determined by mass balances and the latter by equilibrium data. The height of a transfer unit is given by: HTU =

G k m aA tρg

(1.62)

where km is the mass transfer coefﬁcient, a is a speciﬁc area, At is a cross-sectional area of the drier, ρg is the density of the gas phase, and G is the gas ﬂow rate. In practice, it is found that HTU is a property of the type of drier and the material being dried but is independent of size and operating conditions. Therefore, HTU can be calculated from pilot plant experiments in which the height of the drier and the number of transfer units are known. Thus, the design of a similar drier can be obtained by scaling up the pilot plant results. Here again, the Colburn analogy is of great utility. From the arguments used in the section about transfer analogies, a similar expression for the Colburn analogy has been proposed (Le Goff, 1980): NTU DSc2 / 3 NTU H Pr 2 / 3 = = NEU LfD LfH

(1.63)

where the quantity NEU is the number of energy units, and the Le Goff number (Lf) represents the deviation of the Colburn analogy from unity, the Lf number being in the range 1–0.02.

© 2003 by CRC Press LLC

Equations for NTUH and NEU are similar to Equation (1.58) for NTUD: T2

NTU H =

∫ T −T

(1.64)

P1 − P2 ρv2

(1.65)

T1

NEU =

dT

i

b

The number of transfer units is a basic parameter that appears frequently in the design of heat and mass exchangers (Van den Bulck et al., 1985; Khodaparast, 1992; Treybal, 1981).

NOMENCLATURE a At bn C, c * C Cp d D f g G h HTUD j J Jo J1 km k Km K m m m M n n

2

2

Speciﬁc area; cm or m 2 Cross-sectional area of drier; m Roots of Bessel function 3 Molar concentration; kg mol/m 3 Molar concentration at equilibrium; kg mol/m Speciﬁc heat capacity; kJ/kg K Characteristic dimension of a solid body; m or cm 2 2 Diffusion coefﬁcient; m /sec or cm /sec Friction factor; dimensionless 2 Acceleration constant for gravity, m/sec 2 Flow rate; kg/m sec 2 Heat transfer coefﬁcient; W/m K Height of a mass transfer unit, m The mass ﬂux of the mixture with respect to the average bulk velocity; 2 kg/m sec Molar diffusion ﬂux of the mixture with respect to the average bulk velocity; 2 kg mol/m sec Bessel function of ﬁrst kind and order zero Bessel function of ﬁrst kind and order one 2 Mass transfer coefﬁcient; m /sec Thermal conductivity; W/m K Overall mass transfer coefﬁcient based on the gas system concentration driving force Partition coefﬁcient; dimensionless Mass of the mixture; kg in Equation (1.1) Solubility constant between the two phases in Equation (1.48) 2 Mass ﬂux of the mixture relative to ﬁxed coordinates, kg/m sec in Equation (1.11) Molecular weight; kg/kg mol Mole of the mixture; kg mol in Equation (1.4) Relative position in Equations (1.7) and (1.12)

© 2003 by CRC Press LLC

n N NEU NTUD p P q r R R S′ T t u U v V V V w x x X z Z

Mass bulk ﬂux of the mixture relative to stationary coordinates, kg 2 mol/m sec 2 Molar bulk ﬂux of the mixture relative to ﬁxed coordinates; kg mol/m sec Number of energy units Number of mass transfer units Partial pressure; atm Pressure; atm Heat ﬂow rate; W Radial coordinate Radius; cm or m in Equations (1.42) and (1.43) Gas constant; joules/g mol K in Equation (1.38) Shape factor Temperature; K Time; sec Mass diffusion velocity of the system relative to the mass bulk velocity; m/sec Molar diffusion velocity of the system relative to the molar bulk velocity; m/sec Mass bulk velocity of the mixture relative to stationary coordinates; m/sec 3 Volume of the mixture, m in Equation (1.1) 3 Molal volume of the system; m /kg mol in Equation (1.34) Molar bulk velocity measured with respect to ﬁxed coordinates; m/sec Mass fraction of the mixture Rectangular coordinate Mole fraction of the mixture in Equation (1.29) Dimensionless time Rectangular coordinate Height of a drier; m

GREEK SYMBOLS α β δ ε µ ν ρ σAB τ ΩD ϕ

2

Thermal diffusivity; cm /sec Coefﬁcient of thermal expansion; 1/K Thickness of a hypothetical stagnant ﬁlm; cm or m Porosity Viscosity; centipoises 2 Kinematic viscosity; m /sec 3 Mass concentration of the mixture or ﬂuid density; kg/m Collision diameter; °A Tortuosity Collision integral for molecular diffusion; dimensionless Association parameter

REFERENCES Crank, J., The Mathematics of Diffusion, 2nd ed., Oxford University Press, London, 1975. Cussler, E.L., How we make mass transfer seem difﬁcult, Chem. Eng. Educ., 18(3), 124–127, 149–152, 1984.

© 2003 by CRC Press LLC

Geankoplis, C.J., Transport Processes and Unit Operations, 3rd ed., Prentice-Hall., London, 1993. Gekas, V., Transport Phenomena of Foods and Biological Material, CRC Press, Boca Raton, FL, 1992. Khodaparast, K.A., Predict the number of transfer units for cooling towers, Chem. Eng. Progress, 4, 67–68, 1992. Le Goff, P., Performance energétique des echangeurs de matière et de chaleur: interprétation energétique des analogies de Reynolds et de Colburn, Chem. Eng. J., 20, 197–209, 1980. Sherwood, T.K., A review of the development of mass transfer theory, Chem. Eng. Educ., 3, 204–213, 1974. Sherwood, T.K., Pigford, R.L., and Wilke, C.R., Mass Transfer, McGraw-Hill Kogakusha, Ltd., Tokyo, 1975. Treybal, R.E., Mass Transfer Operations, 3rd ed., McGraw-Hill International Editions, 1981. Van den Bulck, E., Mitchell, J.W., and Klein, S.A., Design theory for rotary heat and mass exchangers II. Effectiveness number of transfer units method for rotary heat and mass exchangers, Int. J. Heat Mass Transfer, 28(8), 1587–1595, 1985. Welty, J.R, Wicks, C.E., and Wilson, R.E., Momentum, Heat and Mass Transfer, 3rd ed, John Wiley & Sons, New York, 1984. White, F.M., Heat and Mass Transfer, Addison-Wesley, Reading, MA, 1988.

© 2003 by CRC Press LLC

2

Heat Transfer in Food Products D.R. Sepúlveda and G.V. Barbosa-Cánovas

CONTENTS 2.1 2.2

Introduction General Background 2.2.1 Thermal Properties of Foods 2.2.1.1 Speciﬁc Heat 2.2.1.2 Thermal Conductivity . 2.2.1.3 Thermal Diffusivity 2.2.1.4 Surface Heat Transfer Coefﬁcient 2.2.2 Heat Transfer by Conduction 2.2.2.1 Steady State 2.2.2.2 Nonsteady State 2.2.3 Heat Transfer by Convection 2.2.3.1 Natural Convection 2.2.3.2 Forced Convection 2.2.4 Heat Transfer by Radiation 2.3 Conclusions References

2.1 INTRODUCTION Heating and cooling are common activities in food processing. Several operations involving heating of raw foods are performed for different purposes, such as reduction of the microbial population, inactivation of enzymes, reduction of the amount of water, modiﬁcation of the functionality of certain compounds, and of course, cooking. On the other hand, heat is removed from foods to reduce the rate of its deteriorative chemical and enzymatic reactions and to inhibit microbial growth, extending shelf life by cooling and freezing. Heat transfer plays a central role in all of these operations; therefore, food engineers need to understand it in order to achieve better control and avoid under- or over-processing, which often results in detrimental effects on food characteristics. In practice, heat transfer to or from foods can be attained either by indirect or direct methods. Indirect methods involve the use of heat exchangers that isolate the product from the medium used as a source or sink

© 2003 by CRC Press LLC

TABLE 2.1 Examples of Direct and Indirect Heating and Chilling

Direct Indirect

Heating

Chilling

Frying, boiling, baking, and grilling solid foods Fluid food pasteurization; canned products sterilization

Fluidized bed individual quick freezing (IQF) Fluid food cooling; ice production

of heat. Direct methods allow contact between the food and the heating/cooling medium. Examples of these methods can be found in Table 2.1. Indirect heating methods use gases and vapors, such as steam or air, and liquids, such as water or organic compounds, as a source of thermal energy. Chilling by  indirect methods involves the use of coolant gases, such as ammonia or Suva , or the use of coolant liquids, such as water or ethylene glycol. Direct heating can be attained by means of hot air, oil, infrared energy, and dielectric or microwave methods, among others. Direct chilling can be achieved by the use of cold air or by the application of the Peltier effect.

2.2 GENERAL BACKGROUND The ﬁrst step in understanding heat transfer is to deﬁne what heat is and how it diffuses through a single body or is transferred from one body to another. Heat is a nonmechanical form of energy transferred between regions of different temperature. Heat transfer, therefore, is a natural energy transfer process in which energy tends to travel from a hotter point to a colder point in order to reach an equilibrium temperature. Now that we know that the temperature gradient is the driving force in heat transfer processes, and therefore that if a temperature difference exists, energy transference will occur, a couple of questions arise. How fast will this energy transfer process occur? How will the energy diffuse through foods? The answers to these questions are not easy. Great efforts have been made to try to answer these questions, and several models have been developed to describe heat transfer behavior in different systems under different conditions. The heat transfer mode governing the process is deﬁned by the physical state of the bodies and their relative position. If a heat gradient exists between two solid bodies in contact, the heat transfer will proceed by conduction. If the same gradient exists between two ﬂuids, or between a ﬂuid and a solid, the energy will be transferred by convection. Finally, any body with a temperature above absolute zero will radiate energy in the form of electromagnetic waves transferring heat by radiation. Besides the physical state or relative position, other physical properties of the bodies involved in these processes inﬂuence the heat transfer rate. Characteristics such as form, size, structure, thermal conductivity, speciﬁc heat, density, and viscosity, among others, are of paramount importance in the deﬁnition of the behavior of a system. Early developments in the study of heat transfer in the chemical engineering ﬁeld assumed controlled situations dealing with well-deﬁned substances with ﬁxed

© 2003 by CRC Press LLC

physical characteristics and clearly deﬁned heat transfer modes. However, actual situations in food engineering involve more than one mode of heat transfer simultaneously, and frequently some of the physical characteristics of food, such as density, form, or viscosity, change as heat modiﬁes the chemical structure, affecting the food’s thermal behavior. Furthermore, foods usually have neither regular form nor homogeneous or isotropic behavior. Finally, some particular features of food being heated, such as nonuniform evaporation of water, crust formation, or closing or opening of pores, are of such complexity that they make the modeling of this process difﬁcult or impracticable. Nevertheless, some of these drawbacks have been overcome, and the modeling of several speciﬁc practical situations is possible, mainly due to the development of knowledge of empirical relations that properly suit these speciﬁc processes. Present-day analytical techniques, such as the ﬁnite element method, allow for the modeling of situations characterized by nonuniform thermal properties that change with time, temperature, and location, so that great developments can be expected in the modeling of heat transfer processes in foods. The objective of this chapter is not to describe all of these speciﬁc models, but to introduce the reader to a practical approach to the study of heat transfer in foods. Classic models constructed over assumptions of homogeneity and isotropy will be introduced in order to provide a basic knowledge that will enable the modeling of simple systems and the understanding of more elaborate and speciﬁc models. Now we will focus on some of the most important engineering properties of foods and how they can be measured or calculated in order to use them in further modeling of heat transfer processes.

2.2.1 THERMAL PROPERTIES

OF

FOODS

As stated before, the modeling of heat transfer processes is dependent on some of the physical properties of the foods involved. As mathematical techniques become more elaborate, a higher accuracy is needed in the measurement or calculation of properties such as speciﬁc heat, thermal conductivity, thermal diffusivity, and surface heat transfer coefﬁcient. These properties will be discussed below. 2.2.1.1 Speciﬁc Heat Speciﬁc heat (Cp) is an exclusive property of every substance, and it is deﬁned as the amount of energy needed to increase the temperature of one kilogram of matter by one degree Celsius; therefore, its units are J/kg°C. This property is not dependent upon temperature or mechanical structure (e.g., density). It has been found that a strong correlation exists between a food’s composition and its speciﬁc heat. Derived from the deﬁnition of speciﬁc heat, the amount of heat Q required to increase the temperature of a body with mass m from an initial temperature T1 to a ﬁnal temperature T2 is: Q = m Cp (T2 – T1)

(2.1)

In order to determine the Cp value for a speciﬁc substance or food, differential scanning calorimetry (DSC) is used. Comprehensive data have been gathered, and tables containing Cp values for many products are available in the literature (American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1985).

© 2003 by CRC Press LLC

However, as the water content and composition of foods have been found to affect the Cp value, the data presented in the literature are bound to speciﬁc water contents and formulations, thus reducing their usefulness. For a more practical way to ﬁnd the Cp value, several empirical mathematical expressions have been developed. These expressions can vary from product to product and sometimes even from author to author. Some of these expressions are based only on the water content, having the form Cp = C1 + C2W, where W stands for water content and the constants are deﬁned depending on the situation and product. Examples of these expressions are: Cp = 0.837 + 3.349W

Siebel, 1982

(2.2)

Cp = 1.382 + 2.805W

Dominguez et al., 1974

(2.3)

Cp = 1.470 + 2.720W

Lamb, 1976

(2.4)

More complex expressions including other food components besides water have been developed, and some examples are shown below. Cp = 2.309Xf + 1.256Xs + 4.187W

Charm, 1971

(2.5)

Cp = 1.424Xc + 1.549Xp + 1.675Xf + 0.837Xa + 4.187W Heldman and Singh, 1981 (2.6) where Xc stands for mass fraction of carbohydrates, Xp for proteins, Xf for fat, Xa for ash, and W for water. Generic expressions for mixtures are also available: Cp =

∑ (C Cp ) i

i

Choi and Okos, 1986a

(2.7)

i

where Ci is the mass concentration of each constituent i and Cpi its corresponding Cp. 2.2.1.2 Thermal Conductivity Thermal conductivity (k) is a characteristic that tells us how effective a material is as a heat conductor. As stated in Fourier’s law for heat conduction, this constant is a proportionality factor needed for calculations of heat conduction transfer processes. This physical property can be directly measured from a food material using a thermocouple and a heater, as described in detail by Mohsenin (1980). The suited units for this property are W/m°C. Some data have been gathered and can be found in the literature (American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1985). Thermal conductivity of foods depends mainly on the composition of the food, but factors such as ﬁber orientation and void spaces have an inﬂuence on the heat ﬂow paths through food; therefore, it is important to describe the bulk condition in addition to the composition when reporting a k value. As in the case of speciﬁc heat, some empirical expressions to calculate thermal conductivity values for different foods have been developed. Some examples are: For fruits and vegetables: k = 0.148 + 0.493W where W is the mass fraction of water.

© 2003 by CRC Press LLC

Sweat, 1974

(2.8)

For sucrose solutions, fruit juices and milk: −3

2

k = 1.73 × 10 (326.8 + 1.0412T – 0.00337T )(0.44 + 0.54W)

Riedel, 1949 (2.9)

where T is temperature expressed in degrees Celsius. Other applicable more general expressions for mixtures are of the type: k=

∑ (k X ) i

v i

(2.10)

i

v

th

where ki is the thermal conductivity of the i component and Xi its volume fraction. When heat is ﬂowing through wrappings or compound layer materials, a total thermal conductivity coefﬁcient is needed. This expression can be calculated if the individual thermal conductivity coefﬁcients are known. For heat ﬂowing parallel to two layers, the total thermal conductivity coefﬁcient is given by kT = k1 (1 – c) + k2c

Hallstrom et al., 1988

(2.11)

where c is the volume fraction of material two. On the other hand, if the heat ﬂow is perpendicular to the material’s layer orientation: kT =

k1k 2 ck1 + (1 − c)k 2

Hallstrom et al., 1988

(2.12)

In the case of material mixtures with random size and orientation particles, the value for the total thermal conductivity value will be found between the value for parallel ﬂow and the value for perpendicular ﬂow. For mixtures of more than two components, the same method is followed, taking two materials at a time. 2.2.1.3 Thermal Diffusivity Thermal diffusivity (α) is a compounded thermal property of materials and is calculated from the values found for thermal conductivity, speciﬁc heat, and density of a particular product. α=

k Cpρ

(2.13)

where k is thermal conductivity, Cp speciﬁc heat, and ρ mass density. This thermophysical property links conductivity of the materials with their ability to store heat, thereby showing how heat will diffuse throughout the materials when heated. The units 2 for thermal diffusivity are m /sec. Although the recommended method to determine thermal diffusivity is a calculation based on experimentally measured values of thermal conductivity, speciﬁc heat, and density, other heat diffusivity measurement methods have been developed (Choi and Okos, 1983). Expressions based on water content and temperature of foods have also been developed. Some examples are: –8

–10

α = 5.7363 × 10 W + 2.8 × 10 T

© 2003 by CRC Press LLC

Martens, 1980

(2.14)

where W is the mass fraction of water and T is the temperature expressed in degrees Kelvin, and –8

α = 8.8 × 10 (1 – W) + α wW

Dickerson, 1969

(2.15)

where α w is the thermal diffusivity of water at the studied temperature. As in the cases of other properties, the thermal diffusivity of mixtures can be calculated with a general expression: α=

∑ (α X ) i

i

Choi and Okos, 1986b

(2.16)

i

th

where αi is the thermal diffusivity of the i component and Xi its mass fraction. As thermal diffusivity can be calculated from other thermal properties, data are not frequently found in the literature. 2.2.1.4 Surface Heat Transfer Coefﬁcient The heat transfer coefﬁcient (h) is not a property of materials themselves, but rather a property of convective heat transfer systems involving a solid surface and a ﬂuid. This coefﬁcient is used as a proportionality factor in Newton’s law of cooling, adjusting for the characteristics of the system under study. To deﬁne the value of this factor, it is necessary to characterize the convective medium and the surface involved in the convective heat transfer process. Some of the characteristics involved in the calculation of the heat transfer coefﬁcient are the ﬂuid’s velocity, viscosity, density, thermal conductivity, and speciﬁc heat. The form and surface texture of the solid involved are also important. As can be determined from a dimensional analysis of Newton’s cooling law, the units for the heat transfer 2 coefﬁcient are W/m °C. Since the heat transfer coefﬁcient is a property of the system rather than of the material, its measurement is difﬁcult, and several empirical expressions have been developed to overcome this problem. Some of these expressions will be reviewed below in the section dealing with heat transfer by convection. A compilation of surface heat transfer coefﬁcient data and empirical expressions to calculate this coefﬁcient can be found in the 1985 edition of the ASHRAE Handbook of Fundamentals. Further information regarding measurement of the heat transfer coefﬁcient can be found in the literature (Arce and Sweat, 1980). Now that we have shown methods for determining the most relevant thermal properties of foods, we will ﬁnd out how to use them to model heat transfer processes. The particulars of the different heat transfer modes will be dealt with in the following sections.

2.2.2 HEAT TRANSFER

BY

CONDUCTION

Heat transfer in solids or highly viscous materials takes place by conduction. In this mode, energy is transferred among particles touching each other with no movement of material. As a solid material is heated on one of its faces, a gradient is established between the hot face and the opposite cooler face. This gradient is the driving force promoting the heat ﬂow from one face to the other. As heat penetrates the body,

© 2003 by CRC Press LLC

the interior temperature changes from point to point and across time. This period of time is known as the unsteady state period. Later, when heat has traveled all the way across the body and equilibrium in temperatures has been reached, the interior temperature of each point will remain the same with respect to time and will only depend on its relative position inside the body. At this moment, the steady state transfer regime has been reached, and the body is working as a heat conductor with a determined heat ﬂux going through it. Thus, the study of heat conduction can be divided into two main areas: the study of heat conduction in the steady state and the study of heat conduction in the nonsteady state. 2.2.2.1 Steady State The study of heat conduction in the steady state is useful in modeling the performance of insulators, heat exchangers, and other equipment used to transfer heat from one point to another, such as containers, pans, and walls. In these, the initial variations in internal temperature dependent on time have settled, and the temperature proﬁle inside the material is stationary. The important issue here is to determine the amount of heat a particular material of a given thickness will allow to ﬂow through it. This mechanism can be modeled using Fourier’s law for heat conduction (Equation 2.17), which establishes that the heat ﬂux Qx transmitted through a solid in the direction x is inversely proportional to the thickness x and directly proportional to both the perpendicular transmission area A and to the temperature difference between its two opposite faces ∆T. The proportionality constant needed by this model is the thermal conductivity (k), one of the physical characteristics previously described. In some materials, thermal conductivity may vary with temperature. In these situations, the value corresponding to the average temperature should be used. Q x = − kA

∂T(x) ∂x

(2.17)

The negative sign represents the heat ﬂow from the hottest to the coolest surface, thereby rendering a positive value for the heat ﬂux. As can be seen, this equation describes heat ﬂow only in one direction. For a complete mathematical description, we would need to write similar equations for the other two directions in a three-dimensional system and to integrate over the entire volume. However, most steady state processing applications involve heat conduction in only one direction, as when heat ﬂows across walls or heat exchangers. For practical purposes, these materials can be considered as inﬁnite slabs, so we do not need to be concerned with a general mathematical solution. Qx = − k

A∆T x

(2.18)

Equation (2.18) is the integrated form of Fourier’s law for unidirectional steady state heat conduction over a path of constant cross-sectional area in a parallelepiped. It can be used directly to calculate the heat ﬂux through a body. Besides heat ﬂowing through ﬂat surfaces, another common situation in food engineering is the use of

© 2003 by CRC Press LLC

cylindrical containers or pipes; therefore, an expression for Fourier’s law on cylindrical surfaces is necessary. That expression is shown in Equation (2.19), Qx = − k

A lm ∆T x

(2.19)

where all the terms stand for the same characteristics as in the previous expression except for Alm, which in this case is the logarithmic mean of the inner and outer areas: A lm =

A1 − A 2 A ln 1 A   2

(2.20)

Another common situation is the presence of compounded walls. The introduction of the concept of thermal resistance can be of help when studying heat conduction in this kind of system. If thermal resistance R is deﬁned as the ratio of the thickness x over the area A and thermal conductivity k, R=

x kA

(2.21)

Fourier’s law takes a form identical to Ohm’s law for electric current ﬂow, and all mathematical manipulations can be performed as in electrical calculations. I=

∆V R

(2.22)

Q=

∆T R

(2.23)

Here, the ﬂow of electric current I is directly proportional to the voltage difference ∆V and inversely proportional to the electric resistance R. In the same way, the heat ﬂow Q is directly proportional to the temperature difference ∆T and inversely proportional to the thermal resistance R. This analogy shows that in the case of several different layers placed in series (normal heat ﬂow), the overall temperature difference is the sum of the individual temperature differences, and the same Q ﬂows through all the resistances. Therefore, the total thermal resistance is simply the sum of the individual resistances. On the other hand, when there is parallel heat ﬂow through several layers, the analogy indicates that we have a parallel system. Therefore, the total Q is the sum of the Qx through the individual resistances, and the temperature differences for the individual resistances are all the same and equal to the overall temperature difference. In this case, the reciprocal of the total thermal resistance is equal to the sum of the reciprocals of the individual resistances. The use of these analogies allows us to predict heat transfer in compound systems. 2.2.2.2 Nonsteady State The study of heat conduction in the nonsteady state is pertinent when calculating processes in which the focus is to heat or cool a body instead of using it as a heat conduction medium. Such processes include freezing, cooking, and thermal sterilization

© 2003 by CRC Press LLC

of foods. In these cases, the main concern is to ﬁnd out how long it will take the coldest/hottest point in the body to reach the desired temperature. Moreover, the study of this phenomenon allows us to determine the time needed to process foods at a desired temperature or the temperature at a determined point at a given time. In nonsteady state heat transfer processes in which more than one heat transfer mode applies, conduction usually governs the process, as it is the slowest heat transfer mode. It is important to consider that heat conduction in foods is frequently a threedimensional phenomenon, as the food has ﬁnite dimensions and sometimes is immersed in the heat transfer medium, with heat being transferred through all its surfaces (as in oven baking or deep fat frying). Fourier’s second law of heat transfer for three-dimensional nonsteady state heat conduction states that:  ∂2 T ∂2 T ∂2 T  ∂T = α 2 + 2 + 2  ∂t ∂y ∂z   ∂x

(2.24)

where T stands for temperature, t for time, x, y, and z for the distance on the x, y and z axes, respectively, and α for thermal diffusivity, which is a physical characteristic of the materials, as previously discussed. To arrive at the analytical solution to this complex expression can be difﬁcult or impracticable. However, the analysis of some practical situations may be simpliﬁed through a couple of useful assumptions. The ﬁrst assumption supposes that we are dealing with a semi-inﬁnite body, also known as a thick solid. This semi-inﬁnite body is deﬁned as one with inﬁnite width, length, and depth. If a body with these characteristics is immersed in the heating medium, we can assume that heat will be transferred just from the surface toward the interior, following a straight trajectory to the center; therefore, Fourier’s law can be transformed into: ∂T ∂2 T =α 2 ∂t ∂x

(2.25)

where the x-axis corresponds to any one of the dimensions on a parallelepiped or to the radius on a sphere-like body. The solution to Equation (2.25) becomes simpler now and may be obtained by applying the boundary conditions, which are: T0 Initial temperature of the body at time 0 Tm Heating medium temperature acquired at the surface when immersed in the ﬂuid. The solution takes the form of Equation (2.26), where the temperature T at any point x, measured from the surface, can be determined using a dimensionless temperature ratio: hx

Tm − T  x  k = erf   +e  4αt  Tm − T0

2

 h +   αt  k

  x  h αt  +  erf   4αt  k  

(2.26)

where erf is the Gauss’ error function, which can be obtained from Table 2.2, and k is the thermal conductivity.

© 2003 by CRC Press LLC

TABLE 2.2 Gauss’ Error Function η

η) erf (η

η

η) erf (η

η

η) erf (η

0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64

0.00000 0.45110 0.09008 0.13476 0.17901 0.22270 0.25670 0.30788 0.34913 0.38933 0.42839 0.46622 0.50275 0.53790 0.57162 0.60386 0.63459

0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70

0.66278 0.69143 0.71754 0.74210 0.76514 0.78669 0.80677 0.82542 0.84270 0.88020 0.91031 0.93401 0.95228 0.96610 0.97635 0.98379

1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.20 3.40 3.60

0.98909 0.99279 0.99532 0.99702 0.99814 0.99886 0.99931 0.99959 0.99976 0.99987 0.99993 0.99996 0.99998 0.999994 0.999998 1.000000

Since, in this case, the heat is transferred from a ﬂuid to a solid surface, the surface heat transfer coefﬁcient h is incorporated into the solution. For situations where the heat transfer between the ﬂuid and the solid proceeds very efﬁciently, that is, if h is inﬁnite, the solid surface takes the medium temperature instantaneously, and Equation (2.26) can be simpliﬁed to: Tm − T  x  = erf    4αt  Tm − T0

(2.27)

Now that we know how to handle semi-inﬁnite bodies, a problem arises. The deﬁnition of a semi-inﬁnite body describes a body with inﬁnite dimensions, which in reality is not a possible situation. When can a body be considered as a semi-inﬁnite body for practical purposes? The concept of a semi-inﬁnite body in practice is better related to the system’s behavior than to the body dimensions. The surface heat transfer coefﬁcient, along with the thermal conductivity, plays a fundamental role in determining whether a body will exhibit a thick body response. If a ﬁnite body of a given thickness is studied in the early steps of heat penetration, it will exhibit a semi-inﬁnite body response as heat has only ﬂowed from the outside to the center; therefore, the ratio of thickness to time plays an important role as well. Schneider (1973) found a critical Fourier number to deﬁne when a body ceases to exhibit a thick body response: –0.3

Focritical = 0.00756 Bi

© 2003 by CRC Press LLC

+ 0.02

for 0.001 ≤ Bi ≥ 1000

(2.28)

The Fourier and Biot numbers are: Fo =

αt ( L )2

(2.29)

Bi =

hL k

(2.30)

where L is half the thickness of the body and t is the time the body has been exposed to the conditions studied. If the actual Fourier number exceeds the critical value, the body can no longer be considered to be a semi-inﬁnite body, and a different approach must be taken. Another possible approximation used to solve practical problems regarding heat conduction in a nonsteady state involves the assumption of inﬁnite bodies with simple geometry. Again, the concept of an inﬁnite body is just theoretical, as in practice no such bodies occur and, therefore, a practical deﬁnition is needed. An inﬁnite body is a body in which two of its dimensions are much larger than the third. In this situation, it can be expected that heat will reach the center of the body ﬁrst traveling the shortest way; that is, following the axis corresponding to the thinner dimension. Heat transfer through the remaining axes becomes negligible. This assumption applies to inﬁnite slabs with thickness 2xo and inﬁnite longitude and width, inﬁnite cylinders with radius r and inﬁnite length, and spheres. Analytical solutions for this kind of problem can be developed using dimensionless ratios. Expressions for temperature Y and position n are: Y=

Tm − T Tm − T0

(2.31)

x x0

(2.32)

n=

where Tm is the temperature of the cooling or heating ﬂuid surrounding the solid, T0 is the initial temperature of the body, T is the temperature at a point x, x0 is the distance from the center or midplane to the surface, depending on the body’s shape, and x is the distance from the center or midplane to the selected point. Time and thermal diffusivity are introduced using Fourier module τ, while surface heat transfer coefﬁcient and thermal conductivity are both included using the Biot module in m: τ = Fo =

αt x 20

(2.33)

1 k = Bi hx 0

(2.34)

∂T ∂2 Y =α 2 ∂t ∂n

(2.35)

m= Modifying Equation (2.25), we obtain:

© 2003 by CRC Press LLC

which is the dimensionless form for Fourier’s second law. Applying boundary conditions, Equation (2.35) can be analytically solved by partial derivatives for different situations. However, the analytical solutions for an inﬁnite slab, an inﬁnite cylinder, and a sphere have already been developed and can be found in graphic form as shown in Figures 2.1, 2.2, and 2.3. Using these ﬁgures, it is possible to ﬁnd the Y value for a given set of conditions. First, the correct group of lines is chosen based on the calculated m value. Next, one of the lines is picked depending on the n value. Finally, by ﬁnding the intersection between the selected line and the calculated Fourier modulus τ, the proper Y value will be determined. Once the Y value is obtained, only a simple substitution from Equation (2.31) is needed. A deviation from the assumption of an inﬁnite body is apparent in several cases where the ratio of length or width to thickness is not too large. In these cases, the application of Newman’s rule can be of help. Newman demonstrated that for a ﬁnite solid body being heated or cooled, the internal variation of temperature as a function of time and position could be stated as: Y = YxYyYz

(2.36)

1 m=∞ m=6

m m

x

x

=2

=2 n = 1.0 0.8 0.6 0.4 0.2 0.0

m = 1

m

0.1

0

= 1 m= 0.5

m= 0.5

Y m= 0

m= 0

n = 1.0 0.8 0.6 0.4 0.2 0.0

0.01 n = 0.8 0.6 0.4 0.2 0.0

n = 1.0 0.8 0.6 0.4 0.2 0.0

m=0 n=1

0.001 0

0.5

1

1.5

2

2.5

3

τ = (Fo) FIGURE 2.1 Dimensionless temperature chart for an inﬁnite cylinder.

© 2003 by CRC Press LLC

3.5

1

m=∞

x x?

m=6

m= m=

x?

n = 1.0 0.8 0.6 0.4 0.2 0.0

2

2

0.1 m = 1

m =

n = 1.0 0.8 0.6 0.4 0.2 0.0

1

Y m .5 =0

m .5

=0

m= 0

m=

0.01

0

n = 1.0 0.8 0.6 0.4 0.2 0.0

n = 0.8 0.6 0.4 0.2 0.0

m=0 n=1

0.001 0

1

2

3

4

5

6

τ = (Fo) FIGURE 2.2 Dimensionless temperature chart for an inﬁnite slab.

where Y is the dimensionless temperature deﬁned in Equation (2.31), and values Yx, Yy and Yz are the dimensionless temperature values with respect to the x, y, and z axes, respectively, which can be obtained from Figures 2.1, 2.2, and 2.3. Newman’s rule can be applied in the calculation of heat transfer processes on ﬁnite parallelepipeds and cylinders, as it can be understood that a ﬁnite body results from the conjunction of three inﬁnite bodies.

2.2.3 HEAT TRANSFER

BY

CONVECTION

Heat transfer within a ﬂuid will occur by convection. In this heat transfer mode, energy ﬂows as a result of bulk movement of the ﬂuid due to a temperature gradient. The molecules in the ﬂuid will move due to density changes and will interact with each other at different points of the ﬂuid, exchanging energy. Since the efﬁciency of this process depends on the extent of mixing within the ﬂuid, ﬂow characteristics are as important as thermal properties in determining heat ﬂow rate. Most processing applications of heat transfer by convection involve steady state heat transfer from a solid surface to a ﬂuid in contact with it or vice versa. Heat transfer is deﬁned as the rate of heat ﬂowing through the interface between the ﬂuid and the solid. The amount of energy ﬂowing through this interface is proportional to the temperature gradient and to the interchange surface. This relationship is deﬁned by Equation (2.37),

© 2003 by CRC Press LLC

1

m=∞

x m=

m m

0.1

=

x

6

=

0

2

2

m= 1

m=

m=

1

0.5

m=

Y

n = 1.0 0.8 0.6 0.4 0.2 0.0

0.5

n = 1.0 0.8 0.6 0.4 0.2 0.0

m=0

m=0

n = 1.0 0.8 0.6 0.4 0.2 0.0

0.01 n = 0.8 0.6 0.4 0.2 0.0

m=0 n=1

0.001 0

0.5

1

1.5

2

2.5

3

3.5

τ = (Fo) FIGURE 2.3 Dimensionless temperature chart for a sphere.

known as Newton’s law of cooling: Q = hA ∆T

(2.37)

where Q corresponds to heat ﬂux, A to the interchange area, ∆T to the difference between the ﬂuid and solid temperatures, and h to the proportionality coefﬁcient, known as the heat transfer coefﬁcient. Bulk molecular motion can be induced by differences in the ﬂuid’s temperature at different points within it, developing a buoyant force. This process is known as natural convection. The coefﬁcient of thermal expansion of a ﬂuid (β) is the main property governing natural convection. Without the existence of gravity and thermal expansion, natural convection would not be possible. Mixing efﬁciency in natural convection depends on the temperature gradient. A small temperature difference between the ﬂuid and solid in contact will promote weak currents with a low heat transfer coefﬁcient. On the other hand, when a ﬂuid is forced to ﬂow past a surface by mechanical means such as a pump or a fan, higher velocities are obtained and strong currents are induced regardless of natural convection. High heat transfer coefﬁcients can be reached due to more efﬁcient mixing. This regime is known as forced convection. In practice, forced convection is the most used convective heat transfer mode, as greater heat transfer can be accomplished and better control of the system can be easily established.

© 2003 by CRC Press LLC

As stated by Newton’s cooling law, heat ﬂux is proportional to the contact area and temperature gradient, both easily measurable. However, several problems arise when determining the proportionality constant h. This constant depends on several factors, including the ﬂuid’s properties such as viscosity, density, speciﬁc heat, and thermal conductivity; the nature of the ﬂow (i.e., its velocity, natural or forced convection, streamline or turbulent ﬂow); and other physical characteristics of the system such as size and shape. In practice, exact derivation of heat transfer coefﬁcients from the basic ﬂuid ﬂow and heat conduction equations is not possible, and the use of empirical correlations is needed. These empirical correlations, which have been developed from a theoretical basis and experimental observations, are expressed in dimensionless numbers, allowing us to apply these generic expressions to different ﬂuids and systems. A basic general dimensionless expression that connects the heat transfer coefﬁcient to particular characteristics of ﬂuids and systems has been proposed. This expression states that the Nusselt number Nu is proportional to the product of the Reynolds (Re), Prandtl (Pr), and Grashof (Gr) numbers, as shown in Equation (2.38): Nu = φ [(Re)(Pr)(Gr)]

(2.38)

The Nusselt number is a dimensionless form for the heat transfer coefﬁcient. The other factors involved in this ratio are the thermal conductivity of the ﬂuid k and the characteristic dimension of the system d, which is the diameter for a round pipe or the length for a ﬂat surface. Nu =

hd k

(2.39)

The Reynolds number introduces information about the ﬂuid characteristics and ﬂow regime. It can be considered as the ratio of macroscopic ﬂow to internal friction. When this ratio exceeds a certain value, the inertial force predominates, converting ﬂow from a laminar form into a turbulent one. This number involves the characteristic dimension d, and the ﬂuid’s properties density ρ, viscosity η, and velocity v. For physical properties such as viscosity or density that vary with temperature, the value at the arithmetic mean temperature between the inlet and outlet points will be used. Re =

ρvd η

(2.40)

The Prandtl ratio deals only with physical properties of the ﬂuid and behaves as a physical constant. This expression involves speciﬁc heat Cp, viscosity η, and thermal conductivity k. Pr =

Cpη k

(2.41)

Finally, the Grashof number represents the ratio of buoyancy to internal friction. This quantity involves the characteristic dimension of the system d, the acceleration

© 2003 by CRC Press LLC

due to gravity g, the thermal expansion coefﬁcient β, the density of the ﬂuid ρ, the viscosity η, and the temperature difference between a surface and the ﬂuid ∆T: Gr =

β g ∆T d 3ρ2 η2

(2.42)

As can be seen, all the process variables included in these dimensionless ratios, with the exception of h, can be measured; therefore, a heat transfer coefﬁcient value for a given set of conditions can be calculated using Equation (2.38). However, a difﬁculty remains, as the exact proportionality factor has not been stated. This exact proportionality factor varies from situation to situation, and empirical values have been found for several speciﬁc situations, as a general expression is not possible. Equation (2.38) can be further modiﬁed into two generic expressions. From simple examination of the meaning of each of the dimensionless ratios, it is apparent that when dealing with natural convection, the buoyancy effect governs the process, and the importance of the Reynolds number subsides under the importance of the Grashof number, leading to: Nu = φ [(Pr)(Gr)]

(2.43)

On the other hand, Equation (2.38) can be practically modiﬁed for forced convection as the Reynolds number turns out to be more important than the Grashof number under this ﬂow regime; hence: Nu = φ [(Pr)(Re)]

(2.44)

Now we will review some empirical expressions developed for particular, though frequent, situations. More information about expressions regarding heat transfer by convection in different situations is found extensively throughout the specialized literature. 2.2.3.1 Natural Convection The most common expression used for natural convection in Newtonian ﬂuids is: a

Nu = K [(Pr)(Gr)]

(2.45)

where values for constants K and a in some speciﬁc situations are given in Table 2.3. 2.2.3.2 Forced Convection The relationship most commonly used for turbulent ﬂow inside tubes is known as the Dittus–Boelter equation: 0.8

n

Nu = 0.023 (Re) (Pr)

(2.46)

where n = 0.4 for a ﬂuid being heated or n = 0.3 for a ﬂuid being cooled. This 4 expression is valid for Re > 10 and 0.7 < Pr < 160.

© 2003 by CRC Press LLC

TABLE 2.3 Values of K and a for Equation (2.45) Conﬁguration

(Pr)(Gr)

K

a

<10 4 9 10 . < (Pr)(Gr) < 10 9 >10 –5 <10 –5 –3 10 < (Pr)(Gr) < 10 –3 10 < (Pr)(Gr)r < 1 –4 1 < (Pr)(Gr) < 10 –4 9 10 < (Pr)(Gr) < 10 9 >10 5 7 10 < (Pr)(Gr) < 2 × 10 (FU) 7 10 2 × 10 < (Pr)(Gr) < 3 × 10 (FU) 5 10 3 × 10 < (Pr)(Gr) < 3 × 10 (FD)

1.36 0.59 0.13 0.49 0.71 1.09 1.09 0.53 0.13 0.54 0.14 0.27

1/5 1/4 1/3 0 1/25 1/10 1/5 1/4 1/3 1/4 1/3 1/4

4

Vertical surfaces L = vertical dimension 0.9 m Horizontal cylinder L = diameter 0.2 m

Horizontal ﬂat surfaces

Note: FU = Facing upward; FD = Facing downward. Data from Heldman, D.R., and Singh, R.P., Food Process Engineering, 2nd ed., AVI, Westport, CT, 1981.

For liquid ﬂowing inside tubes in a laminar ﬂow (Re < 2100), a suitable equation is 1

d  3 η   Nu = 1.86 (Pr)(Re)     L    ηW  

0.14

(2.47)

where d/L is the diameter/length ratio and η/ηW is the ratio of the bulk viscosity to the viscosity at the wall. The equation used for a liquid ﬂowing in turbulent ﬂow outside a solid body is 0.52

Nu = [0.35 + 0.47(Re)

0.3

] (Pr)

(2.48)

and the equation for a liquid ﬂowing in laminar ﬂow (Re < 200) outside a solid body is 0.43

Nu = 0.86(Re)

2.2.4 HEAT TRANSFER

BY

0.3

(Pr)

(2.49)

RADIATION

Heat radiation is another way to dissipate energy. Any body with a temperature above absolute zero emits electromagnetic radiation. The wavelength of this radiation varies as a function of the body temperature. The higher the temperature, the more

© 2003 by CRC Press LLC

energetic the radiation; therefore, the smaller the wavelength. Heat radiation does not need a material in which to propagate and can travel through a vacuum. Additionally, heat transfer by radiation does not require a temperature gradient to proceed and therefore occurs constantly throughout nature. However, for practical purposes, use of heat transfer by radiation in food engineering is limited to the use of infrared radiation, dielectric heating, and microwave heating. Use of infrared radiation implies the use of electromagnetic radiation with wavelengths between visible light and radio waves (0.76–1000 µm). Often, the infrared source has a high temperature (500–3000°C), and heat transfer by convection is also taking place and cannot be ignored unless the process occurs under vacuum, as in the case of freeze drying. Examples where heat transfer by infrared radiation is present are grilling and the use of electrical resistances. As penetration of this kind of radiation is poor, the heating effect of infrared radiation has an impact only on the surface of the body, and heat transfer through the body proceeds by conduction or convection. Although infrared radiation is almost always present in heat transfer processes, generally its effect is not as important as the effect of convection, and its contribution has already been taken into account by the empirical equations used to model heat transfer by convection. Dielectric heating such as microwave or radio frequency heating is generally used when large objects need to be quickly and uniformly heated. The principle underlying the operation of these methods lies in the ability of some wavelengths to induce vibration in some dipolar molecules such as water, producing intermolecular friction and thereby increasing the temperature. Using these methods, food products are heated volumetrically, that is, at all points at the same time. The frequencies used for radio frequency heating are in the range of 10 to 100 MHz, while the frequencies used for microwave heating are a little higher, normally 915 to 2450 MHz. The dielectric heating methods described above involve the “instantaneous” generation of heat within the product. Conduction and convection take command of the heat transfer process after heat has been generated. The study of heating processes such as microwave heating, radio frequency heating, and ohmic heating is beyond the scope of this chapter, and no further details will be discussed here.

2.3 CONCLUSIONS The modeling of heat transfer in foods is a difﬁcult task. Often, two or even three heat transfer modes proceed in a system at the same time. Some thermal properties of foods can vary with changes in temperature, and further problems arise because food is seldom regular in shape or homogeneous. However, some assumptions and empirical relations allow the development of practical models that describe certain processes with sufﬁcient precision. Nowadays, some efforts are being made to apply ﬁnite element method to take into account the changing properties of foods and to better model complex food heating or cooling processes. Most empirical heat transfer models applicable to foods are highly speciﬁc, and general analytical models are seldom encountered.

© 2003 by CRC Press LLC

REFERENCES American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., ASHRAE Handbook of Fundamentals, American Society of Heating, Refrigerating and AirConditioning Engineers, Inc., Atlanta, 1985. Arce, J.A. and Sweat, V.E., Survey of lashed heat transfer coefﬁcients encountered in food refrigeration processes, ASHRAE Trans., 86(2), 235–260, 1980. Charm, S.E., Fundamentals of Food Engineering, AVI, Westport, CT, 1971. Choi, Y. and Okos, M.R., The thermal properties of tomato juice concentrates, Trans. ASAE, 26, 305–311, 1983. Choi, Y. and Okos, M.R., Effects of temperature and composition on the thermal properties of foods, in Food Engineering and Process Applications, vol. 1, Maguer L. and Jelen, P., Eds., Elsevier, New York, 1986a. Choi, Y. and Okos, M.R., Thermal properties of liquid foods: review, in Physical and Chemical Properties of Foods, Okos, M.R., Ed., American Society of Agricultural Engineers, St. Joseph, MI, 1986b. Dickerson, R.W., Thermal properties of foods, in The Freezing Preservation of Foods, vol. 2, 4th ed., Tressler, D.K., Van Arsdel, W.B., and Copley, M.J., Eds., AVI, Westport, CT, 1969. Dominguez, M., De Elvira, C., and Fuster, C., Inﬂuence of air velocity and temperature on the two-stage cooling of perishable large-sized products, Annexe Bressanone, Bull. IT Regrig., Annexe 83–90, 1974. Hallstrom, B., Skjoldebrand, C., and Tragardh, C., Heat Transfer and Food Products, Elsevier, New York, 1988. Heldman, D.R. and Singh, R.P., Food Process Engineering, 2nd ed. AVI, Westport, CT, 1981. Lamb, J., Inﬂuence of water on the thermal properties of foods, Chem. Ind., 24, 1046–1048, 1976. Martens, T., Mathematical model of heat processing in ﬂat containers, in Operaciones Unitarias en la Ingenieria de Alimentos, Ibarz, A. and Barbosa-Canovas, G., Eds., Technomic Publishing Company, Lancaster, PA, p. 317. Mohsenin, N.N., Thermal Properties of Foods and Agricultural Materials, Gordon and Breach Science Publishers, Inc., New York, 1980. Riedel, V.L., Wärme leitfähigkeitsmessungen an Zuckerlösungen, Frucht säften und Milch, Chem. Ing. Technik., 21, 340, 1949. Schneider, P.J., Conduction, in Handbook of Heat Transfer, Rohsenow, W.M. and Hartnett, J.P., Eds., McGraw-Hill, New York, 1973. Siebel, J.E., Speciﬁc heat of various products, Ice Refrigeration, 2, 256–257, 1982. Sweat, V.E., Experimental values of thermal conductivity of selected fruits and vegetables, J. Food Science, 39, 1080, 1974.

© 2003 by CRC Press LLC

3

Introductory Aspects of Momentum Transfer Phenomena J.F. Vélez-Ruiz

CONTENTS 3.1 3.2

Introduction Momentum Transfer Variables 3.2.1 Flux of Momentum 3.2.2 Mass Conservation 3.2.3 Energy Balance 3.3 Laminar and Turbulent Flow 3.3.1 Laminar Flow 3.3.2 Turbulent Flow 3.3.3 Transportation of Fluids 3.4 Rheological Properties of Foods 3.4.1 Rheology 3.4.2 Rheological Models 3.4.3 Temperature and Concentration Variables 3.5 Simultaneous Transfer Phenomena 3.6 Final Remarks Nomenclature References

3.1 INTRODUCTION Momentum transfer is a physical phenomenon present in almost any process of the food industry; often the heat and/or mass transfer phenomena occur in association with ﬂow, and it is difﬁcult to imagine a unit operation without moving streams. This phenomenon necessarily involves a convection mechanism between molecules or groups of molecules, or the momentum gradient would be null. In other words, momentum transfer is characterized by the tendency toward equilibrium. When momentum transfer is analyzed in the food ﬂuid ﬁeld, some particular considerations should be taken into account. Foodstuffs are biological materials consumed by humans and animals for nutritional purposes; in order to process the

© 2003 by CRC Press LLC

ﬁnal food products, the raw food material must be transformed to achieve the proper and desirable properties, providing a diversity of satisfactory factors. A food may be considered a multi-component mixture in which carbohydrates, lipids, proteins, and water are the macro constituents, and minerals and vitamins, among others, are the micro components. The type of component, its concentration, and its speciﬁc characteristics play important roles in the structure and engineering properties of each food product, particularly in ﬂuid motion. Food materials are inﬂuenced by many aspects such as variety, time of harvesting, ripeness stage, handling during transport, and of course, by process treatments. The nonNewtonian behavior of many food ﬂuids makes transfer momentum a complicated phenomenon. To explain transfer phenomena, a rigorous mathematical approach leads to differential equations that often are too difﬁcult to be solved analytically, especially when a transient instead of a steady state condition is involved; furthermore, the presence of many molecules or groups of molecules in natural or forced convection complicates analytical solution. For this reason, empirical and numerical methods have been developed to reach faster, more practical, and useful solutions. In food processing, the utilized raw materials are exposed to process conditions that transform, to a minor or major degree, the food’s native state. Differences in concentration, mechanical force, pressure, temperature, and/or velocity, which act as driving forces of the three transport phenomena, importantly affect the food product’s characteristics. Thus, mathematical and/or engineering modeling favors the predictability of those transport phenomena, particularly of momentum transfer, in order to control food quality and to produce a well speciﬁed end product. The fundamentals and applications of momentum transfer are themes widely covered by many authors. Therefore, the main purpose of this chapter is to present the basic principles and main process variables involved in momentum transfer phenomena. Two major ﬂuid motions are introduced: laminar and turbulent ﬂows. Rheological properties and simultaneous transfer phenomena are commented on brieﬂy, and ﬁnally, some general comments are given.

3.2 MOMENTUM TRANSFER VARIABLES The momentum of a ﬂuid may be deﬁned as the product of its mass and velocity at a given point; hence, changes in velocity per unit mass can result in momentum transport. Therefore, momentum transfer or ﬂuid motion depends upon the interrelation of three fundamental variables: mass, velocity, and time (Bennet and Myers, 1983; Fahien, 1983).

3.2.1 FLUX

OF

MOMENTUM

Considering that the velocity is a vector and the velocity gradient is a second-order tensor, the corresponding moment ﬂux or shear stress is also a second-order tensor,

© 2003 by CRC Press LLC

which for an incompressible ﬂuid is given by the following equation (Brodkey and Hershey, 1988): τ = − µ[∇v + (∇v)T ]

(3.1)

Equation (3.1) shows that the stress tensor (τ) is a function of the shear rate T tensor (∇v) and its transpose (∇v) . Velocity, a vector quantity, has three components, and any of these can vary in three directions. Since Equation (3.1) must be homogeneous, the stress tensor (ττ) must be a second-order tensor:  τ xx τ xy τ xz    τ =  τ yx τ yy τ yz       τ zx τ zy τ zz 

(3.2)

This stress tensor has a complicated physical interpretation due to the fact that it is utilized both as a momentum ﬂux and as a shear stress. The application/interpretation of this stress tensor, or force imposed on a unit of surface area, for a given material is conducted as a function of the speciﬁc conditions controlling a physical situation; for instance, in a steady simple shear ﬂow the number of components of the stress tensor is reduced to ﬁve (Rao, 1999; Steffe, 1992). Because the complete analysis of momentum transfer is too complicated, the solution for each particular physical situation has been studied and solved by many researchers, using both simple and complex analytical methods (Gekas, 1992; Toledo, 1991). And even though the solution for many practical situations has been developed, many physical phenomenon problems involving food ﬂuids remain to be solved. Furthermore, whatever the physical problem, the elementary variables are dimensions of the system, involved forces, particular properties of the process material, shear and normal stresses, time, and velocities, among the most important. Most of these variables are combined in those driving force balances known as dimensionless numbers, in which the variable’s participation depends on the physical phenomenon. Table 3.1 includes the common dimensionless numbers related to momentum transfer of Newtonian ﬂuids; the list could be extended if non-Newtonian behavior were considered (Bennet and Myers, 1983; Fahien, 1983; Welty et al., 1976; Vélez-Ruiz, 2001).

3.2.2 MASS CONSERVATION Sometimes it is not necessary to formulate a complete force balance in the solution of a new ﬂow problem; instead, it is more practical to start with the equations of mass conservation, momentum balance, and mechanical energy conservation, also known as equations of change (Bird et al., 1960).

© 2003 by CRC Press LLC

© 2003 by CRC Press LLC

TABLE 3.1 Momentum Transfer Dimensionless Numbers Variables Density, drag force, surface area, velocity Density, pressure, velocity Density, stress, velocity Characteristic dimension, gravity, velocity Agitator speed, diameter, density, power Agitator speed, diameter, volumetric ﬂow Characteristic dimension, density, velocity, viscosity Characteristic dimension, density, velocity, stress Same variables, including rheological properties

Relationship 2

FD/ρv A 2 P/ρv 2 τ/ρv 2 v /dg 3 5 P/ρN D 3 Q/ND vdρ/µ 2

v dρ/σ

Involved Forces

Name

Symbol

Drag force/inertial force Pressure force/inertial force Wall shear force /inertial force Inertial force /gravity force Power/inertial force Flow force /inertial force Inertial force /viscous force

Drag coefﬁcient Euler Friction factor Froude Power Pumping Reynolds

CD Eu f Fr Po P Re

Kinetic energy force/surface force

Weber

We

Generalized Hedstrom (GHe) and Reynolds (GRe), Hedstrom (He), and Plasticity (Pl) numbers

The developed mass conservation over a stationary volume element generates the equation of continuity:  ∂  ∂ρ ∂ ∂ = − ρv x + ρv y + ρvz  = −(∇ ⋅ ρv) ∂t ∂ x ∂ y ∂ z  

(3.3)

This equation describes the density rate of change resulting from the changes in the mass velocity vector (ρv) at a given point, the right hand term being the point product of ρv. The equation of motion for a volume element at a ﬁxed point, even though it is complicated for the x, y, and z directions, takes a single vector expression form (Bird et al., 1960; Liu and Masliyah, 1998): ∂ ρv = −[∇ ⋅ ρvv] − ∇P − [∇τ] + ρg ∂t

(3.4)

in which the different mathematical terms represent the contributions to the momentum balance: ∂ ρv = rate of momentum increase ∂t [∇ ⋅ ρvv] = rate of momentum gained by convection ∇P = pressure force on the element ∇τ = rate of momentum gained by viscous transfer ρg = gravitation force For an incompressible Newtonian ﬂuid, the x-component of the Navier–Stokes equations for the three components of the velocity vector for x, y, z coordinates appears as (Molerus, 1997):  ∂2 v  ∂v ∂v ∂v ∂v  ∂2 vx ∂2 vx  ∂P + µ 2x + + 2  ρ x + v x x + v y x + vz x  = − ∂x ∂y ∂z  ∂x ∂y 2 ∂z   ∂t  ∂x

(3.5)

3.2.3 ENERGY BALANCE Similarly, the mechanical energy balance can be applied to a stationary volume element through which the ﬂuid ﬂows, generating the corresponding equation with several terms: ∂  1 2 1 ρv = − ∇ ⋅ ρv 2 v − (∇ ⋅ Pv) − P( −∇ ⋅ v) − (∇ ⋅ [τ ⋅ v]) − ( − τ: ∇v) + ρ(v ⋅ g)     ∂t 2 2 (3.6) In which the meaning of each term is: ∂  1 2 ρv , rate of increase in the kinetic energy  ∂t  2 1  ∇ ⋅ ρv 2 v , net rate of input of kinetic energy due to bulk flow  2 

© 2003 by CRC Press LLC

(∇ ⋅ Pv), rate of work done by surrounding pressure P( −∇ ⋅ v), rate of reversible conversion to internal energy (∇ ⋅ [τ ⋅ v]), rate of work done by viscous forces ( − τ: ∇v), rate of irreversible conversion to internal energy ρ(v ⋅ g), rate of work done by gravity force As may be noted, the three preceding relationships were obtained in rectangular coordinates; thus, if the ﬂow problem involves curvilinear coordinates, the cylindrical or spherical corresponding equations should be applied. Additionally, the speciﬁc characteristics of the physical system and its properties will have to be considered.

3.3 LAMINAR AND TURBULENT FLOW Among the many types of ﬂow developed by ﬂuids, laminar and turbulent ﬂows are very important and commonly found, no matter what the speciﬁc physical situation. Several geometries, such as cylinder, coil, cube, helix, oven, parallel plates, shell and tubes, tube, and vessels containing food ﬂuids are frequently utilized in food process operations. It can be observed from Table 3.1 that the ratio of the inertial variables to the viscous force (Re) is determinant in the presence of streamline or turbulent ﬂow; therefore, the rheological nature of the food plays an outstanding role in ﬂow deﬁnition. From a practical viewpoint, the type of ﬂow may be established with the evaluation of the Reynolds number for Newtonians, whereas for non-Newtonian behavior the Generalized Reynolds and the critical Generalized Reynolds numbers should be computed.

3.3.1 LAMINAR FLOW Of the several geometries involved in food processing, tube ﬂow is the most important due to easy pipe manufacturing and a very high rate of handled volume to amount of construction material. In it, the shear stress and the velocity proﬁle are functions of the rheological behavior. The corresponding equations are introduced next and are extremely useful for most food ﬂuid systems: For shear stress: τ rz =

r( ∆P ) 2L

(3.7)

For the velocity distribution, the type of ﬂuid implies different relationships: 1. In the case of a Newtonian ﬂuid: 1  ∆P  2 vx =    (R − r 2 )  2   2µL 

© 2003 by CRC Press LLC

(3.8)

2. In cases of non-Newtonian behavior: a. Power law model: n   ∆P  vx =   n + 1  2 KL 

( 1n)

 R( n +1 n ) − r ( n +1 n )   

(3.9)

b. Herschel–Bulkley model (when R0 ≤ r ≤ R):

vx =

2L  1  1n ∆P + 1 K H  nH  H

 1    n +1  1   H    n +1  H   r∆P − τ   ( τ − τ ) − 0 0  2L   w    

(3.10)

c. Bingham plastic model (when R0 ≤ r ≤ R): vx =

1 µP

 ∆P R 2 − r 2 − τ R − r  ) 0(  4 L 

(

)

(3.11)

Similar equations can be developed or have been obtained for other geometries. For the aforementioned equations, four assumptions were considered: 1. 2. 3. 4.

Steady ﬂow Constant rheological properties and density No entrance or exit effects Prevalence of laminar ﬂow

Even though most industrial process ﬂows are turbulent, food materials may be the exception during transport due to their non-Newtonian nature.

3.3.2 TURBULENT FLOW There are many considerations and equations for ﬂows under turbulent conditions; in this type of ﬂow, the average and the instantaneous/point velocity are normally different as a consequence of the velocity ﬂuctuation for a given volume element of ﬂuid. Several approaches, such as the Boussinesq theory, Prandtl mixing length, analogies between the transport phenomena, and ﬁlm and penetration theories, among others, have been proposed for the modeling of turbulence (Brodkey and Hershey, 1988). The mathematical relationships for velocity distribution, when turbulent ﬂow is present, are known as “universal velocity distribution” equations. They are valid inside channels and smooth tubes in which the ﬂow has been fully developed, with most of the boundary layer arising from Prandtl’s theory:

© 2003 by CRC Press LLC

+

For the wall region or viscous sublayer, y ≤ 5: v+ = y+

(3.12)

+

For the buffer or generation zone, 5 < y < 30: v + = 5.0 ln y + − 3.05

(3.13)

+

For the turbulent zone, y ≥ 30: v + = 2.5 ln y + + 5.5

(3.14)

These velocity proﬁles, also known as the law of the wall, have been veriﬁed experimentally for Newtonian ﬂuids with very good results, but such is not the case for non-Newtonian ﬂuids, in which some differences have been observed. Both groups of velocity equations, for viscous and turbulent ﬂows, may be used in the involved unit operation not only for velocity proﬁles mass and volumetric ﬂows, but also for computation of residence time, design parameters, and dimensions inside process units. Furthermore, temperature distribution, heat transfer area, and concentration proﬁles in heat exchangers or in mass transfer related equipment may be obtained with incorporation of momentum transfer considerations.

3.3.3 TRANSPORTATION

OF

FLUIDS

As previously mentioned, there are process conditions involving different geometries, but the cylindrical shape is the most commonly encountered ﬂow situation. Also, it is the most studied in relation to momentum phenomena and related topics, such as pump needs, pressure losses, and friction factors through pipe systems. Accurate prediction of pressure drop/ﬂow relationships for non-Newtonian ﬂuids in ducts is consequently of great importance. Additionally, when ﬂuid ﬂows through ﬁttings (bends, elbows, entrances, expansions, reductions, and valves), the ﬂow patterns become more complex than those in a straight tube and are characterized by altered velocity distributions and the presence of centrifugal forces and secondary ﬂows (Das et al., 1991). In the unit operation of ﬂuid foods’ transportation, there is a lack of information for non-Newtonian materials. Some studies related to the prediction of friction factors, pressure losses, and power consumption evaluations as part of the mechanical energy have been completed. Bernoulli’s equation (Equation 3.15), in which the input of mechanical energy is conserved through the output for uncompressible, isothermal, and steady ﬂow in one direction, is the fundamental mathematical model for the aforementioned evaluations. v12 P Zg v22 P Zg + 1 + 1 + ηp Wp = + 2 + 2 + Ef 2α1g c ρ gc 2α 2 g c ρ gc

(3.15)

Some advances for non-Newtonian behavior, particularly those related to the correction factor for the kinetic energy, friction factor, and related coefﬁcients have

© 2003 by CRC Press LLC

been made recently; they are summarized in Table 3.2 for both Newtonian and nonNewtonian ﬂuids. There are many proposed explicit and implicit equations for Newtonian ﬂuids as a function of Reynolds number and relative roughness that were not included in Table 3.2, and although some contributions have been proposed to characterize non-Newtonian food ﬂuid transportation, it remains a complex ﬂow and an incompletely understood phenomenon.

3.4 RHEOLOGICAL PROPERTIES OF FOODS 3.4.1 RHEOLOGY Rheology, deﬁned as the science of ﬂow and deformation of material, is a fundamental interdisciplinary science that has been gaining increasing importance in the ﬁeld of foods. According to Rao (1986), Steffe (1992), Kokini (1992) and VélezRuiz (1996), among other authors, there are numerous topics of interest to the food industry related to rheological behavior, such as: 1. Process engineering applications involved in equipment and process design 2. Development of new products or reformulation of existing products 3. Quality control of intermediate and ﬁnal products 4. Correlation with sensory evaluation 5. Understanding of food structure Rheology can be used to characterize not only ﬂow behavior of foods and other materials, but also structural characteristics. The knowledge of ﬂow food properties, such as consistency, pourability, thickness, viscoelasticity, viscosity, and yield stress, contributes substantially to facilitating transport and commercial processing, as well as to promoting consumer acceptance. Insight into structural arrangement helps to predict the behavior or stability of a given material with storage, change in humidity and/or temperature, and handling (Motyka, 1996). Consequently, basic rheological information on materials is important not only to engineers, but also to food scientists, processors, and others who may utilize this information and ﬁnd new applications. Many foods are neither solid nor liquid, but exist in an intermediate state of aggregation known as semiliquid or semisolid. As a consequence of the complex nature and lack of precise boundaries between solids/semisolids and liquids/semiliquids, many foods may exhibit more than one rheological behavior depending on their speciﬁc characteristics and the measuring conditions used during the physical characterization. Due to the complex composition and particular structure of foods, the approaches for characterizing a food’s rheological behavior may be classiﬁed into ﬁve methods: empirical, phenomenological (including fundamental and imitative), linear viscoelastic, nonlinear viscoelastic, and micro-rheological. In the case of foods, empirical and phenomenological approaches have been predominant in studies associated with ﬂow properties (Rao, 1992; Vélez-Ruiz and BarbosaCánovas, 1997b). With respect to viscoelastic nature, the approaches mainly include

© 2003 by CRC Press LLC

© 2003 by CRC Press LLC

TABLE 3.2 α) Friction Factors (F) and Related Coefﬁcient (K) for Newtonian and Non-newtonian Fluids Kinetic Energy Factor (α Factor

Regimen

Considerations

Kinetic Energy Correction Factor Newtonian ﬂuids, Re ≤ 2100

References

α = 0.5

Laminar

(2n + 1)(5n + 3) α= 3(3n + 1) 2

Laminar

Power law ﬂuids, and evaluation of GRec

Heldman (1975) Ibarz et al. (1996)

Laminar

Bingham plastic ﬂuids, and evaluation of GRec

Skelland (1967) Ibarz et al. (1996)

α=

α=

1 2−

τ0 τw

Charm (1971)

[(1 + 3n + 2 n 2 + 2 n 2 C + 2 nC + 2 n 2 C 2 )3 (2 + 3n )(3 + 5n )(3 + 4 n )] [[(1 + 2 n) (1 + 3n ) ][18 + n(105 + 66 C) + n (243 + 306C + 85C 2 ) + n 3 (279 + 522C + 350C 2 ) + n 4 (159 + 390C + 477C 2 ) + n 5 (36 + 108C + 216C 2 )]] 2

2

2

Laminar

Herschel-Bulkley ﬂuids, and evaluation of GRec

Osorio and Steffe (1984) Ibarz et al. (1996)

ln(2α ) = 0.168C − 1.062 nC − 0.954 n 0.5 − 0.115 C 0.5 + 0.831

For 0.06 ≤ n ≤ 0.38

Briggs and Steffe (1995)

ln(2α ) = 0.849C + 0.296 nC − 0.600 n

For 0.38 ≤ n ≤ 1.60

Briggs and Steffe (1995)

Turbulent

Newtonian ﬂuids, c:6 − 10 depending of Re

Ibarz et al. (1996)

Laminar and turbulent

Values obtained as a function of Re

Foust et al. (1980)

Laminar

Newtonian ﬂuids, fD = 4 fF

Foust el al. (1980)

Laminar ﬂow

Power law Fluids, GRe instead of Re

Ibarz et al. (1996)

α=

4c (3 + c)(3 + 2c) ≈ 1.0 (1 + c) 3 (1 + 2c) 3

0.5

− 0.602C

0.5

+ 0.733

4

0.5 < α < 1.0

Friction factor 16 64 fF = ;f = Re D Re fF =

16 G Re

© 2003 by CRC Press LLC

f 1 (He) 4 He = F − + Re B 16 6(Re B )2 3fF3 (Re B )8

Laminar ﬂow

Implicit equation for Bingham plastic ﬂuids

Ibarz et al. (1996)

Laminar ﬂow

Herschel-Bulkley ﬂuids, GRe and GHe need to be considered

Garcia and Steffe (1986)

 1.255 1 1 ε = −4 log  +  1/ 2 (fF )1/ 2 Re( f ) 3 .7 D  F 

Turbulent ﬂow

Newtonians, Re: 4000 − 10

ε 1  5.62 = −2 log  0.9 + 0.27  ( 4 fF )1/ 2 D  Re

Turbulent ﬂow

Newtonians, rough pipes

1 4 0.4 log G Re ff(1− n / 2 ) − 1.2  = (fF )1/ 2 n 0.75 n  

Turbulent ﬂow

fF =

16 ψGR ε

 (1 − C)2 2C(1 − C) C 2  ψ = (3n + 1) n (1 − C)1+ n  + + 2n + 1 n + 1   3n + 1

n

1 = 2.27 log(1 − C) + 2.27 log[Re B f F0.5 ] − 1.15 ( 4 f F ) 1/ 2 fF from ﬁgures

k from graphical representations −0.896

k = 191 G Re −0.504 k = 29.4 G Re −0.492 k = 30.3 G Re

Laminar and Turbulent ﬂow

8

Power law ﬂuids, GRe: 2900-36000

Levenspiel (1993)

Levenspiel (1993) Dodge and Metzner (1959)

Implicit equation for Bingham ﬂuids

Ibarz et al. (1996)

Values obtained as a function of GRe and GHe for n = 0.2 and 0.5

Garcia and Steffe (1986)

Friction Loss Coefﬁcients Different ﬁttings Values obtained as a function D and equivalent length. Newtonians 90° short radius elbow Laminar ﬂow of power law ﬂuids Tee, line to branch Laminar ﬂow of power law ﬂuids Fully open three-way plug valve Laminar ﬂow of power law ﬂuids

Foust et al. (1980) Steffe et al. (1984) Steffe et al. (1984) Steffe et al. (1984)

fundamental and linear. Most food systems are considered to be linear viscoelastic materials at small strains. Any of the available commercial instruments that allow objective characterizations are appropriate for measuring the rheological properties and identifying the rheological behavior of food materials. The accuracy of these rheometers has been improved due to the incorporation of modern mechanical devices and microcomputer technology.

3.4.2 RHEOLOGICAL MODELS The relationship between applied stress and resulting strain shown by any food material can be expressed either empirically or in terms of a rheological equation of state, also known as a rheological model. There exists a particular approach in which the rheological behavior of a material is analyzed on a simpliﬁed deformation called single shear or uniaxial deformation. This approach is the basis for many rheological measurement techniques and permits the analysis of many food materials. Fluid, solid, and viscoelastic behaviors have been observed in food products. Juices, milk, vegetable oils, and water behave as Newtonian ﬂuids; but dressings, fruit concentrates, ketchup, and yogurt behave as non-Newtonian. Gels, meat emulsions, and some types of cheese have been characterized as solids with elastic behavior. Other food products such as ice cream, mayonnaise, and whipped cream have been characterized by their viscoelastic nature. Among the many mathematical relationships proposed to characterize the rheological nature of liquid materials, four models are particularly useful for describing the behavior of ﬂuid foods. One is Newton’s model for Newtonians, expressing the concept of viscosity, and the other three (Power Law, Bingham Plastic and Herschel and Bulkley models) are for non-Newtonian behavior; the corresponding equations are: Newtonian model Power law model Bingham model Herschel–Bulkley model

τ = µγ˙

(3.16)

τ = K( γ˙ )n

(3.17)

τ = τ 0 + ηP γ˙

(3.18)

τ = τ 0 + K( γ˙ )n

(3.19)

Many other more complex or more speciﬁc models have been proposed for different ﬂuid materials. Consequently, these models are utilized for particular products. Some of them are included in Table 3.3. In addition, if time is considered as another variable, the ﬂuids may show a thixotropic or a rheopectic behavior. Thixotropy refers to a reversible decrease in apparent viscosity with time at constant shear rate. This is generally due to a reversible change in structure of the material with time under shear, with a limiting viscosity ultimately being approached. Rheopexy is, in essence, the reverse of thixotropy; that is, it represents an increase of apparent viscosity with time at a constant

© 2003 by CRC Press LLC

TABLE 3.3 Additional Rheological Models for Time-Independent Fluids Model

Application

Casson

τ 0.5 = τ 00.5 + K( γ˙ ) 0.5

Vocadlo

1   τ =  ( τ 0 ) n + Kγ˙   

Modiﬁed Casson

τ 0.5 = τ 00.5 + K( γ˙ ) n

Generalized H-B Power Series

⋅

Casson, 1959

Fruit and puree concentrates

Food ﬂuids

Parzonka and Vocadlo, 1968 Mizrahi and Berk, 1972 Ofoli et al., 1987

Food ﬂuids

Whorlow, 1992

Concentrated orange juice

γ = K1τ + K 2 τ + K 3 τ ... ⋅

Chocolate, fruit dispersions and products

n

τ n1 = τ 0n1 + K( γ˙ ) n 2 3

Reference

5

τ = K1 γ + K 2 ( γ˙ ) + K 3 ( γ˙ ) ... 3

5

shear rate. To model thixotropic and rheopectic behavior, several models have been developed. The model expressed by Equation (20) is a modiﬁcation proposed by [Mason et al. (1987)] to another previously established model (Barbosa-Cánovas et al., 1993).   t  Σb i exp −     λi   τ = K( γ˙ )n 1 + ( b 0 t( γ˙ ) − 1)   Σb i    

(3.20)

Sometimes the rheological behavior of foods depends on the experimental conditions; for example, evaporated milk has been characterized as Newtonian by Fernández-Martín (1972), Bloore and Boag (1981), and Wayne and Shoemaker (1988), and as a non-Newtonian ﬂuid by Randhahn (1973) and Schmidt et al. (1980), and during its ﬂow has shown thixotropic behavior (Ibarz et al., 1987). Also, sweetened condensed milk has been characterized as non-Newtonian by Alvarez De Felipe et al. (1991), as a thixotropic ﬂuid by Higgs and Norrington (1971), and as a viscoelastic material by Patil and Patel (1992). The same material may even develop different ﬂow behaviors depending on the applied range of shear rate or shear stress. A viscoelastic material may show either linear or nonlinear behavior. A linear viscoelastic material has properties that are dependent upon time alone and not upon the magnitude of the stress that is applied to the material. Nonlinear viscoelastic materials exhibit mechanical properties that are a function of time and the magnitude of stress used. To express the viscoelasticity of a linear food material, mechanical models incorporating two basic elements have been utilized. These elements are the elastic spring, which represents the instantaneous elastic nature, and the dashpot, which expresses the pure viscous ﬂow. These two elements when in a series constitute a Maxwell body, and when parallel, a Kelvin–Voigt body (Vélez-Ruiz, 1996).

© 2003 by CRC Press LLC

3.4.3 TEMPERATURE

AND

CONCENTRATION VARIABLES

The inﬂuence of temperature on the viscosity of Newtonian and the consistency coefﬁcient of non-Newtonian ﬂuid foods is commonly expressed in terms of an Arrhenius type equation (Equation 3.21). Furthermore, the effects of both variables, concentration and temperature at a given shear rate range, can be combined in terms of single relationships (Vélez-Ruiz and Barbosa-Cánovas, 1997a). Fernández-Martín (1972) and Bloore and Boag (1981) have proposed a polynomial relationship (Equation 3.22) to ﬁt the viscosity of concentrated milk (considered a Newtonian ﬂuid) as a function of total solids and temperature, which also has been ﬁtted to other food ﬂuids.

η, µ a , K = A 0 exp 2

 Ea   RT 

(3.21)

2

2

2

log η = A0 + A1t + A2t + (B0 + B1t + B2t )S + (C0 + C1t + C2t )S

(3.22)

Vitali and Rao (1984) used an exponential relationship to model the apparent viscosity of concentrated orange juice inﬂuenced by temperature and concentration: B

η = φ (T, C) = KT,C exp (Ea/RT)⋅C

(3.23)

Reddy and Datta (1994) employed a combined exponential potential functionality to relate the consistency coefﬁcient, absolute temperature, and concentration: X

K = B1 exp (C2/T) 1.25

(3.24)

Generally, the effect of concentration and temperatures on rheological behavior has been expressed by power and/or exponential equations for different types of food ﬂuids (Vélez-Ruiz and Barbosa-Cánovas, 1997a).

3.5 SIMULTANEOUS TRANSFER PHENOMENA Industrial equipment often involves simultaneous transfer phenomena, hence ﬂow effects must be considered when designing and evaluating heating/cooling processes and mass transfer operations. The velocity proﬁle of any phase will depend on the rheological properties of the food ﬂuid, used geometries, and other speciﬁc factors, such as the solids loading, particle diameter, and density differences in the case of solids–food liquids, and density differences and interface in the case of oil–water and gas non-Newtonian liquid mixtures. Other important factors should be considered, including temperature and thermal properties for heat transfer operations and concentration and density for mass transfer processes.

© 2003 by CRC Press LLC

Since non-Newtonian ﬂuids are often very viscous, most thermal treatment methods assume the ﬂow of foods in tubular ducts as a laminar regime. Thus, the process calculations need to be very accurate in order to avoid under- or overprocessing; in most cases the Arrhenius relationship has been used to describe the effect of temperature on the rheological behavior of non-Newtonian food ﬂuids. To take account of the rheological behavior, Pereira et al. (1989), for instance, considered the rheological parameters as part of the Generalized Reynolds (Equation 3.25), Generalized Prandtl (Equation 3.26), and Generalized Grashoff (Equation 3.27) numbers and the “viscosity correction term” (Kb/Kw), in a double tube heat exchanger modeling for laminar ﬂow:

G Re =

8v 2 − n D n ρ n 3n + 1 2 n K  n 

  3n + 1 n n −1  2  K Cp   n    G Pr = 1− n n −1 k t  4v D    G Gr =

gβρ2 D3∆T   3n + 1 n    K n    1− n n −1   4v R  

2

(3.25)

(3.26)

(3.27)

Flow properties are also closely related to those unit operations involving heat transfer phenomena. Cooling, heating, pasteurization, sterilization, and evaporation are the most common heat transfer operations utilized in food processing, and whatever the main purpose, heat transfer implies ﬂow of food ﬂuids inside the exchanger, mostly with non-Newtonian behavior. Since the ﬂow proﬁle controls mixing and thermal–times effects in the heat equipment, it is essential to know how ﬂow regime inﬂuences the heat transfer phenomenon. On the other hand, there are mass transfer operations in which food ﬂuids are handled and ﬂow behavior will affect the operation performance importantly. Therefore, engineers who work with air and spray drying, fermentation processes, membrane separations, and vacuum drying should consider the ﬂow properties of the ﬂuid materials. Other unit operations, such as extraction, frying, leaching, and osmotic dehydration, have less dependency on rheological properties. Table 3.4 presents a summary of studies in which the heat and mass transfer operations have been related to momentum transfer, such as rheological properties or velocity proﬁles.

© 2003 by CRC Press LLC

TABLE 3.4 Examples of Heat and Mass Transfer Operations Related to Rheological Properties of Food Fluids Application/Fluids

Purpose

Important Remarks

Continuous sterilization/Bingham plastic ﬂuids

Modeling continuous a sterilization for a NN ﬂuid

Gauriguata et al., 1979

Thin ﬁlm evaporation/water and sugar solutions Double tube heat exchanger/guar gum b and CMC solutions c UHT process/starch solutions and water

Simulation of fruit juices evaporation

Understanding the effect of temperature on the rheology is necessary for good sterilization process Evaporation regimes were related to ﬂow Correlations were developed for a nonNewtonian ﬂuid d h for particles heated in e N ﬂuids were 20% higher than in NN ﬂuids

Pereira et al., 1989

Aseptic treatment/particles in CMC solutions Scraped surface heat/NN ﬂuids Spray drying/power law liquid Drum drying/power law ﬂuids

Spray drying/soy protein milk a b c d e

Predicting heat exchange during laminar ﬂow Evaluations of the particle/ﬂuid interface convective heat transfer coefﬁcient Determination of ﬂuid convective heat transfer coefﬁcient Effect of heat transfer on ﬂow proﬁles and numerical simulation Prediction of drop diameter; theoretical deprivation Film thickness of drying material for a drum dryer; theoretical approach Effect of viscosity on drying rates of soy protein milk

d

h was signiﬁcantly affected by ﬂuid viscosity Figures of velocity proﬁles for three NN ﬂuids An equation for drop diameter of NN ﬂuids was developed Thickness of the ﬁlm was equated as a function of velocity ratio of cylinders and ﬂow behavior index The viscosity must be controlled for good atomization and milk quality

Reference

Stankiewics and Rao, 1988

Awuah et al., 1993

Bhamidipati and Singh, 1995 Wang et al., 1999 Weberschinke and Filková, 1982 Daud, 1989

Hayashi, 1996

NN = non-Newtonian CMC = carboxy methylcellulose UHT = ultra high temperature h = convective heat transfer coefﬁcient N = Newtonian

3.6 FINAL REMARKS This chapter is an overall review of an extensive topic in which many aspects of the complex phenomena remain unknown. Therefore, the main momentum transfer parameters and variables have been only brieﬂy commented upon. In process design, momentum transfer is most likely present; thus, some simple or complex approach

© 2003 by CRC Press LLC

must be taken into consideration, not only with respect to the ﬂow nature, but also with respect to heat and mass transfer, as well as biochemical reactions. Rheological behavior has some impact on all unit operations involving food liquids. Nowadays, several computer programs have been developed to solve various transport equations, and they are commercially available. Furthermore, continuous advances in computer capacity in terms of computational speed, disposability, and memory will enable application of rigorous analytical models to speciﬁc momentum transfer problems. Also, the utilization of modern instrumental techniques, such as nuclear magnetic resonance and magnetic resonance imaging, will contribute to the experimental approach for measuring velocity proﬁles and rheological behavior of non-Newtonian ﬂuids, including ﬂuid/particle mixtures, and therefore to a better understanding of the momentum phenomenon.

NOMENCLATURE A A0, Ai b0, bi B, B0, Bi c C C0 , Ci CD Cp d D Ea Ef Eu f fD fF FD Fr g g GGr GHe GPr GRe GRec He k kt K

2

Surface area or transfer area (L ) Constants model Constants model Constants model Constant value (with a magnitude between 6 and 10) Constant ratio (τ0/τw) (dimensionless); solids content (ºBx) Constants model Drag coefﬁcient (dimensionless) Fluid speciﬁc heat (E/MT) Characteristic dimension (L) Tube diameter (L) Activation energy (E/Mol) Friction losses energy (FL/M) Euler number (dimensionless) Friction factor (dimensionless) Darcy’s friction factor (dimensionless) Fanning’s friction factor (dimensionless) Drag force (F) Froude number (dimensionless) 2 Gravitational constant (L/t ) 2 Vector representing the acceleration due to a gravitational ﬁeld (L/t ) Generalized Grashoff number (dimensionless) Generalized Hedstrom number (dimensionless) Generalized Prandl number (dimensionless) Generalized Reynolds number (dimensionless) Critical generalized Reynolds number (dimensionless) Hedstrom number (dimensionless) Friction loss coefﬁcient Thermal conductivity (E/LtT) Consistency coefﬁcient, or model constant for rheological relationships n 2 (Ft /L )

© 2003 by CRC Press LLC

K1, K2, K3 L n np N P Pl Po Q r R R0 Re S t ∆T T Tbav Tw v +

v ∇v T (∇v) We X + y Z

Constants model Pipe length (L) Flow behavior index or in general, power law exponent (dimensionless) Pump efﬁciency Agitator speed or rotational velocity (rev/t) 2 Pressure (F/L ) or power (FL/t) Plasticity number (dimensionless) Power number (dimensionless) 3 Volumetric ﬂow (L /t) Radial coordinate (L) Pipe inner radius (L); universal gas constant (Equation 21) (E/MolT) Plug radius (L) Reynolds number (dimensionless) Solids content (%) Time; temperature (°C) Temperature difference (Tw – Tbav) Absolute temperature (K) Bulk average ﬂuid temperature (T) Wall temperature (T) Flow velocity vector (L/t); v is the magnitude of v, which is composed of vx, vy, and vz; velocity components in directions x, y, z Time averaged velocity (dimensionless) Shear rate tensor (1/t) Transpose of the shear rate tensor (1/t) Weber number (dimensionless) Milk concentration (% w/w) Time averaged distance, distance from the wall (dimensionless) Vertical position (L)

GREEK SYMBOLS α β ρ ε γ λi Ψ σ τ τ0 τrz τw µ, η

Kinetic energy correction factor (dimensionless) Thermal expansion coefﬁcient (1/T) 3 Fluid density (Μ/L ) Relative roughness (dimensionless) Shear rate (1/t) (dimensionless) Time constant (t) Constant for NN friction factor Surface force (F/L) 2 Shear stress tensor or momentum ﬂux (F/L ) which is composed of τxy , τyz, etc., the components of the shear stress tensor 2 Yield stress (F/L ) 2 Shear stress (F/L ) 2 Shear stress at wall (F/L ) 2 Viscosity coefﬁcient or absolute viscosity (Ft/L or M/Lt)

© 2003 by CRC Press LLC

2

µa Apparent viscosity (Ft/L or M/Lt) 2 µp, ηp Plastic viscosity (Ft/L or M/Lt)

REFERENCES Alvarez De Felipe, A.I., Melcón, B., and Zapico, J., Structural changes in sweetened condensed milk during storage: an electron microscopy study, J. Dairy Res., 58, 337–344, 1991. Awuah, G.B., Ramaswamy, H.S., and Simpsom, B.K., Surface heat transfer coefﬁcients associated with heating of food particles in CMC solutions, J. Food Process Eng., 16, 39–57, 1993. Barbosa-Cánovas, G.V., Ibarz, A., and Peleg, M., Rheological properties of ﬂuid foods: review, Alimentaria, April 1993, pp. 39–89. Bennet, C.O. and Myers, J.E., Momentum, Heat and Mass Transfer, McGraw-Hill, Tokyo, 1983. Bhamidipati, S. and Singh, R.K., Determination of ﬂuid-particle convective heat transfer coefﬁcient, Trans. ASAE, 38, 857–862, 1995. Bird, R.B., Stewart, W.E., and Lightfoot, E.N., Transport Phenomena, John Wiley and Sons, New York, 1960. Bloore, C.G. and Boag, I.F., Some factors affecting the viscosity of concentrated skim milk, New Zealand J. Dairy Sci. Technol., 16, 143–154, 1981. Briggs, J.L. and Steffe, J.F., Kinetic energy correction factor of a Herschel-Bulkley ﬂuid, J. Food Process Eng., 18, 115–118, 1995. Brodkey, R.S. and Hershey, H.C., Transport Phenomena: A Uniﬁed Approach, McGraw-Hill, New York, 1988. Casson N., A ﬂow equation for pigmented-oil suspensions: the printing ink type, in Rheology of Dispersed Systems, Mill, C.C., Ed., Pergamon Press, London, 1959, pp. 84–104. Charm, S., The Fundamentals of Food Engineering, AVI, Westport, CT, 1971. Das, S.K., Biswas, M.N., and Mitra, A.K., Non-Newtonian liquid ﬂow in bends, Chem. Eng. J., 45, 165–171, 1991. Daud, W.R.B.W., Theorical determination of the thickness of ﬁlm of drying material in a top loading drum dryer, in Drying ’89, Mujumdar, A.S. and Roques, M., Eds., Hemisphere Publishing Corporation, New York, 1989, pp. 496–500. Dodge, D.W. and Metzner, A.B., Turbulent ﬂow of non-Newtonian systems. AIChE J., 5, 189–204, 1959. Fahien, R.W., Fundamentals of Transfer Phenomena, McGraw-Hill, New York, 1983. Fernández-Martín, F., Inﬂuence of temperature and composition on some physical properties of milk and milk concentrates. II. Viscosity, J. Dairy Res., 39, 75–82, 1972. Foust, A.S., Wenzel, L.A., Clump, C.W., Maus, L., and Andersen, L.B., Principles of Unit Operations, John Wiley and Sons, New York, 1980. García, E.J., and Steffe J.F., Comparison of friction factor equations for non-Newtonian ﬂuids in pipe ﬂow, J. Food Process Eng., 9, 93–120, 1986. Gekas, V., Transport Phenomena of Food and Biological Materials, CRC Press, Boca Raton, FL, 1992. Guariguata, C., Barreiro, J.A., and Guariguata, G., Analysis of continuous sterilization processes for Bingham plastic ﬂuids in laminar ﬂow, J. Food Sci., 44, 905–910, 1979. Hayashi, H., Effect of viscosity on spray drying of soy protein milk, in Proceedings of the 5th World Congress of Chemical Engineering at San Diego, Vol. II, 1996, 98–102.

© 2003 by CRC Press LLC

Heldman, D., Food Process Engineering, AVI, Westport, CT, 1975. Higgs, S.J. and Norrington, R.J., Rheological properties of selected foodstuffs, Proc. Biochem., May 1971, pp. 52–54. Ibarz, A., García, J.L., and Puy Llorens, J., Thixotropic analysis of condensed milks, Alimentaria, Oct. 1987, pp. 35, 37–38. Ibarz, A., Vélez, J., and Barbosa, G., Transport of Food Fluids through Pipes, unpublished document, 1996. Kokini, J.L., Rheological properties of foods, in Handbook of Food Engineering, Heldman, D.R. and Lund, D.B., Eds., Marcel Dekker, New York, 1992, pp. 1–38. Levenspiel, O., Engineering Flow and Heat Exchange, Plenum Press, New York, 1993. Liu, S. and Masliyah, J.H., On non-Newtonian ﬂuid ﬂow in ducts and porous media, Chem. Eng. Sci., 53, 1175–1201, 1998. Mason, P.L., Bistany, K.L., Puoti, M.G., and Kokini, J.L., A new empirical model to simulate transient shear stress growth in semi-solid foods, J. Food Process Eng., 6, 219–233, 1983. Mizrahi, S. and Berk, Z., Flow behavior of concentrated orange juice: mathematical treatment, J. Texture Stud., 3, 69–79, 1972. Molerus, O., Appropriately deﬁned dimensionless groups for the description of ﬂow phenomena in dispersed systems, Chem. Eng. Sci., 53, 753–759, 1997. Motyka, A.L., An introduction to rheology with emphasis on application to dispersions, J. Chem. Educ., 73, 374–380, 1996. Ofoli, R.Y., Morgan, R.G., and Steffe, J.F., A generalized rheological model for inelastic ﬂuid foods, J. Texture Stud., 18, 213–230, 1987. Osorio, F.A. and Steffe, J.F., Kinetic energy calculations for non-Newtonian ﬂuids in circular tubes, J. Food Sci., 49, 1295–1296, 1315, 1984. Parzonka, W. and Vocadlo, J., Méthode de la caractéristique du comportement rhéologique des substances viscoplastiques dápres les mesures au viscosimétre de coutte (modéle nouveau a trois paraméters), Rheol. Acta., 7, 260–265, 1980. Patil, G.R. and Patel, A.A., Viscoelastic properties of sweetened condensed milk as inﬂuenced by storage, Milchwissenschaft, 47, 12–14, 1992. Pereira, E.C., Bhattacharya, M., and Morey, R.V., Modeling heat transfer to non-Newtonian ﬂuids in a double tube heat exchanger, Trans. ASAE, 32, 256–262, 1989. Randhahn, H., Flow properties of milk and milk concentrates, Milchwissenschaft, 28, 620–628, 1973. Rao, M.A., Rheological properties of ﬂuid foods, in Engineering Properties of Foods, Rao, M.A. and Rizvi, S.S.H, Eds., Marcel Dekker, New York, 1986, pp. 1–47. Rao, M.A., Rheology of Fluid and Semisolid Foods. Principles and Applications, Aspen Publishers, Inc., Gaithersburg, MD, 1999. Rao, V.N.M., Classiﬁcation, description and measurement of viscoelastic properties of solid foods, in Viscoelastic Properties of Foods, Rao, M.A. and Steffe, J.F., Eds., Elsevier Applied Science, London, 1992, pp. 3–48. Reddy, C.S. and Datta, A.K., Thermophysical properties of concentrated reconstituted milk during processing, J. Food Eng., 21, 31–40, 1994. Schmidt, R.H., Sistrunk, C.P., Richter, R.L., and Cornell, J.A., Heat treatment and storage effects on texture characteristics of milk and yogurt systems fortiﬁed with oilseed proteins, J. Food Sci., 45, 471–475, 1980. Skelland, A.H.P., Non-Newtonian Flow and Heat Transfer, John Wiley and Sons, New York, 1967. Stankiewics, K. and Rao, M.A., Heat transfer in thin-ﬁlm wiped-surface evaporation of model liquid foods, J. Food Process Eng., 10, 113–131, 1988.

© 2003 by CRC Press LLC

Steffe, J.F., Rheological Methods in Food Process Engineering, Freeman Press, East Lansing, MI, 1992. Steffe, J.F., Mohamed, I.O., and Ford, E.W., Pressure loss in valves and ﬁttings for pseudoplastic ﬂuids in laminar ﬂow, Trans. ASAE, 27, 616–619, 1984. Toledo, R.T., Fundamentals of Food Process Engineering, Chapman and Hall, New York, 1991. Vélez-Ruiz, J.F., Rheological Properties of Concentrated Milk, Ph.D. thesis, Washington State University, Pullman, 1996. Vélez-Ruiz, J.F., Notes of Food Engineering I, unpublished document, 2001. Vélez-Ruiz, J.F. and Barbosa-Cánovas, G.V., Rheological properties of concentrated milk as a function of concentration, temperature and storage time, J. Food Eng., 35, 177–190, 1997a. Vélez-Ruiz, J.F. and Barbosa-Cánovas, G.V., Rheological properties of selected dairy products, CRC Crit. Rev. Food Sci. Nutr., 37, 311–359, 1997b. Vitali, A.A. and Rao, M.A., Flow properties of low-pulp concentrated orange juice: effect of temperature and concentration, J. Food Sci., 49, 882–888, 1984. Wang, W., Walton, J.H., and McCarthy, K.L., Flow proﬁles of power law ﬂuids in scraped surface heat exchanger geometry using MRI, J. Food Process Eng., 22, 11–27, 1999. Wayne, J.E. and Shoemaker, C.F., Rheological characterization of commercially processed ﬂuid milks, J. Texture Stud., 19, 143–152, 1988. Weberschinke, J. and Filková, I., Apparent viscosity of non-Newtonian droplet on the outlet of wheel atomizer, in Drying ’82, Mujumdar, A.S., Ed., Hemisphere Publishing Corporation, New York, 1982, pp. 165–170. Welty, J.R., Wilson, R.E., and Wicks, C.E., Fundamentals of Momentum, Heat and Mass Transfer, John Wiley and Sons, New York, 1976. Whorlow, R.W., Rheological Techniques, Ellis Horwood Ltd., Chiclester, U.K., 1992.

© 2003 by CRC Press LLC

Part II Mass Transfer

© 2003 by CRC Press LLC

4

Structural Effects of Blanching and Osmotic Dehydration Pretreatments on Air Drying Kinetics of Fruit Tissues S.M. Alzamora, A. Nieto, and M.A. Castro

CONTENTS 4.1 4.2

Introduction Materials and Methods 4.2.1 Experiment 4.2.2 Moisture Diffusivity Calculation 4.3 Results 4.3.1 Effect of Blanching 4.3.2 Effect of Osmotic Treatment 4.4 Conclusions Nomenclature References

4.1 INTRODUCTION Typical commercial fruit processing currently involves predrying treatments aimed at either quality improvement of the ﬁnal product or improved drying kinetics (Lewicki, 1998). The most popular pretreatments are blanching and sugar or salt osmotic dehydration. Blanching prior to drying is sometimes performed to inactivate enzymes that adversely affect product quality, denature cell membranes to reduce drying times, remove intercellular air, and/or reduce microbial load. Osmotic pretreatment results in substantial dewatering; it has also been reported to prevent excessive shrinkage of the tissue undergoing drying and to improve rehydration of dry material. Literature results pertaining to the drying behavior of fruit and vegetable tissues as affected by blanching and the osmotic process are apparently contradictory, as

© 2003 by CRC Press LLC

reviewed by Alvarez et al. (1995). For example, moisture diffusivity of water in sugar beet root plates, carrot cubes, and potato slices was reported to decrease because of the uptake of sugar and/or salt. In contrast, sucrose osmotic treatment did not affect the dehydration rate of pineapple. Blanching increased the rate of drying of sugar beet and carrot, decreased the moisture transport rate in potato, and had only a small effect on avocado dehydration behavior. This dissimilarity can be ascribed to the intricate simultaneous heat and mass transfer drying process and to the wide variation in physical and structural properties among vegetables and fruits. A schematic view of the various transfer mechanisms that can be present during drying of fruit tissues is presented in Figure 4.1a. A signiﬁcant (a)

Molecular diffusion CONDUCTION

Capillary motion Knudsen flow Vapor diffusion in pores

CONVECTION

Liquid diffusion Evaporation - condensation

(b)

tt

cwp

tt st

cl = chloroplast; cw = cell wall; cwp: the cell wall pathway; g = Golgi; is = intercellular space; nu = nucleolus; n = nucleus; ml = middle lamella; pl = plasmodesmata; pm = plasmalemma; rer = rough endoplasmic reticulum; st: the symplastic; tt: the transmembrane transport; v = vacuole

FIGURE 4.1 (a) Major mechanisms during drying of parenchymatous fruit tissue. (b) Possible pathways for water transport in a parenchymatous fruit cell (courtesy of Dr. Ancíbor).

© 2003 by CRC Press LLC

number of mechanisms for moisture transport within porous foods has been proposed, including molecular diffusion, capillary motion, liquid diffusion through solid pores, Knudsen ﬂow, vapor diffusion in air-ﬁlled pores, and hydrodynamic ﬂow, none of them prevailing throughout the whole drying process (Zogzas et al., 1996). Usually, a series, parallel, and/or series–parallel combination of the aforementioned mechanisms contributes to the total ﬂow, and the relative contributions show product and drying system speciﬁcity as well as drying time dependence. Structural heterogeneity of biological materials, such as fruit, brings an additional complexity to the water migration in a porous solid system.As Figure 4.1b shows, cellular tissues are multiphase systems (i.e., vacuole, cytoplasm, tonoplast and plasmalemma membranes, cell wall, intercellular spaces), and water can migrate out of cells in three possible ways: transmembrane transport (through tonoplast and plasmalemma membrane boundaries), symplastic transport (via cytoplasmic strands or plasmodesmatas), or cell wall pathway (the apoplastic way), this last being the preferred pathway for small nonionic species such as water (Molz and Ikenberry, 1974; Tyree, 1970). Because of this complexity, the macroscopic (also called the “black box”) approach to quantifying the transport of water during the ﬁrst falling rate period of air drying commonly involves the determination of an empirical single experimental effective water diffusivity (Deff). This parameter, obtained by applying Fick’s second law for species diffusion in a single phase, takes into account the internal porosity and the tortuosity of the sample, but it also lumps together the deformation of the fruit matrix, the volume changes, the composition and structure of the fruit, the material–water interactions, and the multiphase water transport (Zogzas et al., 1996; Achanta and Okos, 1996). Hence, Deff is an empirical parameter useful as a quick engineering design tool but without physical signiﬁcance. A phenomenological understanding of the dehydration kinetics and the effect of pretreatments, however, requires, among others, a microscopic analysis to address the structural and ultrastructural changes produced at the cellular level and their potential inﬂuence on drying rates and quality of the ﬁnal products. Food structure is a process variable usually neglected in engineering design and transport kinetics analysis. But cell wall resistance to water ﬂux, as well as membrane integrity, are modiﬁed to different degrees due to the predrying treatments, depending on the type of fruit considered. In this chapter, ultra-, micro- and macrostructural effects of blanching and osmotic dehydration (atmospheric or in vacuum) pretreatments on the moisture transport rate during the ﬁrst falling rate period of air drying of fruits are illustrated. Drying behavior of strawberry, mango, and apple is discussed under the following headings: shrinkage of fruit piece, porosity, sugar content, cell membrane integrity, and cell wall architecture.

4.2 MATERIALS AND METHODS 4.2.1 EXPERIMENT The experimental process has been well described by Alvarez et al. (1995) and Nieto et al. (1998, 2001). Brieﬂy, apples (Malus pumila, Granny Smith cv.; ≅85–88% w/w moisture content, wet basis) and mangoes (Mangifera indica Linn, Keitt var.; ≅85– 88% w/w moisture content, wet basis) were hand peeled and cut into an inﬁnite plate

© 2003 by CRC Press LLC

shape (dimensions at the end of the pretreatment ≅4 × 4 × 0.4 cm). Strawberries (Pájaro or Tioga Leico var.; ≅86% w/w moisture content, wet basis) were washed, decapped by hand, and selected to obtain samples of uniform size and maturity. For steam blanching, apple and mango plates were exposed to steam for 1 min at atmospheric pressure and then cooled in water at 5°C. Whole strawberries were exposed to steam for 3 min and cooled in similar conditions. For osmotic dehydration at atmospheric pressure, samples were immersed into different glucose aqueous solutions with (mango and apple) or without (strawberry) forced convection at 25°C until the desired ﬁnal water activity (aw) value was reached (≅3 h for mango and apple and 48 h for strawberry). For vacuum glucose impregnation, fruit samples were immersed in a 59.0% w/w glucose aqueous solution (aw = 0.84) at 25°C, and a pressure equal to 60 mmHg was applied to the system for 10 min. After the vacuum treatment, the system was placed at atmospheric pressure for 10 min; the ﬁnal aw value reached by fruits was 0.97. After osmosis, fruit samples were drained and dried at 60°C (mango and apple) or 55°C (strawberry) with air at high constant velocity (about 15 m/sec) to eliminate or minimize external resistance to moisture loss.

4.2.2 MOISTURE DIFFUSIVITY CALCULATION The Deff value was obtained by applying Fick’s second law for species diffusion in a single phase, with boundary conditions of internal resistance controlling and uniform initial moisture content, integrated over the volume of the slab (apple, mango) or sphere (strawberry) (Luikov, 1968). The Deff values for spheres were affected by a shape factor to take into account that strawberries are ellipsoids (Becker, 1959; Aguerre et al., 1987). Uniform internal fruit temperature was assumed due to the low Biot number for heat transfer usually found for conventional air drying of fruits (Alzamora et al., 1979). Negligible external heat transfer effects were also considered. Assuming diffusion in an isotropic medium, constant diffusion coefﬁcient, and isothermal process, and using the moisture concentration converted to moisture content on a dry basis, Fick’s second law for one-dimensional unsteady diffusion is given as:  ∂2 m C ∂m  ∂m = Deff  2 +  ∂t x ∂x   ∂x

(4.1)

where x is the spatial coordinate, C is a constant (0 for inﬁnite plate; 2 for sphere), and Deff is the effective moisture diffusivity. For uniform moisture distribution (assuming no constant drying period takes place) and internal control to mass transfer, initial and boundary conditions are: m(x, 0) = m0

at t = 0

(4.2)

m(xS, t) = me

at x = xS (at the surface)

(4.3)

m(0, t) = ﬁnite

© 2003 by CRC Press LLC

at x = 0 (at the center)

(4.4)

Solutions for the different geometrical conﬁgurations can be expressed as: m − me 8 = m0 − me π2

∞

∑ n =1

2   1 2 π D eff t exp ( 2 1 ) − n +  2 2  (2 n + 1) 4 l0  

(4.5)

for a slab, where l0 is the half-thickness of the slab; m − me = m0 − me

∞

∑ n 6π 2

2

n =1

 D t exp − n 2 π 2 eff2  Re  

(4.6)

for a sphere, where Re is the radius. For long drying times, only the ﬁrst term of Equations (4.5) and (4.6) is signiﬁcant, and the values of Deff may be estimated from the linear relationship m − me/m0 − me vs. time on semilogarithmic coordinates. Strawberries were assumed to be ellipsoids, having three characteristic diameters (2 rM1 ≅ 2 rM 2 ≤ 2 rM ). For bodies having an ellipsoid shape, the Fourier number may be extended to (Aguerre et al., 1987; Becker, 1959): F0 =

Deff t  Vp  3 S   p

2

(4.7)

where Vp is the volume and Sp is the surface of the body. Generally, the equivalent spherical radius (Re) is used as the characteristic length. F0′ =

Deff t R 2e

(4.8)

where Re = 3(VS/SS), and SS and VS are the surface area and the volume of the sphere, respectively. If VS = VP = V, the relationship between F0 and F0′ is given by 2

Deff t  Sp  Deff t F0′ F0 = 2 = 2   = Ψ2 R2 = Ψ2 S  V  V  S e 3 S  3 S   S  p Deff t

(4.9)

where Ψ is deﬁned as SS/Sp, and SS is the surface area of a sphere of volume equal to that of the fruit with surface area Sp, which is assumed to be an ellipsoid. The 2 intrinsic diffusivity Deff is given by Ψ D′eff. Ψ is the shape factor of a solid, commonly known as the sphericity (Becker, 1959). The diffusion coefﬁcient calculated from 2 Equation (4.6) is D′eff, and it must be corrected by the factor Ψ when the product shape can be assumed as an ellipsoid: Expressing the surface area of an ellipsoid as Sp = 2 π rm2 + 2 π

© 2003 by CRC Press LLC

 rm R m  sin −1 e  e 

(4.10)

and calculating the eccentricity, e, as (Aguerre et al., 1987): e = 1 − ( rm / R m )2

(4.11)

the shape factor results in: Ψ=

SS = Sp

4 π R 2e r R  2 π rm2 + 2 π m m sin −1 e  e 

(4.12)

4.3 RESULTS 4.3.1 EFFECT

OF

BLANCHING

Table 4.1 summarizes the main structural features that may be produced by fruit scalding (Ilker and Szczesniak, 1990; Alzamora et al., 1997). Depending on the preponderant phenomenon/a, drying rates of blanched tissues could be decreased or increased compared to the moisture transport rate for the fresh fruit. The photomicrographs in Figure 4.2 compare the structures of the fruits with and without blanching. All raw fruits (Figure 4.2A, C, F, G) exhibited parenchymatous cells containing intact membranes, cytoplasm, and organelles and had intact cell walls without degradation, disruption, or dissolution. The plasma and tonoplast membranes were closely associated with the cell wall, and the middle lamella was clearly seen cementing adjacent cells. On the contrary, in the three blanched fruits (Figure 4.2B, D, E, H, I), plasmalemma and tonoplast were disrupted, and numerous vesicles of the cytoplasm had been formed. In blanched strawberry, the electronic density of the cell wall was much lower than that of fresh fruit walls (Figure 4.2B). The middle lamella practically disappeared, and microﬁbrils appeared distorted. Reduction in fruit volume was small (<10%) (Alvarez et al., 1995). In mango, heated cell walls exhibited disorganized microﬁbrils and longitudinal striations with zones of high and low electron density (Figure 4.2I). Protoplasm appeared TABLE 4.1 Major Reported Structural Phenomena Due to Blanching in Connection with Water Transport Rate During Drying of Fruit Tissues (from Various Sources) Disruption of cell membranes and increased permeability to water as well as loss of solubles to the surrounding medium and/or redistribution of solubles within the material during drying Shrinkage of tissues due to contraction of some biopolymers and/or displacement of occluded air Loosening of the hemicellulose–cellulose and the pectin networks due to cleavage and solubilization of polymers, increasing the cell wall porosity and decreasing cellular adhesion along the middle lamella 2+ Crosslinking of pectic polysaccharides by Ca and by ester linkages (facilitated by deesteriﬁcation of pectin chains due to activation of pectin methylesterase) Starch gelatinization and protein insolubilization

© 2003 by CRC Press LLC

FIGURE 4.2 Parenchyma tissue from strawberry, apple, and mango as affected by vapor blanching. A,B: strawberry. A: fresh control. Cell wall with a nitid middle lamella and a very tightly packed pattern of microﬁbrils mainly toward the margin. B: blanched. Less densely stained wall. C–E: apple. C: fresh control. Intact membranes close to cell walls and conspicuous middle lamella. D, E: blanched. Disrupted membranes and densely stained wall with some striations; formation of vesicles. F–I: mango. F,G: fresh control. Polygonal cells closely aligned to one another, with grouped starch granules and protein–carbohydrate slime; cell walls with good electron density. H, I: blanched. Dense protoplasm due to gelatinization of starch and thermal denaturation of slime. Rounded cells, disorganized microﬁbrils and longitudinal striations. A–E, G, I: TEM micrographs; F, H: LM micrographs. Scale: A, B, G, I: 0.5 µm; C–E: 1 µm; F, H: 100 µm. cw: cell wall; p: plasmalemma; T: tonoplast; ML: middle lamella; s: starch granule; sl: slime; ve: vesicle.

© 2003 by CRC Press LLC

dense probably due to gelatinization of starch and thermal denaturation of the protein– carbohydrate slime typical of the fruit (Figure 4.2H). Blanching also produced a slight volume shrinkage (≅10%) and decreased intercell contact (Nieto et al., 2001). Cell walls of blanched apple showed good optical density, only slightly lower than that of raw apples. Striations with zones of high and low electron density were observed but were less pronounced compared with those in heated mango. Separation of adjacent cells caused by dissolution of the middle lamella was not observed (micrographs not shown). Shrinkage of apples due to blanching was approximately 23%, a value very similar to the reported porosity of the fruit (air spaces comprise 20–30% of ﬂesh tissue volume) (Nieto et al., 1998). These alterations in the ultrastructure and microstructure of heated apple, mango, and strawberry tissues might explain, at least partially, the drying behavior (Figure 4.3). For strawberry, blanching would enhance Deff value due to: 1. The elimination of the cell membrane’s resistance to water diffusion 2. A decrease in the resistance of the cell walls to water ﬂux In apple, the effect of blanching on Deff could be ascribed to the increase in density of apples due to air exhaustion and the slight contraction of tissues, all phenomena predominating over the slight modiﬁcation of cell wall resistance to water ﬂux and/or the decreased transmembrane transport resistance due to membrane disruption. The decrease of Deff in mango could be attributed to: 1. The slight increase in density due to the cell collapse 2. The alteration of cellular contents (gelatinization of starch and denaturation of slimes) Both of these phenomena are more noticeable than the low ultrastructural damage of the cell wall and the disruption of membranes that would facilitate water ﬂow. 2.50E-05

Deff(cm2/s)

2.00E-05

1.50E-05

1.00E-05

5.00E-06

0.00E+00

apple

strawberry

control;

mango

steam blanched

FIGURE 4.3 Experimental Deff values for the ﬁrst falling rate period of air drying of raw and blanched fruits (drying temperature: 60°C for mango and apple; 55°C for Pájaro var. strawberrry).

© 2003 by CRC Press LLC

4.3.2 EFFECT

OF

OSMOTIC TREATMENT

Drying rate can be also affected by various structural modiﬁcations produced in the fruit tissue by osmotic treatments (Table 4.2) (Alzamora et al., 1997). A general aspect of the drying curves of mango and apple as affected by glucose dipping at atmospheric pressure or in vacuum to reach aw 0.97 is seen in Figure 4.4.

m (g H2O / g DM) 10 9

(a)

8 7 6 5 4 3 2 1 0 0

100

200

300

400

500

600

2

2

t / lo (min / cm ) _

m (g H2O / g DM)

6

(b) 5

4

3

2

1

0 0

100

200

300

400

500

600

t / lo2 (min / cm2)

control (raw) ; x blanched; * osmotically dehydrated to aw 0.97 (atmospheric); osmotically dehydrated to aw 0.97 (in vacuum).

FIGURE 4.4 Effect of blanching and glucose osmotic dehydration on drying curves of (a) apple and (b) mango at 60°C.

© 2003 by CRC Press LLC

TABLE 4.2 Major Reported Structural Phenomena Due to Osmotic Dehydration in Connection with Water Transport Rate during Drying of Fruit Tissues (Various Sources) Collapse of the tissue due to water removal Loss/redistribution of native sugars and solutes due to decompartmentation and/or passive transport through membranes; uptake of osmotic solute(s) Alteration of cell wall ultrastructure due to (a) leakage of soluble pectins to the osmotic medium that reduces the cohesiveness of the polysaccharide matrix and/or (b) speciﬁc interactions among solute(s) and cell wall components that modify to different degrees the strength of the walls as well as the porosity of the pectin matrix Starch gelatinization Stabilization of three-dimensional structure of proteins Plasmolysis and/or disruption of tonoplast and plasmalemma

Osmotic treatment appreciably reduced the moisture content of the fruits. No constant drying period was observed at any of the conditions studied. For both fruits, experimental Deff values decreased as the glucose concentration of the impregnation solution increased, that is, as aw of the slabs decreased (Figure 4.5). When glucose impregnation was performed under vacuum, the Deff value was similar to that of the atmospheric treated slab with the same aw (0.97) for mango, but vacuum impregnated apple exhibited a Deff value much lower than that corresponding to apple impregnated at atmospheric pressure with aw 0.97 and similar to the Deff value of the atmospheric impregnated fruit with aw 0.93. Shrinkage of mango and apple tissues before drying depended on the pretreatment (Figure 4.5). The percentage volume reduction shown by atmospheric osmotically dehydrated mango or apple to aw 0.97 was similar to that exhibited by blanched tissues (≅10% and ≅23%, respectively), while treatments in glucose solutions with aw 0.95 or 0.93 resulted in a more severe volume change (≅40–43%). Vacuum treated samples showed a greater shrinkage compared with the atmospheric impregnated fruit with the same aw (19 vs. 10% for mango and 37 vs. 24% for apple). Sugar composition of mango and apple tissues was signiﬁcantly inﬂuenced by the osmotic process (Table 4.3). Sugar exchange during osmosis (glucose gain and loss of “natural” sugars, fructose and glucose) resulted in modiﬁed sugar proﬁles of the ﬁnal products. Glucose content of mango and apple tissues impregnated at atmospheric pressure increased with the increasing glucose concentration of the solution. Vacuum glucose impregnated mango showed a lower uptake of glucose and a lower loss of “natural” sugars than the slabs impregnated at atmospheric pressure with aw 0.97, while the glucose content of the vacuum treated apple was 35% greater than that of atmospheric impregnated slabs with the same aw. Light microscopy observations of atmospheric glucose impregnated apples to reach aw 0.97 showed original arrangements of cells rather well maintained (micrographs not shown). Cells looked rounded but well deﬁned, with plasmalemma separated from the wall. Examinations with transmission electron microscopy (TEM) indicated electronic

© 2003 by CRC Press LLC

50

Sv,%

40 30 20 10 0 apple

mango

2.50E-05

Deff(cm2/s)

2.00E-05 1.50E-05 1.00E-05 5.00E-06

0.00E+00 apple

control;

strawberry

osmotically dehydrated, atmospheric pressure, aw 0.97;

osmotically dehydrated, vacuum, aw 0.97; pressure, aw 0.95;

mango

osmotically dehydrated, atmospheric

osmotically dehydrated, atmospheric pressure, aw 0.93

FIGURE 4.5 Experimental Deff values and volume shrinkage (Sv, %) for osmotically dehydrated apple, mango, and strawberry (Tioga Leico, var.).

dense cell walls and a network of microﬁbrils and a pectic matrix very similar to those of the fresh fruit (Figure 4.6C). When impregnation was made in vacuum, more rounded cells were observed in light microscopy (LM) (micrographs not shown), with some spaces between cells, but the degree of cell-to-cell contact did not decrease. Cell walls appeared with a very pronounced staining, exhibiting a very densely packed ﬁbrillar material (Figure 4.6D). Original arrangements of cells were also maintained in atmospheric glucose impregnated mango tissues with aw 0.97 or 0.93. Tonoplast and plasmalemma appeared

© 2003 by CRC Press LLC

TABLE 4.3 Sugar Content (% W/W) of Glucose Impregnated Mango and Apple Slabs Mango Pretreatment

Fructose

Control

3.6 ± 0.1

Glucose

Fructose

Glucose

Sucrose

At Atmospheric Pressure 2.3 ± 0.1 4.3 ± 0.1 5.6 ± 0.1

4.1 ± 0.1

2.6 ± 0.1

3.8 ± 0.1 4.0 ± 0.1 3.8 ± 0.1

12.6 ± 0.3 20.9 ± 0.1 27.4 ± 0.9

1.5 ± 0.1 2.4 ± 0.1 1.3 ± 0.2

7.2 ± 0.1

3.7 ± 0.1

2.5 ± 0.2

7.0 ± 0.1

16.5 ± 0.3

1.5 ± 0.2

Immersed in aqueous glucose solution of aw 0.97 2.3 ± 0.1 17.6 ± 0.3 aw 0.95 — — aw 0.93 2.6 ± 0.1 35.7 ± 0.9

Control

3.6 ± 0.1

Apple Sucrose

1.8 ± 0.01 — 1.9 ± 0.2

In Vacuum 2.3 ± 0.1 4.3 ± 0.1

Vacuum impregnated with glucose solution of aw 0.84 (ﬁnal fruit 2.9 ± 0.1 6.9 ± 0.1 3.8 ± 0.2 aw = 0.97)

intact, and cellular contents were plasmolyzed; this effect was very pronounced at aw 0.93. Due to plasmolysis, starch granules were localized near the center of the cells (micrographs not shown). As seen in TEM (Figure 4.6A), ﬁbrillar material appeared darkly stained and tightly packed, and the middle lamella, either cementing adjacent cells or lining the walls at the intercellular spaces (micrographs not shown), exhibited high electron density. Mango tissues impregnated under vacuum (aw 0.97) also showed a cell assembly similar to that of the control and cytoplasm plasmolysis. In some zones, disrupted membranes were observed. Ultrastructure observations indicated densely stained cell walls with clear reticulate pattern and a nitid middle lamella (Figure 4.6B). On the contrary, the optical density of cell walls of osmotically dehydrated strawberries was lower than the optical density of fresh strawberry cell wall. The middle lamella partially disappeared, and distortion of mioﬁbrils occurred (micrographs not shown), indicating degradation of the hemicellulose polysaccharides present in the cell wall, breakdown of pectins, and changes in the “crystallinity” of cellulose. The many changes in ultrastructure, microstructure, and composition induced by predrying osmosis could affect drying behavior in many ways. In mango and apple, cell walls of glucose-impregnated tissues were not modiﬁed (hence, neither were the wall transport properties of the wall) to a great extent compared with the control. But shrinkage and glucose uptake during the impregnation step would increase the overall water transport resistance. The magnitude of the increase would be dependent on the degree of cell collapse and sugar incorporation. In strawberry, glucose infusion would cause no effect on drying rate due to two counter-blanching effects: increased water transport resistance due to solute uptake

© 2003 by CRC Press LLC

FIGURE 4.6 Ultrastructure (TEM) of parenchyma tissue of mango and apple as affected by osmotic dehydration. A, B: mango; C, D: apple. A: immersed in glucose solution of aw 0.97. Densely stained wall and plasmolyzed cytoplasm; intermixed microﬁbrillar pattern; conspicuous middle lamella. B: vacuum impregnated, aw 0.97. Interrupted membranes; visible middle lamella; moderate electronic density of the walls. C: immersed in glucose solution of aw 0.97. Mioﬁbrillar disorganization but moderately electron dense wall. D: vacuum impregnated, aw 0.97. Walls darkly stained; very densely packed ﬁbrillar material; broken membranes with formation of vesicles. Scale: A, D: 500 nm; B, C: 1 µm.

and the reduction of the cell wall resistance due to degradation/solubilization of polysaccharides of the cell wall.

4.4 CONCLUSIONS There is a close relation between drying kinetics and structural modiﬁcations undergone by fruits under blanching and osmotic dehydration pretreatments. Resistance of fruit tissues to water ﬂux could be decreased by disruption of membranes and degradation/solubilization of the cell wall matrix, while drying rate would be adversely inﬂuenced by cell collapse, solute(s) gain, starch gelatinization, and protein denaturation.

© 2003 by CRC Press LLC

NOMENCLATURE l0 Re F0 DM aw m

mo m me Deff x Ψ

Half-thickness of the slab (cm) Sphere radius (cm) Fourier number Dry matter (g) Water activity Average moisture content, dry basis (kg water/kg dry matter) Initial moisture content, dry basis (kg water/kg dry matter) Moisture content, dry basis (kg water/kg dry matter) Moisture content in equilibrium with the surrounding temperature and humidity conditions, dry basis (kg water/kg dry matter) 2 Effective moisture diffusivity in the solid (cm /sec) Characteristic dimension (cm) Shape factor of a solid, adimensional

REFERENCES Achanta, S. and Okos, M.R., Predicting the quality of dehydrated food and biopolymers: research needs and opportunities, Drying Technol., 14, 1329–1368, 1996. Aguerre, R.J., Gabitto, J.F., and Chirife, J., Shape factors for the analysis of diffusion in air drying of grains, Int. J. Food Sci. Technol., 22, 701–705, 1987. Alzamora, S.M., Chirife, J., and Viollaz, P.E., A simpliﬁed model for predicting the temperatures of foods during air dehydration, J. Food Technol., 14, 369–380, 1979. Alzamora, S.M, Gerschenson, L.N., Vidales, S.L., and Nieto, A., Structural changes in minimal processing of fruits: some effects of blanching and sugar impregnation, in Food Engineering 2000, Fito, P., Ortega-Rodríguez, E., and Barbosa-Cánovas, G.V., Eds, Chapman and Hall, New York, 1997. Alvarez, C.A., Aguerre, R., Gómez, R., Vidales, S., Alzamora, S.M., and Gerschenson, L.N., Air dehydration of strawberries: effects of blanching and osmotic pretreatments on the kinetics of moisture transport, J. Food Eng., 25, 167–178, 1995. Becker, H.A., A study of diffusion in solids of arbitrary shape, with application to the drying of the wheat kernel, J. Appl. Polym. Sci., 1, 212–216, 1959. Ilker, R. and Szczesniak, A.S., Structural and chemical bases for texture of plant foodstuffs, J. Texture Stud., 21, 1–36, 1990. Lewicki, P.P., Effect of pre-drying treatment, drying and rehydration on plant tissue properties: a review, Int. J. Food Prop., 1, 1–22, 1998. Luikov, A.V., Analytical Heat Diffusion Theory, Academic Press, London, 1968. Molz, F.J. and Ikenberry, E., Water transport through plant cells and cell walls: theoretical development, Soil Sci. Soc. Am. Proc., 38, 699–704, 1974. Nieto, A.B., Castro, M.A., and Alzamora, S.M., Kinetics of moisture transfer during air drying of blanched and/or osmotically dehydrated mango, J. Food Eng., 50(3), 175–185, 2001. Nieto, A., Salvatori, D., Castro, M.A., and Alzamora, S.M., Air drying behavior of apples as affected by blanching and glucose impregnation, J. Food Eng., 36, 63–79, 1998. Tyree, M.T., The symplast concept: a general theory of symplastic transport according to the thermodynamics of irreversible processes, J. Theor. Biol., 26, 181–214, 1970. Zogzas, N.P., Maroulis, Z.B., and Marinos-Kouris, D., Moisture diffusivity data compilation in foodstuffs, Drying Technol., 14, 2225–2253, 1996.

© 2003 by CRC Press LLC

5

Pretreatment Efﬁciency in Osmotic Dehydration of Cranberries S. Grabowski and M. Marcotte

CONTENTS 5.1 5.2

Introduction Experimental Procedure 5.2.1 Osmotic Dehydration 5.2.2 Pretreatment Techniques 5.3 Results and Discussion 5.3.1 Selection of the Best Pretreatment 5.3.1.1 Coefﬁcient of Pretreatment Efﬁciency 5.3.1.2 Taste Acceptability 5.3.2 Simple Diffussivity Model for Cut Cranberries 5.4 Conclusions Nomenclature Acknowledgments References

5.1 INTRODUCTION Dehydration of small fruits, such as grapes, blueberries, cranberries, cherries, and gooseberries, is restricted by the fruit outer surface (cuticle), which plays a major role in the control of transpiration, and in protecting the fruit against weather inclemencies or attacks from insects and parasites (Mazliak, 1970; Somogyi and Luh, 1986; Somogyi et al., 1996). This cuticle, if it has not been damaged, has little permeability to moisture (Suarez et al., 1984). It includes two classes of compounds: natural waxes and cutin. The waxes contain a particular kind of lipid, which is an ester of high molecular weight, resulting from the combination of a fatty acid with a long chain monoalcohol. With the exception of the wax esters, natural fruit waxes contain a mixture of hydrocarbons (parafﬁns and oleﬁns), fatty acids (normal, hydroxylated, and ethylenic), ketones, alcohols, and aldehydes. All of these compounds have high molecular weights and similar physical properties, especially insolubility in water and a melting point between 40 and 100°C. Ursolic acid is

© 2003 by CRC Press LLC

widespread on the surface of apples, cranberries, pears, and prunes, among other fruits. This acid is very difﬁcult to dissolve from the fruit skin. For example, at 15°C one part of this acid dissolves in 88 parts of methanol, in 178 parts of ethanol (or in 35 parts of boiling ethanol), or in 140 parts of ether and is soluble in glacial acetic acid and 2% alcoholic NaOH (Mercks Index, 1983). The second layer of the fruit skin (cutin) is poorly soluble in most organic solvents, as the chains of constituents are ﬁrmly ﬁxed by cross-polymerization in the membrane (Mazliak, 1970). In practice, many different pretreatment techniques before fruit dehydration have been developed and applied. Saravacos and Charm (1962) divided fruits and vegetables into three general groups: those with a homogenous structure (carrot, blanched potato, garlic); those with a porous structure (apples, peaches, pears); and those possessing a surface skin (grapes, cranberries, cherries, gooseberries, etc.). The fruits from the third group need special pretreatments, as drying without pretreatment is not practical and requires a long time and much energy. The authors also speciﬁed conditions for the proper surface agent selection. The agent should be nontoxic, water soluble or easily dispersible, relatively low in molecular weight, and inexpensive. Detailed outlines of the California pretreatment practices for sun drying of fruits were presented by Heid and Joslyn (1967). Short (3–30 sec) hot or cold lye dip (0.25–1% of lye in water) is the most typical pretreatment for prunes, grapes, apricots, peaches, and nectarines. Most recently, a review of predrying treatment techniques and their effects on drying and rehydration of plant tissues was presented by Lewicki (1998). The author divided all pretreatments into two main groups: chemical (inorganic and organic) and nonchemical (heating, blanching, freezing, etc.). According to the author, the main beneﬁcial effects of pretreatment included reduced drying time, denaturation or inactivation of surface enzymes, removal of intracellular air, softening of the texture, and increased rehydration rate. According to Kostaropoulus and Saravacos (1995), Grabowski et al. (1994), and Masi and Riva (1988), the drying time of surface pretreated grapes (immersed in ethyl oleate, etc.) was reduced by about half. Venkatachalapathy and Raghavan (1997) found a positive effect using a combination of ethyl oleate (3%) and NaOH (0.5%) for microwave drying of strawberries. However, the convective drying rate of the strawberries was improved by only about 10% as a result of this pretreatment. In another study, surfactant pretreatment of basil leaves increased the drying rate by a factor of 14 (Rocha et al., 1993). In light of the above, the main objective of this study was to compare the effect of some of the most typical surface pretreatment techniques on osmotic dehydration and sugar infusion of cranberries. Some of the techniques tested in this study were theoretical rather than practical. They were selected based on knowledge of the characteristics of ursolic acid, the main component of the cranberry skin waxes.

5.2 EXPERIMENTAL PROCEDURE 5.2.1 OSMOTIC DEHYDRATION The experimental procedure enabled measurement of two important parameters of osmotic dehydration: water loss (WL) and mass reduction (MR). The third parameter of the process, solid gain (SG), which is mainly the infusion of sugar into the fruit

© 2003 by CRC Press LLC

structure, is the difference between the water loss and the mass reduction, as shown in Equations (1–3). All three parameters were calculated on the basis of 100 g of initial mass of fresh (control) or surface pretreated fruits: MR = 100 – M2

(5.1)

WL = 100 × b1 – M2 × b2

(5.2)

SG = WL – MR

(5.3)

Small scale laboratory equipment (Figure 5.1) was used to perform osmotic dehydration tests for fresh whole (control) and pretreated cranberries. Five vertical cylindrical columns of 250 ml each (5.08 cm diameter, 12.7 cm high) were connected in parallel to a positive displacement pump (Speed-trol, Sterling Electric Inc., New York) with a variable ﬂow rate (1–20 l/min). Using control valves, the syrup ﬂow rate was adjusted to be equal and constant through each column during the entire process (1 l/min for each column). Sucrose syrup at 67.5°Brix (commercially called liquid sugar) was recirculated from a tank (30 l) equipped with a heating jacket, through the test columns ﬁlled with cranberries, and back to the tank. Heating of the syrup in the tank was controlled to obtain a constant temperature at the inlet of the columns of 50 ± 2°C. The actual mass of the samples and the moisture content were determined after removing the samples one by one from the columns after a given period of time. All tests were performed at least in triplicate. The moisture content in the cranberry samples was determined using a standard procedure by drying the samples in a vacuum oven at 70°C for 6 h (AOAC, 1984). The sugar content of the cranberry samples was determined using a high pressure

5

2

4 1 3

Steam Condensate

FIGURE 5.1 Laboratory osmotic dehydration unit: (1) osmotic syrup tank; (2) mixer; (3) variable speed pump; (4) ﬂow regulating valves; (5) dehydration columns ﬁlled with cranberry samples (250 ml each).

© 2003 by CRC Press LLC

liquid chromatography (HPLC) after grinding a deﬁned quantity in distilled water (Marcotte and LeMaguer, 1991, 1992). The sugar concentration of the syrup was assumed to be constant during the process, as the mass of syrup circulating into the system was approximately 40 times more than the mass of cranberries in the columns. At the beginning and end of each run, the concentration of sugar in the syrup was measured (refractometer, Minolta Co., Ltd., Osaka, Japan) and adjusted to 67.5°Brix, if necessary.

5.2.2 PRETREATMENT TECHNIQUES Frozen cranberries (Vaccinium macrocarpon) of Stevens or Early Black varieties were purchased from a local cranberry farm and stored in a cold room (−4°C) until use. Each time, ﬁve samples of cranberries (about 100 g each) were thawed to +4°C and pretreated using one of the 13 procedures presented in Table 5.1. Among pretreatments, NaOH (2%) in 95% ethanol (pretreatment No. 4) and pectinase (pretreatment No. 5) have a theoretical rather than practical importance. These were included in the pretreatment list because of the solubility characteristics of ursolic acid (Mercks Index, 1983). Ethyl oleate, ethanol, NaOH, and enzyme (pectinase) applied in the pretreatment were supplied by Sigma-Aldrich Chemical Co. (Milwaukee, WI) and sodium oleate by J.T. Baker (Philipsburg, NJ).

TABLE 5.1 Characteristics of the Pretreatment Techniques Applied and Experimental Values of Coefﬁcients of Pretreatment Efﬁciency (ζζDEH for Moisture Removal and ζINF for Sugar Infusion) Pretr. No.

Type

Description

Conc. (% mass)

Time (min)

Temp (ºC)

ζDEH

ζINF

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

CH CH CH CH CH T T M M CO CO CO CO

Ethyl oleate Sodium oleate NaOH in water NaOH in ethanol (95%) Pectinase Steaming Boiling water Cut into halves a Perforating Ethyl oleate: hot dip Sodium oleate: hot dip NaOH in water: hot dip Ethyl oleate + NaOH: hot dip

3 3 0.5 2 0.3 — — — — 3 3 0.5 3 + 0.5

3 3 3 3 10 3 3 — — 3 3 3 3

20 20 20 20 20 100 100 20 20 100 100 100 100

2.8 2.6 3.15 2.7 1.1 5.7 5.6 6.1 3.5 5.6 5.5 5.8 6.3

2.45 2.3 3.1 2.0 1.1 5.05 4.5 5.1 2.5 4.9 4.7 4.95 5.4

Note: CH, chemical; T, thermal; M, mechanical; CO, combined (chemical + thermal). a

10 small holes (1 mm diameter) per berry.

© 2003 by CRC Press LLC

5.3 RESULTS AND DISCUSSION 5.3.1 SELECTION

OF THE

BEST PRETREATMENT

Pretreatment techniques applied before osmotic dehydration of cranberries were evaluated for their effect on cranberry moisture reduction and sugar infusion. The faster osmotic dehydration and sugar infusion were achieved, the better the pretreatment effect obtained. Two speciﬁc measurements of pretreatment efﬁciency were determined: 1. Coefﬁcient of pretreatment efﬁciency (ζ) 2. Taste acceptability of the cranberries after 5 h of osmotic process 5.3.1.1 Coefﬁcient of Pretreatment Efﬁciency Weitz et al. (1989) deﬁned the coefﬁcient of pretreatment efﬁciency as: ζ = τN/τP

(5.4)

MOISTURE CONTENT, X, dry basis

where τN and τP are the process times to reach an assumed dehydration (or infusion) level in the food, without (N) and with (P) a given type of pretreatment, respectively. Normally, unless atypical changes in the food structure arise, a coefﬁcient of pretreatment efﬁciency higher or equal to 1 (ζ ≥ 1) is found. Table 5.1 presents experimental results of different pretreatment tests. A ﬁnal moisture content of 50% (w.b.) and a mass reduction of 18% were assumed. Figure 5.2 shows data of dehydration kinetics of pretreated cranberries. The best result was achieved by combining chemical and thermal methods (pretreatment No.13 [NaOH and ethyl oleate in boiling water]: ζDEH = 6.3 and ζINF = 5.4). Similar results were obtained for cranberries cut into halves (ζDEH = 6.1 and ζINF = 5.1)

8 Halves

7 Steamed

6 Sodium oleate

5 4

Ethyl oleate

3

Pectinase

2

Untreated

1

0

12

Thousands

24

36

PROCESSING TIME, sec FIGURE 5.2 Effect of different pretreatments on cranberry dehydration kinetics.

© 2003 by CRC Press LLC

and other combinations of chemical and thermal pretreatments (pretreatments No. 10, 11, 12). The main problem associated with the combined pretreatments was the high sensitivity of the process to even small differences in initial temperature, size, and variety of tested cranberries. The range of effective pretreatment times for these techniques (pretreatments No. 10–13) and other thermal methods (pretreatments No. 6 and 7) was very narrow. Overprocessing of berries resulted in the destruction of texture, while underprocessing was an insufﬁcient pretreatment effect. Thus, based on the results presented in Table 5.1, cutting cranberries into halves was found to be the most practical pretreatment before osmotic dehydration of cranberries. For cranberries cut into halves, approximately 30% of the total surface was exposed to an effective mass transfer (dehydration and infusion), and the rest of the surface (approximately 70%) was covered by the skin with a mass transfer resistant to the layer of wax. 5.3.1.2 Taste Acceptability A panel of 10 untrained testers evaluated the taste of cranberries pretreated with 13 different techniques and then subjected to 5 h osmotic dehydration in a sugar syrup of 67.5° Brix at 50°C. An evaluation scale of 0–100 points was applied (0 = totally rejected; 100 = maximum preference). Figure 5.3 shows the average values. The lowest values were given to all chemically pretreated cranberries, medium to thermal and combined (chemical and thermal), and the highest to cranberries cut into halves. According to comments of the testers, each of the chemical or thermal pretreatments

100

TASTE ACCEPTABILITY, %

90 80

CHEMICAL MECHANICAL THERMAL COMBINED

70 60 50 40 30 20 10 0 1

2

3

4

5

6

7

8

9 10

11 12 13

PRETREATMENT TYPE (Number) FIGURE 5.3 Results of taste panel acceptability evaluation. The numbers of the pretreatments refer to Table 5.1.

© 2003 by CRC Press LLC

caused some speciﬁc changes in the taste or texture of the berries. Thus, the mechanical cutting of cranberries into halves was the most effective pretreatment tested. The other mechanical pretreatment, perforating the skin, was not successful, probably because a very low proportion of the skin was opened to the osmotic syrup. If it were possible to obtain a high enough number of perforations (or surface area opened by perforation), for example, 20–30% or more, this technique could also be practical.

5.3.2 SIMPLE DIFFUSSIVITY MODEL

FOR

CUT CRANBERRIES

After selection of the most effective pretreatment technique, attention was given to the mathematical description of the mass transfer between cut cranberries and the osmotic syrup. It is obvious that water and sucrose are mainly transferred through the cut surface of the berries, with only a small proportion being transferred through the uncut surface covered by the skin. Therefore, the entire mass transfer is the sum of two quantities: one related to the cut surface of the berry, and the second to the unaffected surface. Introducing a surface ratio parameter (α), which is the ratio of the cut surface area divided by total surface of the cut cranberry, α = Fopen by cut/Ftotal

(5.5)

and introducing different moisture (or infused sugar) effective diffusivity for the cut (Deff cut) and the uncut (Deff uncut) surface, the following simpliﬁed model of mass exchange between cut cranberry and osmotic syrup is proposed: Deff = αDeff cut + (1 – α)Deff uncut

(5.6)

To verify this model, a special set of tests was performed. Cranberries of uniform size were cut into halves and additionally from both sides, to achieve approximately 50% of open surface. Samples of uncut cranberries (reference: α = 0), cranberries cut into halves (30% open surface: α = 0.3), and cranberries cut from both sides (for 50% of open surface: α = 0.5) were placed into the osmotic dehydration unit (Figure 5.1). The osmotic dehydration and infusion treatment was performed in a sucrose syrup of 67.5° Brix at 50°C. Figure 5.4 shows examples of the dehydration kinetics. Figure 5.5 shows examples of sugar infusion kinetics of cut and uncut cranberries. At ﬁrst, no signiﬁcant differences in osmotic process of either variety of cranberries were observed. As predicted, the water content of cranberries cut to 50% of open surface (α = 0.5) was reduced at a higher rate than that of those cut into halves (α = 0.3). The dehydration time of uncut or whole cranberries was many times longer than for cut cranberries. For the sugar infusion, a similar situation was observed (Figure 5.5). Based on Fick’s second law of unsteady state mass diffusion (Crank, 1975), and assuming a spherical geometry and a uniform initial temperature and concentration distribution inside the berry, an effective coefﬁcient of diffusion (Deff) was calculated from the following equations (Crank, 1975; Nsonzi and Ramaswamy, 1997): 2

2

2

WR = 6/π exp(–Deffπ τ/a ) 2

2

Deff = Ba /π

© 2003 by CRC Press LLC

(5.7) (5.8)

WATER CONTENT, X, dry basis

7 6 5 4 3

Untreated

Halves "Early Black"

Halves "Stevens"

Cut (50% open surface)

2 1 0

0

10

20

30

40

Thousands PROCESSING TIME, sec

FIGURE 5.4 Kinetics of moisture removal (osmotic dehydration) from samples of cut and uncut (reference) cranberries.

kg SUGAR CONTENT (S), kg dry basis

0.4

Untreated (whole) Halves "Stevens" Halves "Early black" Cut (to 50% open)

0.3

0.2

0.1

0 0

5

10

15

20

Thousands

PROCESSING TIME, sec FIGURE 5.5 Kinetics of sugar infusion into uncut (reference) and cut cranberries.

© 2003 by CRC Press LLC

where τ is the process time; a is a characteristic dimension of the cranberry, and B is the slope of the kinetic curves ln(WR) or ln(SI) against time (t). Figure 5.6 shows the moisture reduction, and Figure 5.7 shows the sugar infusion. 2 Based on the statistical analysis (R = 0.91 − 0.96), effective diffusion coefﬁcient values were found to obey the following equations: 1 0

ln(WR)

-1 -2 Untreated

-3

Halves "Stevens"

-4 Halves "Early Black"

-5 -6

Cut (50% open surface)

0

7200 14400 PROCESSING TIME, sec

21600

FIGURE 5.6 Calculation of the effective moisture diffusivity for moisture reduction of cranberries. 2

ln(SI)

0

-2

-4

Untreated (whole) Halves "Stevens" Halves "Early black" Cut (to 50% open) -6 0

7200

14400

21600

PROCESSING TIME, sec FIGURE 5.7 Calculation of the effective diffusivity for sugar infusion into cranberries.

© 2003 by CRC Press LLC

For water loss (osmotic dehydration): –9

–11

Deff = 2.38 10 α + 1.7 10 (1 − α)

(5.9)

For sugar gain (infusion): –9

–11

Deff = 10 α + 1.65 10 (1 − α)

(5.10)

Equations (5.9) and (5.10) show that the effective diffusion coefﬁcient for the cut area of a cranberry is around 100 times higher than that of the uncut surface of the berry. The values of effective diffusivity for dehydration and infusion varied with process temperature and concentration of the osmotic syrup. In this work, both parameters were kept constant to study the clear effect of pretreatment techniques. For cranberries cut into halves (30% of open surface or α = 0.3), average effective –10 2 –10 2 mass diffusivities of about 7 × 10 m /sec and 3.1 × 10 m /sec were obtained for dehydration and sugar infusion, respectively. In osmotic dehydration literature, similar values have been reported (Rastogi and Raghavarao, 1997; Kaymak and Kincal, 1994; Marcotte and LeMaguer, 1992; Lewicki et al., 1984). Lower values –10 2 –10 2 of Deff, i.e., 2–5 × 10 m /sec for dehydration and 0.2–2 × 10 m /sec for infusion, were determined by Nsonzi and Rawaswamy (1997) for blueberries that were untreated before the osmotic process. To validate our mathematical model, shown in Equation (5.6), a special osmotic dehydration test for cranberries cut from one side to obtain 15% of open surface (α = –10 2 0.15) was performed. Experimental values of mass diffusivity of 4 × 10 m /sec for –10 2 dehydration and 1.9 × 10 m /sec for sugar infusion were obtained. These values –10 2 compared well with values calculated from Equations (5.9) and (5.10) (3.7 × 10 m /sec –10 2 for dehydration and 1.64 × 10 m /sec for sugar infusion). Therefore, this simple model can be applied to other fruits and vegetables cut before the next steps of processing.

5.4 CONCLUSIONS From the point of view of efﬁciency and taste acceptability, the best practical pretreatment of cranberries before osmotic dehydration and infusion was to cut the berries into halves. Taking into account the ratio of the open surface from cutting to the total surface of cut cranberries, a simple proportional model for the effective moisture loss and sugar gain diffusivities was proposed. Within the range of experimental data, effective diffusion coefﬁcients for moisture loss and sugar gain were approximately 100 times higher for the cut surface than for the uncut cranberries. The model was validated experimentally by comparing theoretical values to experimental data generated for berries with 15% of open surface. This model could be applied to other fruits and vegetables that are cut before other processing operations.

NOMENCLATURE a B

Characteristic dimension of cranberry, m –1 Slope of the kinetic curves (absolute value from Equation 5.8), s

© 2003 by CRC Press LLC

b Deff F MR S SG SI WL WR X α τ ζ

Cranberry moisture content, w.b. 2 Effective coefﬁcient of diffusion, m /sec 2 Surface of the single berry, m Mass reduction, g/100 g of initial mass Sugar content, kg/kg dry basis Solid gain, g/100 g of initial mass Dimensionless sugar intake: (S – SEQ)/(S1 − SEQ) Water loss, g/100 g of initial mass Dimensionless water reduction: (X – XEQ)/(X1 – XEQ) Moisture content, kg/kg dry basis Surface ratio: open by cut to total Process time, sec Coefﬁcient of pretreatment efﬁciency (Equation 5.4)

SUBSCRIPTS 1, 2 DEH EQ INF N, P

Initial and ﬁnal, respectively Dehydration Equilibrium Infusion of sugar Without pretreatment and pretreated, respectively

ACKNOWLEDGMENTS Financial support from the Ofﬁce of Energy Research and Development of Canada (Program PERD) is gratefully acknowledged. Special thanks go to Francois Brunet for the HPLC sugar tests.

REFERENCES AOAC, Ofﬁcial Methods of Analysis, 14th ed., Association of Ofﬁcial Analytical Chemists, Washington, DC, 1984. Crank, J., The Mathematics of Diffusion, Clarendon Press, Oxford, 1975, pp. 89–103. Grabowski, S., Mujumdar, A.S., Ramaswamy, H.S., and Strumillo, C., Osmo-convective drying of grapes, Drying Technol., 12, 1211–1219, 1994. Heid, J.L. and Joslyn, M.A., Fundamentals of Food Processing Operations, AVI, Westport, CT, 1967, p. 510. Kaymak, F. and Kincal, N.S., Apparent diffusivities of reducing sugars in potato strips blanched in water, Int. J. Food Sci. Technol., 29, 63–70, 1994. Kostaropoulos, A.E. and Saravacos, G.D., Microwave pre-treatment for sun-dried raisins, J. Food Sci., 60, 344–347, 1995. Lewicki, P., Effect of pre-drying treatment, drying and rehydration of plant tissue properties: a review, Int. J. Food Prop., 1, 1–22, 1998. Lewicki, P., Lenart, A., and Turska, D., Diffusive mass transfer in potato tissue during osmotic dehydration, Food Technol. Nutr. — Annals of Warsaw SGGW-AR, 16, 25–32, 1984.

© 2003 by CRC Press LLC

Marcotte, M. and LeMaguer, M., Repartition of water in plant tissues subjected to osmotic processes, J. Food Process Eng., 13, 297–320, 1991. Marcotte, M. and LeMaguer, M., Mass transfer in cellular tissues. Part II: Computer simulations vs. experimental data, J. Food Eng., 17, 177–199, 1992. Masi, P. and Riva, M., Modeling grape drying kinetics, in Preconcentration and Drying of Food Materials, Bruin, S., Ed., Elsevier, Amsterdam, 1988, pp. 203–214. Mazliak, P., Lipids, in The Biochemistry of Fruits and Their Products, Hulme, A.C., Ed., Academic Press, New York, 1970, pp. 209–221. Mercks Index, An Encyclopedia of Chemicals, Drugs, and Biologicals, Mercks & Co., Inc., Rahway, NJ, 1983, pp. 1413–1414. Nsonzi, F., and Ramaswamy, H.S., Osmotic dehydration kinetics of blueberries, Drying Technol., 15, 705–723, 1997. Rastogi, N.K. and Raghavarao, K.S., Water and solute diffusion coefﬁcient of carrot as a function of temperature and concentration during osmotic dehydration, J. Food Eng., 34, 429–440, 1997. Rocha, T., Lebert, A., and Marty-Andonin, C., Effect of pretreatments and drying conditions on drying rate and color retention of basil (Ocimum basilicum), Lebensm.-Wiss. Technol., 26, 456–463, 1993. Saravacos, G.D. and Charm, S.E., Effect of surface active agents on the dehydration of fruits and vegetables, Food Technol., 16, 91–93, 1962. Somogyi, L.P. and Luh, B.S., Dehydration of foodstuffs, in Commercial Fruit Processing, 2nd ed., Woodroof, J.G. and Luh, B.S., Eds., AVI, Westport, CT, 1986, pp. 353–405. Somogyi, L.P., Ramaswamy, H.S., and Hui, Y.H., Processing Fruits: Science and Technology— Biology, Principles and Applications, Technomic, Lancaster, PA, 1996, pp. 14–24 and 185–220. Suarez, C., Loncin, M., and Chrife, J., A preliminary study of the ethyl oleate dipping treatment on drying rate of grain corn, J. Food Sci., 49, 236–238, 1984. Venkatachalapathy, K. and Raghavan, G.S.V., Effect of chemical pretreatment on microwave drying of strawberries, Proceedings of the Annual Conference of the Canadian Society of Agricultural Engineering., May 27–30, 1997, Sherbrooke, Canada, Volume A, pp. 215–224. Weitz, D.A., Lara, M.A., Piacentini, R.D., and Feldman, S., Dipping treatment effects on simulated prune solar drying, Can, Inst. Food Sci. Technol. J., 22, 133–136, 1989.

© 2003 by CRC Press LLC

6

Mass Transfer Description of the Osmodehydration of Apple Slabs E. Azuara-Nieto, G.F. Gutiérrez-López, and C.I. Beristain-Guevara

CONTENTS 6.1 6.2 6.3 6.4

Introduction Theoretical Frame Materials and Methods Results 6.4.1 Mathematical Modeling 6.5 Discussion 6.6 Conclusions Nomenclature Acknowledgments References

6.1 INTRODUCTION Over the past few years, a number of reports related to mass transfer during osmotic dehydration (OD) have appeared in the technical literature. However, a full understanding of the mechanisms involved in the simultaneous countercurrent mass ﬂows has not been reached. Transport phenomena during OD depend on the diffusion coefﬁcient and on the driving force for water and solutes. By manipulating processing factors affecting these parameters, it is possible to reach different levels of dehydration or impregnation of the material under treatment. A common property of foodstuffs subjected to osmotic dehydration is the formation of a layer of high solute concentration on the product surface. Osmotically dehydrated gels and plant tissues in sucrose solutions display a solute impregnation localized on a superﬁcial layer 2–3 mm from the surface. Solute layer formation plays a role in mass transfer control during osmotic dehydration,

© 2003 by CRC Press LLC

enhancing water loss and reducing both solute uptake and losses of soluble solids from the foodstuff as ascorbic acid and fructose (Vial et al., 1991; Saurel et al., 1994). Additionally, the presence of the solute layer may have an effect on product behavior during storage or further dehydration (Karathanos et al., 1995). Only a limited number of reports suggest the existence of three stages during the osmotic dehydration process (Toupin et al., 1989; Le Maguer and Yao, 1995). Among these, the model proposed by Le Maguer and Yao is the only one that attempts to explain the mass transfer in each stage. These authors were able to model the operation closely to the behavior of the real tissue by employing thermodynamic concepts for irreversible processes. However, the main drawbacks of the model were the vast number of biophysical properties that have to be known for a given foodstuff and the need to develop a numerical solution of the equations. The purpose of this work was to develop a kinetic model based on shrinking core theory (Levenspiel, 1976), in order to describe the osmotic dehydration stages of apples and to obtain information about the mass transfer mechanisms along the process.

6.2 THEORETICAL FRAME Variability of raw materials is one of the most important sources of error when collecting mass transfer data during osmodehydration. Agricultural practices, variety of the product, and level of maturity, among other factors, affect composition and physical–chemical properties of fruits and vegetables. The complex heterogeneous structure of natural tissues makes it difﬁcult to study and understand countercurrent mass transfer mechanisms arising during this operation. Nobel (1983) claimed that cell tissues may be considered as individual cells within a continuous cell wall with porous matrixes forming channels through which water ﬂows. Individual cells containing over 90% water act as springs that supply water to the channels. These cells are separated from the cell wall by a cellular membrane. This organ allows water ﬂow and also may function as a solids barrier depending on the nature of the solids. The space occupied by cells is called intracellular volume and the free space is called extracellular volume. When tissues are put into contact with the osmotic solution, solids enter the extracellular volume. Penetration of solids induces a difference in the chemical potential of water on both sides of the cellular membranes, and water leaves the intracellular volume, reaching the osmotic solution before passing this extracellular volume. The amount of water leaving the system is proportional to the mass of solids entering the tissue. During osmodehydration, the volume of water ﬂowing out of the system is much higher than the entering volume of solids. Driving forces are maintained due to this difference in ﬂows, and shrinkage of the tissue also arises as a consequence. Pseudodiffusion has frequently been used to model osmotic dehydration. A heterogeneous material is assumed to be homogeneous to allow the usage of the second degree diffusion equation for nonsteady conditions and thus to ﬁnd an approximate solution for the evaluation of transferred mass. An effective diffusion coefﬁcient is introduced to allow for the resistance due to the effects of the cell membrane and shrinkage of tissues.

© 2003 by CRC Press LLC

Stahl and Loncin (1979) used a one-dimensional equation to model mass transfer in potatoes with and without peel. These authors found that the diffusion phenomena may be predicted by means of a boundary layer model incorporating a mass transfer coefﬁcient for the peel. They also concluded that effective diffusion found during the experiments is strongly dependent on time and cannot be considered as a constant. Diffusion of sucrose in sugar beet root submerged in water was modeled by means of the unstable diffusion equation, considering that all the sucrose can diffuse freely in the material (Soddu and Gioia, 1979). In this work, the effect of cellular structures on mass transfer was taken into account by the use of an apparent diffusion coefﬁcient. The authors found that in the fresh vegetable, a driving force smaller than the one based on the total sucrose concentration regulates sucrose diffusion. This means that not all the sucrose contained in the tissue takes an active role in diffusion. Part of it is bound to cellular structures, and this amount strictly depends on the conﬁguration of such structures. Conway et al. (1983) modeled water loss from 1 cm thick apple rings, considering the slices as inﬁnite homogeneous slabs. For this purpose, Fick’s unsteady state equation was used to predict water loss, assuming no surface resistance and no solids gain. Beristain et al. (1990) used the same equation to model water loss during osmodehydration of pineapple slices in sucrose solutions. The authors obtained diffusion coefﬁcients for water at different temperatures and concentrations by means of the Park method (Crank, 1975). They concluded that for a high sucrose concentration (70°Bx), the diffusion coefﬁcient is not constant. Hough et al. (1993) developed a model for osmotic dehydration of apple slices, assuming unidirectional unsteady state pure diffusion. Mass balances for dehydration and impregnation were applied separately. These authors took into account shrinkage, and their model involves a numerical solution to the transport differential equations. According to Yao and Le Maguer (1997), volumetric ﬂow and changes in cellular structure that take place during osmotic dehydration are the main factors that differentiate mass transfer in osmodehydration from pure diffusion. Volume ﬂow is strongly inﬂuenced by changes in the cellular structure of the tissue. In pure diffusion, dimensionless change of mass may be represented as a unique function of the Fourier number for mass 2 transfer (Fo = Dit/l ) (Crank, 1975), in which Di is the diffusion coefﬁcient of specie i, t is time of contact, and l is the half thickness of the slab. These criteria may be applied to check for pure diffusion, considering variations in thickness of the slab. Simpler models also exist based on mass balances, such as those reported by Raoult-Wack et al. (1991) and Azuara et al. (1992). Parjoko et al. (1996) and Mujaffar and Sankat (1998) successfully applied the Azuara et al. model to osmodehydration of pineapple in palm tree sugar solutions and shark ﬁllets in brine. There have been studies involving complex microscopic models, which consider nonreversible thermodynamic concepts in order to work out the contribution of each component and a description of the role of the natural tissues in the process (Toupin et al., 1989; Toupin and Le Maguer, 1989; Marcotte et al., 1991; Marcotte and Le Maguer, 1992; Le Maguer and Yao, 1995; Yao and Le Maguer, 1996). In these models, the cell is assumed to pass through three dehydration stages, which are a function of the decrease in cellular volume (Toupin et al., 1989). Detailed microscopic models are useful for explaining mass transfer at the cellular level. Water lost is related to osmotic

© 2003 by CRC Press LLC

phenomena through natural membranes acting as semipermeable barriers (Le Maguer, 1988). However, studies carried out with agar gels by Raoult-Wack et al. (1991) showed that it is possible to ﬁnd the same dehydration effect without the existence of selective membranes. Other works using normal and frozen (to eliminate the selectiveness of membranes) apples conﬁrmed that osmosis is not the main mechanism in dehydration (Saurel et al., 1994). In frozen tissues, the dehydration mechanism was diffusive and markedly related with a dense layer of solids on the surface of the product. Analysis of these ﬁndings suggests that osmodehydration of homogeneous materials may be modeled as a diffusion process with a variable diffusion coefﬁcient.

6.3 MATERIALS AND METHODS Golden Delicious apples were obtained from a local market. The fruits were cut into disk-shaped pieces 46 mm in diameter and 4 mm thick and immediately immersed into a 20 g/l solution of ascorbic acid for 5 min to control browning. In osmotic dehydration, it is necessary to count with reliable kinetics the changes in mass that are attributed to the process and not to variability of the product. To overcome this, a continuous method of evaluation of the kinetics was used. With this method, it is possible to obtain all the kinetics by measuring weight losses in the same sample along the processing time (Azuara et al., 1998). The apple disks were dehydrated by immersing into a 500 g/l sucrose solution set at 30, 40, or 50°C. A food:solution ratio greater than 1:20 was maintained at all times. Samples were withdrawn periodically up to a total drying time of 5 h. Immediately after sample withdrawal, the disks were blotted with drying paper to remove excess solution. Each disk was weighed and its thickness measured at at least three different points using a Mitutoyo micrometer. After these measurements, the disks were returned to the osmotic solution to continue the process. At the end of the experiment, moisture content was determined in each sample by placing it into vacuum oven for 24 h at 70°C (AOAC, 1984).

6.4 RESULTS 6.4.1 MATHEMATICAL MODELING Work on concentration proﬁles along osmotic dehydration of apples carried out by Salvatori et al. (1997) has shown the existence of a zone in the center of the samples that keeps the initial conditions of the fresh fruit and that decreases in size with time. This experimental evidence may suggest the possibility of developing a kinetic equation based on the shrinking core model (Levenspiel, 1976). Given that the thickness/diameter ratio of the apple disks was smaller than 0.1 (actual ratio = 0.086), the samples can be considered as semiinﬁnite plates, in which ﬂuxes of water and soluble solids are unidirectional (Vaccarezza et al., 1974). According to the shrinking core theory, during the drying process the moist center decreases and a crust is formed. The crust contains less moisture than the initial water content between the surface and the moist core. At all times, core properties are similar to those of the initial stages (Levenspiel, 1976). The shrinking core model

© 2003 by CRC Press LLC

proposes that the total resistance to water transfer from the sample to the osmotic solution can be explained by the existence of two resistances acting in series: an internal one represented by an effective diffusion coefﬁcient through the dried shell, and an external one located in the ﬁlm of ﬂuid around the particle. The contribution of each resistance towards the total one along OD is different, and the limiting one will be that of higher value (Levenspiel, 1976). Water loss (WFL) and solids gain (SG) during osmotic dehydration were calculated using equations derived from mass balances (Azuara et al., 1992). WFL =

SG =

s1tWFL ∞ 1 + s1t

(6.1)

s2 tSG ∞ 1 + s2 t

(6.2)

Apple samples had different initial moisture and solids content, causing the scatter observed in WFL and SG values (Karathanos et al., 1995). To minimize the variation, constants s1, s2, WFL∞, and SG∞ were calculated with equations developed for a method for continuous evaluation of osmotic dehydration kinetics (Azuara et al., 1998). The rate of water transfer per unit area from the moist core to the surface and through the dehydrated crust is given by: 2  − dWFS  = Dw − dCw   dx  πdo(do + 4 x)  dt 

(6.3)

Azuara et al. (1992) proposed the following equation to calculate the effective diffusion coefﬁcient for foodstuffs having a ﬂat slab geometry: π tF 2  s110  Dw = 4  1 + s1t 

2

(6.4)

Figure 6.1 shows that a variable diffusion coefﬁcient such as the one evaluated with Equation (6.4) is a unique function of the Fourier number and thus can be modeled as pure diffusion. The rate of water transfer per unit surface area of the disk, from the food surface to the ﬂuid, is given by: 2  − dWFS  = hw (C int sol − Cso) πdo(do + 4 lt )  dt 

(6.5)

By manipulating Equations (6.3), (6.4), and (6.5), it is possible to arrive at:

−

 d + 4 lt  8 lt + do   1 πd 0 (d 0 + 4 lt )(1 + s1t )2 (Cwi − Cwo) = −(1 + α ) 0 ln   + 2s1WFL ∞  8 lc + do   hw  4Dw

© 2003 by CRC Press LLC

(6.6)

1

WFL/WFLα

0.8

0.6

thickness 2 mm

0.4

thickness 4 mm thickness 6 mm

0.2

0 0

0.5

1

1.5

2

Fourier number

FIGURE 6.1 Dimensionless water loss vs. Fourier number for different thicknesses of apple disks (T = 30°C).

Equation (6.6) shows that total resistance to mass transfer is the algebraic sum of an internal diffusive resistance (shell resistance) plus a solids uptake resistance through the ﬁlm of solution surrounding the foodstuff. Therefore, the model can be written in the following form: Total resistance to = shell resistance + ﬁlm resistance to mass transfer to water ﬂow waterﬂow

(6.7)

Equation (6.6) can be written in its dimensionless form: −

π 2 d 0 F 2 l 0 2 (Cwi − Cwo)(1 + s1t )ML  8l + d 0  2 WFL ∞ ( WFL ∞ − SG ∞ ) ln  t   8l c + d 0  4Dw(1 + s1t )ML =

 8l + d 0  hws1t( WFL ∞ − SG ∞ )(d 0 + 4l t ) ln  t   8l c + d 0 

− (1 + α )

2

Ymod = (πs1lo /hw(WFL∞ – SG∞))Xmod. – (1 + α)

(6.8)

(6.9)

The expression to estimate the half thickness of the moist core (lc) is: lc =

© 2003 by CRC Press LLC

lo 1 + s1t

(6.10)

The half thickness of the apple disk at time t (lt) was adjusted with the following equation: l  l  l t = l e + (l o − l e ) c  + cs1t  c  l  t  lo 

2

(6.11)

Activation energy (Ea) can be estimated using an Arrhenius-type equation of the following form: Dw = Do e − Ea / RT

(6.12)

Goodness of ﬁt was estimated with the mean relative deviation modulus (P%) between the experimental and predicted values: P(%) =

100 N

m

∑

| M i − M pi |

i =1

(6.13)

Mi

6.5 DISCUSSION Figure 6.2 shows the volume change of the apple disks (Vt/Vo) vs. moisture content at 30°C. Three stages during the osmotic dehydration can be observed. The same behavior was obtained when the drying process was carried out at 40 and 50°C. These experimental results obtained using macroscopic measurements are in agreement 0

0.9

-0.2

0.8

-0.4

0.7

Stage 3

Stage 2

-0.6

Stage 1

-0.8 0.6 -1.0 0.5

-1.2

0.4

Total resistance x 10-4 (min/cm)

Vt/Vo

1

-1.4 0.5

0.6

0.7

0.8

0.9

Moisture (g water/g wet solid) FIGURE 6.2 Changes in volume and total resistance during osmotic dehydration of apple disks.

© 2003 by CRC Press LLC

TABLE 6.1 Parameters of the Model Temperature (ºC)

WFL∞/Mo

SG∞/Mo

30

0.7156

0.1476

0.0317

40

0.7505

0.1747

0.0531

50

0.7602

0.2354

0.0903

s1 min

−1

Stage of O.D. st

1 nd 2 rd 3 st 1 nd 2 rd 3 st 1 nd 2 rd 3

hw (g water–m/g solids–s) 1.244 2.900 2.200 3.543 3.013 4.472 3.221 5.047 3.922

× × × × × × × × ×

−6

10 −7 10 −8 10 −7 10 −8 10 −9 10 −7 10 −8 10 −9 10

(1 + α) 1.5118 2.4073 7.8034 1.9612 5.8864 14.5240 2.5626 7.5624 21.6112

with the three stages theory proposed at the microscopic level by Toupin et al. (1989) and Le Maguer and Yao (1995). The mathematical model based on the shrinking core theory also predicted three stages as a function of the total resistance to water ﬂow (Figure 6.2). In the model, α is a dimensionless parameter that is characteristic for each stage and that increases with the amount of impregnated solids into the apple disk, which decreases as the amount of washed solids by water ﬂow increases. The parameters of each stage are reported in Table 6.1. It can be observed that α increased as the osmotic dehydration took place. A similar effect was observed when the temperature was increased. In addition, the mass transfer coefﬁcient for water (hw) had an opposite behavior as compared with that of α. This may be due to the fact that impregnation on the surface raised the ﬁlm resistance to water ﬂow. In Figure 6.3 (dimensionless form of Equation (6.9)), the presence of the three stages of osmodehydration at 40 and 50°C can be observed. At the end of each stage and the beginning of the next one, an increment of (1 + α) and a decrease of hw are observed. As seen in Figure 6.4, the diffusion coefﬁcient of water (Dw) decreased as the moisture content decreased. On the other hand, Dw increased with temperature. However, it should be noted that there is a zone of high moisture where Dw increased as the moisture content decreased (Figure 6.4). In this zone, the osmotic solution penetrates into the apple tissue to expel the trapped air from intercellular spaces, facilitating the diffusion of water contained in the superﬁcial cells. As a consequence, the apple–solution interface increases and Dw also increases. At the beginning of the second stage, an increase in the length of the water diffusion path around the cells on the surface and the cells in the moist core occurs, which leads to a decrease of Dw. The third stage is beyond collapse and Dw diminishes as moisture content decreases. Figure 6.5 depicts the variation of lt and lc with time. It can be seen that lt and lc diminish faster along the ﬁrst stage than in the second and third stages. Moreover, in the third stage, the half thickness of the moist core (lc) is close to zero because the equilibrium has almost been reached.

© 2003 by CRC Press LLC

0

-1 -2

Stage 1 Stage 2

-4

-4 -6 -5 -8 -6 Stage 3

40°C

-10

50°C

-12

Ymod (50°C)

Ymod (40°C)

-3

-2

-7 -8

-14

-9 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Xmod FIGURE 6.3 Stages of osmotic dehydration (OD) obtained with Equation (6.9).

14 Stage 1 30°C 40°C 50°C

10

Stage 2

2

(m /s)

12

Dw × 10

10

8 Stage 3 6 4 2 0 0.3

0.4

0.5

0.6

0.7

0.8

0.9

Moisture (g water/g wet solid) FIGURE 6.4 Variation in the diffusion coefﬁcient during osmotic dehydration of apple disks.

© 2003 by CRC Press LLC

0.2

lt or lc (cm)

0.15

lt 30°C

0.1

lt 40°C lt 50°C lc 30°C

0.05

lc 40°C lc 50°C

0 0

50

100

150

200

250

300

350

Time (min) FIGURE 6.5 Variation of lc and lt with time during osmotic dehydration of apple disks.

TABLE 6.2 Parameters for Equation (6.11) Temperature (ºC)

le (cm)

c (cm)

P (%)

30 40 50

0.14057 0.13079 0.13740

−0.04205 −0.01848 +0.02926

1.952 1.755 0.657

As shown in Table 6.2, lt can be calculated as a function of lc and the half-thickness of the apple disk at equilibrium (le). A good ﬁt was obtained with P values ≤1.952%. Also, as the increment of temperature favors solids entrance and diminishes shrinkage, correction factor c is less negative. Activation energy (Ea) for water diffusion increased as the moisture content of the apple disks decreased. For stage 1, the moisture content varied from 0.83 to 0.78 g water/g wet solid, and Ea was in the range of 8.6 to 10.5 kcal/mol. For stage 2, the moisture content varied from 0.78 to 0.56 g water/g wet solid, and Ea was in the range of 10.5 to 13.0 kcal/mol. For stage 3, the moisture content varied from 0.56 to 0.50 g water/g wet solid, and Ea was in the range of 13.0 to 17.7 kcal/mol.

© 2003 by CRC Press LLC

6.6 CONCLUSIONS To model osmotic dehydration as a pure diffusion process, it is necessary to account for a nonconstant diffusion coefﬁcient (Dw), which varies in such a way that the dimensionless variation of mass can be represented as a unique function of the Fourier number. It is possible to determine macroscopically the stages of the process by measuring volume changes of a sample during the process. The shrinking core model applied to this operation predicts the same stages as volume change measurements do. This model takes into account water losses, solids entrance, weight losses, and variation of sample thickness. The greater the impregnation, the lower the water ﬂux from the product to the solution. This may be due to the fact that impregnated sugar molecules on the surface of the slices interact with water molecules, creating an additional resistance to water ﬂux from the sample to the medium. Shrinkage of the discs decreases with impregnation and temperature. It was possible to predict the change in sample thickness along the OD process, considering initial thickness and size of the wet core.

NOMENCLATURE c Cintsol Cso Cw Cwi Cwo do Do Dw Ea 2 Fo = Dw t/lt mod exp F = WFL∞ /WFL∞ hw lo lt lc le Mi Mo Mpi ML N

© 2003 by CRC Press LLC

Constant for correction of thickness for solids gained and temperature (cm) 3 Interfacial solids concentration (g/cm ) 3 Volumetric concentration of sucrose in the solution (g/cm ) 3 Volumetric concentration of water in the apple (g/cm ) Volumetric concentration of water inside the apple disk at 3 time 0 (g/cm ) Volumetric concentration of water inside the osmotic solution 3 (g/cm ) Initial diameter of the apple disk (cm) 2 Frequency factor (m /sec) 2 Effective diffusion coefﬁcient of water (m /sec) Activation energy (kcal/mol) Fourier number Correction factor Mass transfer coefﬁcient of water based on the concentration of osmotic solution (g of water–m/g of solids–sec) Half-thickness of the apple disk at time 0 (cm) Half-thickness of the apple disk at time t (cm) Half-thickness of the moist core (cm) Half-thickness of the apple disk at equilibrium (cm) Experimental values Initial weight of the apple disk (g) Predicted values Weight lost by the food at time t (g) Number of experimental data

P R s1 s2 SG SG∞ t T Vo Vt WFL WFL∞ mod WFL∞ exp WFL∞ WFS x α

Mean relative deviation modulus between the experimental and predicted values (%) Universal gas constant (1.987 cal/mol K) –1 Constant related to water loss (min ) –1 Constant related to solids gain (min ) Amount of solids gained by the apple disk at time t (g) Amount of solids gained by the apple disk at equilibrium (g) Time (min, sec) Absolute temperature (K) 3 Volume of the apple disk at time 0 (cm ) 3 Volume of the apple disk at time t (cm ) Amount of water lost by the apple disk at time t (g) Amount of water lost by the apple disk at equilibrium (g) Value for WFL∞ obtained from Equation (1) Value for WFL∞ obtained experimentally Amount of water that remains in the apple disk at time t, but that could leave the disk by diffusion (g) Position of a point in the circular plate in Cartesian coordinates, measured in axial direction (cm) Unidimensional characteristic parameter for each stage

ACKNOWLEDGMENTS To CYTED Project XI.13, IPN–México and Universidad Veracruzana–México for support.

REFERENCES AOAC, Ofﬁcial Methods of Analysis, Association of Ofﬁcial Analytical Chemists, Washington, DC, 1984. Azuara, E., Beristain, C.I., and Gutiérrez, G.F., A method for continuous kinetic evaluation of osmotic dehydration, Lebensm.-Wiss. Technol., 31, 317–321, 1998. Azuara, E., Cortés, R., Garcia, H.S., and Beristain, C.I., Kinetic model for osmotic dehydration and its relationship with Fick’s second law, Int. J. Food Sci. Technol., 27, 409–418, 1992. Beristain, C.I., Azuara, E., Cortes, R., and Garcia, H.S., Mass transfer during the osmotic dehydration of pineapple rings, Int. J. Food Sci. Technol., 25, 576–582, 1990. Conway, J., Castaigne, F., Picard, G., and Vovan, X., Mass transfer considerations in the osmotic dehydration of apple, Can. Inst. Food Sci. Technol. J., 16, 25–29, 1983. Crank, J., The Mathematics of Diffusion, 2nd ed., Clarendon Press, Oxford, 1975. Hough, G., Chirife, J., and Marini, C., A simple model for osmotic dehydration of apples, Lebensm.-Wiss. Technol., 26, 151–156, 1993. Karathanos, V.T., Kostaropoulos, A.E., and Saravacos, G.D., Air-drying kinetics of osmotically dehydrated fruits, Drying Technol., 13, 1503–1521, 1995. Le Maguer, M., Osmotic dehydration: review and future directions, in Proc. Int. Symposium Progress in Food Preservation Process, CERIA, Brussels, vol. 1, 1988, pp. 283–309.

© 2003 by CRC Press LLC

Le Maguer, M. and Yao, Z.-M., Mass transfer during osmotic dehydration at the cellular level, in Food Preservation by Moisture Control, Fundamentals and Applications, BarbosaCánovas, G.V. and Welti-Chanes, J., Eds., 1995, pp. 325–350. Levenspiel, O., Solid-ﬂuid reactions, in Chemical Reaction Engineering, 2nd. ed., Wiley, New York, 1976, p. 357–377. Marcotte, M. and Le Maguer, M., Mass transfer in cellular tissues. II: Computer simulation vs. experimental data, J. Food Eng., 17, 177–199, 1992. Marcotte, M., Toupin, C.J., and Le Maguer, M., Mass transfer in cellular tissues. I: The mathematical model, J. Food Eng., 13, 199–220, 1991. Mujaffar, S. and Sankat, C.K., The osmotic dehydration of shark ﬁllets, Proceedings of the 11th International Drying Symposium, Akritidis, C.B., Marinos-Kouris D., and Saravakos, G.D., Eds., ZITI Editions, Thessaloniki, Greece, 19–22, vol. A, 1998, pp. 911–921. Nobel, P.S., Biophysical Plant Physiology and Ecology, W.H. Freeman and Company, New York, 1983. Parjoko, Rahman, M.S., Buckle, K.A., and Perera, C.O., Osmotic dehydration kinetics of pineapple wedges using palm sugar, Lebensm.-Wiss. Technol., 29, 452–459, 1996. Raoult-Wack, A.L., Petitdemange, F., Giroux, F., Ríos, G., Guilbert, S., and Lebert, A., Simultaneous water and solute transport in shrinking media. 2: A compartmental model for the control of dewatering and impregnation soaking process, Drying Technol., 9, 613–630, 1991. Salvatori, D., Andrés, A., Chiralt, A., and Fito, P., Concentration proﬁles in apple tissue during osmotic dehydration, Proceedings of the Seventh International Congress on Engineering and Food, Jowitt, R., Ed., Sheﬁeld Academic Press, Brighton, U.K., 1997. Saurel, R., Raoult-Wack, A.L., Rios, G., and Guilbert. S., Mass transfer phenomena during osmotic dehydration of apple. I. Fresh plant tissue, Int. J. Food Sci. Technol., 29, 531–542, 1994. Soddu. A. and Gioia, F., Diffusion through living systems: sugar loss from sugar beets, Chem. Eng. Sci., 34, 763–773, 1979. Stahl, R. and Loncin, M., Prediction of diffusion in solid foodstuffs, J. Food Process. Preserv., 3, 213–223, 1979. Toupin, C.J. and Le Maguer, M., Osmotically induced mass transfer in plant storage tissues: a mathematical model—Part 2, J. Food Eng., 10, 97–121, 1989. Toupin, C.J., Marcotte, M., and Le Maguer, M., Osmotically induced mass transfer in plant storage tissues: a mathematical model—Part 1, J. Food Eng., 10, 13–38, 1989. Vaccarezza, L.M., Lombardi, J.L., and Chirife, J., Kinetics of moisture movement during air drying of sugar beet root, J. Food Technol., 9, 317–327, 1974. Vial, C., Guilbert, S., and Cuq, J., Osmotic dehydration of kiwifruits: inﬂuence of process variables on the color and ascorbic acid content, Sci. Aliment., 11, 63–84, 1991. Yao, Z. and Le Maguer, M., Mathematical modelling and simulation of mass transfer in osmotic dehydration processes. I: Conceptual and mathematical models, J. Food Eng. 29, 349–360, 1996. Yao, Z. and Le Maguer, M., Osmotic dehydration: an analysis of ﬂuxes and shrinkage in cellular structure, Trans. ASAE, 39, 2211–2216, 1997.

© 2003 by CRC Press LLC

7

Combined Effect of High Hydrostatic Pressure Pretreatment and Osmotic Stress on Mass Transfer during Osmotic Dehydration N.K. Rastogi, A. Angersbach, and D. Knorr

CONTENTS 7.1 7.2

Introduction Materials and Methods 7.2.1 Raw Material Preparation 7.2.2 High Pressure Pretreatment 7.2.3 Osmotic Dehydration of Potato Slices 7.2.4 Determination of Water and Solute Diffusion Coefﬁcients during Osmotic Dehydration 7.2.5 Determination of Cell Disintegration Index (Zp) 7.3 Results and Discussion 7.4 Conclusion Nomenclature Acknowledgments References

7.1 INTRODUCTION Osmotic dehydration is a process of partial removal of water from plant tissues by immersion in a concentrated solution of sugar or salt. Due to the difference in osmotic pressure between the food and the solution, water is transported from the

© 2003 by CRC Press LLC

material into the solution. The diffusion of water is accompanied by the simultaneous counterdiffusion of solute from the osmotic solution into the tissue. Since the membrane responsible for osmotic transport is not perfectly selective, other solutes present in the cells can also be leached into the osmotic solution (Dixon and Jen, 1977; Lerici et al., 1985; Giangiacomo et al., 1987). The rate of diffusion of water from any material made up of such tissues depends upon factors such as: • • • •

The The The The

temperature and concentration of the osmotic solution size and geometry of the material solution to material mass ratio level of agitation of the solution

A number of recent publications have described the inﬂuence of these variables on mass transfer rates during osmotic dehydration (Roult-Wack et al., 1992; Torreggiani, 1993; Roult-Wack, 1994; Rastogi and Raghavarao, 1994, 1995, and 1997a and b; Rastogi et al., 1997). Given the low rate of mass transfer observed, a number of techniques have also been tried to improve mass transfer rate. These techniques include the application of a partial vacuum (Rastogi and Raghavarao, 1996; Fito, 1994) or ultrasound (Simal et al., 1999) during treatment, and ultra high hydrostatic pressure (Rastogi and Niranjan, 1998) or high intensity electrical ﬁeld pulses (Rastogi et al., 1999) to the material prior to osmotic treatment. Mass transfer during osmotic treatment occurs through semipermeable cell membranes present in biological materials, which offer the dominant resistance to the process. The state of the cell membrane can change from being partially to being totally permeable, and this can lead to signiﬁcant changes in tissue architecture. During osmotic removal of water from foods, the osmotic dehydration front moves from the surface of the food in contact with surrounding osmotic solution to the center, which results in disintegration of cells due to osmotic stress. A mechanism of osmotic water removal from biological materials has recently been proposed by Rastogi et al. (2000a). High hydrostatic pressure (HHP) pretreatment results in cell disintegration. The cell disintegration index (Zp, as measured by an electrophysical measurement based on electrical impedance analysis) after high pressure treatment increases with time. It is well known that application of high pressures (100–800 MPa) causes permeabilization of the cell structure (Farr, 1990; Dornenburg and Knorr, 1993; Rastogi et al., 1994 and 2000b; Eshtiaghi et al., 1994). This phenomenon is exploited here to enhance mass transfer rates during osmotic dehydration by pretreating the samples at such high pressures. Osmotic dehydration of HHP-treated pineapple has been reported to be faster than for untreated pineapple (Rastogi and Niranjan, 1998). The aims of the present work are to investigate the combined effect of high hydrostatic pressure and osmotic stress on the extent of membrane permeabilization and to explain the mechanism of mass transfer during osmotic removal of water from high pressure treated foods.

© 2003 by CRC Press LLC

7.2 MATERIALS AND METHODS 7.2.1 RAW MATERIAL PREPARATION Fresh potatoes were purchased locally in large quantities and stored at low temperature in order to have uniformity of the raw material. The potatoes were cut into circular pieces of diameter 3.5 cm and thickness 1.0 cm. The average moisture content of the potatoes was 86.5% on a wet basis.

7.2.2 HIGH PRESSURE PRETREATMENT The potato slices were subjected to high hydrostatic pressures in an isostatic pressure vessel (National Forge Europe, Belgium). The unit had a working volume of 700 ml, and its maximum recommended working pressure was 600 MPa. Maximum pressure could be reached within 2 min, and the decompression time was about 10 sec. Potato samples were vacuum sealed in double polyethylene pouches and subjected to pressures of 200, 300, and 400 MPa for 10 min at 25°C. The maximum temperature experienced by the sample during pressurization was 35°C, and samples were cooled to about 15°C during decompression. A mixture of distilled water and press oil (97:3 v/v) was used as the medium for transmitting pressure.

7.2.3 OSMOTIC DEHYDRATION

OF

POTATO SLICES

High pressure treated and untreated potato slices were blotted with tissue to remove external moisture and then subjected to osmotic dehydration. The samples were weighed and suspended in the vessel containing the sugar solution (50°Brix) maintained at 25°C. The temperature was controlled using a constant temperature stirred water bath. The ratio of the volume of the pieces to that of the medium was maintained at 1:25 in order to ensure that the concentration of the osmotic solution did not change signiﬁcantly during the experiment. The samples were withdrawn at regular intervals of 1 h, rinsed quickly, and blotted gently with tissue paper to remove adhering water. The potato slices after osmotic treatment were cut longitudinally into nine layers, ~1 mm length, and used to determine the moisture content and Zp values with respect to the distance from the center of the sample. The samples were then weighed and dried in a vacuum oven at 70°C for 18 h. The moisture and solid content were expressed in terms of kg of water/kg of initial dry solids and kg of solid/kg of initial dry solids, respectively. All the experiments were done in triplicate, and average values have been reported. Relative moisture and solid content are deﬁned as follows: Relative Moisture Content =

Relative Solid Content =

© 2003 by CRC Press LLC

Moisture content at any time (M) Initial moisture content (Mo ) Solid content at any time (S) Initial solid content (So )

7.2.4 DETERMINATION OF WATER AND SOLUTE DIFFUSION COEFFICIENTS DURING OSMOTIC DEHYDRATION The solution of Fick’s second law for diffusion from an inﬁnite slab (thickness 2l) being dehydrated from both sides, with suitable assumptions and boundary conditions, can be written for diffused moisture (Mr) and solid ratio (Sr) as (Crank, 1975): ∞

(m t − m ∞ ) 8 Mr = = (m o − m ∞ ) π2 Sr =

(st − s∞ ) 8 = (so − s∞ ) π 2

∑ n=0

∞

∑ n=0

2   1 1 exp − n +  π 2 Fow  2   (2 n + 1) 2  

2   1 1 2  exp − n + π Fos    (2 n + 1)2 2  

(7.1)

(7.2)

where Fow and Fos are the Fourier numbers for water and solute diffusion, respectively, and are given by the following equations: 2

Fow = Dew t/l

(7.3)

2

(7.4)

Fos = Des t/l

where Dew and Des are the effective diffusion coefﬁcients of water and solute, respectively, and l is the half thickness of the inﬁnite slab. The values of Fow and Fos can be obtained using Equations (7.1) and (7.2) at different moisture and solid ratios, and the values thus obtained are plotted against the corresponding “t” values. The Dew and Des values are estimated from the slopes of these plots (Rastogi and Raghavarao, 1997a and b).

7.2.5 DETERMINATION

OF

CELL DISINTEGRATION INDEX (ZP)

The conductivity–frequency spectra of high pressure treated and control samples of potato were obtained (Angersbach et al., 1997, 1999; Knorr and Angersbach, 1998). The cell disintegration index (Zp) was deﬁned as: Zp = 1 − b

(K′h − K′l ) ; (K h − K l )

0 ≤ Zp ≤ 1

(7.5)

where b = Kh/K′h, Kl and K′l are the electrical conductivity of control and treated samples measured in a low frequency ﬁeld (1–5 kHz), and Kh and K′h are the electrical conductivity of control and treated samples measured in a high frequency ﬁeld (3–50 MHz). The cell disintegration index characterizes the proportion of cells with highly permeable cell walls. Zp takes values between 0 and 1 corresponding to 100% intact cells and total cell disintegration, respectively. It is an integral parameter that indicates the relative reduction in the portion of intact cells in the cell system. A homogeneous distribution of intact and permeabilized cells and noncellular compartments in the measured system is a prerequisite for correct measurement. During osmotic treatment, a reduction in cells can occur due to disintegration or shrinkage of cell membranes.

© 2003 by CRC Press LLC

The conductivity of control and treated samples was determined with impedance measurement equipment (Electronic Manufacture Company, Mahlsdorf, Germany) between parallel disc electrodes (9.7 mm diameter) spaced 8 mm apart. The phase voltages were of equal amplitude (between 1 and 5 V, peak to peak) and the frequency changed between 3 and 50 MHz. A correction for the capacitance and inductance (of about 1.2 µH) arising from the measuring cell was incorporated using Schwan’s method (Schwan, 1963, 1968). The cell disintegration index (Zp) values were measured immediately after the high pressure treatment. The variation of Zp values with time was also measured for the samples treated at 200, 300, and 400 MPa.

7.3 RESULTS AND DISCUSSION Typical plots of variation of moisture and solid content of control and high pressure treated samples with immersion time during the course of osmotic dehydration are shown in Figures 7.1a and 7.1b. The moisture and solid diffusion both increased due to high pressure pretreatment. They also increased with an increase in pretreatment pressure. In order to compare the mass transfer characteristics, the effective diffusion coefﬁcients of water diffusing out of the sample and solute infusing into the sample were calculated. The rate of change of moisture as well as solid content was obtained from Figures 7.1a and 7.1b for all the data and plotted against the average moisture content and average solid content (Figures 7.2a and 7.2b), respectively, in order to infer equilibrium moisture and solid content. In order to calculate the Dew and Des values considering the unsteady state osmotic dehydration, the typical values of Fow and Fos (at different moisture ratios corresponding to t) obtained from Equations (7.1) and (7.2) are plotted against t (Figures 7.3a and 7.3b). The values of the effective diffusion coefﬁcients are inferred from the slopes of such plots. The relevant values are reported in Table 7.1. It is evident that the diffusion coefﬁcient for water increased due to high pressure pretreatment, giving shorter dehydration times. There was also a simultaneous increase in solute diffusion coefﬁcients. This is attributed to the increase in cell permeability due to high pressure pretreatment. In order to represent the exponential increase of water and solute diffusion coefﬁcients (Dew and Des) with the applied pressure, the values of –ln(Dew) and –ln(Des) were plotted against 1/P (as shown in Figure 7.4), and correlations similar

TABLE 7.1 Effective Diffusion Coefﬁcient for Water (Dew) and Solute (Des) at Different Pressures Treatment Pressure (MPa) Control 200 300 400

© 2003 by CRC Press LLC

9 2 Dew × 10 (m /sec)

9 2 Des × 10 (m /sec)

0.37 0.45 0.64 0.84

0.31 0.41 0.57 0.67

Moisture Content (kg/kg)

5.0 Control 200 MPa 300 MPa 400 MPa

4.5

4.0

3.5

3.0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

5.0

6.0

Immersion Time (h)

(a)

2.4 Control

Solid Content (kg/kg)

2.2

200 MPa 300 MPa

2.0

400 MPa

1.8 1.6 1.4 1.2 1.0 0.0

1.0

2.0

3.0

4.0

Immersion Time (h) (b)

FIGURE 7.1 Variation of (a) moisture and (b) solid content of control and high pressure treated potato samples during the course of osmotic dehydration.

to the Arrhenius relation were obtained as:   B  Dew = A w exp − w    P    B  Des = As exp − s    P 

© 2003 by CRC Press LLC

2

(R = 0.98) 2

(R = 0.99)

(7.6) (7.7)

0.4 Control 200 MPa 300 MPa 400 MPa

–dm/dt

0.3

0.2

0.1

0.0 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

Av. Moisture Content (kg/kg)

(a) 0.4 Control 200 MPa 300 MPa 400 MPa

ds/dt

0.3

0.2

0.1

0.0 1.0

1.5

2.0

2.5

3.0

Av. Solid Content (kg/kg)

(b)

FIGURE 7.2 Variation of (a) moisture removal (−dm/dt) and (b) solid uptake (−ds/dt) of control and high pressure treated potato samples during the course of osmotic dehydration with average moisture content and solid content, respectively. –9

2

–9

2

The values of Aw, As, Bw, and Bs were 1.50 × 10 m /sec, 1.09 × 10 m /sec, 244.19 MPa, and 196.63 MPa, respectively. The cell disintegration index (Zp) increases with an increase in high hydrostatic pressure applied to the potato sample (Figure 7.5a). The Zp values were recorded immediately after the high pressure treatment. The Zp values of the pressure-treated potato increased with time at atmospheric pressure, and the equilibrium Zp values also increased with pressure (Figure 7.5b). The Zp values of the center layer after

© 2003 by CRC Press LLC

0.7

Fow

Control

0.6

200 MPa

0.5

300 MPa 400 MPa

0.4 0.3 0.2 0.1 0.0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

5.0

6.0

Immersion Time (h) (a)

0.7

Fos

Control

0.6

200 MPa

0.5

300 MPa 400 MPa

0.4 0.3 0.2 0.1 0.0 0.0

1.0

2.0

3.0

4.0

Immersion Time (h) (b)

FIGURE 7.3 Variation of Fourier number of (a) water, Fow and (b) solute, Fos diffusion with time.

high pressure pretreatment were 0.039, 0.065, and 0.091 at 200, 300, and 400 MPa and could reach 0.35, 0.45, and 0.53 within 6 h, respectively (Figure 7.6). The Zp values of the center layer after 5 h in the case of samples treated at 400 MPa reached up to 0.82, which is due to the combined effect of osmotic stress and high pressure induced permeabilization (Figure 7.6c). The increase in Zp values (or tissue softening or loss of texture) following high pressure treatment was due to destruction of cell membranes and partial liberation of cell substances. Upon high pressure treatment, polymethylesterase (PME) enzyme, which is bound to the cell wall, is liberated and not completely inactivated and brought in close contact with its substrate, the methylated pectin. This causes deesteriﬁcation not only during high pressure treatment, but also during the standing

© 2003 by CRC Press LLC

–ln(Dew) or –ln(Des)

21.9

21.6

Dew Des

21.3

21.0

20.7 0.002

0.003

0.004

0.005

0.006

1/P

FIGURE 7.4 Plot of −ln(De) with 1/P, representing the exponential increase of diffusion coefﬁcients with pressure applied. 0.10 0.08

Zp

0.06 0.04 0.02 0.00 0

100

200

300

400

Pressure (MPa) (a)

0.6 200 MPa 300 MPa 400 MPa

0.5

Zp

0.4 0.3 0.2 0.1 0.0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

Time (h) (b)

FIGURE 7.5 (a) Variation of cell disintegration index (Zp) with applied pressure. The Zp values were measured immediately after high pressure treatment; (b) Variation of cell disintegration index (Zp) with time at atmospheric pressure after high pressure treatment.

© 2003 by CRC Press LLC

1.0 1h 2h 3h 4h 5h

Zp

0.8

0.6

0.4

0.2

0.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.8

0.9

1.0

Relative distance (l/lo) (a) 1.0 1h 2h 3h 4h 5h

Zp

0.8

0.6

0.4

0.2

0.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Relative Distance (l/lo) (b)

FIGURE 7.6 Distribution of cell disintegration index with respect to distance from the center of the potato samples (thickness 10 mm) during osmotic dehydration of control sample (a) and samples pressure pretreated at 200 MPa (b) and 400 MPa (c) for 10 min. (Reprinted from Rastogi, N.K., Angersbach, A., and Knorr, D., J. Food Eng., 45, 25–31, 2000 with permission from Elsevier Science.)

time after the release of high pressure. The pressure treatment also causes partial inactivation of PME. This reaction continues with time even after high pressure treatment and results in time dependent softening of potato tissue. The alteration in pectin results in loss of water and soluble solids (or extractable pectin) after high pressure treatment (Stute et al., 1996). It has been reported in the literature that

© 2003 by CRC Press LLC

1.0

Zp

0.8

0.6

0.4 1h 2h 3h 4h 5h

0.2

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.8

0.9

1.0

Relative Distance (l/lo) (c)

FIGURE 7.6 (Continued).

Relative Moisture Content (M/Mo)

1.0

0.9

0.8 1h 2h 3h 4h 5h

0.7

0.6 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Relative Distance (l/lo)

(a)

FIGURE 7.7 Distribution of relative moisture content with respect to distance from the center of the potato samples (thickness 10 mm) during osmotic dehydration of control sample (a) and samples pressure pretreated at 200 MPa (b) and 400 MPa (c) for 10 min. (Reprinted from Rastogi, N.K., Angersbach, A., and Knorr, D., J. Food Eng., 45, 25–31, 2000 with permission from Elsevier Science.)

following high pressure treatment, some fruits and vegetables soften over time at atmospheric pressure (Basak and Ramaswamy, 1998; Rastogi et al., 2000b). The proﬁles of the cell disintegration index (Zp) were different for samples treated at 200, 300, and 400 MPa, due to differences in the degree of cell disintegration with

© 2003 by CRC Press LLC

Relative Moisture Content (M/Mo)

1.0

0.9

0.8

1h 2h 3h 4h 5h

0.7

0.6 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.8

0.9

1.0

Relative Distance (I/Io)

(b)

Relative Moisture Content (M/Mo)

1.0

0.9

0.8

1h 2h 3h 4h 5h

0.7

0.6 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Relative Distance (l/lo)

(c)

FIGURE 7.7 (Continued).

the applied pressures (Figures 7.5a and 7.5b). The Zp values of the untreated sample did not change with time and remained at zero. A typical variation in cell disintegration index (Zp) of pressure-treated (200 and 400 MPa) and untreated potato samples with distance from the center of the material for different dehydration times is shown in Figure 7.6. It may be inferred from the ﬁgures that as the dehydration front moved within the sample, it resulted in sudden increases in Zp values. The Zp values of the center layer of potato after 5 h of osmotic dehydration for the control and samples treated at 200, 300, and 400 MPa were 0.18, 0.28, and 0.82, respectively, which showed that the variation in Zp values was due to the combined effect of osmotic stress as the dehydration proceeded and high pressure induced permeabilization.

© 2003 by CRC Press LLC

Relative Soild Content (S/So)

2.4 1h 2h 3h 4h 5h

2.2 2.0 1.8 1.6 1.4 1.2 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.8

0.9

1.0

Relative Distance (l/lo)

(a)

Relative Soild Content (S/So)

2.4 1h 2h 3h 4h 5h

2.2 2.0 1.8 1.6 1.4 1.2 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Relative Distance (l/lo)

(b)

FIGURE 7.8 Distribution of relative solid content with respect to distance from the center of the potato samples (thickness 10 mm) during osmotic dehydration of control sample (a) and samples pressure pretreated at 200 MPa (b) and 400 MPa (c) for 10 min. (Reprinted from Rastogi, N.K., Angersbach, A., and Knorr, D., J. Food Eng., 45, 25–31, 2000 with permission from Elsevier Science.)

There was a progressive increase in Zp values as the osmotic dehydration proceeded. The Zp values of all the layers, in the case of samples pressure treated at 400 MPa, were higher than the control and the sample treated at 200 MPa at the corresponding distances and immersion times (Figure 7.6). The variations in relative moisture (M / Mo) and solid (S/So) content with respect to the distance from the center of the material for the pressure-treated and control potato samples for different treatment times are shown in Figures 7.7 and 7.8. It may be noted that the relative moisture was reduced and solid content

© 2003 by CRC Press LLC

Relative Soild Content (S/So)

2.4 1h 2h 3h 4h 5h

2.2 2.0 1.8 1.6 1.4 1.2 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Relative Distance (l/lo)

(c)

FIGURE 7.8 (Continued).

increased in the case of samples treated at 200 and 400 MPa as compared to the control.

7.4 CONCLUSION High hydrostatic pressure pretreatment results in cell permeabilization. The cell permeabilization index after high pressure treatment increases with time. Osmotic dehydration of high hydrostatic pressure treated foods is faster than that of untreated foods. The state of the cell membrane during osmotic dehydration of high pressure pretreated samples can change from being partially to totally permeable, which leads to signiﬁcant changes in the tissue architecture, resulting in increased mass transfer rates during osmotic dehydration as compared to untreated samples, due to the combined effect of cell permeabilization due to osmotic stress and high pressure induced permeabilization.

NOMENCLATURE As, Bs Aw, Bw Des Dew Fos Fow Kl, K′l Kh, K′h

Coefﬁcients for solute diffusion in Equation (7.7) Coefﬁcients for water diffusion in Equation (7.6) 2 Effective diffusion coefﬁcient of solid (m /sec) 2 Effective diffusion coefﬁcient of water (m /sec) Fourier number of solid diffusion Fourier number of water diffusion Electrical conductivity of control and treated samples, respectively, measured in a low frequency ﬁeld (1–5 kHz) (mS/cm) Electrical conductivity of control and treated samples, respectively, measured in a high frequency ﬁeld (3–50 MHz) (mS/cm)

© 2003 by CRC Press LLC

l m m∞ mo P s s∞ so t Zp

Half thickness of inﬁnite slab (m) Moisture content at t = t (kg/kg) Moisture content at t = ∞ (kg/kg) Initial moisture content at t = 0 (kg/kg) Pressure (MPa) Solid content at t = t (kg/kg) Solid content at t = ∞ (kg/kg) Initial solid content at t = 0 (kg/kg) Immersion time (h) Cell disintegration index

ACKNOWLEDGMENTS Author NKR gratefully acknowledges the support of the German Academic Exchange Service (DAAD) for providing a research fellowship at Berlin University of Technology to carry out this work. NKR is also grateful to Dr. V. Prakash, Director, CFTRI and H. Krishna Murty, Head, Dept. of Food Engineering, for constant encouragement.

REFERENCES Angersbach, A., Heinz, V., and Knorr, D., Elektrische Leitfähigkeit als maß des Zellaufschlußgrades von zellulären Materialien durch Verarbeitungsprozesse, Lebens. Verpackungstech., 42, 195–200, 1997. Angersbach, A., Heinz, V., and Knorr, D., Electrophysiological model of intact and processed plant tissues: cell disintegration criteria, Biotechnol. Prog., 15, 753–762, 1999. Basak, S. and Ramaswamy, H.S., Effect of high pressure processing on the texture of selected fruits and vegetables, J. Texture Stud., 29, 587–601, 1998. Crank, J., Mathematics of Diffusion, 2nd ed., Clarendon Press, Oxford, 1975, pp. 24–25. Dixon, G.M. and Jen, J.J., Changes of sugar and acid in osmovac dried apple slices, J. Food Sci., 42, 1126–1131, 1977. Dornenburg, H. and Knorr, D., Cellular permeabilisation of cultured plant tissue by high electric ﬁeld pulse and ultra high pressure for recovery of secondary metabolites, Food Biotechnol., 7, 35–48, 1993. Eshtiaghi, M.N., Stute, R., and Knorr, D., High pressure and freezing pretreatment effects on drying, rehydration, texture and colour of green beans, carrots and potatoes, J. Food Sci., 59, 1168–1170, 1994. Farr, D., High pressure technology in food industry, Trends Food Sci. Technol., 1, 14–16, 1990. Fito, P., Modelling of vacuum osmotic dehydration of food, J. Food Eng., 22, 313–328, 1994. Giangiacomo, R., Torreggiani, D., and Abbo, E., Osmotic dehydration of fruit. I: Sugar exchange between fruit and extracting syrup, J. Food Process. Preserv., 11, 183–195, 1987. Knorr D. and Angersbach, A., Impact of high electric ﬁeld pulses on plant membrane permeabilization, Trends Food Sci. Technol., 9, 185–191, 1998. Lerici, C.L., Pinnavaia, G., Dalla Rosa, M., and Bartolucci, L., Osmotic dehydration of fruit: inﬂuence of osmotic agents on drying behavior and product quality, J. Food Sci., 50, 1217–1219, 1985.

© 2003 by CRC Press LLC

Rastogi, N.K., Angersbach, A., and Knorr, D., Evaluation of mass transfer mechanisms during osmotic treatment of plant materials, J. Food Sci., 65, 1016–1019, 2000a. Rastogi, N.K., Angersbach, A., and Knorr, D., Synergistic effect of high hydrostatic pressure pretreatment and osmotic stress on mass transfer during osmotic dehydration, J. Food Eng., 45, 25–31, 2000b. Rastogi, N.K., Eshtiaghi, M.N., and Knorr, D., Accelerated mass transfer during osmotic dehydration of high intensity electrical ﬁeld pulse pretreated carrots, J. Food Sci., 64, 1020–1023, 1999. Rastogi, N.K., and Niranjan, K., Enhanced mass transfer during osmotic dehydration of high pressure treated pineapple, J. Food Sci., 63, 508–511, 1998. Rastogi, N.K. and Raghavarao, K.S.M.S., Effect of temperature and concentration on osmotic dehydration of coconut, Lebensm.-Wiss. Technol., 27, 264, 1994. Rastogi, N.K. and Raghavarao, K.S.M.S., Kinetics of osmotic dehydration of coconut, J. Food Process Eng., 18, 187–197, 1995, Rastogi, N.K. and Raghavarao, K.S.M.S., Kinetics of osmotic dehydration under vacuum, Lebensm.-Wiss. Technol., 29, 669–672, 1996. Rastogi, N.K. and Raghavarao, K.S.M.S., Mass Transfer During Osmotic Dehydration of Carrot: Comparison of Different Methods for the Estimation of Effective Diffusion Coefﬁcients, Proceedings of 7th International Congress on Engineering and Food (ICEF), Brighton, U.K., 1997a, vol. 2, G 73–76. Rastogi, N.K. and Raghavarao, K.S.M.S., Water and solute diffusion coefﬁcients of carrot as a function of temperature and concentration, J. Food Eng., 34, 429–440, 1997b. Rastogi, N.K., Raghavarao, K.S.M.S., and Niranjan, K., Mass transfer during osmotic dehydration of banana: Fickian diffusion in cylindrical conﬁguration, J. Food Eng., 31, 423–432, 1997. Rastogi, N.K., Subramanian, R., and Raghavarao, K.S.M.S., Application of high pressure technology in food industry, Indian Food Ind., 13, 30–34, 1994. Roult-Wack, A.L., Advances in osmotic dehydration, Trends Food Sci. Technol., 5, 255–260, 1994. Roult-Wack, A.L., Lenart, A., and Guilbert, S., Recent advances during dewatering through immersion in concentrated solution, in Drying of Solids, Majumdar, A.S., Ed., International Science Publisher, New York, 1992, pp. 21–51. Schwan, H.P., Determination of biological impedance, in Physical Techniques in Biological Research, vol. 6, part B, Nastuk, W.L, Ed., Academic Press, New York, 1963, p. 323. Schwan, H.P., Electrode polarization impedance and measurements in biological materials, Ann. N.Y. Acad. Sci., 148, 191–209, 1968. Simal, S., Benedito, J., Sanchez, E.S., and Rossello, C., Use of ultrasound to increase mass transport rates during osmotic dehydration, J. Food Eng., 36, 323–336, 1999. Stute, R., Eshtiaghi, M.N., Boguslawski, S., and Knorr, D., High pressure treatment of vegetables, in High Pressure Chemical Engineering, von Rohr, P.R. and Trepp, C., eds., Elsevier, New York, 1996. Torreggiani, D., Osmotic dehydration in fruits and vegetable processing, Food Res. Int., 26, 59–68, 1993.

© 2003 by CRC Press LLC

8

Hydrodynamic Mechanisms in Plant Tissues during Mass Transport Operations P. Fito, A. Chiralt, J. Martínez-Monzó, and J. Barat

CONTENTS 8.1 8.2 8.3 8.4

Introduction HDM Promoted by External Pressure Changes HDM Promoted by Cell Shrinkage in Osmotic Processes HDM Promoted by Cell Matrix Relaxation in Long-Term Osmotic Processes 8.5 Conclusions Nomenclature Acknowledgments References

8.1 INTRODUCTION In the processing of fruit and vegetables, solid–ﬂuid systems (SFS) frequently occur in different operations, such as osmotic dehydration, rehydration, candy processing, boiling, and cooking, among others. The heat and mass transfer processes in such systems have usually been modeled considering the food solid as a continuous phase. Nevertheless, the cellular structure (intercellular spaces and cell compartmentation) plays an important role in the deﬁnition of mechanisms involved in the process and therefore in process kinetics. Recently, several studies have been carried out to determine the inﬂuence of porosity on the response of fruit tissue to solid–liquid operations (Fito, 1994; Fito and Pastor, 1994; Fito et al., 1996; Fito and Chiralt, 1997). In this way, a fast mass transfer mechanism (hydrodynamic mechanism, HDM) has been described as occurring in process operations in which a porous solid is immersed in a liquid phase; changes in temperature or pressure also take place. The occluded gas inside the product pores is compressed or expanded according to the pressure or temperature changes, while the external liquid is pumped into the

© 2003 by CRC Press LLC

pores in line with the gas compression. An effective exchange of the product internal gas with the external liquid is promoted in vacuum impregnation (VI) operations, where a vacuum pressure (p1~50–100 mbar) is imposed on the system for a short time (t1); afterwards, the atmospheric pressure (p2) is reestablished while the product remains immersed in the liquid for a time t2 (Fito et al., 1996; Salvatori et al., 1998a). The volume fraction of the initial sample (X) impregnated by the external liquid when mechanical equilibrium is achieved in the sample has been modeled as a function of the compression ratio r (given by Equation (8.1), where pc is capillary pressure), sample effective porosity (εe), and sample volume deformations at the end of the process (γ) and the vacuum step (γ1) (Equation (8.2)) (Fito et al., 1996). If γ = γ1 = 0, Equation (8.1) gives the relationship for VI of stiff products. r=

p2 + pc p1

ε e ( r − 1) = ( X − γ )r + γ 1

(8.1) (8.2)

When there are no pressure changes (p1 = p2) in the system, capillary impregnation will occur due to the capillary pressure; the lower the pressure in the system, the greater the liquid penetration, according to Equations (8.1) and (8.2). The possibility of introducing an external solution containing speciﬁc/selected solutes inside the product pores has made VI a tool in fruit processing. The addition of preservatives (antimicrobials, antibrowning agents, pH reducers, and others) or nutrients (minerals, vitamins, etc.), fast water activity depression, and modifying physical properties, among others, may be some of the possible applications of VI (Chiralt et al., 1999). Impregnation of the fruit pores due to hydrodynamic mechanisms has been seen to occur without external pressure changes when the cellular tissue remains immersed in a liquid phase for a long time (e.g., syrup canned and candied fruits). This has been explained in terms of the capillary forces, pressure and temperature ﬂuctuations in the system, and relaxation phenomena of the shrunken cellular matrix when hypertonic solutions are used in the treatments (Barat et al., 1998). Fito et al. (2000) reported a contribution of HDM to the total mass transfer throughout the osmotic process due to the pressure gradients in the tissue associated with internal volume generation in line with cell water losses. The aim of this work is to analyze the role of hydrodynamic mechanisms in different kinds or times of processing in plant tissue–ﬂuid systems and their implications in process kinetics, as well as the inﬂuence of the action of these mechanisms on plant tissues in terms of product quality or process advantages.

8.2 HDM PROMOTED BY EXTERNAL PRESSURE CHANGES The most effective action of HDM in the product pores is promoted by vacuum impregnation operations. The compression ratio can reach very high values by using common industrial pumps and, additionally, the product remains are impregnated at the end of the process when normal pressure is recovered. Impregnation promoted by

© 2003 by CRC Press LLC

applying high pressure in the system is not effective because the liquid introduced into the pores in the compression step ﬂows out when the system returns to atmospheric conditions. For stiff matrices, the kinetics of impregnation are very fast, depending on the pore size (length and diameter) and tortuosity and the liquid viscosity. Equation (8.3) gives the relationship between the liquid penetration level and time, in terms of the volume fraction of the pore impregnated (xv) at time t (t2) in a reduced way (xr) (Equation (8.4)). The value of xve corresponds to the impregnated volume at mechanical equilibrium, which can be obtained by Equation (8.2) when γ = γ1 = 0, since xv = X/εe. Parameters B and k are described by Equations (8.5) and (8.6) (Chiralt et al., 1999).   1 − xr   1 t = − (x 2r − x 2r 0 ) − k ( x r − x r 0 ) + ln  2 B  1 − x r 0    xr =

xv x ve

k = 1+

1 x ve

(8.3)

(8.4)

(8.5)

2

 eF  p2 B = 8µ t  2  rp  ( p2 − p1 )

(8.6)

Figure 8.1 shows the predicted development of xr as a function of time (t2) after the vacuum step for different values of the external liquid viscosity, and by considering a stiff matrix with pore size of 100 µm diameter, 1 cm length, and a tortuosity factor Ft = 2. It can be observed that even for high viscosity liquids such as hydrocolloids or concentrated sugars, the penetration times needed to reach the xve are on the order of a few minutes (Figure 8.1a). This process length is near the time required to achieve stationary pressure in the tank after the valve is opened to restore the atmospheric pressure. In real systems with a viscoelastic character, the kinetics of pore impregnation are coupled with deformation–relaxation of the sample volume. A fast mechanical pseudoequilibrium can be achieved in the ﬁrst step, with a notable reduction of product porosity coupled with partial liquid penetration. Afterwards, the true equilibrium is reached through relaxation of the deformed porous matrix, which leads to progressive liquid entry in line with sample volume recovery while the product remains immersed. This two-step behavior will be especially promoted when long penetration times, associated with high liquid viscosity or/and small pore diameter, occur. For cylindrical (2 cm diameter and height) apple samples, Figure 8.1b shows the sample volume fraction impregnated (X) and deformed (γ) after VI (10 min at 50 mbar) with a sugar isotonic solution and with 3% pectin sugar isotonic solution, as a function of the length of the VI second step at atmospheric pressure. It can be observed that at very short times, the sample volume reduces by about 5% and slowly recovers in line with time increase. The impregnation levels increase more quickly in the less viscous solution.

© 2003 by CRC Press LLC

1

xr 0.8 3 (m /m ) 3

0.6 0.4 0.01 Pa·s 0.1 Pa·s 1.0 Pa·s

0.2 0 0

20

40

60

t (s) (a)

X /γ

0.2

0.1

0

-0.1 0

1000

2000

3000

4000 t(s)

(b)

FIGURE 8.1 (a) Impregnation kinetics of an ideal pore (100 µm diameter, 1 cm length, 2 tortuosity factor) for different viscosities (Pa s) of the external solution. (b) Development of sample volume fraction impregnated (X, closed symbols) and deformed (γ, open symbols) with time (t2), during VI of cylindrical apple (var. Granny Smith) samples with isotonic sugar solution (squares) and 3% pectin isotonic sugar solution (circles).

It is remarkable that when solutions with high viscosity are used for VI, it is advantageous to carry out the vacuum step with samples suspended above the solution, rather than immersed in it. If not, difﬁculties of sample gas outﬂow cause great sample deformation and very limited impregnation. Throughout the release of the gas, it becomes entrapped in the external solution, thus forming stable foam around the sample with much higher viscosity than the original ﬂuid. During the second VI step, part of the entrapped gas ﬂows into the pores again, thus reducing the impregnation effectiveness. Table 8.1 shows the levels of deformation and impregnation of cylindrical apple samples at the end of the vacuum step and of the process as a function of the

© 2003 by CRC Press LLC

TABLE 8.1 Impregnation (X) and Deformation (γ) Levels of Apple (var. Granny Smith) Cylindrical Samples (2 cm Diameter and Height) Reached in a VI Operation (p1 = 50 mbar, t1 = 10 min, t2 = 15 min) with Isotonic Sugar Solutions Containing Different Concentrations of Pectin Pectin concentration %

Viscosity µ (Pas)

X1

γ1

X

0 1 2 3 d 3

0.0068 0.0202 0.0917 0.179 0.179

−0.035 −0.043 −0.011 0.028 −0.040

0.013 0.03 0.10 0.14 0.01

0.14 0.12 0.07 0.09 0,13

a b c d

a

a

b

b

c

γ

εe

−0.05 −0.02 −0.05 −0.06 .0,05

0.20 0.15 0.14 0.13 0.19

At the end of the vacuum step. At the end of the process. Determined on the basis of theoretical model (Equation (8.2)) assuming mechanical equilibrium. Samples were not immersed in the solution during the vacuum step.

impregnating solution viscosity. Effective sample porosity, calculated by Equation (8.2), assuming mechanical equilibrium, also appears in Table 8.1. The decreasing values of εe, in line with the solution viscosity increase, suggest that mechanical equilibrium was not reached for t2 = 15 min. On the other hand, a greater effectiveness of sample impregnation when the sample is not immersed in the viscous solution during the vacuum step can be observed. VI may promote fast compositional changes in fruit, which is useful in many cases to ensure processed fruit stability (decrease of pH or water activity, introduction of antibrowning agents or microbial preservatives) or quality (the improvement of the sweet–sour taste relationship, fortiﬁcation with speciﬁc nutrients). Prediction of compositional changes in short VI treatments can be easily obtained by applying Equations (8.7) and (8.8), if the value of the impregnated volume fraction (X) and the density 0 IS of the initial product (ρ ) and the impregnating solution (ρ ) are known (Chiralt et al., 1999). From these equations, the required solution mass fraction (yi) of a determined component (i.e., water, sugar, acid, additive, etc.) to achieve the desired level in the VI ﬁnal product (mass fraction: xi ) can be calculated. Composition changes promoted by concentration gradients between external solution and product were not taken into account in Equation (8.7) due to the short length of VI processes. In Equation (8.7), 0 xi corresponds to the initial mass fraction of component i in the product. x iVI =

x 0i + x HDM y i 1 + x HDM

x HDM = X

© 2003 by CRC Press LLC

ρIS ρ0

(8.7)

(8.8)

8.3 HDM PROMOTED BY CELL SHRINKAGE IN OSMOTIC PROCESSES Throughout osmotic processes in fruit and vegetables, a great cell volume reduction occurs due to intracellular water loss. This implies the generation of internal voids that provoke internal pressure depression, which promotes hydrodynamic ﬂow of the external solution from the sample interface to the internal voids. These pressure gradients also contribute to the structural development pathway of cells, depending on the kind of ﬂuid (gas or liquid) in the tissue pores (Fito et al., 2000). Figure 8.2 shows a scheme of how HDMs were promoted into the tissue, as well as the sample cellular structure development. When the intercellular spaces are full of liquid, osmosis promotes plasmolysis but no signiﬁcant folding of the cell wall, whereas the space between plasmalemma and cell wall is ﬂooded by the extracellular liquid (Martínez-Monzó et al., 1998a). In contrast, when intercellular spaces are occupied by gas, osmosis provokes cell wall shrinkage without plasmalemma separations (Salvatori et al., 1998b). This difference in behavior has been explained in terms of the different pressure drop of gas or liquid phases during their ﬂux towards the intercellular space generated volumes (isgv in Figure 8.2). The balance of forces acting on both sides of the plasmalemma–cell wall layer during cell water volume loss leads to the separation of the double layer and to the ﬂux of the external liquid through the cell wall, or to cell wall deformation together with the plasmalemma (Fito et al., 2000). In osmotic treatments of cellular tissues, HDM may act to a great extent at the beginning of the process if a vacuum pulse is applied in the tank for a short period (Pulsed Vacuum Osmotic Dehydration, PVOD), since the sample impregnation with the osmotic solution is promoted. In treatments at atmospheric conditions (OD) or at vacuum conditions (Vacuum Osmotic Dehydration, VOD) capillary pressure also provokes HDM near the sample interface to a lesser extent. The different extent of the external liquid ﬂow into the tissue and the subsequent differences in the cellular structure development will affect the tissue response to mass transport. Figure 8.3 shows a comparison of the effective diffusivity values (De) in the fruit liquid phase obtained in OD and PVOD treatments in apple slices (1 cm thick)

is containing gas phase

B

isgv

is A JHDM

ic

B JW Jw

A is

JHDM M

is containing liquid phase

FIGURE 8.2 Scheme of cellular structure development during osmotic treatments depending on the ﬂuid present in the intercellular spaces (is) and water (Jw) and hydrodynamic (JHDM) ﬂuxes (isgv, intercellular space generated volume; ic, intracellular content; A and B, cell bonding points).

© 2003 by CRC Press LLC

De × 1010(m2/s) (PVOD)

12 10

25° Brix

8

35° Brix

6

45° Brix

4

55° Brix

2

65° Brix

0

0

2

4 6 8 10 De × 1010(m2/s)(OD)

12

2

FIGURE 8.3 Comparison of values of the effective diffusion coefﬁcient (De, in m /sec) in apple (Granny Smith) liquid phase (water plus solutes) obtained in OD and PVOD processes carried out with different sucrose solutions (25 to 65°Brix) at 30, 40, and 50°C.

0

4000

8000

t (s)

12000

Ln Y 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 FIGURE 8.4 Kinetics of fruit liquid phase composition changes in cylindrical apple samples (2 cm diameter and height) osmosed in 62°Brix rectiﬁed grape must, for nonimpregnated ♦), samples impregnated with an isotonic solution (••), and samples impregnated samples (♦ with a 3% pectin isotonic solution ( ).

osmosed with different sucrose syrups (25–65°Brix) at 30, 40, and 50°C. Compositional change promoted by the vacuum pulse was corrected to make the De values more comparable (Barat et al., 1997). Higher values of De in the PVOD process can be observed; the higher the De value in OD, the greater the difference. On the other hand, Figure 8.4 shows the inﬂuence of VI with isotonic solutions of different viscosity on the kinetics of fruit liquid phase composition changes for apple cylindrical samples. The reduced concentration of each component (Yi) was deﬁned in terms of the solute or water mass fractions (zi, i = water or solutes) in the fruit liquid phase (water plus solutes) by Equation (8.9). The value of z at equie librium (zi ) was taken to be equal to that of the osmotic solution. The acceleration of kinetics in line with the ﬁlling of the pores, without any changes in the initial value of the process driving force, can be observed. Nevertheless, if the impregnating

© 2003 by CRC Press LLC

solution viscosity is high, slower kinetics are observed. These results agree with a great promotion of diffusion through the noncompartmented intercellular spaces when ﬁlled with liquid phase, which is greatly affected by the liquid viscosity (Martínez-Monzó et al., 1998b).

Yi =

(z it − z ei ) (z 0i − z ie )

(8.9)

8.4 HDM PROMOTED BY CELL MATRIX RELAXATION IN LONG-TERM OSMOTIC PROCESSES In long-term osmotic processes such as those carried out in fruit candying, HDM plays an important role in tissue development after compositional equilibrium between the sample and the external solution has been reached. Sample mass and volume decrease in line with osmotic dehydration until a minimum value is reached at compositional equilibrium time tc. From this point, sample mass and volume begin a slowly increasing pathway until almost all of the initial values are recovered. This was observed initially in apple samples (Barat et al., 1998; Fito et al., 1998) and was conﬁrmed for other fruits (Barat, 1998). Mass and sample volume recovery has been explained in terms of pressure gradients generated in the shrunken cellular structure due to relaxation of cell walls, where a great amount of free energy was stored during cell dehydration–shrinkage. True equilibrium in the system implies free energy reduction by release of mechanical stress. If the product remains immersed in the external solution, volume recovery is coupled with liquid suction and therefore with mass gain. In this sense, the pressure drop of liquid inﬂow will affect the sample volume relaxation rate, causing the system (fruit plus external liquid) to behave as a viscoelastic solid. The overall relaxation rate of the system will be greatly dependent on liquid viscosity and the elastic character of the cellular matrix. The relative relaxation level will be determined by the total volume lost during osmotic treatment and the irreversible structural damage in the tissue. In this sense, cellular turgor will not be recovered, and so the ﬁnal sample volume will be reduced with respect to the initial value by the intercellular volume associated with the turgid cell packaging. HDM ﬂow in this matrix relaxation process has been modeled on the basis of a viscoelastic model (Equation (8.10)) (Peleg, 1980). In Equation (8.10), F0 and Ft are respectively the initial force on the sample associated with a given deformation and the force at a determined relaxation time. The constants A and B represent, respectively, the total relative relaxation level and the relaxation rate. To ﬁt Equation (8.10) to the experimental mass recovery data, the following hypotheses are considered: the mechanical stress on the matrix is released as ﬂow pressure drops in the external liquid; likewise, a laminar ﬂow was assumed. From these hypotheses, force will be given by Equation (8.11), thus obtaining Equation (8.12) to describe mass recovery. 0 The M values are the relative mass gain of the sample at each time. The function 0 (dM (t)/dt) was obtained by ﬁtting a bi-exponential function to the experimental

© 2003 by CRC Press LLC

0

curve (M vs. time) and calculating the derivative equation and its values at each time. F0 t 1 t = + F0 − Ft AB A F=

(8.10)

8πµFt e  ∂M 0 (t )    ρIS  ∂t 

(8.11)

(∂M 0 ( t ) / ∂t )0 t 1 t t = = + (∂M 0 ( t ) / ∂t )0 − (∂M 0 ( t ) / ∂t )t YF AB A

(8.12)

Figure 8.5 shows a linear relationship between experimental points plotted as deﬁned by Equation (8.12) for OD and PVOD treatments of 1 cm thick apple slices, with 55°Brix sucrose solution, at 30, 40, and 50°C. The scarce inﬂuence of temperature and kind of treatment on the kinetics of HDM mass ﬂow during sample stress relaxation can be observed. Table 8.2 shows the mean values obtained for A and B parameters for OD and PVOD treatments of apple slices in the 30–50°C range. The values of A are near one in all cases, indicating that samples recover about 100% of their initial mass throughout the examined time, with the relaxation rate being affected by the syrup concentration. The relaxation is faster as the sucrose concentration is lower (below 25°Brix), in agreement with the lower viscosity values of the solutions.

4000 t/YF (h) 3000 55 55 55 55

2000 1000

OD 30°C OD 40°C OD 50°C PVOD 30°C

55 PVOD 40°C 55 PVOD 50°C

0 0

1000

2000

3000

4000

t – tc (h) FIGURE 8.5 Kinetics of HDM mass ﬂow in long-term osmotic processes after compositional equilibrium time (tc). Points correspond to osmosed apple slices (1 cm thick) in 55°Brix sucrose solution for OD and PVOD treatments at different temperatures.

© 2003 by CRC Press LLC

TABLE 8.2 A and B Parameters of Equation (10) for OD and PVOD Treatments of Osmosed Apple Slices in Sucrose Syrups (OS) of Different Concentrations OD

PVOD

°Brix (OS)

A

B

A

B

65 55 45 35 25 20

1.02 1.05 1.02 1.01 0.98 1.01

0.002 0.004 0.012 0.024 0.162 0.024

0.98 1.07 1.05 1.00 0.96 1.01

0.009 0.005 0.037 0.094 0.082 0.080

8.5 CONCLUSIONS HDM plays an important role in solid–liquid operations with cellular products such as fruit and vegetables. Through understanding and modeling the action of these mechanisms, better process control will be possible. Promotion of these mechanisms through the control of process variables may be a tool in designing new product composition.

NOMENCLATURE p µ xv xve xr εe r X1 X 1

γ γ

e rp Ft

Pressure (mbar), (subscript c: capillary; 1: at the vacuum step; 2: atmospheric) Solution viscosity (Parsec) 3 3 Pore volume fraction impregnated by the solution (m /m ) Pore volume fraction impregnated by the solution at mechanical equilibrium 3 3 (m /m ) Reduced pore volume fraction impregnated by the solution (xv/xve) Sample effective porosity Compression ratio Sample volume fraction impregnated by the solution at the end of the ﬁrst VI step Sample volume fraction impregnated by the solution at the end of the VI process Relative volume deformation of the sample due to pressure change at the end of the ﬁrst VI step Relative volume deformation of the sample due to pressure change at the end of the VI process Sample characteristic dimension (m) Pore radius (m) Tortuosity factor of the sample pores

© 2003 by CRC Press LLC

k B 0 ρ IS ρ xHDM yiiv xi0 xi Yi t zi De 0 M t F

Dimensionless parameter of the model of VI kinetics Time dimension parameter of the model of VI kinetics 3 Density of the initial product (kg/m ) 3 Density of the impregnating solution (kg/m ) Mass ratio of the impregnated solution in the initial product (kg/kg) Mass fraction of the component i in the impregnating solution (kg/kg) Mass fraction of component i in the impregnated product (kg/kg) Mass fraction of component i in the initial product (kg/kg) Reduced driven force referred to component i Mass fraction of component i in the food liquid phase at time t of the process (kg/kg) 2 Pseudodiffusion coefﬁcient (m /sec) Mass relative change of the sample at each time (kg/kg) Process time (sec) Force (N)

ACKNOWLEDGMENTS The authors thank the Comisión Interministerial de Ciencia y Tecnología (Spain), CYTED program, and European Union (DGXII) for their ﬁnancial support.

REFERENCES Barat, J.M., Osmotic Dehydration Model Development as Unit Operation, Ph.D. Thesis, Universidad Politécnica, Valencia, Spain, 1998. Barat, J.M., Alvarruiz, A., Chiralt, A., and Fito, P., A mass transfer modelling in osmotic dehydration, in Engineering and Food at ICEF 7, Jowitt, R., Ed., Shefﬁeld Academic Press, Shefﬁeld, 1997, pp. G 81–84. Barat, J.M., Chiralt, A., and Fito P., Equilibrium in cellular food osmotic solution systems as related to structure, J. Food Sci., 63, 1–5, 1998. Chiralt, A., Fito, P., Andrés, A., Barat, J.M., Martínez-Monzó, J., and Martínez-Navarrete, N., Vacuum impregnation: a tool in minimal processing of foods, in Processing of Foods: Quality Optimization and Process Assessment, Oliveira, F.A.R. and Oliveira, J.C., Eds., CRC Press, Boca Raton, FL, 1999, pp. 341–356. Fito, P., Modelling of vacuum osmotic dehydration of food, J. Food Eng., 22, 313–328, 1994. Fito, P., Andrés, A., Chiralt, A., and Pardo, P., Coupling of hydrodynamic mechanism and deformation relaxation phenomena during vacuum treatments in solid porous foodliquid systems, J. Food Eng., 27, 229–240, 1996. Fito, P. and Chiralt, A., Osmotic dehydration: an approach to the modelling of solid foodliquid operations, in Food Engineering 2000, Fito, P., Ortega-Rodríguez, E., and Barbosa-Cánovas, G., Eds., Chapman and Hall, New York, 1997, pp. 231–252. Fito, P., Chiralt, A., Barat, J.M., and Martínez-Monzó, J., Vacuum impregnation in fruit processing, in Trends in Food Engineering, Lozano, J.E., Barbosa-Cánovas, G., Parada Arias, E., and Añón, M.C., Eds., Technomic, Lancaster, PA, 2000, pp. 149–164. Fito, P., Chiralt, A., Barat, J., Salvatori, D., and Andrés, A., Some advances in osmotic dehydration of fruits, Food Sci. Technol. Int., 4, 329–338, 1998.

© 2003 by CRC Press LLC

Fito, P. and Pastor, R., Non-diffusional mechanism occurring during vacuum osmotic dehydration, J. Food Eng., 21, 513–519, 1994. Martínez-Monzó, J., Martínez-Navarrete, N., Fito, P., and Chiralt, A., Mechanical and structural changes in apple (var. Granny Smith) due to vacuum impregnation with cryoprotectants, J. Food Sci., 63, 499–503, 1998a. Martínez-Monzó, J., Martínez-Navarrete, N., Chiralt, A., and Fito, P., Osmotic dehydration of apple as affected by vacuum impregnation with HM pectin, in Drying ’98, vol. A., Akritidis, C.B., Marinos-Kouris, D., and Saravacos, G.D., Eds., Ziti Editions, Thessaloniki, 1998b, pp. 836–843. Peleg, M., Linearization of relaxation and creep curves of solid biological materials, J. Rheol., 24, 451–463, 1980. Salvatori, D., Andrés, A., Chiralt, A., and Fito, P., 1998a. The response of some properties of fruits to vacuum impregnation, J. Food Process. Eng., 21, 59–73, 1998a. Salvatori, D., Andrés, A., Albors, A., Chiralt, A., and Fito, P., Structural and compositional proﬁles in osmotically dehydrated apple, J. Food Sci., 63, 606–610, 1998b.

© 2003 by CRC Press LLC

9

Effect of Pretreatment on the Drying Kinetics of Cherry Tomato (Lycopersicon esculentum var. cerasiforme) P.M. Azoubel and F.E.X. Murr

CONTENTS 9.1 9.2

Introduction Basic Concepts 9.2.1 Osmotic Dehydration 9.2.2 Sorption Isotherms 9.2.3 Drying 9.3 Mathematical Models 9.4 Materials and Methods 9.5 Results and Discussion 9.5.1 Cherry Tomato Characterization 9.5.2 Osmotic Dehydration 9.5.3 Sorption Isotherms 9.5.4 Air Drying 9.6 Conclusions Nomenclature Acknowledgment References

9.1 INTRODUCTION The cherry tomato (L. esculentum var. cerasiforme) is considered the ancestral form of tomato (Folquer, 1976). This tomato type is an excellent source of vitamins A and C (Gould, 1974) and is used in salads and has been used as a supplement in astronauts’ diet during long periods of residence in space, due to its fast in vitro production (Kaur-Sawhney et al., 1996).

© 2003 by CRC Press LLC

The tomato is a very perishable fruit, necessitating the removal of water for its preservation. The drying of solids is a common form of preservation, allowing the foodstuff to be kept for a longer period than would otherwise have been possible (Hawlader et al., 1991). In addition, dried food can be stored and transported at a relatively low cost. However, water removal leads to a serious decrease in food nutritive and organoleptic values, such as ligniﬁed texture, slow or incomplete rehydration, and loss of juiciness characteristics of fresh fruit and vegetables. Moreover, color and smell are affected in a negative way. It is generally known that dried food of the best quality is obtained by means of freeze-drying, but this is one of the most expensive methods. For these reasons, efforts are being made to perfect the convection drying process. The preliminary treatment of the raw material is of crucial importance. The utilization of an osmotic prestep can have important advantages in terms of product quality and cost (Lenart, 1996). The present study was carried out to determine the inﬂuence of osmotic pretreatment on the drying kinetics of cherry tomato, using a ﬁxed bed dryer.

9.2 BASIC CONCEPTS 9.2.1 OSMOTIC DEHYDRATION Osmotic dehydration of foods has recently gained attention as a processing method to obtain better quality fruit products. It is based on the immersion of foods, whole or in pieces, in hypertonic solution (sugars, sodium chloride, glycerol, sorbitol), originating two simultaneous counter-current ﬂows: an exit of water from the product to the solution and a migration of solutes from the solution to the solid. A third ﬂow consists of the loss of some natural components, such as sugars, organic acids, and mineral salts; although these may be quantitatively of no signiﬁcant meaning in the mass exchange, they can be important to the ﬁnal nutritive value and organoleptic properties of the food (Raoult-Wack et al., 1989). The quantity and rate of water removal depend on several variables and processing parameters. In general, the weight loss in osmosed fruit is increased by increasing solute concentration of the osmotic solution, immersion time, temperature, solution/ fruit ratio, and speciﬁc surface area of the food and by using a low pressure system (Lerici et al., 1985). Osmotic dehydration has generally been applied to fruit, vegetables, meat, and ﬁsh (Raoult-Wack et al., 1994). This process will not yield a moisture low enough to make the product shelf stable, but it is considered a prestep to air, freeze, and vacuum drying (Lenart, 1996; Uddin et al., 1990). Since the osmotic process generally results in some solute uptake, changes in the composition of the food material that can inﬂuence the subsequent drying step must be considered. One important property of a material relative to drying is its water sorption isotherm, since this will determine the degree of drying required to obtain a stable product (Islam and Flink, 1982).

© 2003 by CRC Press LLC

9.2.2 SORPTION ISOTHERMS Moisture sorption isotherms can be used to predict changes in food stability and to select appropriate package materials and ingredients (Zhang et al., 1996). The isotherm curve can be obtained in one of two directions. An adsorption isotherm is made by placing a completely dry material into various atmospheres of increasing relative humidity and measuring the weight gain due to water. The desorption isotherm is found by placing the initially wet material under the same relative humidities, but in this case measuring the loss in weight (Iglesias and Chirife, 1982). There are several experimental means to determine sorption isotherms (Gal, 1972). The principal methods are: • Gravimetric—The sample weight change in equilibrium with different water vapor pressures is determined. • Manometric—The vapor pressure of water in equilibrium with a food at a given moisture content is measured by a sensitive manometric device. • Hygrometric—The equilibrium relative humidity of a small amount of air in contact with a food at a given moisture content is measured by a hygrometric device. A number of mathematical models have been proposed for correlation, analysis, and prediction of sorption data, including Guggenheim–Anderson–de Boer (GAB) (van den Berg and Bruin, 1981), Brunauer–Emmett–Teller (BET) (Brunauer et al., 1938), and the models of Halsey (1948) and Oswin (1946), as respectively described in the following equations: X=

X m CGAB K GAB a w [(1 − K GAB a w ) (1 − K GAB a w + CGAB K GAB a w )]

(9.1)

X m C BET a w (1 − a w ) [1 − (C BET − 1) a w ]

(9.2)

X=

−A a w = exp  B  X   a  X=A w   1 − aw 

(9.3)

B

(9.4)

where X is the moisture content (kg/kg, dry basis); Xm is the monolayer moisture content (kg/kg, dry basis); CGAB and KGAB are GAB constants; aw is the water activity; CBET is BET constant; A and B are Halsey and Oswin constants.

© 2003 by CRC Press LLC

9.2.3 DRYING Dehydration or drying operations are important steps in the chemical and food processing industries. The basic objective in drying food products is the removal of water from the solids to a level at which microbial spoilage is minimized (Vagenas et al., 1990). Drying is a process of simultaneous heat and mass transfer. Heat transfer occurs during evaporation of the moisture removed from the drying solid object, while mass transfer takes place during the removal of moisture from the object’s surface by an external drying ﬂuid, which is usually air (Dincer and Dost, 1995). The drying curve includes a constant drying rate region and a falling rate region. The constant rate period indicates that a ﬁlm of water is freely available at the drying surface for evaporation into the drying medium, while the falling rate period indicates an increased resistance to both heat and mass transfer and occurs when the surface water no longer exists, and water to be evaporated comes from within the structure and must be transported to the surface. However, for some material, only the falling rate regions are observed (Hawlader et al., 1991). A wide variety of dehydrated foods (snacks, dry mixes and soups, dried fruits, etc.) are available today (Vagenas et al., 1990). In the tropics, fresh tomatoes are available throughout the year, while in temperate regions tomatoes are a seasonal crop, and hence, a surplus exists in one season and a shortage in another. Currently, tomatoes are preserved in the forms of ketchup, paste, and juice (Hawlader et al., 1991).

9.3 MATHEMATICAL MODELS The prediction of the kinetics of osmotic dehydration of cherry tomato was based on a two-parameter equation from mass balance, using data obtained during a relatively short period of time, as developed by Azuara et al. (1992) and adapted to spherical geometry:

Dt =

 π t  S1 r   WLmod ∞ ⋅   exp   36  1 + S1t   WL ∞   2

2

(9.5)

mod

exp

where Dt is the apparent diffusion coefﬁcient (m /sec) at time t; WL ∞ and WL ∞ are the amounts of water (g water/100 g of sample) leaving the solid after inﬁnite time, predicted by the model and experimental data, respectively; r is the radius of the sample; and S1 is a constant related to the water loss, calculated from the following linear regression that associates the water lost (WL) with time (t) (Azuara et al., 1992): t 1 t = + WL S1 ( WL ∞ ) WL ∞

© 2003 by CRC Press LLC

(9.6)

The value at equilibrium, WL ∞, is ﬁxed for the established conditions of temperexp ature, time, and fruit to solution rate. When WL ∞ is unknown, by assuming that it mod equals WL ∞ , Equation (9.5) may be used to obtain a good estimation for Dt, as long as the kinetics data are adequately ﬁtted by Equation (9.6). The value of WL is a function of the rate of water loss and time. WL increases as these variables increase, and can be calculated as: WL =

ww o − ( tw − ws) × 100 wso + ww o

(9.7)

where wwo and wso are the initial water and solid contents (g), respectively, and tw is the total wet weight. The average apparent diffusion coefﬁcient is calculated by: n

Davg =

∑D

t

1

n

(9.8)

where n is the number of data points used. For drying kinetics, considering the cherry tomato slice as a ﬂat plate with initially uniform moisture distribution, negligible external resistance to mass transfer, and no shrinkage, the solution for Fick’s equation is (Crank, 1975): w − we 8 = 2 wo − we π

∞

∑ (2i + 1) i=0

1

2

t exp −(2i + 1)2 .π 2 .Deff. . 2  L  

(9.9)

where w, we and w0 are the moisture content at t, the equilibrium, and the initial moisture content, respectively (g water/g dry mass); t is drying time (sec); L is length of plane thickness (m); and Deff is effective diffusion coefﬁcient for moisture in 2 solids (m /sec). The equilibrium moisture content of a sample being dried depends upon the moisture content of the air and the structure and type of material (Hawlader et al., 1991) and was obtained from water sorption isotherms for cherry tomatoes with and without the osmotic pretreatment. For conditions where L is small and t is large, the terms in the summation in Equation (9.9) corresponding to n > 1 are small, and the following approximation can be made (Hawlader et al., 1991): 2  w − we   8  π Deff t ln   = ln 2  − π L2  wo − we 

(9.10)

where Deff can be measured from the slope of the plot of ln ww −−wwe against t or t/L . o e 2

© 2003 by CRC Press LLC

The mean relative deviation modulus (E, %) was used as a criterion to evaluate the ﬁt of the tested model, as applied to the experimental data. Values of E were calculated using the following equation:

E=

100 N

∑

ν0 − ν p ν0

(9.11)

where ν0 and νp are the observed and the predicted values, respectively. Values of E less than or equal to 10% are considered to ﬁt the experimental data satisfactorily.

9.4 MATERIALS AND METHODS Fresh cherry tomatoes harvested between the end of January and the middle of May were purchased from a local market. The fruits were sorted visually for color (completely red), size (approximately 2.8 cm diameter), and lack of physical damage, and the physicochemical characteristics were determined according to Ranganna (1977). As the cherry tomato waxy skin presents a high resistance to mass transfer, the fruits were washed and perforated with needles (1 mm diameter) (Shi et al., 1997) 2 to pin hole density of 16 holes/cm . The perforated cherry tomatoes were immersed in NaCl and NaCl + sucrose (3:2) solutions of different concentrations (10 and 25% w/w) at 25°C (room temperature) and agitation of 70 r/min, maintained in a temperature– agitation controlled shaker (Tecnal, TE-421). In order to avoid any signiﬁcant dilution effect on the osmotic solution, a 1:10 fruit-to-solution ratio was used. At different processing times, samples were withdrawn from the solution, rinsed with cold water to remove adhering osmotic solution, and gently blotted to remove surface moisture. The water content of cherry tomato samples was determined gravimetrically by vacuum oven drying at 70°C for 24 h. The salt content was determined by Mohr’s titration method (Ranganna, 1977). Three replications were made. Desorption isotherms of the samples were determined using the static gravimetric method. Saturated salt solutions were prepared to give deﬁned constant water activity (Greenspan, 1977). Three replications of the same experiment were carried out. After equilibrium was reached, the equilibrium moisture content was determined (vacuum oven at 70°C for 24 h). The adequacy of the mathematical models of BET, GAB, Halsey, and Oswin was veriﬁed. For air drying experiments, a cabinet dryer was used, and the tests were conducted at three different temperatures (50, 60, and 70°C) and two air velocities (0.75 and 2.60 m/sec). The tomatoes were cut into quarters along the longitudinal axis and the seeds were removed. The samples (length of 1.8 mm) were spread uniformly on a perforated stainless steel tray in a ﬁxed bed dryer. The processing temperature was controlled using precalibrated cooper-[constantan] thermocouples and the air ﬂow rate was monitored by an anemometer (TSI, 8330-M). The drying curves were determined by periodic weighing of the tray on a semianalytical scale.

© 2003 by CRC Press LLC

9.5 RESULTS AND DISCUSSION 9.5.1 CHERRY TOMATO CHARACTERIZATION The physicochemical characteristics of the cherry tomatoes used in the experiments are shown in Table 9.1. The total solids content, acidity, and soluble solids content were similar to the values obtained by Gould (1974) for tomato, but the NaCl content was higher and the reducing sugars content was lower. Sugars and organic acids were the majority of the total dry matter content of the tomato fruit. Similar results for cherry tomato were obtained by Picha (1987). The pH value was similar to the results of PetroTurza (1987) for tomato and the density to tomato pulp (Ranganna, 1977).

9.5.2 OSMOTIC DEHYDRATION Characterizing the effect of osmotic dehydration on the air drying kinetics of cherry tomatoes was the main objective of this study. The effect of the osmotic agent (NaCl and the NaCl–sucrose mixture) and solution concentration (10 and 25% w/w), at room temperature (25°C), was evaluated by determining moisture and salt contents, as shown in Figure 9.1. The more concentrated the solution, the higher the percentages of water loss and solid uptake, due to an increase in osmotic pressure gradient resulting in increased mass transfer. This ﬁnding is in agreement with the results of Rastogi and Raghavarao (1994) for the osmotic dehydration of carrots in sucrose solutions, and of Vijayanand et al. (1995) for cauliﬂower in salt solutions. The rate of water loss was faster in the ﬁrst 2 h of the process, decreasing gradually while approaching the end of the experiment, which was not sufﬁcient in length for equilibrium to be reached, except for the 10% solution. Figure 9.1(b) shows the salt gain during the osmotic dehydration of cherry tomato. It was observed that an increase in the concentration of the osmotic solution gave higher salt gain within 6 h of processing. By ﬁxing the concentration of the

TABLE 9.1 Physicochemical Characteristics of Cherry Tomatoes Analysis Moisture content (%) Acidity (% citric acid) NaCl (%) Reducing sugars (%) pH Brix Ascorbic acid (%) Density (g/ml)

© 2003 by CRC Press LLC

Mean Value 94.39 0.64 0.65 1.03 4.04 5.53 31.39 0.99

TABLE 9.2 Average Water Apparent Diffusion Coefﬁcient (Davg) Obtained from the Osmotic Dehydration Process 2

Sample Sodium Sodium Sodium Sodium

S1(10 ) chloride chloride chloride chloride

(10%) (25%) + sucrose (10%) + sucrose (25%)

1.76 2.28 0.40 1.75

100

10

2

m /sec)

E (%)

11.69 14.42 2.17 11.66

8.85 0.12 3.68 10.01

10 NaCl 10% NaCl 25% NaCl+sucrose 10% NaCl+sucrose 25%

96

8

Salt gain (%)

Water content (%)

Davg (10

92

88

NaCl 10% NaCl 25% NaCl+sucrose 10% NaCl+sucrose 25%

6

4

2 84 0

60

120

180

240

300

360

0 0

60

120

180

240

Time (min)

Time (min)

(a)

(b)

300

360

FIGURE 9.1 Moisture (a) and salt gain (b) proﬁles of osmotically dehydrated cherry tomato.

solution, the effect of the osmotic agent can be evaluated. Our results showed that the salt gain was lower when the mixed NaCl–sucrose solution was used. The experimental water loss results were used to estimate the apparent water diffusion coefﬁcients. The time used for prediction by the proposed model was 180 min. Table 9.2 presents the obtained average water apparent diffusivities (Davg) and S1 values. Increasing the osmotic solution concentration (10 to 25% w/w) caused an increase in Davg. Changing the osmotic medium from salt to a mixed salt–sucrose solution, at the same temperature, resulted in a decrease of the diffusion coefﬁcient. This is due to sodium chloride ionization in solution, and as the molecular weight of sodium chloride is lower than that of sucrose, its rate of penetration into vegetable tissues is higher. Higher values for S1 indicate a higher diffusion of water per unit of time. The model was able to predict the entire osmotic dehydration process up to equilibrium, using data obtained over a short period of time, with satisfactory mean relative modulus. Consumer demand for fresh, convenient, and safe vegetables has promoted interest in processed products with fresh-like qualities (Shi et al., 1997). The osmotic dehydration process was carried out within a short period of time in order to achieve

© 2003 by CRC Press LLC

we (kg/kg)

0.5 0.4 0.3

T= 50°C (fresh) T= 70°C (fresh) T=50°C (NaCl 10%)

0.2 0.1 0.0 0.0

0.2

0.4

aw

0.6

0.8

1.0

FIGURE 9.2 Sorption isotherms for fresh and osmoticly dehydrated cherry tomato.

a high degree of dewatering with relatively small solids gain. Pretreatment with sodium chloride, 10% w/w for 2 h, was chosen for the air drying experiments, and desorption isotherms of these samples were determined.

9.5.3 SORPTION ISOTHERMS The results of the experimental measurements of the equilibrium moisture content (we) of cherry tomato with and without pretreatment, at relative humidity ranging from 10.75 to 81.20%, are shown in Figure 9.2. The pretreated sample obtained lower values of water activity than the fresh fruit. Sloan and Labuza (1976) noted that components such as glycerol or salt are particularly effective in reducing the water activity. No temperature dependence of the experimental data of the fresh fruit can be seen. Similar behavior was observed by Bolin (1980) for prunes. The results for 50°C were considered for all samples, and temperature independence was assumed for the osmotically pretreated samples. It can be seen that the desorption isotherms do not intersect. For products with high sugar content, the intersection of sorption isotherms can be observed (Saravacos et al., 1986). For products with low sugar, high protein, or high starch, there is no intersection point with increased temperature (Benado and Rizvi, 1985). The results of direct nonlinear regression analysis of ﬁtting the GAB, BET, Halsey, and Oswin models to the experimental points (Tables 9.3, 9.4, and 9.5) showed that the GAB equation was satisfactory in predicting the equilibrium moisture content of fresh cherry tomato, and that the Halsey model presented the best ﬁt for samples pretreated in 10% NaCl osmotic solution for 2 h (Figure 9.3).

9.5.4 AIR DRYING The effect of air temperature (50, 60, and 70°C) at air velocities of 0.75 and 2.60 m/sec on the drying kinetics of cherry tomato is illustrated in Figure 9.4. Increasing the temperature of the drying medium increased the drying potential and the moisture removal rates. When the ﬂow rate was increased at constant temperature, similar behavior was observed. The effect of osmotic pretreatment was clearly veriﬁed at a temperature of 50°C and air velocity of 2.60 m/sec. In this condition, the drying time was reduced, with higher drying rates and effective diffusion coefﬁcients (Table 9.6). For the other conditions studied (60 and 70°C at both air velocities), the drying time of pretreated samples with 10% NaCl solution was not faster when compared

© 2003 by CRC Press LLC

TABLE 9.3 Estimated Parameters for Fresh Cherry Tomato ο at 50 C Parameters

Model BET GAB Halsey Oswin

Xm 0.133 Xm 0.138 A 0.026 A 0.227

C 20.087 C 95.615 B 2.205 B 0.335

R

2

E (%)

n S K 0.781

0.979

3.221

0.990

2.278

—

0.995

2.341

—

0.990

2.171

TABLE 9.4 Estimated Parameters for Fresh Cherry Tomato ο at 70 C Parameters

Model BET GAB Halsey Oswin

Xm 0.145 Xm 0.135 A 0.036 A 0.231

C 11.154 C 51.868 B 1.988 B 0.370

R

2

E (%)

n S K 0.822

0.97

8.022

0.99

3.747

—

0.99

6.617

—

0.99

3.353

TABLE 9.5 Estimated Parameters for Osmosed Cherry ο Tomato at 50 C Parameters

Model BET GAB Halsey Oswin

© 2003 by CRC Press LLC

Xm 0.575 Xm 0.074 A 0.069 A 0.120

C 0.11 C 5.973 B 1.099 B 0.751

R

2

E (%)

n S K 0.991

0.98

6.060

0.99

2.573

—

0.99

2.211

—

0.99

3.353

we (kg/kg)

0.5 0.4

fresh (GAB)

0.3 0.2 0.1 0.0 0.0

NaCl 10% (Halsey)

0.2

0.4

0.6

0.8

1.0

aw

FIGURE 9.3 Equilibrium moisture content at 50°C and the predictions of the GAB and Halsey models for fresh and preteated cherry tomato, respectively.

(w – we)/(wo – we)

1.0

fresh (T = 50°C) 10% NaCl (T = 50°C)

0.8

fresh (T = 60°C) 10% NaCl (T = 60°C)

0.6

fresh (T = 70°C)

0.4

10% NaCl (T = 70°C)

0.2 0.0

0

20

40

60

80

100

120

140

Time (min) (a)

(w – we)/(wo – we)

1.0

fresh (T = 50°C) 10% NaCl (T = 50°C)

0.8

fresh (T = 60°C) 10% NaCl (T = 60°C)

0.6

fresh (T = 70°C)

0.4

10% NaCl (T = 70°C)

0.2 0.0

0

20

40

60

80

100

120

140

Time (min) (b)

FIGURE 9.4 Effect of temperature on water removal for fresh and osmotically dehydrated cherry tomato at constant air velocities of 0.75 m/sec (a) and 2.60 m/sec (b).

to the untreated samples at the same air temperature and velocity, The effective diffusion coefﬁcients were lower, indicating a less favored diffusional process. The differences in the effective diffusion coefﬁcients can be attributed to the compositional changes that occur following osmosis. The uptake of salt and the loss of water that occur in osmosis give increased internal resistance to moisture movement. However, the dried cherry tomato in 10% NaCl solution presented a ﬂexible structure, smaller shrinkage, and a more natural coloration when compared with the dried

© 2003 by CRC Press LLC

TABLE 9.6 Effective Diffusion Coefﬁcients of Air Dried Cherry Tomatoes 11

2

Deff (10 m /sec) o

T ( C) 50 60 70

v (m/sec)

Fresh

10% NaCl

0.75 2.60 0.75 2.60 0.75 2.60

12.02 13.66 17.49 26.78 20.77 37.70

12.02 17.49 14.21 19.67 18.03 21.86

TABLE 9.7 Activation Energy for Diffusion in Cherry Tomatoes Sample Fresh 10% NaCl

v (m/sec)

Ea (kJ/mol)

R

0.75 2.60 0.75 2.60

25.39 46.61 18.31 10.56

0.99 0.99 0.99 0.99

fruit with no preliminary treatment. The same behavior was found by Lenart (1996) for osmodehydrated dried apples. Figure 9.5 shows the variation in the drying rate for all samples as a function of moisture content with air velocity and temperature. For the given experimental conditions, the samples did not show a constant rate of drying. Higher temperature, higher air velocity and the pretreatment for the lower temperature increased the potential for the transport of moisture, thus increasing the drying rate. For temperatures of 60 and 70°C, the untreated samples showed higher drying rates in the beginning, due to a higher free water content. The activation energy was estimated by an Arrhenius type equation, using the value of effective diffusivity for each temperature from Table 9.6: Deff = A exp

 − Ea   RT 

(9.12)

where Ea is activation energy (kJ/mol), R is the universal gas constant (8.314 J/mol K), A is the integration constant, and T is temperature (K). The values of activation energy and the correlation coefﬁcient are presented in Table 9.7. The pretreated samples’ activation energy was much lower than that of the fresh samples, indicating that temperature has less inﬂuence on drying rate for

© 2003 by CRC Press LLC

0.04 0.03

2

–dw/dt (10 kg/kg sec)

0.05

0.02

fresh (T = 50°C) 10% NaCl (T = 50°C) fresh (T = 60°C) 10% NaCl (T = 60°C) fresh (T = 70°C) 10% NaCl (T = 70°C)

0.01 0.00 0.0

0.2

0.4

0.6

0.8

1.0

0.8

1.0

w (kg/kg)

2

–dw/dt (10 kg/kg sec)

(a) 0.08 0.06 0.04

fresh (T = 50°C) 10% NaCl (T = 50°C) fresh (T = 60°C) 10% NaCl (T = 60°C) fresh (T = 70°C) 10% NaCl (T = 70°C)

0.02 0.00 0.0

0.2

0.4

0.6

w (kg/kg)

(b)

FIGURE 9.5 Drying rate vs. moisture content at constant air velocities of 0.75 m/sec (a) and 2.60 m/sec (b).

salt osmosed fruits. These results are similar to those of Islam and Flink (1982) for osmotically dehydrated potatoes in NaCl solution.

9.6 CONCLUSIONS The rate of moisture removal and solids gain in the osmotic dehydration of cherry tomato was directly related to the concentration of the solution, the osmotic agent and the immersion time. In order to obtain a processed product with fresh-like qualities, pretreatment with 10% NaCl solution for 2 h was the condition used prior to drying. The water apparent diffusivity for osmotic dehydration ranged from 2.17 × –10 –10 2 10 to 14.42 × 10 m /sec and the calculated effective diffusivity ranged from –11 –11 2 –11 12.02 × 10 to 37.70 × 10 m /sec for fresh fruit and from 12.02 × 10 to 21.86 × –11 2 10 m /sec for cherry tomatoes pretreated in 10% NaCl solution for 2 h. For the given experimental conditions, the samples did not show a constant rate of drying. Osmotic dehydration of cherry tomato in 10% NaCl solution for 2 h before air drying was efﬁcient in increasing the water removal rate and the effective diffusion o coefﬁcient, and in decreasing the drying time at 50 C with air velocity of 2.60 m/sec.

© 2003 by CRC Press LLC

For all conditions studied, the osmodehydrated dried samples presented a ﬂexible structure, smaller shrinkage, and a more natural coloration when compared to dried cherry tomato with no preliminary treatment. The activation energy for effective diffusivity was lower for osmosed samples, indicating less inﬂuence of temperature on drying rate.

NOMENCLATURE Davg Deff Ea L R R t w we w0 WL WL∞ T

2

Moisture apparent diffusion coefﬁcient, m /sec 2 Moisture effective diffusion coefﬁcient, m /sec Activation energy, kJ/mole Thickness, m Universal gas constant, J/mol K Radius, m Time, sec Moisture content, kg/kg Equilibrium moisture content, kg/kg Initial moisture content, kg/kg Water loss, g water/100 g sample Amount of water leaving the solid at equilibrium, g water/100 g sample Temperature, K

ACKNOWLEDGMENT The authors gratefully acknowledge the ﬁnancial support of CAPES.

REFERENCES Azuara, E., Beristain, C.I., and Garcia, H.S., Development of a mathematical model to predict kinetics of osmotic dehydration, J. Food Technol., 29, 239, 1992. Benado, A.L. and Rizvi, S.S.H., Thermodynamic properties of water on rice as calculated from reversible and irreversible isotherms, J. Food Sci., 50, 101, 1985. Bolin, H.R., Relation of moisture to water activity in prunes and raisins, J. Food Sci., 56, 1190, 1980. Brunauer, S., Emmet, T.H., and Teller, F., Adsorption of gases in multimolecular layers, G. Am. Chem. Soc., 60, 309, 1938. Crank, J., Mathematics of Diffusion, Clarendon Press, Oxford, 1975. Dincer, I. and Dost, S., An analytical model for moisture diffusion in solid objects during drying, Drying Technol., 13, 425, 1995. Folquer, F., El Tomate: Estudio de la Planta y su Produccion Comercial, Editorial Hemisferio Sur, Buenos Aires, 1976. Gal, S., Recent developments in techniques for the determination of sorption isotherms, in Water Relations of Foods, Duckworth, R.B., Ed., Academic Press, London, 1972, p. 89. Gould, W.A., Tomato Production, Processing and Quality Evaluation, AVI, Westport, CT, 1974.

© 2003 by CRC Press LLC

Greenspan, L., Humidity ﬁxed points of binary saturated aqueous solutions, J. Res. Stand. A. Phys. Chem., 81, 89, 1977. Halsey, G., Physical adsorption on uniform surfaces, J. Chem. Phys., 16, 931, 1948. Hawlader, M.N.A., Uddin M.S., Ho, J.C., and Teng A.B.W., Drying characteristics of tomatoes, J. Food Eng., 14, 259–268, 1991. Iglesias, H.A. and Chirife, J., Handbook of Food Isotherms: Water Sorption Parameters for Food Components, Academic Press, New York, 1982. Islam, M.N. and Flink, J.N., Dehydration of potato II. Osmotic concentration and its effect on air drying behaviour, J.Food Technol., 17, 387, 1982. Kaur-Sawhney, R., Applewite, P.B., and Galston, A.W., Formation in vitro of ripe tomato fruits from thin layer explants of ﬂower pedicels, J. Fruit Nuts, 18, 191, 1996. Lenart, A., Osmo-convective drying of fruits and vegetables: technology and application, Drying Technol., 14, 391, 1996. Lerici, C.R., Pinnavara, G., Dalla Rosa, M., and, Bartolucci, L., Osmotidehydration of fruits: inﬂuence of osmotic agents on drying behavior and product quality, J. Food Sci., 50, 1217–1219, 1985. Oswin, C.R., The thickness of package life. III. Isotherm, J. Chem. Ind., 65, 419, 1946. Petro-Turza, M., Flavour of tomato and tomato products, Food Ver. Int., 2, 309, 1987. Picha, D.H., Sugar and organic acid content of cherry tomato fruit at different ripening stages, Hort. Sci., 22, 94, 1987. Ranganna, S., Manual of Analysis of Fruit and Vegetables Products, McGraw-Hill, New Delhi, 1977. Raoult-Wack, A.L., Lafont, F., Rios, G., and Guilbert, S., Osmotic dehydration: study of mass transfer in terms of engineering properties, in Drying of Solids, Mujumdar, A.S. Roques, M.A., Eds., Hemisphere Publishing Company, New York, 1989, p. 487. Raoult-Wack, A.L., Rios, G., Saurel, R., Giroux, F., and Guilbert, S., Modeling of dewatering and impregnation soaking process (osmotic dehydration), Food Res. Int., 27, 207, 1994. Rastogi, N.K. and Raghavarao, K.S.M.S., Effect of temperature and concentration on osmotic dehydration of coconut, Lebensm.-Wiss. Technol., 27, 564, 1994. Saravacos, G.D., Tsiourvas, D.A., and Tsami, E., Effect of temperature on the water adsorption isotherms of sultana raisins, J. Food Sci., 51, 381, 1986. Shi, J.X., Le Maguer, M., Wang, S.L., and Liptay, A., Application of osmotic treatment in tomato processing: effect of skin treatments on mass transfer in osmotic dehydration of tomatoes, Food Res. Int., 30, 669, 1997. Sloan, A.E. and Labuza, T.P., Investigating alternative humectants for use in foods, Food Prod. Devel., 9, 75, 1976. Uddin, M.S., Hawlader, M.N.A., and Rahman, M.S., Evaluation of drying characteristics of pineapple in the production of pineapple powder, J. Food Process. Preserv., 14, 375, 1990. Vagenas, G.K., Marinos-Kouris, D., and Saravacos, G.D., An analysis of mass transfer in airdrying of foods, Drying Technol., 8, 323, 1990. Van den Berg, C. and Bruin, S., Water activity of and its estimation in food systems: theoretical aspects, in Water Activity: Inﬂuences on Food Quality, Rockland, L.B. and Stewart, G.F., Eds., Academic Press, New York, 1981. Vijayanand, P., Nagin, C., and Eipeson, W.E., Optimization of osmotic dehydration of cauliﬂower, J. Food Process. Preserv., 14, 391, 1995. Zhang, X.W., Liu, X., Gu, D.X., Zhou, W., Wang, R.L., and Liu, P., Desorption isotherms of some vegetables, J. Sci. Food Agric., 70, 303, 1996.

© 2003 by CRC Press LLC

10

Determination of ConcentrationDependent Effective Moisture Diffusivity of Plums Based on Shrinkage Kinetics A.L. Gabas, F.C. Menegalli, and J. Telis-Romero

CONTENTS 10.1 Introduction 10.2 Mathematical Model 10.3 Methodology 10.3.1 Material 10.3.2 Drying Apparatus and Conditions 10.3.3 Shrinkage Kinetics 10.4 Shrinkage and Effective Diffusivity 10.5 Conclusions Nomenclature Acknowledgment References

10.1 INTRODUCTION Air drying is one of the most used unit operations in food processing, and mathematical modeling of the dehydration process is very useful in the design and optimization of dryers (Madamba, 1997; Arrouz et al., 1998). Nevertheless, theoretical simulations of drying processes require a substantial amount of computing time as a consequence of the complexity of diffusion equations governing the process. A drying process can be described completely using an appropriate drying model made

© 2003 by CRC Press LLC

up of differential equations of heat and mass transfer in the interior of the product and its interface with the drying agent (air). Knowledge of transport and material properties is necessary to apply any transport equation. Such properties as diffusivity and mass and heat transfer coefﬁcients, as well as thermal conductivity, must be accurately estimated. Knowledge of additional properties such as equilibrium moisture content, shrinkage, bulk density, speciﬁc volume, and porosity, is also required. Many articles have recently been published concerning the estimation of the abovementioned properties (Zogzas et al., 1994; Madamba et al., 1994; Barbanti et al., 1994; Newman et al., 1996; Sabarez et al., 1997; Karathanos, 1999; Telis et al., 2000). Shrinkage is common during drying, and volume changes may affect the moisture removal rate. Study of the shrinkage phenomenon is essential to better understand drying kinetics and to improve the reliability of diffusivity based models (Raghavan et al., 1995; Simal et al., 1996; Sanjuán et al., 1996). Drying of plums (Prunus domestica) in drying tunnels produces prunes generally at about 14–19% moisture content (wet basis), which have sufﬁciently low water activity to avoid the problems of microbial spoilage, allowing long-term storage of the fruit. These fruits are then rehydrated (35–40%) prior to packing and sale. Many countries have a ﬂourishing prune industry, including the U.S., France, Italy, Turkey, Chile, Argentina, and Australia (Price et al., 1997). The drying kinetics of plums have been investigated as a function of temperature in the range of 50 to 80°C using a laboratory pilot plant. The volume change or shrinkage of grapes during thin layer convective air drying has been described by a correlation with respect to water content (Gabas et al., 1999). The method for evaluating effective diffusivity as a function of moisture content and shrinkage during drying of plums is based on numerical solution to Fick’s diffusion equation. A number of studies have focused on modeling the drying process of fruits and vegetables and solving the mass transfer equation analytically. Córdova-Quiroz et al. (1996) obtained a simpliﬁcation of boundary conditions of the mass transfer equation in cylindrical slabs of carrots. They developed an alternative simpliﬁcation for the mathematical description of interfacial mass transfer, introducing a modiﬁed Biot number. Hernández et al. (2000) proposed an analytical solution of a mass transfer equation with concentration dependence of shrinkage and constant average water diffusivity for mango slices and cassava parallelepipeds. Although the drying behavior of a range of fruits and vegetables has been extensively studied, there is relatively little work on the kinetics of drying of plums, especially simultaneously considering shrinkage and diffusivity as a function of moisture content.

10.2 MATHEMATICAL MODEL A mass balance for the drying process of plums can be applied by considering the fruit as a sphere (Figure 10.1), according to the system of coordinates presented in Figure 10.2. The partial differential equation resulting from the mass balance at a differential 2 volume element r (senφ)∆φ∆ψ∆r is shown as (Bird et al., 1960): → → → ∂ ρA  → + ∇⋅ ρA v  =  ∇⋅ D AB ∇ ρA  + q A     ∂t

© 2003 by CRC Press LLC

(10.1)

r(senφ)∆ψ r ∆φ

∆r

flesh stone rs rp

2

FIGURE 10.1 Differential volume element r (senφ)∆φ∆ψ∆r by considering the plum as a sphere.

∆r r∆φ r

∆φ φ

r(sen φ)∆ψ

∆ψ r senφ 2

FIGURE 10.2 System of spherical coordinates with the volume element r (senφ)∆φ∆ψ∆r for the mass balance.

The following hypotheses are generally used to describe the mass transfer in solid drying: unsteady state system, constant temperature and pressure, constant mass density and diffusion coefﬁcient, negligible convective mass transfer, and absence of chemical reactions. Thus, assuming that internal resistance controls the drying rate, the differential equation for spherical coordinates in terms of Fick’s

© 2003 by CRC Press LLC

second law is (Bird et al., 1960): r ∂ρA = D AB∇2ρA ∂t

(10.2)

Most cereals (rice, corn, wheat, etc.) experience little change of volume during the drying process. Therefore, the analytical solution of Equation (10.2) applies satisfactorily to the study of these materials. On the other hand, for high moisture content foods (potato, apple, persimmon, grape, plum, etc.) the volume variation is important, and the analytical solution of Equation (10.2) obtained for diffusivity and volume constant is not applicable, since the shrinkage and values of diffusivity as a function of moisture content should be taken into account. The drying process of plums can be studied by solving the second Fick’s law by numerical methods, considering moving boundary conditions and diffusion coefﬁcient as a function of moisture content (Murray and Landis, 1959; Gabitto and Aguerre, 1985; Sobral, 1987). The plum is viewed as a composite spherical body comprised of two concentric materials (stone and ﬂesh). The ﬂesh component of the spherical plum is divided into N concentric spherical shells of equal thickness. The radial length of the fruit decreases due to shrinkage; consequently, the thickness of each shell reduces as drying progresses. The following dimensionless groups are necessary in order to have Equation (10.2) in a dimensionless form: X − Xe Xo − Xe

(10.3)

r , in (r > rs) rpo

(10.4)

Deff t r2

(10.5)

M= ξ=

Fo =

Substituting and rearranging the differential of Equations (10.3) and (10.4), and using the deﬁnition of Fourier mass number (Equation (10.5)), the second Fick’s law in spherical coordinates is developed and presented in the following form: ∂M 2 ∂M ∂2 M = + 2 ∂Fo ξ ∂ξ ∂ξ

(10.6)

with the initial and boundary conditions: Fo = 0, ξ = 1, ξ=

© 2003 by CRC Press LLC

rs , rpo

M=1

(10.6a)

∂M = − Bi m Ms ∂ξ

(10.6b)

∂M =0 ∂ξ

(10.6c)

Equation (10.6) cannot be integrated, since it does not represent a moving boundary system, and shrinkage was not considered. In order to allow its integration, the following substantial derivative is deﬁned: dM ∂M ∂M ∂ξ = + dFo ∂Fo n ∂ξ ∂Fo n

(10.7)

as well as the expression that relates the position of an arbitrary nodal point with the interface position: ξ=

n ξ N p

(10.8)

Equation (10.8) can be derived to give: ∂ξ n ∂ξ p = ∂Fo N ∂Fo

(10.9)

Substituting equations (10.7), (10.8) and (10.9) in Equation (10.6), the representative differential equation of the moving boundary system is: dM  2 N n  ∂ξ p   ∂M ∂2 M = + + 2 dFo  nξ p N  ∂Fo   ∂ξ ∂ξ

(10.10)

with the initial and boundary conditions: Fo = 0, ξ = ξp, ξ=

M=1

(10.10a)

∂M = − Bi m Ms ∂ξ

(10.10b)

∂M =0 ∂ξ

(10.10c)

rs , rpo

Equation (10.10) represents the second Fick’s law expressing the drying process considering shrinkage and diffusivity varying with average moisture content. Considering that this equation can be expressed in ﬁnite differences, it is solved using Equations (10.11), (10.12), and (10.13):

© 2003 by CRC Press LLC

dM M n ,i +1 − M n ,i = dFo ∆Fo

(10.11)

∂M M n +1,i +1 − M n −1,i +1 = ∂ξ 2 ∆ξ

(10.12)

∂2 M M n −1,i +1 − 2 M n ,i +1 + M n +1,i +1 = ∂ξ 2 ∆ξ 2

(10.13)

Combination of equations (10.10), (10.11), (10.12) and (10.13) leads to: + M n −1,i +1  M M n ,i +1 − M n ,i = λ 2 k  n +1,i +1  + λ1 (M n −1,i +1 − 2 M n ,i +1 + M n +1,i +1 ) (10.14)   2 where: λ1 =

∆Fo ∆ξ 2

(10.14a)

λ2 =

∆Fo ∆ξ

(10.14b)

k=

2 N n  ∂ξ p  + nξ p N  ∂Fo 

(10.14c)

i = temporary coordinate index; n = space coordinate index; with the following initial and boundary conditions: Fo = 0, ξ = ξp, ξ=

rs , rpo

M=1

(10.14d)

(M N − M N −1 ) = − Bi m M N ∆ξ

(10.14e)

M0 = M1

(10.14f)

A rearrangement of Equation (10.14) will result in: λ k λ k   − λ1 + 2  M n −1,i +1 + (1 + 2λ1 )M n ,i +1 −  λ1 + 2  M n +1,i +1 = M n ,i (10.15)   2  2  In this way, the integration of Equation (10.2) consists of the solution of a system constituted by the development of Equation (10.15) in a matrix form (n = 1 to n = N – 1). For evaluation of Equation (10.14c), the particle radius and its derivation are determined by applying the ﬁnite difference: ∂ξ p ∂Fo

=

rpi − rpi −1 ∆Fo ⋅ rpo

(10.16)

The particle radius at a time ti and ti−1 is calculated from the relation between volume and moisture content experimentally obtained for the total drying time. The ∆Fo term is evaluated as follows: ∆Fo =

Deff ( x ) ∆t 2 rpo

(10.17)

where ∆t is a time interval between the sample collection in the drying experiments, and Deff ( x ) (effective moisture diffusivity) is calculated through an iterative

© 2003 by CRC Press LLC

procedure aiming to adjust the experimental and calculated values of average residual moisture. The group of equations (10.14a, b, c) was completed considering ∆ξ equal to 1/N, since the nodal points number is constant. In order to apply the boundary condition corresponding to Equation (10.14e), it is necessary to evaluate the Biot mass number (Bim) by assuming a linear relationship between the food material and the air moisture at equilibrium (Córdova-Quiroz et al., 1996): k c K eq rpo

Bi m =

(10.18)

Deff

Y∗ = K eq X

(10.18a)

The parameter Keq represents an average partition constant. It may be evaluated with the equation suggested by Hernández et al. (2000):

K eq

∫ =

Xe

(Y∗ / X)dX

Xo

(10.18b)

Xo − Xe

where Y∗ =

a w ( Pvap / P )

18 1 − a w ( Pvap / P ) 28

(10.18c)

Data on water activity can be obtained from Gabas et al. (2000), showing the desorption isotherms of plum pulp described by the Guggenheim–Anderson–de Boer (GAB) model. The mass transfer coefﬁcient in Equation (10.18) can be calculated by an empirical equation (Equation (10.19)) applied to mass transfer between spheres and air for turbulent ﬂow in ﬁxed bed (Saravacos, 1986): 1

Sh = 2 + 0.6 Re p 2 Sc

1

3

(10.19)

The water vapor diffusivity in the air is evaluated by the Schmidt correlation (Dãscãlescu, 1969): D vap = 0.083

(Ta + 273)1.81 273

(10.20)

A computational program written in Fortran is applied to the numerical integration of Equation (10.2). Equation (10.15) is written in a matrix form and solved using the Gauss-elimination procedure, obtaining the moisture proﬁle. The spaceaveraged moisture content in a plum material is given by:

X =

© 2003 by CRC Press LLC

∫

rp

rs

X drp rp − rs

(10.21)

and, in the dimensionless form:

∫ M =

ξp

ξs

M d ξp

ξ p − ξs

(10.22)

Equation (10.22) is integrated by using the composite Simpson’s rule to calculate the average moisture content.

10.3 METHODOLOGY 10.3.1 MATERIAL All the experimental measurements were made with plums of the Angeleno variety acquired in a local market and kept at 7°C prior to use. The plums were pretreated in a solution of 1.5% ethyloleate for 1 min at 50°C and then rinsed in a current of water for 2 min.

10.3.2 DRYING APPARATUS

AND

CONDITIONS

The dryer used to conduct the experiments is a pilot-scale piece of equipment consisting of three basic parts: an airﬂow rate control system, a drying air heating section, and a drying chamber; it is equipped with a process control system based on Fieldbus technology supplied by SMAR Industrial Equipment Ltd. As indicated in Figure 10.3, a centrifugal fan (1) was used to force the air through the drying chamber. The fan was driven by an electric motor with the airﬂow rate being controlled by a frequency modulator (2) (Siemens, model MMV). An oriﬁce plate (3) connected to a pressure transmitter (SMAR, model LD302) (4) was installed after the fan to measure the airﬂow during the process. Dry bulb (5) and wet bulb (6) temperatures of the air stream were measured online using temperature transmitters (SMAR, model TT302). The drying air was heated by passing through electric resistances (7) controlled by a power converter (8) (Therma, model TH 6021A/80). Before the drying chamber, a “beehive” (9) was installed for better distribution of air in the product. The drying compartment (10) consisted of two square metal trays, placed perpendicular to the airﬂow. These compartments were designed for experiments of through drying. Thermocouples connected with temperature transmitters (SMAR, model TT302) were placed before and after the trays (11,14), and at the center (12) and surface (13) of the plums to analyze the evolution of temperature in the product during the experiments. In order to integrate the instruments with the Fieldbus system, a 4–20 mA current converter (SMAR, model IF302) (15) was used. The equipment operation was monitored and controlled by means of a computer  (16) running the software AIMAX -WIN. The drying experiments were carried out in air at temperatures in the range of 50 to 80°C and with an air velocity of approximately 1.5 m/sec.

© 2003 by CRC Press LLC

14

16

10 13 12 11

9

15

6

5

4 2

7

8 3 1

FIGURE 10.3 Experimental drying apparatus: (1) centrifugal fan, (2) frequency modulator, (3) oriﬁce plate, (4) pressure transmitter, (5) dry bulb temperature, (6) wet bulb temperature, (7) electric resistance heaters, (8) power converter, (9) beehive, (10) square metal trays, (11) thermocouple before the trays, (12) thermocouple at the center of the plum, (13) thermocouple at the surface of the plum, (14) thermocouple after the trays, (15) current converter, (16) computer.

10.3.3 SHRINKAGE KINETICS The shrinkage kinetics of the particles was used to correlate instantaneous size (spherical equivalent diameter) as a function of material moisture content. The dimensional change of the plum was assumed to occur only in the ﬂesh section (rs < r < rp), and the volume of the stone component was considered constant throughout the drying process. Samples were placed on the tray in a single layer. The volume change was determined with about 48 plums, from which samples of three were taken out periodically from the dryer, to measure the total volume by the water displacement method. Moisture content of the samples was determined by drying at 60°C under vacuum for 48 h (AOAC, 1990).

10.4 SHRINKAGE AND EFFECTIVE DIFFUSIVITY The volume change or shrinkage during thin layer convective air drying of plums is described as a linear function of moisture content by the following equation: V/Vo = A + BX

(10.23)

Table 10.1 shows the constants A and B at different temperatures and the coefﬁcient 2 of determination (r ), which presented satisfactory values. This equation is used to estimate the particle radius of the plum in the numerical solution described previously.

© 2003 by CRC Press LLC

TABLE 10.1 Constants of Equation (23), Which Describes the Volume Change during Drying of Plums at Different Temperatures o

T ( C)

A

50 60 70 80 a

a

B

0.174 0.181 0.191 0.193

a

r

0.172 0.174 0.175 0.178

2

0.998 0.988 0.997 0.998

All ﬁts had a signiﬁcance level less than 5%.

1.0

0.8

V/Vo

0.6

0.4

T = 80°C T = 70°C T = 60°C

0.2

T = 50°C

0.0 0

1

2

3

4

5

Moisture content (dry basis)

FIGURE 10.4 Shrinkage during drying of plums.

Figure 10.4 shows the volume change of the plums at 50–80°C, where considerable shrinkage is observed, although with little inﬂuence of temperature. This can be attributed to the viscoelastic nature of the material, which suffers a structural collapse during drying. Similar results were obtained for thin layer drying of Thompson seedless grapes by Rhagavan et al. (1995), who found a linear relationship of volume change as a function of the moisture content of the berries. Simal et al. (1996) employed a diffusivity model with moving boundary conditions to simulate the drying kinetics of seedless grapes of the Flame variety, with the volume change represented by plotting V/V0 vs. X/X0 and by ﬁtting a linear equation with similar constants. The initial moisture content was similar for all samples of plums. The inﬂuence of air drying temperature on the drying curves can be observed in Figure 10.5. As expected, increases in the air temperature substantially shortened the drying time in o comparison with that observed at 50 C. The drying time required to evaporate 90% o of water was shorter by 39.8, 57.7, and 70.5% at 60, 70, and 80 C, respectively, o compared to that at 50 C. Therefore, it is evident that at the same water content, the

© 2003 by CRC Press LLC

4.0

Moisture content (dry basis)

3.5 3.0 T = 80°C

2.5

T = 70°C

2.0

T = 60°C T = 50°C

1.5 1.0 0.5 0.0 0

500

1000

1500

2000

2500

Drying time (min)

FIGURE 10.5 Drying curves of plums at different temperatures; symbols refer to experimental ) numerical solution from data; (— —) analytical solution from Equation (10.2); ( Equation (10.15).

drying rate is dependent on air temperature. Induction periods or constant drying rate periods were not observed, and the drying was characterized only by the falling rate period. Barbanti et al. (1994), writing about air drying kinetics of cultivar plums, also observed that there was no constant drying rate period in this process. The existence of only the falling rate period could be indicative of a diffusion-controlled mechanism of drying. It can be also seen in Figure 10.5 that the analytical model of Fick’s Law, considering radius and effective diffusivity constants, is not applicable to ﬁt the experimental data in the ﬁnal drying period. However, during the drying period ﬁtted by this model, the plums had not reached the commercially desirable moisture content (approximately 0.15 kg water/kg dry matter). In addition, according to Figure 10.4, the radius of the plum is a function of moisture content, showing that shrinkage has to be taken into account during the drying process. The apparent agreement between the analytical solution of Equation (10.2) applied to plums and the experimental data in a great part of the drying curves (Figure 10.5) could be explained by supposing a simultaneous decrease in the effective diffusivity and in the radius, in such a way that these effects compensated for each other. The numerical solution ﬁtted to the experimental data can be also seen in this ﬁgure. As expected, a good adjustment was obtained for all drying curves, including for the ﬁnal drying period. From the numerical solution of Fick’s second law, the effective diffusivity as a function of simultaneous shrinkage and moisture content can be calculated. Figure 10.6 presents the effective diffusivity behavior with decreasing moisture content of the plums, and it can be observed that the effective diffusivity parameter is far from being constant during the process. The effective diffusivity is more inﬂuenced by o moisture content at 80 C than at other temperatures. On the other hand, neglecting o the initial inductive period, the effective diffusivity at 60 and 50 C changes almost

© 2003 by CRC Press LLC

1.00E-009

Effective diffusivity (m2/s)

T = 80°C

8.00E-010

T = 70°C

6.00E-010 T = 60°C

4.00E-010

T = 50°C

2.00E-010

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Moisture content (dry basis)

FIGURE 10.6 Variation of effective diffusivity with moisture content of plums at different temperatures. 90 T = 50°C T = 60°C T = 70°C T = 80°C

Temperature (°C)

80 70 60 50 40 30 20 0

1

2

3

4

Moisture content (dry basis)

FIGURE 10.7 Evolution of temperature inside plums during drying.

linearly with decreasing moisture content. The increase of effective diffusivity in this initial period could be attributed to the time necessary for the temperature of the plum to increase until it reaches the drying process temperature. According to Figure 10.7, in general, the temperature of the fruit begins to reach equilibrium with the drying air at a moisture content of approximately 3.0 kg/kg dry mass. Sabarez et al. (1997) reported that the resistance to moisture transfer through the skin layer is important during drying of plums, particularly in the early stages of drying. These authors concluded that the skin layer limits the maximum effective evaporation rate from the plum surface and provides signiﬁcant resistance to initial moisture loss.

© 2003 by CRC Press LLC

Activation energy (kJ/mol)

39 38 37 36 35 34 33 32 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Moisture content (dry basis)

FIGURE 10.8 Relationship between activation energy for water diffusion and moisture content in plums undergoing drying

Raghavan et al. (1995) obtained effective diffusivity values varying with moisture content under convective and microwave drying of grapes, and these values were found to decrease with decreasing water content. Effective diffusivity coefﬁcients considering shrinkage but not varying with moisture content were reported by Hawlader et al. (1991) for tomatoes and by Simal et al. (1996), who obtained diffusivities of around –10 –9 2 –1 4.7 × 10 to 1 × 10 m sec for grapes. Sabarez and Price (1999) studied the drying of plums of the d’Agen variety and obtained Deff values in the range of 4.3 to 7.6 × –10 2 –1 10 m sec at 70, 75, and 80°C. The temperature dependence of the diffusivity can be represented by an Arrhenius type equation (Simal et al., 1996; Lewick et al., 1998; Simal et al., 2000). The activation energy for diffusion is calculated by taking a log plot of effective diffusivity at constant moisture content, against the reverse of the absolute air drying temperature. The relationship between activation energy and moisture content is presented in Figure 10.8. The tendency of increasing activation energy with decreasing moisture content is expected, and the majority of researchers have recognized this effect, especially for the low moisture content range. Satisfactory values of the determination coefﬁcient (0.99) were obtained during the ﬁtting procedure.

10.5 CONCLUSIONS The volumetric shrinkage of plums results in a linear correlation with respect to the moisture content. The ﬁnite difference method can be used for more accurate predictions and simulation of the drying process, and effective diffusivity values can be obtained as a function of moisture content, taking into account the shrinkage of the material. In general, these values are found to decrease with decreasing moisture content. The reported moisture diffusivity data at different temperatures falls between

© 2003 by CRC Press LLC

–10

–10

2

1.2 × 10 and 8.9 × 10 m /sec. These results lead to the conclusion that shrinkage and moisture content cannot be neglected in establishing reliable values of effective diffusivity. The activation energy for diffusion is also dependent on the moisture content. It increases with decreasing water content in plums undergoing drying.

NOMENCLATURE A aw B Bim d DAB Deff Dvap Ea Fo Keq kc m M Ms N n P Pvap qA R Rep rs rp rpo Sc Sh T Ta t v V Vo X Xo Xe ∗ Y

Constant in Equation (10.23) Water activity Constant in Equation (10.23) Biot mass number ([kc ⋅Keq ⋅rpo]/Deff) Sphere diameter (m) 2 Diffusion coefﬁcient (m /sec) 2 Effective diffusivity (m /sec) 2 Water vapor diffusivity in the air at a temperature Ta (m /h) Activation energy (kJ/mol) 2 Fourier mass number ([Deff ⋅t]/[rpo] ) Average partition constant Mass transfer coefﬁcient (m/sec) Mass (kg) Residual moisture content Dimensionless moisture content at the surface of the plums Number of nodal points Arbitrary nodal point Total pressure (atm) Vapor pressure of water (atm) Chemical reaction in Equation (10.1) Universal gas constant (8.314 J/mol K) Modiﬁed Reynolds number ([ρ⋅v⋅d]/µ) Radius of the stone (kernel + shell) component (m) Radius of the whole plum (m) Radius of the plum at t = 0 (m) Schmidt number (µ/ρ⋅Dvap) Sherwood number ([kc ⋅d]/Dvap) Absolute temperature (K) Air temperature (°C) Time (sec) elocity (m/sec) 3 Volume (m ) 3 Initial volume (m ) Moisture content dry basis (kg/kg dry matter) Initial moisture content (dry basis) Equilibrium moisture content (dry basis) Molar fraction at equilibrium

© 2003 by CRC Press LLC

GREEK SYMBOLS ξ Radial coordinate (m) ξp Dimensionless particle radius (rp(t)/rpo) 3 ρ Density (kg/m ) µ Viscosity (kg/m sec)

ACKNOWLEDGMENT The authors acknowledge ﬁnancial support from São Paulo State Research Fund Agency, FAPESP (Processes: 98/12283–5; 98/08738–7 and 98/05130–8).

REFERENCES AOAC, Ofﬁcial Methods of Analysis, 15th ed., Association of Ofﬁcial Analytical Chemists, Washington, DC, 1990. Arrouz, S., Jomaa, W., and Belghith, A., Drying Kinetic Equation of Single Layer of Grapes, Drying ’98 — Proceedings of the 11th International Drying Symposium, August 19–22, 1998, B, pp. 988–997. Barbanti, D., Mastrocola, D., and Severine, C., Air drying of plums: a comparison among twelve cultivars, Sci. Aliment., 14, 61–73, 1994. Bird, R.B., Stewart, W.E., and Lightfoot, E.N., Transport Phenomena, John Wiley & Sons, Inc., New York, 1960, pp. 554–560. Córdova-Quiroz, A.V., Ruiz-Cabrera, M.A., and García-Alvarado, M.A., Analytical solution of mass transfer equation with interfacial resistance in food drying, Drying Technol., 14, 1815–1826, 1996. Dãscãlescu, A., Le Sechage et ses Applications Industrielles, Dunod, Paris, 1969. Gabas, A.L., Menegalli, F.C., and Telis-Romero, J., Effect of chemical pretreatment on the physical properties of dehydrated grapes, Drying Technol., 17, 1215–1226, 1999. Gabas, A.L., Menegalli, F.C., and Telis-Romero, J., Water sorption enthalpy-entropy compensation based on isotherms of plum skin and pulp, J. Food Sci., 65, 680–684, 2000. Gabitto, J.F. and Aguerre, R.J., Solucion numerica del processo de secado com cambio de volumen, Revista Latinoam. Transf. Cal. Mat., 9, 231–240, 1985. Hawlader, M.N.A., Uddin, M.S., Ho, J.C., and Teng, A.B.W., Drying characteristics of tomatoes, J. Food Eng., 14, 259–268, 1991. Hernández, J.A., Pavón, G., and García, M.A., Analytical solution of mass transfer equation considering shrinkage for modeling food-drying kinetics, J. Food Eng., 45, 1–10, 2000. Karathanos, V.T., Determination of water content of dried fruits by drying kinetics, J. Food Eng., 39, 337–344, 1999. Lewick, P.P., Witrowa-Rajchert, D., and Nowak, D., Effect of drying mode on drying kinetics of onion, Drying Technol., 16, 59–81, 1998. Madamba, P.S., Optimisation of the drying process: an application to the drying of garlic, Drying Technol., 15, 117–136, 1997. Madamba, P.S., Driscoll R.H., and Buckle, K.A., Shrinkage, density and porosity of garlic during drying, J. Food Eng., 23, 309–319, 1994. Murray, W.D. and Landis, F.L., Numerical and machine solutions of transient heat conduction problems involving melting or freezing, J. Heat Transfer, Trans. ASME, May 1959, 106–112.

© 2003 by CRC Press LLC

Newman, G.M., Price, W.E., and Woolf, L.A., Factors inﬂuencing the drying of prunes 1. Effects of temperature upon the kinetics of moisture loss during drying, Food Chem., 57, 241–244, 1996. Price W.E., Sabarez, H.T., Laajoki, L.G., and Woolf, L.A., Dehydration of prunes: kinetic aspects, Agro-Food-Industry Hi-Tech, 8, 29–33, 1997. Raghavan, G.S.V., Tulasidas, T.N., Sablani, S.S., and Ramaswamy, H.S., A method of determination of concentration dependent effective moisture diffusivity, Drying Technol., 13, 1477–1488, 1995. Sabarez, H.T. and Price W.E., A diffusion model for prune dehydration, J. Food Eng., 42, 167–172, 1999. Sabarez, H.T., Price W.E., Back, P.J., and Woolf, L.A., Modelling the kinetics of drying of d’Agen plums (Prunus domestica), Food Chem., 60, 371–382, 1997. Sanjuán, N., Bermejo, M.V., Vivanco, D., Cañellas, J., and Mulet, A., Drying Kinetics of Moscatel Cultivar Grapes, Drying ’96 — Proceedings of the 10th International Drying Symposium, July 30 – August 2, 1996, B, pp. 1069–1076. Saravacos, G.D., Mass transfer properties of foods, in Engineering Properties of Foods, Rao, M.A. and Rizvi, S.S.H., Eds., Marcel Dekker, New York, 1986, pp. 169–221. Simal, S., Femenía, A., Llull, P., and Rosselló, C., Dehydration of aloe vera: simulation of drying curves and evaluation of functional properties, J. Food Eng., 43, 109–114, 2000. Simal, S., Mulet, A., Catalá, P.J., Cañellas, J., and Rosselló, C., Moving boundary model for simulating moisture movement in grapes, J. Food Sci., 61, 157–160, 1996. Sobral, P.J.A., Secagem de sangue bovino incorporado a proteína texturizada de soja, em leito ﬂuidizado e em leito ﬁxo, thesis, FEA, UNICAMP, 1987. Telis, V.R.N., Gabas, A.L., Menegalli, F.C., and Telis-Romero, J., Water sorption thermodynamic properties applied to persimmon skin and pulp, Thermochim. Acta, 343, 49–56, 2000. Zogzas, N.P., Maroulis, Z.B., and Marinos-Kouris, D., Densities, shrinkage and porosity of some vegetables during air drying, Drying Technol., 12, 1653–1666, 1994.

© 2003 by CRC Press LLC

11

Modeling Dehydration Kinetics and Reconstitution Properties of Dried Jalapeño Pepper R. Olivas-Vargas, F.J. Molina-Corral, A. Pérez-Hernández, and E. Ortega-Rivas

CONTENTS 11.1 Introduction 11.2 Materials and Methods 11.3 Results and Discussion 11.4 Conclusions Nomenclature Acknowledgments References

11.1 INTRODUCTION Drying is a physical separation process that has the objective of removing a liquid from a solid phase by means of thermal energy. The liquid is generally water and is liberated by vaporization rather than by breaking chemical bonds between the liquid and the solid; i.e., the liquid is not chemically bound to the solid. In most industrial drying applications, it is neither necessary nor economically feasible to remove every vestige of water from the solid; thus, commercially dry solids will usually contain a certain amount of residual moisture, the amount of which is determined by a compromise between product quality and economic factors. In food and biological materials, low moisture levels are necessary to stop or slow the growth of spoilage microorganisms, as well as the occurrence of undesirable biochemical and enzymatic reactions. The fundamental principles underlying drying processes are, in general, those typical of the science of heat and mass transfer. Drying, as a unit operation in food and chemical engineering, is characterized by the separation, usually partial, of a

© 2003 by CRC Press LLC

liquid contained within a solid by the process of vaporization of the liquid into a gas phase. The mechanism of the drying process, as controlled by the principle of heat and mass transfer, consists of the transport of mass from the interior of the solid to the surface, the vaporization of the liquid at or near the surface, and the transport of the vapor into the bulk gas phase. Simultaneously, heat is transferred from the bulk gas phase to the solid phase, where all or a portion of it provides for vaporization, and the remainder accumulates in the solid as a sensible heat. The overall rate by which the above sequence of steps takes place deﬁnes the drying rate and is inversely related to the drying time. Regardless of how heat is provided, the drying cycle generally consists of three steps: 1. Before any evaporation takes place, sensible heat must be added to the drying mass until the boiling point of the liquid under the given operating conditions is reached. 2. Once the boiling point is reached, evaporation takes place at a rate related to the moisture level in the solid, and this rate is normally constant over a certain moisture range. 3. At some condition, a critical moisture point is reached and the drying rate begins to fall. Constant rate drying is the ﬁrst stage, in which drying occurs at or near the boiling point of the liquid. There is no resistance to vaporization, since the moisture appears on the surface of the solid, completely wetting the outer surface. The constant drying rate is proportional to the difference between the vapor pressure of the liquid covering the surface of the solid and that of the vapor surrounding the wetted solid. It has been found that the vapor pressure of the wetting liquid is very close to that of the pure liquid at the same temperature. At the critical moisture content of the solid, the drying rate begins to fall because there is not enough moisture to completely cover the solid surface. The reduced amount of moisture being evaporated comes from the interstices of the solid through the porous structure. Falling rate drying is controlled by the physical properties of the liquid and solid. The rates of movement of the liquid and its vapor depend on capillary size, glazing of the solid, pressure gradients between trapped liquid and vapor, and the environs of the solid, as well as on cracking, checking, etc. At the same time, the heat transfer rate to the interior of the solid is being slowed because of the receding boundary of the liquid-wetted portion of the particle. This boundary movement increases the resistance to heat ﬂow because it reduces the thermal conductivity within the solid. Cracking and checking disrupt the paths of heat transfer, further reducing the rate. Moisture migration during drying has been explained by different models. Four mechanisms are recognized: capillarity, concentration gradient diffusion, vapor diffusion by pressure difference, and layer diffusion across solid–ﬂuid interfaces (Brennan, 1994). Capillary forces are responsible for water retention in porous solids or those of rigid construction, while osmotic pressure is responsible in aggregates of ﬁne powders and on the surface of the solid (Toei, 1983). It has been reported that

© 2003 by CRC Press LLC

moisture migration by diffusion is the predominant mechanism in drying of many food products, such as vegetables (Geankoplis, 1983). Drying data are usually expressed as total weight of the material as a function of time during the drying process. These data can also be expressed in terms of drying rate by recalculation of some values. The moisture content is deﬁned as the ratio of the amount of water in the food to the amount of dry solids, i.e.,: Xt =

Wt − Fs Fs

(11.1)

where Xt is the moisture expressed as weight of water/weight of dry solids, Wt is the total weight of the material at time t, and Fs is the weight of the dry solids. An additional important quantity used in designing drying processes is the free moisture content X, which can be evaluated considering the equilibrium moisture content Xeq, by the simple relation: X = X t − X eq

(11.2)

As previously mentioned, moisture contents can be recalculated to obtain drying rates. The rate of drying R can be expressed proportional to the change in moisture content as a function of time t, by the following relationship: R∝

dX dt

(11.3)

Individual values of dX/dt as a function of time t can be obtained from tangent lines drawn to the curve of X vs. t. Replacing the proportionality condition in Equation (11.3) by Fs /A, the drying rate can be represented by: R=−

 Fs   dX   A   dt 

(11.4)

where A is the drying surface area. Drying of fruits and vegetables follows conventional dehydration theory, which was adapted from drying of inorganic materials and other raw materials in the chemical processing industry (Sarvacos and Charm, 1962). The advantages of reducing moisture content below 5% in biological materials are well known: microbial and enzyme activity are practically stopped, and transport costs are greatly reduced. However, fruits and vegetables can also suffer undesired changes due to the drying process. Shrinkage, case hardening, texture damage, and reconstitution difﬁculty can be caused by drying (Brennan, 1994). Dehydrated vegetables, when reconstituted, cannot match the original texture even if precautions are taken during the entire drying process. The large scale of industrial drying makes the analysis of the process difﬁcult. Operators and process engineers often have only a few variables to use in formulating

© 2003 by CRC Press LLC

any changes needed to control the operation. Typically, the feed rate is held constant and the controlling variable is the drying medium temperature. The operator may use exaggerated safety factors to prevent product build-up or over-drying. Mathematical modeling may be considered an efﬁcient tool to overcome inefﬁciencies of drying plants such as damaged product, wasted energy, wear on the dryer, or decreased throughput. Models to describe dehydration of foods are necessary for process design, improvement, and minimization of energy while keeping quality as unimpaired as possible. Development of mathematical models to describe drying of porous solids has been the topic of many research studies for many years. Heat and mass transfer take place in a porous solid when it contains moisture and is subjected to any or all of the gradients of concentration, partial vapor pressure, temperature, total pressure, and external force ﬁelds. There has been no general agreement among researchers on which driving forces predominate, considering different materials or media and external drying conditions. More and more sophisticated drying models are becoming available based on either a mechanistic classical approach or on nonequilibrium thermodynamics. However, a major question that still remains is the determination of the best driving forces and assumptions to be made for drying model formulation. Another concern should be the determination of the coefﬁcients and parameters used in the model. The measurement or determination of the necessary coefﬁcients should be feasible and practical for general applicability of a drying model. The research described here was directed towards developing a predictive mathematical model of jalapeño pepper drying and thermal damage, due to the economic importance of this commodity, as well as its potential commercialization value as a processed product.

11.2 MATERIALS AND METHODS Fresh green jalapeño peppers (Capsicum annuum L.) obtained from local markets were used for the experiments. They were selected manually in order to obtain peppers in good condition of uniform size (6–7 cm), and then sliced to an approximate thickness of 5 mm using an electrical cutting machine (S.A. Bertuzzi; Brugherio, Milano, Italy). The jalapeño slices were washed to remove seeds and allowed to drain for 10 min. Samples of 180 g were placed over nine trays of a locally manufactured dryer, diagrammatically illustrated in Figure 11.1. Air was heated by a gas burner model HP225B LP (Adams Manufacturing Company; Cleveland, OH) and directed in parallel direction towards the peppers at 5 m/sec and temperatures of 60, 70, and 80°C. The drying time was 150 min. Dry bulb temperatures were recorded using thermometers located at different positions, as shown in Figure 11.1. Air velocity was measured using a Pitot tube (Dwyer Instruments, Inc.; Michigan City, IN) connected to a differential inclined manometer according to ASTM (1995) norm D3154. Moisture changes were determined by weight difference according to AOAC (1990) method 6.004. To determine a rehydration ratio, samples of 5 g dried slices were immersed in 400 ml water baths. The water baths were set at 75°C, and the immersion time was 6 min.

© 2003 by CRC Press LLC

198 cm Trays

Thermometers

Air valve

206 cm

Exhaust

Burner

64 cm

83.5 cm

49.5 cm

FIGURE 11.1 Schematic diagram of the tray dryer used for the experiments.

The results obtained were used to derive drying and rehydration kinetics predictive models by means of regression analysis, using the Statistica 5.5 software (StatSoft, Inc., Tulsa, OK).

11.3 RESULTS AND DISCUSSION In fundamental drying research of food materials, ideally a model would contain a minimum of restrictive assumptions, and all material property values needed for the model would be obtained. The prediction of the drying characteristics based on knowledge of composition and structure is complex due to the nature of solid structures and the limited understanding of the moisture transport mechanism. An alternative is the identiﬁcation of the relevant driving forces and the use of independent experimental tests that isolate the different driving forces to determine the necessary model coefﬁcients. The model should have the most possible theoretical meaning and require the minimum of experimental tests to determine the coefﬁcients. The model developed in this work was derived according to the characteristics described above. Drying kinetics were determined and the data were handled in a mathematical way to evaluate the best ﬁtting equations describing the drying curves. To achieve this, drying conditions had to be controlled very carefully to ensure constant velocity, constant moisture content, and constant temperature of the ﬂowing air. When these conditions were set, it was assumed that the drying rate represented by Equation (11.4) could also be established entirely in terms of the moisture gradient

© 2003 by CRC Press LLC

between the sample and the surrounding drying air, i.e., dX R = K y (X R − Xe ) dt

(11.5)

where XR is the moisture content on a dry basis of the vegetable, Ky is a coefﬁcient governing the mass transfer, and Xe is the moisture content of the air. To give the model a generalized characteristic, the moisture content was normalized using the following dimensionless relation: Θ=

XR − Xe X0 − Xe

(11.6)

where X0 is the moisture content of the material at the initial time, i.e., t = 0. It can be demonstrated (Molina-Corral, 1988) that Equation (11.5) can be rearranged by incorporating the normalized moisture content described by Equation (11.6), to give the following relationship:  X − Xe  d  XR − Xe  = Ky  R    dt  X 0 − X e   X0 − Xe 

(11.7)

The normalized moisture content Θ can be made explicit and transposed to give: dΘ = K y dt Θ

(11.8)

Integrating Equation (11.8), the following relationship is therefore obtained: ln Θ = K y t + C

(11.9)

where C is the integration constant. Taking natural logarithms on both sides of Equation (11.9) transforms it into the following exponential expression: Θ=e

K y +C

(11.10)

Using logarithm’s laws it can be demonstrated (Molina-Corral, 1988) that Equation (11.10) simply becomes the one presented below, which relates the variation of moisture content of the material Θ as a function of time t and temperature T, i.e., Θ=e

© 2003 by CRC Press LLC

Kyt

(11.11)

TABLE 11.1 Regression Parameter Values for the Dehydration and Rehydration Models from Experimental Data Parameter

Dehydration Model

β1 β2 β3 β4 β5 β6

5.209 × 10 −2 3.730 × 10 −2 1.550 × 10 0.0 −4 1.000 × 10 −4 6.000 × 10

−1

Rehydration Model −2

−7.3340 × 10 −5 1.6000 × 10 −3 2.5004 × 10 0.0 −5 −2.4360 × 10 0.0

Equation (11.11) represents a one-exponential model known as the thin ﬁlm drying model. Such a model basically states that the drying constant, Ky in this case, is a combination of the transport properties involved in drying and describes with reasonable accuracy the drying kinetics of hygroscopic materials. When the previously mentioned constant conditions of velocity, moisture, and temperature of the drying air are ensured, the transport properties most inﬂuential in drying of vegetables are time and temperature. The correlation exercises practiced in accordance with the experimental data demonstrated that the best ﬁtting model for the coefﬁcient governing the mass transfer Ky was a quadratic one expressed as: K y = β1 + β2 t + β3T + β 4 t 2 + β5T 2 + β6 tT

(11.12)

where the parameters β1, β2,…, β6 are those presented in Table 11.1. The model for predicting moisture content as a function of time and temperature was therefore given by: Θ = e(β1 +β2 t +β3T +β4t

2

+β5T 2 +β6 tT ) t

(11.13)

Figure 11.2 shows the experimental drying curves contrasted with the correspondinc correspondent ones obtained using Equation (11.13) above at the three temperatures tested. As can be seen, the mathematical model ﬁt the experimental 2 data very well, judging by the high given values of the coefﬁcient of determination R . As stated earlier, moisture migration by diffusion is the predominant mass transfer mechanism in drying of fruits and vegetables. It has also been reported (Toledo, 1991) that diffusivity may be constant if cells do not collapse and pack together. This behavior would be identiﬁed in ﬁrm solids such as grains, or in high moisture products such as fruits and vegetables when physical changes such as water removal are minimal. As shown in Figure 11.3, the presence of only a falling rate period for all the conditions tested was conﬁrmed. This trend was in agreement with the work reported by Turhan

© 2003 by CRC Press LLC

1 0.8 0.6 S = 0.023

0.4

R2 = 0.99

0.2 0 0

30

60

90

120

150

(a)

Moisture content

1 0.8 0.6 S = 0.031

0.4

R2 = 0.99

0.2 0 0

30

60

90

120

150

(b)

1 0.8 0.6 0.4

S = 0.020 R2 = 0.99

0.2 0 0

30

60

90

120

150

(c)

Time (minutes) FIGURE 11.2 Experimental (䉱) and calculated (—) drying curves for 60 (A), 70 (B), and 80°C (C) dehydration temperatures.

© 2003 by CRC Press LLC

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

0.2

0.4

0.6

0.8

1

0.6

0.8

1

0.6

0.8

1

Drying rate (kg/h·m2)

(a)

2 1.5 1 0.5 0 0

0.2

0.4

(b)

2.4 2 1.6 1.2 0.8 0.4 0 0

0.2

0.4

(c)

Moisture content

FIGURE 11.3 Experimental drying rate curves for 60 (A), 70 (B), and 80°C (C) dehydration temperatures.

and Turhan (1997), who found that peppers dehydrated without previous blanching presented only a falling rate period in their drying kinetics. The drying curves presented in Figure 11.2 also show the difference in drying velocities according to the applied temperature. It can be observed that drying

© 2003 by CRC Press LLC

kinetics were higher, with a similar trend, for the processes carried out at 70 and 80°C, but slower for the minimum temperature of 60°C. Thus, it can be argued that drying kinetics were optimal at any of the higher temperatures, and that these levels of heat were moderate enough to prevent undesirable phenomena such as case hardening. It has been observed that in drying of some fruits, vegetables, meat, and ﬁsh, as drying temperatures approach the water boiling range, a hard and impermeable ﬁlm develops on the surface (Brennan et al., 1979). Case hardening can be more severe during ﬁnal stages of drying, where more than one falling rate period is presented. Since there was only one falling rate period in this study, case hardening was not a problem and drying kinetics developed quite well. However, as more undesirable phenomena can be caused by high drying temperatures, it would be advisable to use 70°C as the dehydration processing temperature in further applications, as drying behavior was similar at either 70 or 80°C. In addition to case hardening, shrinkage and texture damage can be caused by drying of vegetables, resulting in poor appearance and loss of some sensory attributes. The amount of thermal damage in drying of vegetables is difﬁcult to evaluate, but it may be related in some way to structural alteration of the tissues due to excessive heat. The degree to which a dehydrated sample will rehydrate is inﬂuenced by such structural and chemical changes. Rehydration is maximized when cellular and structural disruption is minimized. Several measures can be taken to minimize structural alterations in order to improve the reconstitutability of dried food products. The drying method and adjustment of drying conditions can result in a product with good rehydration properties. For example, it has been reported that freeze-drying causes fewer structural changes than any other method, with minimal changes to the product’s hydrophilic properties (Heldman and Singh, 1981). This procedure results in obtaining food pieces with an open pore structure that will absorb water easily when reconstituted. However, freeze-drying is an expensive form of dehydration for foods due to the slowness of the drying rate and the use of vacuum. Since the vapor pressure of ice is very small, freeze-drying requires very low pressures or very high vacuum. For this reason, it is more feasible to try to obtain food products with good reconstitution properties by manipulating the operating variables of dryers. One possibility is to partially dehydrate fruits by immersion in sugar solutions to promote water migration by osmotic pressure difference, then give them a gentle drying cycle in order to obtain crisp products that rehydrate easily (Beltrán-Reyes et al., 1996). Also, the blanching method and drying temperatures can have an effect on reconstitution properties of vegetables (Ortega-Rivas et al., 1997). In this work, the amount of damage produced by the different drying conditions was determined by estimating the rehydration ratio RR using the following relation: RR =

w0 wf

(11.14)

where w0 is the weight of the dry sample and wf is the weight of the rehydrated sample.

© 2003 by CRC Press LLC

Rehydration relation

1 0.9

60°C

0.8 0.7

70°C

0.6 80°C

0.5 0.4 0.3 0.2 0.1 0 0

20

40

60

80

100

120

140

Drying time (minutes)

FIGURE 11.4 Experimental rehydration curves.

Rehydration rates, estimated by Equation (11.14), are shown in Figure 11.4. The best ﬁtting model for the rehydration ratio, obtained using a procedure similar to that in deriving Equation (11.13), was: RR = e(β1 +β2 t +β3T +β4t

2

+β5T 2 +β6 tT ) t

(11.15)

The parameters β1, β2,…, β6 are given in Table 11.1. As can be observed in Figure 11.4, rehydration kinetics showed a trend opposite to that of the drying process, i.e., the dried peppers rehydrated better at the lower drying temperature and at the shorter treatment times. In general terms, the worst rehydration characteristics were demonstrated by the peppers dried at 80°C. This behavior could be due to the extent of tissue damage, which is expected to be more severe at higher drying temperatures. It has been reported (Charm, 1971) that excessive thermal damage, due to high drying temperatures, may be responsible for poor appearance and loss of texture of dehydrated biological materials.

11.4 CONCLUSIONS A mathematical model to describe dehydration of jalapeño pepper at normal operating conditions was developed. The model describes the drying process in terms of the moisture migration as a function of time at different temperatures. The effect of thermal damage as a function of rehydration capacity is also included. The regression equations describing the model were highly correlated. The model can be used to opt for the best compromise between drying capability and product quality. Application of the model to a material similar to the one tested in the experiments would indicate that the use of relatively high temperatures would make a product practically bone dry, but with irreversible thermal damage, as its capacity to absorb water in a reconstitution process would be impaired. A moderate drying temperature, on the other hand, would result in a product with low moisture content and appropriate rehydration properties. Since the model development was based on careful experimental

© 2003 by CRC Press LLC

conditions and the use of fresh materials of random composition, it can be applied with conﬁdence to conditions different from those used at the University of Chihuahua. The model is easy to adapt, and simple calculations could provide guidance in choosing processing times and temperatures in advance as a function of the expected properties of the product, avoiding waste of time, energy, and raw materials.

NOMENCLATURE A β C Fs Θ Ky R RR t T w0 wf Wt X Xe Xeq XR Xt X0

2

Drying surface area, m Parameter of the regression model Integration constant Weight of dry solids, kg Normalized moisture content 2 Coefﬁcient governing the mass transfer, kg mol/sec m 2 Rate of drying, kg water/h m Rehydration relation Time, min Temperature, °C Weight of dry sample, g Weight of rehydrated sample, g Total weight of wet material, kg Free moisture content, kg water/kg dry solid Moisture content of the air, kg water/kg dry air Equilibrium moisture content, kg water/kg dry solid Moisture content of vegetable, kg water/kg dry solid Total moisture content, kg water/kg dry solid Initial moisture content, kg water/kg dry solid

ACKNOWLEDGMENTS The authors thank the National Council for Science and Technology (CONACyT) as well as the Program for Academics Improvement (PROMEP), México, for providing funding to the project.

REFERENCES AOAC, Ofﬁcial Methods of Analysis, 15th ed., Association of Ofﬁcial Analytical Chemists, Washington, DC, 1990. ASTM, Standard test method for average velocity in a duct (Pitot tube method), Annual Book of ASTM Standards, Vol 11.03, 1995, pp. 89–92. Beltrán-Reyes, B., Ortega-Rivas, E., and Anzaldúa-Morales, A., Characterization of reconstituted apple paste in terms of rehydration and ﬁrmness, Food Sci. Technol. Int., 2, 307–313, 1996. Brennan, J.G., Food Dehydration: A Dictionary and Guide, Butterworth-Heinemann, Stoneham, MA, 1994.

© 2003 by CRC Press LLC

Brennan J.G., Butters, J.R., Cowell, N.D., and Lilly, A.E.V., Food Engineering Operations, 2nd ed., Applied Science, London, 1979. Charm, S.E., The Fundamentals of Food Engineering, 2nd ed., AVI, Westport, CT, 1971. Geankoplis, C.J., Transport Processes and Unit Operations, Allyn and Bacon, Boston, MA, 1983. Heldman, D.R. and Singh, R.P., Food Process Engineering, Van Nostrand Reinhold, New York, 1981. Molina-Corral, F.J., Development of a Mathematical Model of Jalapeño Pepper Drying in a Tray Dehydrator with Gas Heating Source, thesis, University of Chihuahua, México, 1988. Ortega-Rivas, E., Moreno-Pérez, L.F., and Gasson-Lara, J.H., Effect of blanching and drying temperatures on rehydration rate and texture of sweet potatoes, in Advances in Food Engineering, Narsimhan, G., Okos, M.R., and Lombardo, S., Eds., Purdue Research Foundation, West Lafayette, IN, 1997, pp. 81–85. Sarvacos, G.D. and Charm, S.E., A study of the mechanism of fruits and vegetables dehydration, Food Technol., 16, 78–81, 1962. Toei, R., Drying mechanism of capillary porous bodies, in Advances in Drying, vol. 2, Mujumdar, A.S., Ed., Hemisphere, New York, 1983. Toledo, R.T., Fundamentals of Food Process Engineering, 2nd ed., Van Nostrand Reinhold, New York, 1991. Turhan, M. and Turhan, K.N., Drying kinetics of red pepper, J. Food Process. Preserv., 21, 209–223, 1997.

© 2003 by CRC Press LLC

12

Application of an Artiﬁcial Neural Network for Moisture Transfer Prediction Considering Shrinkage during Drying of Foodstuffs J.A. Hernández-Pérez, M.A. Garcia-Alvarado, G. Trystram, and B. Heyd

CONTENTS 12.1 Introduction 12.2 Materials and Methods 12.2.1 Neural Network Systems 12.2.2 Learning Algorithm 12.2.3 Database Preparation 12.3 Results and Discussion 12.3.1 Learning Bases of the Model 12.3.2 Validation of the Proposed Model 12.4 Conclusions Nomenclature References

12.1 INTRODUCTION Air drying is an essential activity in food processing industries. On-line state estimation and control of the air drying operation require the mathematical description of food moisture evolution during the process. The dynamics of the food drying process involve simultaneous heat and mass transfer, where water is transferred by diffusion from the inside of food material towards the air–food interface and from the interface to the air stream by convection;

© 2003 by CRC Press LLC

heat is transferred by convection from the air to the air–food interface and by conduction to the interior of the food (Balaban and Pigott, 1988; Karathanos et al., 1990; Kiranoudis et al., 1993; Zogzas and Maroulis, 1996). This phenomenon has been modeled with different levels of complexity; existing models do not permit adequate control of the air drying process in industrial applications, mainly because physical dynamic models (or detailed models), considering the complexity of the process, usually result in coupled nonlinear differential equations with partial derivatives, where numerical simulations require specialized software and are very time consuming. It is important to mention that these detailed models are able to predict within a wide range. The dynamic models can be simpliﬁed (Courtois et al., 1991; Hernández et al., 2000), but these models cannot take into account the complexity of the process, and some still contain ordinary nonlinear differential equations that take too long to simulate for applications of control (Trelea et al., 1997b). Empirical model representations approximate the drying kinetic by several line segments (Daudin, 1982), high order polynomials (Techasena et al., 1992), neural networks (Dornier et al., 1993), etc. These models have a narrower validity range but require only a limited number of simple arithmetic operations for simulation and can be easily incorporated in control software. Shrinkage is an important factor in mathematical models of heat and mass transfer for the prediction of food drying kinetics. Mulet (1994) tested models with different levels of complexity, concluding that the main factor that must be considered in models is product shrinkage. Models that take into account the shrinkage of the product are models in which the volume is considered as a function of the content of moisture. The shrinkage of biological products during drying is not perfectly homogeneous (Ratti, 1994; Hernández, et al., 2000). It is interesting to mention that there is a deviation of some predictions during food drying kinetics considering shrinkage at lower moisture levels (Ψ < 0.05); this is due to the possible conclusion of the shrinkage and the heterogeneous characteristics of the product that could be the product, and this phenomenon’s behavior is typical for foodstuffs (Hernández et al., 2000). The progress of neurobiology has allowed researchers to build mathematical models of neurons to simulate neural behavior. Neural networks are recognized as good tools for dynamic modeling and have been extensively studied since the publication of the perceptron identiﬁcation method (Rumelhart and Zipner, 1985). The interest in such models lies in their modeling without any assumptions about the nature of underlying mechanisms and in their ability to take into account nonlinearities and interactions between variables (Bishop, 1994). Recent results establish that it is always possible to identify a neural model based on the perceptron structure, with only one hidden layer, for either steady state or dynamic operations (with recurrent models) (Hornik et al., 1989; Hornik, 1993). An outstanding feature of neural networks is the ability to learn the solution of the problem from a set of examples and to provide a smooth and reasonable interpolation for new data. Also, in the ﬁeld of food process engineering, neural networks are a good alternative to conventional empirical modeling based on polynomial and linear regressions. For food processes, the neural computing application keeps on growing (Linko and Zhu, 1992; Huang and Mujamdar, 1993; Zhu et al., 1996; Linko et al., 1997; Trelea et al., 1997a; Hernández-Pérez et al., 2000).

© 2003 by CRC Press LLC

The aim of the present work was to test the ability of neural networks to model and predict moisture transfer during air drying in foodstuffs. The model was validated with experimental drying data of cassava parallelepipeds and mango slices.

12.2 MATERIALS AND METHODS 12.2.1 NEURAL NETWORK SYSTEMS Neural networks are composed of simple elements operating in parallel. As in nature, the network function is determined largely by the connections between elements (neurons); each connection between two neurons has a weight coefﬁcient attached to it. A neuron is grouped into distinct layers and interconnected according to a given architecture. The standard network structure for function approximation is the multiple layer perceptron (or feedforward network). The feedforward network often has one or more hidden layers of sigmoid neurons followed by an output layer of linear neurons. Multiple layers of neurons with nonlinear transfer functions allow the network to learn nonlinear and linear relationships between input and output vectors. The linear output layer lets the network produce values outside the range –1 to +1 (Demuth and Beale, 1998; Limin, 1994). For multiple layer networks, we use the number of layers to determine the superscript on the weight matrices. The appropriate notation is used in two-layer networks. A simple view of network structure and behavior is given in Figure 12.1. This network can be used as a general function approximator. It can approximate any function with a ﬁnite number of discontinuities, arbitrarily well, given sufﬁcient neurons in the hidden layer. The numbers of neurons in the input and output layers are given by the number of input and output variables in the process under investigation. In this work, the input layer consisted of ﬁve variables in the process (air temperature, air velocity,

IW1{1,1}

Σ

n1

In2

Σ

n2

In k

Σ

ns

In1

LW2 {2,1}

b1 Input layer

Σ

Out

b2 Hidden layer

Output layer

FIGURE 12.1 The neural network computational model. k = number of inputs, In = inputs, Out = output, thick lines = weights and biases.

© 2003 by CRC Press LLC

shrinkage function of the moisture, time, and air humidity), one for each input. The optimal number of neurons in the hidden layer(s) ns is difﬁcult to specify and depends on the type and complexity of the task; this is usually determined by trial and error. Each neuron in the hidden layer has a bias b, which is added with the weighted inputs to form the neuron input n. This sum, n, is the argument of the transfer function f. n = IW{1,1}In1 + IW{1,2}In2 + ··· + IW{1, k}Ink + b The coefﬁcients associated with the hidden layer are grouped into matrices IW1 (weights) and b1 (biases). The output layer contains one variable (moisture of the product) for mango and cassava, respectively, which computes the weighted sum of the signals provided by the hidden layer; the associated coefﬁcients are grouped into matrices LW2 and b2. Using the matrix notation, the network output can be given by Equation (12.1). 2

1

Out = f (LW2f (IW1*In + b1) + b2)

(12.1)

Hidden layer neurons may use any differentiable transfer function to generate their 1 2 output. In this work we used as f Tan-Sigmoid Function and for f Linear Transfer Function. The number of network coefﬁcients (weights and biases) is given by Equation (12.2). m = n(In + 1) + Out(n + 1)

(12.2)

12.2.2 LEARNING ALGORITHM A learning algorithm is deﬁned as a procedure that adjusts the coefﬁcients (weights and biases) of a network in order to minimize an error function (usually a quadratic one) between the network outputs for a given set of inputs and the correct outputs already known (this procedure may also be referred to as a training algorithm). If smooth nonlinearities are used, the gradient of the error function can be easily computed by the classical backpropagation procedure (Rumelhart et al., 1986). Previous learning algorithms used this gradient directly in a steepest descent optimization, but recent results have shown that second order methods are far more effective. In this work, the Levenberg–Marquardt (trainlm), optimization procedure in the Neural Network Toolbox of Matlab (Demuth and Beale, 1998) was used. The algorithm of Levenberg is an approximation of Newton’s methods; this algorithm was designed to approach second order training speed without having to compute the Hessian matrix (Hagan and Menhaj, 1994). Despite the fact that computations involved in each iteration are more complex than in the steepest descent case, the convergence is faster, typically by a factor of 100. The root mean square error (RMSE) between the experimental values and network predictions was used as a criterion of model adequacy, as shown in Figure 12.2.

© 2003 by CRC Press LLC

Xa t Lv

Process

Va

Ψ

T°C

+ Shrinkage

+

RMSE

Optimization Method (Levenberg-Marquardt)

Neural Network (weights and bias)

ˆ Ψ

FIGURE 12.2 Recurrent network architecture for the drying kinetic considering the shrinkage of the product and procedure used for learning of neural network.

12.2.3 DATABASE PREPARATION Experimental data provided by Hernández et al. (2000), consisting of mass transfer kinetics of mango slices, 4 × 4 cm with three slab thicknesses (0.50, 0.75, and 1.0 cm), and cassava parallelepipeds, 10 cm long with three thicknesses (1.0, 2.0, and 3.0 cm), were used. The experimental drying kinetics were carried out at three different air temperatures and air velocities with a time of 10 h for each kinetic. The arrangement was a 3*3*3 (slab thickness * air temperature * air velocity) complete factorial design for mango and 3*3 (thickness * air temperature) complete factorial design for cassava at constant air velocity, with two replicates. Tables 12.1 and 12.2 give the experimental conditions studied for each kinetic of mango and cassava. Eperimental ﬁles were split into learning and test databases. The inputs of the network were air temperature (T), air velocity (Va), shrinkage (Lv), time (t), and air humidity (Xa); the output of the network was the food moisture content in dimenˆ ) for mango. The same network was used for cassava but without sionless form (Ψ the input (Va). The food moisture evolution during drying was calculated by sample weight loss of the product at times t = 0, 0.25, 0.50, 0.75, 1.0, 1.25, 1.50, 1.75, 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, and 10.0 h. Wet and dry bulb temperatures of the ambient air were measured with glass thermometers to estimate the air moisture content (Xa). Equation (12.3) was used to determine the variation of shrinkage during kinetic drying of mango and cassava, as proposed by Hernández et al. (2000). This equation

© 2003 by CRC Press LLC

TABLE 12.1 Experimental Conditions Studied for Mango File Number

Initial Thickness Lo (cm)

Air Temperature T (°C)

Air Velocity Va (m/sec)

Time t (h)

0.5 0.75 1.0 0.5 0.75 1.0 0.5 0.75 1.0 0.5 0.75 1.0 0.5 0.75 1.0 0.5 0.75 1.0 0.5 0.75 1.0 0.5 0.75 1.0 0.5 0.75 1.0

50 50 50 60 60 60 70 70 70 50 50 50 60 60 60 70 70 70 50 50 50 60 60 60 70 70 70

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75 1.75 3 3 3 3 3 3 3 3 3

0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 M21 M22 M23 M24 M25 M26 M27

is a function of moisture content of the product.   X  Lv = L 0 ∆L f + (1 − ∆L f )    X 0   

(12.3)

where Lv represents the thickness (cm), L0 is the initial thickness (cm), ∆Lf represents the fraction of initial slab thickness at the end of drying (∆Lf = 0.55 for mango and ∆Lf = 0.68 for cassava), and X and X0 are the moisture and initial moisture of the product (g water/g dry matter). The selected experimental ﬁles were split into learning and test databases to obtain a good representation of the situation diversity. In each case:

© 2003 by CRC Press LLC

TABLE 12.2 Experimental Conditions Studied for Cassava File Number

Initial Thickness Lo (cm)

Air Temperature T (°C)

Air Velocity Va (m/sec)

Time t (h)

1 1 1 2 2 2 3 3 3

50 60 70 50 60 70 50 60 70

3 3 3 3 3 3 3 3 3

0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10 0–10

C1 C2 C3 C4 C5 C6 C7 C8 C9

Mango Eighteen experimental kinetics in learning database (M1, M3, M5, M6, M7, M8, M10, M11, M14, M15, M16, M18, M20, M21, M22, M23, M25, and M27) Nine experimental kinetics in test database (M2, M4, M9, M12, M13, M17, M19, M24, and M26) Cassava Six experimental kinetics in learning database (C1, C2, C4, C6, C8, and C9) Three experimental kinetics in test database (C3, C5 and C7) The learning database was obtained to optimize the neural network, and the test database was reserved for the validation of the predictive capability of the model.

12.3 RESULTS AND DISCUSSION The proposed model for mango (Equation (12.4)) involved three neurons ns = 3 in the hidden layer (18 weights and 4 bias) to determine the moisture transfer in a dimensionless form. The same model, but without the input of air velocity (Va), was used for cassava (15 weights and 4 bias). This model includes the effect of shrinkage (Lv) as a function of the last moisture content. It is important to mention that the mango slices were dried on one side, and cassava parallelepipeds were suspended so drying took place on the four sides (two dimensions). The parallelepipeds were of the same size and drying was homogeneous on the four sides, so we used as input one only Lv for mango and cassava. ˆ represents the predicted moisture of the product in dimensionless form; X Ψ e is the moisture in equilibrium (g water/g dry matter). This moisture (Xe) was determined using the relationship of air moisture and the sorption isotherms that were experimentally obtained for mango and cassava in the laboratory (Equations (12.5) and (12.6)). The moisture levels (X/X0) of Equation (12.3) were determined for the last output network, which makes one closed boucle for (Lv), as represented in Equation (12.4).

© 2003 by CRC Press LLC

Lv = L 0 ∆L f + (1 − ∆L f

)

T°

X X0

V L

(X − Xe ) ˆ = Ψ (Xo − Xe )

t

(12.4)

X bia Mango:

aw = 1 – exp[–exp(0.9154 + 0.5639lnX)]

Cassava:

aw = 1 – exp[–exp(–44.8 + 8.66lnT – 6.41lnX −5 2

+ 0.049TlnX – 6.7 × 10 T lnX)]

12.3.1 LEARNING BASES

OF THE

(12.5)

(12.6)

MODEL

Figure 12.3 gives the trial root mean square error (RSME) against the iteration number in the case of mango and cassava, for one to six neurons in the hidden layer. These results showed that the typical learning error decreased when the number of neurons in the hidden layer increased, but for three or more neurons in the hidden layer for mango, and two or more neurons for cassava, respectively, an additional increase in structure complexity did not strongly decrease the RSME. One problem that occurs during neural network training feedforward is called over-ﬁtting. The RSME on the training set is driven to a very small value, but when new data are presented (e.g., test database) to the network, the RSME is large. Therefore, the RSME on the test database is a good criterion to optimize the number of iterations and avoid over-ﬁtting. Figure 12.3 shows that for three (RMSE = 0.001408) or four (RMSE = 0.001323) neurons in the hidden layer, the error is very small for mango, whereas for cassava the same error is obtained with two (RMSE = 0.00149) or three (RMSE = 0.00148) neurons. In order to determine the number of neurons in the hidden layer, we plotted the RMSE (learning and test bases) against the number of neurons, as shown in Figure 12.4. This ﬁgure presents over-ﬁtting because the error on the test database can increase with the number of neurons. The optimal number of neurons in the hidden layer is three for both mango and cassava. Figure 12.5 presents the simulated results against experimental data for test and learning bases of mango and cassava; in all cases the prediction was correct, whatever the level of moisture. However, at lower moisture contents an evident deviation between experimental and simulated data was observed for mango. In order to conﬁrm these deviations, a plot of some drying experimental and predicted kinetics

© 2003 by CRC Press LLC

1

10

Root-mean square error training

0

10

10

10

10

10

- one neuron

-- two neurons

-. three neurons

.. four neurons

- - five neurons

-o- six neurons

-1

MANGO -2

-3

-4

0

20

40

60

80

100

Levenberg-Marquardt 1

Root-mean square error training

10

- one neuron

-- two neurons

-. three neurons

.. four neurons

- - five neurons

-o- six neurons

0

10

10

-1

CASSAVA 10

10

-2

-3

0

20

40

60

80

100

Levenberg-Marquardt

FIGURE 12.3 Test root mean square error (RMSE) vs. number of iterations and various numbers of hidden neurons for mango and cassava.

(experimental M25, M27, C2, C8; see drying conditions in Tables 12.1 and 12.2) are presented in semilog scale in Figure 12.6. This ﬁgure shows that at Ψ < 0.05 the model cannot predict the drying curves. These deviations at lower moisture content are also observed with detailed models (Hernández et al., 2000).

© 2003 by CRC Press LLC

10-1

MANGO

Root-mean square error

-o- Learn 10

-2

- - Test

10-3

10-4 1

2

3

4

5

6

5

6

Number of neurons 10-1

Root-mean square error

CASSAVA -o- Learn - - Test 10

-2

10-3

1

2

3

4

Number of neurons

FIGURE 12.4 Comparison of RSME learn and test vs. the number of neurons in the two cases (mango and cassava).

12.3.2 VALIDATION

OF THE

PROPOSED MODEL

Figure 12.7 depicts the ability of the models to predict drying kinetics at different thicknesses, temperature, and air velocities in the experimental domain. This ﬁgure shows some simulated results generated and experimental data obtained by the test database (M4, M12, M26, C3, C5, and C7; see Tables 12.1 and 12.2). It is evident that

© 2003 by CRC Press LLC

1

Mango

learn

0.9

o test

0.8

Simulated

0.7 0.6 0.5 0.4

y = 0.0101 + 0.9838x

0.3

R=1

0.2 0.1 0 0

0.2

0.4

0.6

0.8

1

Experimental

1 learn

0.9 0.8

o test

Simulated

0.7 0.6 0.5

Cassava

0.4

y = 0.0144 + 0.9763x

0.3

R=1

0.2 0.1 0 0

0.2

0.4

0.6

0.8

1

Experimental

FIGURE 12.5 Simulated vs. experimental data for test and learning bases of mango and cassava.

the model was successful in predicting the experimental drying kinetics, showing the importance of the artiﬁcial neural network to simulate the drying curves of foodstuffs. These models are not complex, and they can be used for on-line estimation of air drying processes in industrial applications.

10 0

PSI = (X–Xe)/(Xo–Xe)

Mango

10 -1

T = 70°C

10 -2 o Lvo = 0.5 cm (M25)

* Lvo = 1 cm (M27) - Predict 0

2

4

6

8

10

8

10

Time (hr)

0

PSI = (X–Xe)/(Xo–Xe)

10

Cassava

-1

10

T = 60°C -2

10

o Lvo = 1.0 cm (C2) * Lvo = 3.0 cm (C8) -3

10

- Predict

0

2

4

6

Time (hr)

FIGURE 12.6 Experimental data and predicted results of the learning bases for mango and cassava.

12.4 CONCLUSIONS This study shows that neural network modeling can be used to obtain accurate simulation of the moisture transfer during food drying over a wide experimental range. This neural network modeling was validated with experimental drying data. Technological interest in this kind of modeling must be related to the fact that it is elaborated without any preliminary assumptions about the underlying mechanisms, and also to its implementation facility and speed of simulation. The applications of

© 2003 by CRC Press LLC

1 * Lvo = 0.5 cm T = 60°C Va = 0.5 m/sec + Lvo = 1 cm T = 50°C Va = 1.75 m/sec o Lvo = 0.75 cm T = 70°C Va = 3m/sec - Prediction

0.9

PSI = (X–Xe)/(Xo–Xe)

0.8 0.7 0.6 0.5 0.4 0.3 0.2

Mango

0.1 0 0

2

1

6 Time (hr)

8

10

* Lvo = 1 cm T = 70°C Va = 3 m/s + Lvo = 2 cm T = 60°C Va = 3 m/s o Lvo = 3 cm T = 50°C Va = 3m/s - Prediction

0.9 0.8

PSI = (X–Xe)/(Xo–Xe)

4

0.7 0.6 0.5 0.4

Cassava

0.3 0.2 0.1 0

0

2

4

6 Time (hr)

8

10

FIGURE 12.7 Experimental data and simulated curves generated with the proposed model in the drying kinetics of mango and cassava. The symbols represent experimental moisture evolution at different conditions.

artiﬁcial neural networks can be used for on-line state estimation and control of drying processes.

NOMENCLATURE k In

Number of input Input variables

© 2003 by CRC Press LLC

Out ns, n IW1, LW2 b1, b2 T Va Lv L0 t Xa X, X0 and Xe aw

Output variables Neuron in the hidden layer Matrix weight Matrix bias Air temperature (°C) Air velocity (m/sec) Thickness (cm) Initial thickness (cm) Time (h) Air moisture content (g water/g dry air) Food moisture content: in each time, initial, and in equilibrium, respectively (g water/g dry matter) Food water activity

GREEK SYMBOLS ˆ Dimensionless variables (experimental and predicted moisture) Ψ, Ψ ∆Lf Fraction of the initial characteristic length at the end of drying period (cm)

REFERENCES Balaban, M. and Piggot, G.M., Mathematical model of simultaneous heat and mass transfer in food with dimensional changes and variable transport parameters, J. Food Sci., 53, 935–939, 1988. Bishop, C.M., Neural networks and their applications, Rev. Sci. Instrum., 65, 1803–1832, 1994. Courtois, F., Lebert, A., Duquenoy, A., Lasseran, J.C., and Bimbenet, J.J., Modeling of drying in order to improve processing quality of maize, Drying Technol., 9, 927–945, 1991. Daudin, J.D., Modélisation d’un séchoir à partir des cinétiques expérimentales de séchage, Ph.D. thesis, ENSIA, Massy, France, 1982. Demuth H. and Beale M., Neural Network Toolbox for Matlab—User’s Guide, version 3, The MathWorks Inc., Natick, MA, 1998. Dornier, M., Rocha M.T., Trystram, G., Bardot, I., Decloux, M., and Lebert, A., Application of neural computation for dynamic modeling of food processes: drying and microﬁltration, Artiﬁcial Intelligence for Agriculture and Food (AIFA Conf.), Nimes, France, 27–29 October, 1993, pp. 223–240. Hagan, M.T. and Menhaj M.B., Training feedforward networks with the Marquardt algorithm, IEEE Trans. Neural Networks, 6, 989–993, 1994. Hernández, J.A., Pavon, G., and Garcia, M.A., Analytical solution of mass transfer equation considering shrinkage for modeling food drying kinetics, J. Food Eng., 45, 1–10, 2000. Hernández-Pérez, J.A., Ramírez-Figueroa, E., Rodriguez-Jimenes, G., and Heyd, B., Spray Dried Yogurt Water Sorption Isotherms Prediction Using Artiﬁcial Neural Network, 12th International Drying Symposium, 28–31 August 28–31, 2000, p. 56. Hornik. K., Some new results on neural network approximation, Neural Network, 6, 1069–1072, 1993.

© 2003 by CRC Press LLC

Hornik, K., Stinchcombe, M., and White, H., Multilayer feedforward networks are universal approximations, Neural Network, 2, 359–366, 1989. Huang B. and Mujumdar, A., Use of neural networks to predict industrial dryers’ performances, Drying Technol., 11, 525–541, 1993. Karathanos, V.T., Villalobos, G., and Saravacos, G.D., Comparison of two methods of estimation of the effective moisture diffusivity from drying data, J. Food Sci., 55, 218–223, 1990. Kiranoudis C.T., Maroulis Z.B., and Marinos-Kouris D., Heat and mass transfer modeling in air drying of foods, J. Food Eng., 26, 329–348, 1993. Limin, F., Neural Networks in Computer Intelligence, McGraw-Hill, New York, 1994. Linko, P. and Zhu, Y.H., Neural networks for real time variable estimation and prediction in the control of glucoamylase fermentation, Prog. Biochem., 27, 275–283, 1992. Linko S., Luopa, J., and Zhu, Y.H., Neural networks as “software sensors” in enzyme production, J. Biotechnol., 52, 257–266, 1997. Mulet, A., Drying modeling and water diffusivity in carrots and potatoes, J. Food Eng., 22, 329–348, 1994. Ratti, C., Shrinkage during drying of foodstuffs, J. Food Eng., 23, 91–105, 1994. Rumelhart D. and Zipner D., Feature discovering by competitive learning, Cognitive Sci., 9, 75–112, 1985. Rumelhart, D.E., Hinton, G.E., and Williams, R.J., Learning internal representations by error propagation, Parallel Data Process., 1, 318–362, 1986. Techasena, O., Lebert, A., and Bimbenet, J.J., Simulation of deep bed drying of carrots, J. Food Eng., 16, 267–281, 1992. Trelea, I.C., Courtois, F., and Trystam, G., Dynamic models for drying and wet-milling quality degradation of corn using neural networks, Drying Technol., 15, 1095–1102, 1997a. Trelea, I.C., Raoult-Wack, A.L., and Trystam, G., Note: application of neural network modeling for the control of dewatering and impregnation soaking process (osmotic dehydration), Food Sci. Technol. Int., 3, 459–465, 1997b. Zogzas, N.P. and Maroulis, Z.B., Effective moisture diffusivity estimation from drying data. a comparison between various methods of analysis, Drying Technol., 14, 1543–1573, 1996. Zhu, Y.H., Rajalahti, T., and Linko, S., Application of neural networks to lysine production, Biochem. Eng, J., 62, 207–214, 1996.

© 2003 by CRC Press LLC

13

Modeling of Prato Cheese Salting: Fickian and Neural Network Approaches A.F. Baroni, M.R. Menezes, E.A.A. Adell, and E.P. Ribeiro

CONTENTS 13.1 Introduction 13.1.1 Mass Transfer Phenomena 13.1.2 Artiﬁcial Neural Networks 13.2 Materials and Methods 13.2.1 Cheese Processing 13.2.2 Cheese Sampling 13.2.3 Analytical Methods 13.3 Mathematical Modeling 13.3.1 Fickian Diffusion Model 13.3.2 Average Concentration 13.3.3 Neural Network Model 13.4 Results and Discussion 13.4.1 Cheese Composition 13.4.2 Salting Process 13.4.3 Performance of the Model Approaches 13.4.4 Statistical Analysis 13.4.5 Effective Diffusion Coefﬁcients 13.5 Conclusions Acknowledgments References

13.1 INTRODUCTION The production of cheese in Brazil is quite recent, having been consolidated from an industrial standpoint in the beginning of the twentieth century, especially after the arrival of Danish and Dutch immigrants in the state of Minas Gerais in 1920

© 2003 by CRC Press LLC

(Furtado, 1991). Prato cheese holds a leading position in Brazilian production with 57,758 tons produced yearly. Within the universe of Brazilian cheese, Prato has the highest technological standardization; it is the best characterized commercial cheese (Oliveira, 1986; Ribeiro, 1996). The expected average composition of ripened Prato cheese is 42 to 44% moisture, 26 to 29% fat, pH ranging from 5.2 to 5.4, and salt concentration 1.6 to 1.9% (Furtado and Neto, 1994). Schiftan and Komatsu (1980) carried out experiments on 50 commercial Prato cheese samples and obtained average values of 40% moisture, 47.5% fat in the dry matter, 1.7% salt, and 3.5% ash. Furtado and WolfschoonPombo (1979) reported the average composition of Prato cheese as 53.0 to 59.2% dry matter, 40.8 to 47.0% moisture, 25.3 to 30.5% fat and 47.7 to 51.5% fat in the dry matter.

13.1.1 MASS TRANSFER PHENOMENA Salting is one of the main steps of cheese production; thus, salt concentration distribution is an important parameter affecting cheese quality and acceptability. Salting plays a number of important roles in cheese, such as controlling the biochemistry of cheese ripening and the water activity of young cheeses. Salting affects the growth and survival of bacteria and the activity of cheese enzymes. Nowadays, brine salting is the most widely used salting technique in the Brazilian cheese industry. It is performed in an empirical way, and many times the distribution of the salt in the ﬁnal product is irregular. Salt is absorbed and penetrates into the cheese, while an outer ﬂux of water takes place. The amount of salt retained and water removal by the cheese depend, mostly, on brine concentration and brining time (Furtado and Neto, 1994). Fick’s law of diffusion is usually used to represent mass changes during brine salting of cheese. However, simpliﬁcations imposed on the model may affect its accuracy. Geurts et al. (1974) modeled the brine salting of Gouda cheese applying Fick’s law of diffusion. They obtained one-dimensional data on salt concentration and moisture proﬁles in cheese pieces, measured as a function of time. The authors noticed that the effective diffusion coefﬁcient of salt within the cheese was considerably lower than in free solution, due to factors such as tortuosity, viscosity, and matrix restriction effects. However, Fick’s ﬁrst law was not able to describe moisture ﬂux during the brining step. An empirical linear relationship between water content and salt concentration was applied, resulting in a coefﬁcient of proportionality of the dewatering process. Guinee and Fox (1983, 1987) found similar results for water and salt diffusion in Romano-type cheese. The same authors published a comprehensive review of salt and moisture diffusion of various cheeses in 1987. Luna and Chavez (1992) and Turhan and Kaletunç (1992) also investigated water movement during brine salting of cheese. Payne and Morison (1999) used a Maxwell–Stefan multi-component approach to model salt and water diffusion in cheese based on published data. This reﬁned approach, taking into account diffusive interactions among salt, water, and cheese matrix, still requires a large number of assumptions during the modeling.

© 2003 by CRC Press LLC

13.1.2 ARTIFICIAL NEURAL NETWORKS Artiﬁcial neural networks (ANNs) have been of interest because they enable direct modeling of nonlinear processes without requiring a prespeciﬁed detailed relationship. ANNs have been increasingly used in food and chemical engineering for several purposes. They have been applied recently in the prediction of quality attributes in beef (Park et al., 1994), the snack frying process (Huang et al., 1998b), and cheddar cheese (Muir et al., 1997); improvement of control loops in food processing (Huang et al., 1998a; Benne et al., 2000); classiﬁcation problems, such as classiﬁcation of beef (Park et al., 1994); and prediction of protein functionality (Arteaga and Nagai, 1993), moisture attained in a rehydration process of dried rice (Ramesh et al., 1996), pressure drop of non-Newtonian ﬂuids in tubes (Adhikari and Jindal, 2000), and drying in a ﬂuidized bed (Balasubramanian et al., 1996), among other applications. Artiﬁcial neural networks consist of a large number of simple interconnected nonlinear processing units (neurons) arranged in a layered structure, having adjustable connection weights. These weights are the internal parameters of the network. The input neurons are connected to the output neurons through layers of hidden nodes. Each neuron receives information in the form of inputs from other neurons and processes it through some function, typically nonlinear, called the activation function (Psichogios and Ungar, 1992). The general structure of a multilayered neural network with one output is shown in Figure 13.1. Due to the parallel structure and the ability to learn by adjusting the connection weights, ANNs can handle nonlinear relationships where mathematical models are not available without need of any previous knowledge on the relationships of the process variables (Psichogios and Ungar, 1992; Balasubramanian et al., 1996; Park et al., 1994; Adhikari and Jindal, 2000; Ramesh et al., 1996). During the network learning procedure, weights are adjusted so that the introduction of a set of inputs produces the desired set of outputs. The most widely used neural network learning method is backpropagation. This method uses an iterative gradient search technique to minimize a performance function, equal to the mean

Hidden 1

Input 1 . . .

Output 1

Input n . . .

1 Threshold value

Hidden n Threshold value

1

FIGURE 13.1 General structure of a multilayered neural network with one output.

© 2003 by CRC Press LLC

difference between the desired and the actual network outputs (Psichogios and Ungar, 1992). The neural network process model should have as few neurons in the hidden layer as possible, respecting accuracy limitations (Huang et al., 1998b). The aims of this work are to model mass transfer during brine salting of Prato cheese by a traditional phenomenological model and an empirical approach and to compare their results.

13.2 MATERIALS AND METHODS 13.2.1 CHEESE PROCESSING The cheese manufacturing trials were carried out in a dairy pilot plant of the Chemistry and Food Engineering Department of the Mauá Institute of Technology. In each experiment, 100 l of milk were used per cheese vat to produce twelve pieces 3 of cheese with a mean weight of 1.0 kg and dimensions of (11.5 × 5.5 × 5.5) cm each. During the cheesemaking process, pasteurised, refrigerated whole milk was ﬁrst heated to 32°C in a cheese vat. It was then inoculated with 1% of Probat 8/12 WIESBY culture (composed of Lactococcus lactis subsp. lactis + L. lactis subsp. cremoris + L. lactis subsp. lactis biovar. diacetilactis + Leuconostoc mesenteroides subsp. cremoris), a calcium chloride solution (23 g/100 l of milk) was added, the “urucum” coloring (10 ml/100 l of milk) was added, and calf rennet (WIESBY) was added (2 g/100 l of milk). The curd was formed during approximately 35 min and was cut to a size of ca. 0.8 to 1.0 cm. The temperature of the curd and whey mixture was raised slowly and maintained at 40°C for 60 min. Whey was subsequently drained, and the curd was placed in Prato hoops and held at room temperature (25°C) throughout pressing (2 kg weights) for 4 h, during which the cheese pieces were inverted ﬁve times, held (2 h), and then brined.

13.2.2 CHEESE SAMPLING The cheese pieces were immersed in nonagitated brine solutions of 15, 20, and 25% NaCl (w/w) at 10°C with a brine:cheese ratio of 2:1 (v/v). These are the usual conditions for Brazilian Prato cheese manufacturing. At each sampling time (30, 60, 120, 240, 360, and 480 min), one sample was removed from the brine vessel. After that, all samples and the control sample were divided into three regions: external, intermediate, and internal, as shown in Figure 13.2. These samples, classiﬁed by region, were weighed, ground, and kept at −10°C prior to chemical analysis. Note that in Figure 13.2 only two cut directions are shown; the third is the same as the vertical cut (B), once these two directions have the same dimensions (B = C = 5.5 cm).

13.2.3 ANALYTICAL METHODS In the control cheese samples, acidity, fat content (Atherton and Newlander, 1981), ash content, pH, total solids, and protein (AOAC, 1984) were analyzed. Salt content and moisture of all ground samples were determined by the Volhard method (AOAC, 1984). Analytical assays were performed in triplicate.

© 2003 by CRC Press LLC

External Intermediate Internal

B/6 B/6 B/3 B/6 B/6

y

C A/6

A/6

A/3

z

A/6 A/6 x

FIGURE 13.2 Schematic representation of cheese cut.

13.3 MATHEMATICAL MODELING 13.3.1 FICKIAN DIFFUSION MODEL Considering tridimensional unsteady state mass transfer, the phenomenon of Fickian diffusion for rectangular geometry is described by the following equation:  ∂2C A ∂2C A ∂2C A  ∂C A = Deff  + +  ∂t ∂y 2 ∂z 2   ∂x 2

(13.1)

where CA is the salt concentration in cheese and Deff is the effective diffusivity. It was assumed that the cheese was homogeneous, that brine concentration remained constant during the experiments and was equal to the salt concentration at cheese surfaces, and that no ﬁlm resistance existed between the brine and cheese faces. These assumptions correspond to an inﬁnite Biot number and unity equilibrium distribution coefﬁcient (K). To solve Equation (13.1), it was necessary to apply the solution suggested by Neumann (Crank, 1975), a product of the solutions of three plane sheets: f (x, y, z, t) = Ψ (x,t)⋅ζ (y, t)⋅ϕ (z, t)

(13.2)

The solution for a single plane sheet is given by: CA − C As = C A0 − C As

∞

∑ n=0

 − Deff (2 n + 1)2 π 2 t  8 exp   (2 n + 1)2 π 2 2a 2  

Initial condition: t = 0,

z > 0,

CA = CA0

t > 0,

z = 0,

CA = CAs

t > 0,

z = a,

∂C A =0 ∂z

Boundary conditions:

© 2003 by CRC Press LLC

(13.3)

where CA0 is the initial salt concentration in cheese, CAs is the salt concentration on the cheese surface, n is the number of terms of the series, and 2a is the plane sheet thickness size in directions x, y, and z. Since all variables of Equation (13.3) are known except Deff, the effective diffu sivity (Deff) was obtained by a least squares estimation using Microsoft Excel (1997) to ﬁt experimental data, with 100 terms of the series considered.

13.3.2 AVERAGE CONCENTRATION The proposed model predicted the average concentration of salt within cheese as a function of time. It was calculated from experimental data measured at three regions (internal, intermediate, and external) of the cheese piece; hence, one divided the total experimental volume V in integrating volumes Vi representing each region of cheese analyzed. The average concentration CA was calculated as follows: 3

∑C V i

CA =

i =1

V

i

(13.4)

13.3.3 NEURAL NETWORK MODEL A neural network model was constructed using a multilayer perceptron architecture. The network had two inputs, brining time and brine concentration, because these variables have a greater effect than other process variables on salt diffusion, and one output, average salt concentration in cheese. The training algorithm used was the well-known backpropagation algorithm, using the experimental data obtained, so as to minimize the differences between desired and calculated values of average salt concentration in cheese. Determination of the number of hidden neurons is commonly done empirically. The procedure used to choose the structure of the artiﬁcial neural network was a systematic trial and error procedure using two data sets (training and testing) in an attempt to avoid overﬁtting and underﬁtting. A description of these phenomena can be found elsewhere (Huang et al., 1998b; Arteaga and Nagai, 1993). From the 21 vectors available, containing the two inputs and the output, 18 were used to form the training set, while the remaining data formed the testing set. Data were presented to training in a random manner in order to achieve a better training. Error for comparison between structures was calculated by the sum of the squared error between the value in the training or test set and the value calculated by the ANNs. The method for choosing the number of nodes in the hidden layer is presented as follows (Zorzetto et al., 2000). Topology of the network was chosen initially to have a large number of hidden nodes, i.e., 10 nodes. Training was carried out until a minimum error for the test set was observed with this number of hidden nodes. This step is shown in Figure 13.3.

© 2003 by CRC Press LLC

5.0

0.25 testing 0.2

3.0

0.15

2.0

0.1

1.0

0.05

0.0 0

50

100

150

200

Squared error - testing

Squared error - training

training 4.0

0 250

Number of iterations

FIGURE 13.3 Squared error for training and testing sets with 10 hidden nodes.

Brine time

Average concentration

Brine concentration 1 Threshold value Threshold value

1

FIGURE 13.4 Neural network model for Prato cheese salting.

As can be observed from Figure 13.3, minimum squared error for the testing set was reached with 100 iterations. Using the same number of iterations found in this structure, i.e., 100 iterations, nodes in the hidden layer were gradually cut off, until the smallest structure that could provide the same performance was reached. Following this procedure, it was noticed that minimum error was reached using 10 nodes in the hidden layer. However, differences in the testing error among the structures were not high. Thus, it was decided to use a smaller network with ﬁve hidden nodes to accelerate the training procedure, while still having an admissible error. From this analysis, the network topology used in this work is shown in Figure 13.4.

© 2003 by CRC Press LLC

13.4 RESULTS AND DISCUSSION 13.4.1 CHEESE COMPOSITION The average pH of Prato cheese before brine salting was 5.20 ± 0.01. Results of the mean centesimal composition analysis are shown in Table 13.1.

13.4.2 SALTING PROCESS It is important to evaluate the changes of salt concentration within the cheese during the salting process to select the best operating conditions (especially salting time and brine concentration). As presented in Figure 13.5, no inﬂuence of brine concentration was observed in the internal portion of the cheese, but it is important to notice that although the values of salt concentration increased with time, the amount of salt permeated is almost null. However, at the intermediate position (Figure 13.6), differences of about 75% can be observed after 240 min between 15 and 20–25% NaCl. These variations become clear for the external region (Figure 13.7), where the solution of 15% NaCl yielded a lower salt concentration for all time periods studied. Nevertheless, no considerable differences between 20 and 25% NaCl were found even in this position.

TABLE 13.1 Composition of Control Cheese Samples (%)

Moisture Fat Fat (dry matter) Total protein Ash

Average

Standard Deviation

48.3 27.2 52.6 20.5 4.00

0.4 0.2 0.4 0.1 0.01

Internal Salt Concentration (%)

0.3 15% NaCl 0.2

20% NaCl 25% NaCl

0.1

0 0

100

200

300

400

Time (min)

FIGURE 13.5 Salt concentration at the internal position.

© 2003 by CRC Press LLC

500

600

Salt Concentration (%)

Intermediate 0.3

0.2

15% NaCl 20% NaCl

0.1

25% NaCl

0.0 0

100

200

300

400

500

600

Time (min)

FIGURE 13.6 Salt concentration at the intermediate position.

Salt Concentration (%)

External 4.0 3.0 15% NaCl 2.0

20% NaCl 25% NaCl

1.0 0.0 0

100

200

300

400

500

600

Time (min)

FIGURE 13.7 Salt concentration at the external position.

Since the initial moisture of cheese samples varied for each trial, normalized values M /Mi (moisture wet basis/initial moisture) were plotted against time (Figure 13.8). It is important to note the greater water loss of cheese treated with 25% NaCl solution—more than 10% of the initial value—when compared to the other solutions (maximum of 5% moisture loss). It can be concluded that the concentration of 15% NaCl in the solution did not provide a gradient of activity coefﬁcient high enough to maintain a driving force for efﬁcient mass transfer between the sodium chloride in solution and the liquid phase in cheese. Besides, Furtado (1991) reported that salt concentrations lower than 17% cause a smoothing of the Prato cheese skin, probably due to hydration of the surface. As can be seen, the water loss of the cheese salted in 15% NaCl brine solution was minimal, with a small moisture increase after 360 min. However, as mentioned before, the increase of brine concentration from 20 to 25% NaCl did not raise the sodium chloride concentration within the cheese for all studied conditions. This behavior can be explained by a greater outward water ﬂux of 25% NaCl solution when compared to 20% NaCl (Figure 13.8). This dewatering could lead to the formation of a hard skin on the surface of the cheese, thus avoiding

© 2003 by CRC Press LLC

1.00

M / Mi

0.98 0.95

15% NaCl 20% NaCl

0.93

25% NaCl 0.90 0.88 0

100

200

300

400

500

600

Time (min)

FIGURE 13.8 Normalized average moisture of cheese samples.

salt penetration. These assumptions agreed with the visual observation that the cheese treated in 25% NaCl concentration showed small ﬁssures on the cheese surface, probably due to shrinkage leading to modiﬁcations of skin permeability.

13.4.3 PERFORMANCE

OF THE

MODEL APPROACHES

Figure 13.9 allows a general visualization of the performance of the models for average salt concentration prediction at different brine salt concentrations. It can be observed from these plots that the neural network model had a better adjustment to the experimental data than Fick’s model did. Although experimental data did not show the expected behavior from the theoretical analysis due to experimental errors as shown in Figure 13.9(a), the neural network model had a good agreement with these data. Hence, the neural model does not require information regarding the understanding of the process, but on the other hand does not bring any additional comprehension. Theoretical knowledge and analysis of data are of principal importance during the selection of training and testing data in order to avoid discrepancy in the neural model. Fick’s model did not present a good ﬁt to the experimental data, probably due to some model assumptions, especially concerning the unity equilibrium distribution coefﬁcient, since it used a nonagitated solution and a low solution:cheese ratio. These factors could lead to a dilution of the solution with time and a varying concentration at the cheese surface.

13.4.4 STATISTICAL ANALYSIS One-way ANOVA (α = 0.01) tests were performed in order to detect signiﬁcant differences between experimental average salt concentrations and those predicted 2 by Fickian and neural models. The correlation index (R ) and the sum of squared errors (SSE) between calculated and experimental data were also calculated.

© 2003 by CRC Press LLC

0.8 Exp 15%

0.6

Neural 15% 0.4

Fick 15%

0.2 0.0 0

100

200

300

400

500

3.0

2.5 2 1.5 Exp 20% Neural 20%

1

Fick 20% 0.5 0

600

0

100

200

Time (min)

Time (min)

Exp. Data

Fick

SE F

300

400

500

600

Average Salt Concentration (%)

1.0

Average Salt Concentration (%)

Average Salt Concentration (%)

© 2003 by CRC Press LLC

1.2

2.5 2.0 1.5

SE N

Time (min)

Exp. Data

Fick

SE F

Neural 25% Fick 25%

0.5 0.0 0

Time (min)

Neural

Exp 25%

1.0

100

200

300

400

500

600

Time (min)

Neural

SE N

Time (min)

Exp. Data

Fick

SE F

Neural

SE N

0

0.000

0.090 0.0081 0.029 0.0009

0

0.000 0.120 0.0144

0.022

0.0005

0

0.000

0.150

0.0226

0.025

0.0006

30

0.306

0.301 0.0000 0.275 0.0009

30

0.373 0.558 0.0343

0.358

0.0002

30

0.433

0.588

0.0243

0.412

0.0004

60

0.344

0.368 0.0006 0.390 0.0020

60

0.656 0.785 0.0166

0.683

0.0007

60

0.704

0.827

0.0152

0.735

0.0010

120

0.470

0.518 0.0023 0.436 0.0012

120

1.129 1.105 0.0006

1.114

0.0002

120

1.205

1.165

0.0016

1.182

0.0005

240

0.670

0.729 0.0035 0.653 0.0003

240

1.728 1.551 0.0315

1.730

0.0000

240

1.829

1.637

0.0367

1.835

0.0000

360

0.876

0.890 0.0002 0.893 0.0003

360

2.211 1.888 0.1040

2.188

0.0005

360

2.256

1.995

0.0680

2.257

0.0000

480

1.086

1.025 0.0037 1.084 0.0000

480

2.349 2.170 0.0323

2.357

0.0001

480

2.565

2.294

0.0732

2.551

SUM

0.2417

SUM

0.0185

(a) 15 % NaCl SE F – Squared error Fick model SE N – Squared error neural model

0.0056

SUM

0.2337

0.0022

(b) 20 % NaCl

FIGURE 13.9 Model performances at brine salting in 15% (a), 20% (b), and 25% (c) NaCl solutions.

(c) 25 % NaCl

0.0002 0.0028

TABLE 13.2 Modeling Results Fickian R 15% NaCl 20% NaCl 25% NaCl

2

0.9893 0.9912 0.9972

Neural 2

FRatio

P

R

1.792E–03 0.002 6.759E–07

0.999 0.932 0.999

0.9933 0.9996 0.9995

FRatio

P

8.387E–06 3.600E–07 6.759E–07

0.995 0.999 0.999

Note: Fratio = Fcalculated/Ftable

TABLE 13.3 Effective Diffusion Coefﬁcients as a Function of the Salt Concentration 7

2

Deff. 10 (cm /sec) 15% NaCl 20% NaCl 25% NaCl

1.64 4.25 3.00

The data analyzed by ANOVA (Table 13.2) showed no signiﬁcant differences (p ≥ 0.01) between the experimental data and Fickian models or between the experimental data and ANN models. It is known that for a reliable statistical investigation some statistical parameters should be analyzed simultaneously, thus preventing a misinterpreted conclusion. One can observe that the better ﬁt to experimental data was obtained by the neural model, 2 which showed greater R value, lower SSE parameters, and smaller F ratios for all brine concentrations tested. The advantage of this procedure is that it is not necessary to have any previous knowledge about the process to model it. On the other hand, from the neural network it was not possible to understand the physical behavior of the process, once it was modeled from a “black box” approach. Hence, this approach is suitable when it is not necessary to have a detailed understanding of the process, or in process control strategies such as Internal Model Control (IMC). Statistical analysis for the Fickian diffusion model also showed good results, making it possible to calculate the effective diffusivity coefﬁcient, which is related to the mass transfer rate. However, some attention must be paid to Fick’s model because of the previous discussions regarding Figure 13.9.

13.4.5 EFFECTIVE DIFFUSION COEFFICIENTS Effective diffusion values were affected by brine concentration. The brine solution of lowest concentration, 15% NaCl, presented the lowest Deff (Table 13.3). On the other hand, the 20% NaCl solution showed the highest effective diffusion coefﬁcient,

© 2003 by CRC Press LLC

rather than 25% NaCl. Reduced effective diffusivity with increasing salt concentration has been previously reported (Turhan and Kalentuç, 1992) for Turkey white cheese. The authors associated this occurrence with a lower outer water ﬂux in relation to inner salt penetration for the solutions of lower concentration. Regardless, Deff values are similar to those presented by Zorrilla and Rubiolo (1996) for Fynbo cheese and slightly slower than those reported by Turhan and Kalentuç (1992), probably due to compositional differences.

13.5 CONCLUSIONS Although statistical analysis demonstrated that neural network as well as Fickian diffusion models can successfully model salt diffusion in Prato cheese, observations on the experimental data plotted together with the applied models showed a noticeably better ﬁt with the ANN approach, mainly because of the inadequacy of some assumptions on the resolution of Fick’s law. No considerable difference in salt concentration as a function of time was detected between brine concentrations of 20 and 25%. However, cheese treated in 25% NaCl solution had a larger moisture loss than that brined at 20% NaCl. For 15% NaCl solution, the salt penetration and water removal were less intense. Marginal salt uptake was found at the internal and intermediate regions even after 480 min of processing. Effective diffusion coefﬁcients were affected by brine concentration. A maximum value was found at the 20% NaCl solution rather than 25% NaCl, due to greater dehydration of the cheese samples treated with the latter solution.

ACKNOWLEDGMENTS The authors gratefully acknowledge Prof. Walter Borzani and Prof. Marcello Nitz for their helpful discussions and suggestions and students Graziela dos Santos Viola and Rafaela R. C. Bandeira de Mello for their valuable assistance during the experiments.

REFERENCES Adhikari, B. and Jindal, V.K., Artiﬁcial neural networks: a new tool for prediction of pressure drop of non-Newtonian ﬂuid foods through tubes, J. Food Eng., 46, 43–51, 2000. AOAC (Association of Ofﬁcial Analytical Chemists), Ofﬁcial Methods of Analysis, 14th ed., Williams, S., Ed., AOAC, Washington, DC, 1984. Arteaga, G.E. and Nagai, S., Predicting protein functionality with artiﬁcial neural networks: foaming and emulsifying properties, J. Food Sci., 58, 1152–1156, 1993. Atherton, H. and Newlander, J.A., Chemistry and Testing of Dairy Products, 4th ed., AVI, Westport, CT, 1981. Balasubramanian, A., Panda, R.C., and Ramachandra Rao, V.S., Modelling of a ﬂuidized bed drier using artiﬁcial neural network, Drying Technol., 17, 1881–1889, 1996. Benne, M., Grondin-Perez, B., Chabriat, J.P., and Hervé, P., Artiﬁcial neural networks for modelling and predictive control of an industrial evaporation process, J. Food Eng., 46, 227–234, 2000. Crank, J., The Mathematics of Diffusion, Oxford University Press, Oxford, 1975.

© 2003 by CRC Press LLC

Furtado, M.M., A Arte e a Ciência do Queijo, Editora Globo S.A., São Paulo, 1991. Furtado, M.M. and Neto, J.P.M.L., Tecnologia de Queijos: Manual Técnico para Produção Industrial de Queijo, Editora Dipemar Ltda, São Paulo, 1994. Furtado, M.M. and Wolfschoon-Pombo, A.F., Fabricação de queijo prato e minas: estudo do rendimento. Parte II. Previsão da gordura no extrato seco, Rev. Instit. Laticínios Cândido Tostes, 34, 3–13, 1979. Geurts, T.J., Walstra, P., and Mulder, H., Transport of salt and water during salting of cheese. 1. Analysis of the processes involved, Neth. Milk Dairy J., 28, 102–129, 1974. Guinee, T.P. and Fox, P.F., Sodium chloride and moisture changes in Romano-type cheese during salting, J. Dairy Res., 50, 511–518, 1983. Guinee, T.P. and Fox, P.F., Salt in cheese: physical, chemical and biological aspects, in Fox, P.F., Cheese: Chemistry, Physics and Microbiology. 1. General Aspects, Elsevier Applied Science, London, 1987. Huang, Y., Whittaker, A.D., and Lacey, R.E., Neural network prediction modeling for a continuous snack food frying process, Trans. ASAE, 41, 1511–1517, 1998a. Huang, Y., Whittaker, A.D., and Lacey, R.E., Internal model control for a continuous snack food frying process using neural networks, Trans. ASAE, 41, 1519–1525, 1998b. Luna, J.A. and Chavez, M.S., Mathematical model for water diffusion during brining of hard and semi-hard cheese, J. Food Sci., 57, 55–58, 1992. Muir, D.D., Hunter, E.A., and Banks, J.M., Aroma of cheese. 2. Contribution of aroma to the ﬂavour of cheddar cheese, Milchwissenschaft, 52, 85–88, 1997. Oliveira, J.S., Queijos: Fundamentos Tecnológicos, 2nd ed., Ícone Editora, São Paulo, 1986. Park, B., Chen, Y.R., Whittaker, A.D., Miller, R.K., and Hale, D.S., Neural network modeling for beef sensory evaluation, Trans. ASAE, 37, 1547–1553, 1994. Payne, M.R. and Morison, K.R., A multi-component approach to salt and water diffusion in cheese, Int. Dairy J., 9, 887–894, 1999. Psichogios, D.C. and Ungar, L.H., A hybrid neural network – ﬁrst principles approach to process modeling, AIChE J., 38, 1499–1511, 1992. Ramesh, M.N., Kumar, M.A., and Srinivasa Rao, P.N., Application of artiﬁcial neural networks to investigate the drying of cooked rice, J. Food Process Eng., 19, 321–329, 1996. Ribeiro, E.P., Aplicação de Ultraﬁltração de Leite no Processo de Fabricação de Queijo Prato, thesis, Universidade Estadual de Campinas, Brasil, 1996. Schiftan, T.Z. and Komatsu, I., Estudos sobre a composição do queijo Prato consumido na cidade de São Paulo, Rev. Instit. Laticínios Cândido Tostes, 35, 33–38, 1980. Turhan, M. and Kaletunç, G., Modeling of salt diffusion in white cheese during long-term brining, J. Food Sci., 57, 1082–1085, 1992. Zorrilla, S.E. and Rubiolo, A.C., Modelling NaCl and KCl movement in Fynbo cheese during salting, J. Food Sci., 59, 976–980, 1994. Zorzetto, L.F.M., Maciel Filho, R., and Wolf-Maciel, M.R., Process modelling development through artiﬁcial neural networks and hybrid models, Comput. Chem. Eng., 24, 1355–1360, 2000.

© 2003 by CRC Press LLC

14

Inﬂuence of Vacuum Pressure on Salt Transport during Brining of Pressed Curd A. Chiralt, P. Fito, C. Gonzalez-Martínez, and A. Andrés

CONTENTS 14.1 Introduction 14.2 Materials and Methods 14.2.1 Cheesemaking 14.2.2 Salting Treatments 14.2.3 Analysis of the Concentration Proﬁles 14.2.4 Analytical Controls 14.3 Results and Discussion 14.3.1 NaCl Concentration Proﬁles 14.3.2 Modeling Salt Transport through Proﬁle Development 14.4 Conclusions Nomenclature Acknowledgments References

14.1 INTRODUCTION Salting of cheese is usually carried out by brine immersion (BI) for a lengthy period of time (24–48 h, depending on the cheese size), and this causes technological and quality problems in cheesemaking. The process implies the management of great amounts of brine and the development of sharp salt concentration proﬁles in the cheese pieces, which may provoke ripening problems in some cases (Guinee and Fox, 1987). Recently, a new salting procedure has been described (vacuum impregnation, VI), which makes the salting process shorter (thus reducing the involved brine volumes) and the salt concentration proﬁle in cheese ﬂatter (Chiralt and Fito, 1997; Andrés et al., 1997). This new process is based on the action of hydrodynamic

© 2003 by CRC Press LLC

mechanisms (HDM) associated with pressure changes. In the VI process, vacuum pressure is applied in the salting tank at the beginning of the process for a time t1, after which the atmospheric pressure is restored for a time t2. During the vacuum period, the occluded gas in the pressed curd is expanded and ﬂows out. When atmospheric pressure is restored, the residual gas is compressed, leading to the entry of the external brine into the curd pores. In this way, a greater salt uptake occurs in the cheese pieces than when using the conventional immersion for the same salting time, and a different salt proﬁle is achieved (Andrés et al., 1997). Salting of cheese by BI has been described as a diffusion process, but capillary mechanisms may also play an important role in the salt uptake (Geurts et al., 1980). The capillary input of the external brine in the curd pores can contribute to quite an extent to the total salt gain when subatmospheric pressure is applied in the salting tank. Capillary penetration in a pore occurs coupled with the compression of the occluded internal gas. The volume fraction of the sample penetrated by the external liquid (Xc) is a function of the capillary pressure (pc), the pressure in the system (p), and the effective porosity of the product (ε) (Fito, 1994; Fito and Pastor, 1994). According to Equation (1), the lower the pressure in the system (p), the greater the capillary penetration. Xc = ε [pc/(p + pc)]

(14.1)

When atmospheric pressure (p2) is restored in the tank at vacuum pressure (p1), the HDM react, leading to a great penetration of external liquid. The volume fraction of the sample penetrated by the external liquid (XHDM) has been modeled by Equations (14.2) and (14.3) in stiff matrices (Fito, 1994). Nevertheless, pressure changes in the system can also promote sample deformations when the solid matrix exhibits a viscoelastic behavior (Fito et al., 1996). The restoring of atmospheric pressure after a vacuum period can promote curd compression and partial collapse of its pores, decreasing the effectiveness of capillary phenomena for salting. XHDM = ε (1 – 1/r)

(14.2)

r = (p2/p1) + (pc/p1)

(14.3)

The aim of this work is to analyze the contribution of the different mass transfer mechanisms in cheese salting in order to minimize the salting time by using subatmospheric pressures. Analysis of the concentration proﬁles in a product throughout a mass transfer process is a good approach to clarify the mass transfer mechanisms involved in the process. In this sense, NaCl and moisture concentration proﬁles have been analyzed in cheeses at different times of salting by using: • BI (brine immersion): salting process at atmospheric pressure • VI (vacuum impregnation): salting process at vacuum pressure (p1) • PVI (pulse vacuum impregnation): a two-step salting process; the former (t1) at vacuum pressure (p1), and the latter (t2) at atmospheric pressure (p2).

© 2003 by CRC Press LLC

14.2 MATERIALS AND METHODS 14.2.1 CHEESEMAKING Cheeses were processed at the food technology pilot plant of the Universitat Autónoma of Barcelona. Ewe’s milk from Manchega sheep was supplied by the university dairy farm. Cheeses were manufactured from pasteurized milk (15 sec at 72°C), in a 250 l vat, according to standard protocol. Milk (100 l in each batch) was heated to 31°C, and 2% lactic starter (Lactococcus lactis ssp. lactis plus L. lactis ssp. cremoris; AM Larbus S.A., Barcelona) was added. After 35 min, the milk coagulum was cut into 8–10 mm cubes with a wire knife. The curds were heated at a rate of 1°C per 5 min to reach 36°C and held at this temperature for 10 min prior to wheying. The curd was molded into cylindrical pieces (10 cm high and 18 cm diameter) of about 2.5 kg and pressed following two steps: ﬁrst, for 1 h at 800 Pa; second, cheeses were turned upside down and pressed again for 3 h at 1600 Pa.

14.2.2 SALTING TREATMENTS Salting treatments were carried out with a 24% (w/w) brine in a stirred tank at 10°C. A pressure of 50 mbar was applied during the vacuum periods. Development of salt and moisture concentration proﬁles throughout the salting process was analyzed in cylindrical samples of cheese (6 cm diameter, 10 cm high), the lateral surface of which was covered with a ﬁlm in order to avoid radial mass transfer during salting. The experiments were carried out using two curd batches and applying different salting times (Table 14.1): t1, time at p1 = 50 mbar and t2, time at atmospheric pressure (p2).

14.2.3 ANALYSIS

OF THE

CONCENTRATION PROFILES

A sharp tubular cork borer (20 mm internal diameter) was used to take out cylindrical samples from salted curd pieces in the axial direction at different times during salting. Starting at the surface in direct contact with the brine, each sample cylinder was TM sliced into disks (1.5 mm thick) with a tissue slicer EMS (Fort, Washington) model OTS-3000–04. The distance to the interface (d) of the disks of each cylinder core was identiﬁed by the order of slicing. At each distance to the interface, moisture and salt were analyzed in respective disks.

TABLE 14.1 Salting Treatments for the Analysis of the Salt Concentration Proﬁle Development Salting Treatment

t1 (h) p1 = 50 mbar

t2 (h) p2 = 1013 mbar

Curd Batch

BI PVI VI

0 0.5 0.5; 2; 8; 17

0.5, 2, 8, 17 0; 1.5; 7.5; 16.5 0

1 2 1, 2

© 2003 by CRC Press LLC

14.2.4 ANALYTICAL CONTROLS For sodium chloride determination, samples were homogenized in distilled water at 9000 r/min in an ULTRATURRAX T25 for 5 min and centrifuged to remove any ﬁne debris present in the sample. An aliquot of exactly 500 µl of centrifuged sample was taken and titrated in a chloride analyzer (Sherwood, Mod. 926). Moisture content was determined by drying of the samples at 105°C until a constant weight was reached.

14.3 RESULTS AND DISCUSSION 14.3.1 NACL CONCENTRATION PROFILES Figure 14.1 shows the NaCl concentration proﬁles for each treatment at 8 and 17 h salting times, in terms of the reduced salt concentration Y(t,d) (Equation (14.4)) in the cheese liquid phase (water plus salt), as a function of the distance d to the interface. In Equation (14.4), z is the salt mass fraction in the cheese liquid phase at time t (zt), t = 0 (z0) and at equilibrium (ze). The equilibrium value has been taken to be equal to the brine concentration, according to previous studies (González et al., 1999). By comparison with the concentration proﬁles in curds from the same production batch, at a determined time of salting, it can be observed that when vacuum pressure was used, salt penetration was deeper than in the traditional BI method because of the capillary mechanisms, especially in the lower part of the cheeses where more pores exist. The effectiveness of the VI process is greater than that of PVI. Y1

Y1

(a)

0.8

0.8

0.6

0.6

0.4

0.4

0.2

d(mm)

0

(b)

0.2

d(mm)

0 0

10

20

30

40

50

0

10

20

30

40

50

Y1

Y1

(c)

0.8 0.6

0.6

0.4

0.4

0.2

d(mm)

0

(d)

0.8

0.2

d(mm)

0 0

10

20

30

40

50

0

10

20

30

40

50

FIGURE 14.1 Experimental concentration proﬁles in the upper (a and c) and lower (b and d) part of the curd, at 8 h (a and b) and 17 h (c and d) of salting by the different procedures (BI—batch1: ο, PVI—batch2: ◊, VI—batch1: 䊐, VI—batch2: ∆).

© 2003 by CRC Press LLC

This suggests that the pore collapses to quite an extent when atmospheric pressure is restored, inhibiting the HDM penetration. After 17 h of salting, the concentration proﬁle was not fully developed in cheeses salted by BI and PVI. However, 8 and 17 h were enough to reach a fully developed proﬁle, in the lower and upper part respectively, of curd pieces salted by VI. Differences in porosity of the lower and upper part of the curd (in relation to the plug position during pressing) have been explained in terms of the viscoelastic response during pressing (Chiralt and Fito, 1997). This leads to heterogeneous salt transport in the piece, especially if hydrodynamic mechanisms are promoted. Y=

14.3.2 MODELING SALT TRANSPORT DEVELOPMENT

zt − ze z0 − ze

(14.4)

THROUGH

PROFILE

A pseudodiffusional approach was used to model salt transport in the cheese liquid phase. Equation (14.5) (Crank, 1975) was ﬁtted to the experimental proﬁles at the different salting times by using a nonlinear optimization method to obtain the effective pseudo diffusion coefﬁcient De for each treatment and curd zone. Equation (14.5) has been applied considering a number of terms (value of n) great enough to satisfy Equation (14.6). The obtained values of De for the different samples are shown in Table 14.2. Despite the scarce physical meaning of De when there is a notable action of hydrodynamic mechanisms, De values reﬂect the differences observed in the proﬁles. Nevertheless, great deviations in the predicted proﬁles with respect to the experimental points were observed. Y(l, t ) =

4 π

∞

( − )n

 − De t(2 n + 1)2 π 2  (2 n + 1)πl  cos 4e 2 2e 

∑ 2n1+ 1 exp n=0

Y (l, t ) − Yn −1 (l, t ) Yn (l, t )

< 0.01

(14.6)

TABLE 14.2 Values of the Pseudo Diffusion Coefﬁcient (De × 10 2 10 , m /sec) Obtained from the Modeling of the Concentration Proﬁle for Each Treatment and Curd Zone (Lower and Upper Part) Treatment BI-1 PVI-2 VI-1 VI-2

© 2003 by CRC Press LLC

(14.5)

Upper Part

Lower Part

4.4 6.1 4.6 9.5

5.2 8.4 7.7 12.3

Ypred 1.00

0.95

0.90

0.85

0.80 0.80

0.85

0.90 Yexp (a)

0.95

1.00

Ypred 1.00

0.95

0.90

BI-1 VI-1 VI-2

0.85

PVI-2

0.80 0.80

0.85

0.90 Yexp (b)

0.95

1.00

FIGURE 14.2 Comparison of experimental Y mean values with those predicted from the models: (a) pseudodiffusional model (PDM) for the different salting treatments in the lower (closed symbols) and upper (open symbols) part of the curd, (b) PDM (䊏) and advancing disturbance front (ADF: ◊) models, for all treatments.

Mean values of Y were calculated for each case by integrating the concentration proﬁles at a determined salting time, and their values were compared with those obtained from the De values applying Equation (14.7) (Crank, 1975). Figure 14.2a shows the comparison between predicted and experimental values, and a greater deviation for treatments carried out under vacuum conditions can be observed. Y = 1− 2

 De t   πl 2 

0.5

(14.7)

On the basis of these results, a model developed to predict concentration proﬁles was applied (Fito et al., 1998; Salvatori et al., 1998; Salvatori et al., 1999). This model

© 2003 by CRC Press LLC

TABLE 14.3 Location of the Advancing Disturbance Front (df; mm) in the Upper (UP) and Lower (LP) Part of the Curd, as a Function of Salting Treatment and Time BI-1

PVI-1

VI-1

VI-2

Salting Time (h)

UP

LP

UP

LP

UP

LP

UP

LP

0.5 2 8 17

7.7 13.1 24.4 30.5

10.5 13.8 26.7 30.1

7.7 13.5 21.1 31.2

10.5 16.8 26.4 32.2

9.3 19.8 33.9

10.8 30.8

20.1 27.0 37.7

22.6 25.9

a

a

a

a

a

a

a

Fully developed proﬁle.

TABLE 14.4 Parameters df0 and ν Describing the ADF Rate in the Upper (UP) and Lower (LP) Part of the Curd Salted by Different Treatments BI-1

PVI-1

VI-1

VI-2

Parameter

UP

LP

UP

LP

UP

LP

UP

LP

df0 ν

3.62 6.66

7.06 6.13

3.62 6.66

7.06 6.13

2.25 11.4

0 20.5

14.7 8.19

15.6 8.5

is based on the deﬁnition of an advancing disturbance front (ADF) in the material where mass transport occurs. ADF has been deﬁned as a virtual plane that separates the zone of the product near the interface where the original concentration status has been disturbed by mass transport phenomena from the rest of the sample where no changes in concentration or mass ﬂuxes are evident. The location of the ADF in the cheese samples has been estimated as the distance (df) to the plane sheet interface where Y(t,d) = 0.99. Table 14.3 gives the values of df for the different treatments at each time. The df vs. time relationships have been modeled by Equation (14.8), where df0 and ν parameters reﬂect the particular inﬂuence of the properties of each curd on salting rate (González, 1999). Table 14.4 gives the obtained values for each treatment. The advanced rate of ADF in the cheese dropped as the salting process progressed and was greatly affected by the curd porosity and water content in VI treatments. d f = d f 0 + ν ⋅ t 0.5

(14.8)

When the values of Y(t,d) were plotted as a function of a reduced distance to the interface z (Equation (14.9)) according to the ADF model, two generalized

© 2003 by CRC Press LLC

1 0.8 0.6 Y 0.4 0.2 0 0

0.2

0.4

z

0.6

0.8

1

0.6

0.8

1

(a) 1 0.8 0.6 Y 0.4 0.2 0 0

0.2

0.4

z (b)

FIGURE 14.3 Generalized proﬁles in terms of the reduced distance to the interface (z) for VI (a) and BI/PVI (b) treatments (VI-1: ο, VI-2: ∆, BI-1: ◊, PVI-2: +). Line: ADF ﬁtted model.

proﬁles were obtained. One of these proﬁles corresponds to the vacuum treatments (VI) and the other to the BI and PVI treatments (Figure 14.3). The ADF model, shown in Equation (14.10), could be ﬁtted to the points of these generalized proﬁles by a nonlinear procedure for z < 1, thus obtaining the characteristic model parameters (K and z0). In the ADF model, K is a facility coefﬁcient to mass transport of the system, whereas z0 is a reduced distance near the interface immediately equilibrated with the external medium (Fito et al., 1998). The obtained values of z0 in all cases were zero, and K values were 1.075 and 1.145, respectively, for VI and BI/PVI

© 2003 by CRC Press LLC

treatments. The close ﬁtting of this model to experimental points can be seen in Figure 14.3 (lines). At z ≥ 1, Y = 1 for all treatments. z = d / df Y=

K( z − z 0 ) (z − z 0 ) + (1 − z 0 ) ⋅ (K − 1)

(14.9) (14.10)

The ADF model also allows prediction of the mean values of Y(t) in the cases where samples were not completely affected by disturbance (concentration proﬁle not fully developed) (Fito et al., 1998). Equation (14.11) gives the Y(t) mean values as a m function of K and the maximum z value (zt ) of each sample at each time (Salvatori et al., 1999). Figure 14.3b shows the close agreement between experimental and predicted values.  1   1   Y( t ) = 1 − 1 − K 1 + (K − 1) ln1 −    m      z t  K  

(14.11)

It can be observed in addition that the ADF model allows prediction of the mean reduced concentrations better than the pseudodiffusional model (PDM), but only for those situations when the concentration proﬁle is not fully developed. Nevertheless, in practical terms, this situation occurs in industrial salting of this kind of cheese for the usual overall amounts of salt required. The common Y mean values range between 0.88 and 0.84, which correspond to salt levels of 1.5–2.0% in the cheese. These values are lower than the mean value of Y in the sample disturbed zone (z < 1) for the BI and PVI treatments and of the order of those reached in the VI treatments. Therefore, at the end of the usual salting process, the cheese status corresponds to the non-fully developed concentration proﬁle, and the ADF model will be applicable with more accurate predictions than those reached with the SDM.

14.4 CONCLUSIONS Brining at vacuum pressure greatly enhances salting kinetics due to the promotion of hydrodynamic transport coupled with diffusion in the cheese liquid phase. The salt concentration proﬁles developed during VI salting can be better modeled by an advancing disturbance front model than by diffusional equations. Curd porosity and moisture greatly affect salt transport kinetics, especially when hydrodynamic mechanisms are promoted in the curd pores by vacuum pressure. The greater the curd porosity and moisture, the faster the salting process. Therefore, special control of these variables will be recommended during cheese production, ensuring a homogeneous salt uptake during the brining process.

NOMENCLATURE d Distance in the sample to the interface (m) df Distance of the advancing disturbance front (ADF) to the interface (m) 2 De Pseudodiffusional coefﬁcient (m /sec)

© 2003 by CRC Press LLC

e K l p t Y z zt z0

Sample half-thickness (m) ADF model parameter (dimensionless) Distance from any point in the sample to center (m) Pressure (mbar) (subscript c, capillary; 1, at the vacuum step; 2, atmospheric) Salting time (sec) Reduced driven force Reduced distance to the sample interface (d/df) Mass fraction of salt in the cheese liquid phase (water plus salt) at time t, (subscript e, equilibrium; 0, initial value) ADF model parameter (dimensionless)

ACKNOWLEDGMENTS The authors thank the Comisión Interministerial de Ciencia y Tecnología (Spain) and CYTED program for their ﬁnancial support.

REFERENCES Andrés, A., Panizzolo, L., Camacho, M.M., Chiralt, A., and Fito, P., Distribution of salt in Manchego type cheese after brining, in Engineering and Food at ICEF 7, Jowitt, R., Ed., Shefﬁeld Academic Press, Shefﬁeld, 1997, pp. 133–136. Chiralt, A. and Fito, P., Salting of Manchego cheese by vacuum impregnation, in Food Engineering 2000, Fito, P., Barbosa-Cánovas, G., and Ortega-Rivas, E., Eds., Chapman and Hall, New York, 1997, pp. 215–230. Crank, J., The Mathematics of Diffusion, Oxford University Press, London, 1975, pp. 44–68. Fito, P., Modelling of vacuum osmotic dehydration of food, J. Food Eng., 22, 313–328, 1994. Fito, P., Andrés, A., Chiralt, A., and Pardo, P., Coupling of hydrodynamic mechanism and deformation relaxation phenomena during vacuum treatments in solid porous foodliquid systems, J. Food Eng., 27, 229–240, 1996. Fito, P., Chiralt, A., Barat, J., Salvatori, D., and Andrés, A., Some advances in osmotic dehydration of fruits, Food Sci. Technol. Int., 4, 329–338, 1998. Fito, P. and Pastor, R., Non-diffusional mechanism occurring during vacuum osmotic dehydration, J. Food Eng., 21, 513–519, 1994. Geurts, T.G., Walstra, P., and Mulder, P., Transport of salt and water during salting of cheese. 2. Quantities of salt taken up and of moisture lost, Neth. Milk Dairy J., 34, 229–254, 1980. González, C., Salado de Quesos Tipo Manchego por Impregnación a Vacío e Inﬂuencia en la Maduración, Ph.D. thesis, Universidad Politécnica de Valencia, Spain, 1999. González, C., Fuentes, C., Andrés, A., Fito, P., and Chiralt, A., Effectiveness of vacuum impregnation brining of Manchego-type curd, Int. Dairy J., 9, 143–148, 1999. Guinee, T.P. and Fox, P.F., Salt in cheese: physical, chemical and biological aspects, in Cheese: Physics and Microbiology, Vol. 1., Fox, P.F., Ed., Elsevier Applied Science, London, 1987, pp. 251–297. Salvatori, D., Andrés, A., Chiralt, A., and Fito, P., Osmotic dehydration progression in apple tissue II: Generalised equations for concentration prediction, J. Food Eng., 42, 133–138, 1999. Salvatori, D., Andrés, A., Albors, A., Chiralt, A., and Fito, P., Structural and compositional proﬁles in osmotically dehydrated apple, J. Food Sci., 63, 606–610, 1998.

© 2003 by CRC Press LLC

15

Effects of Water Concentration and Water Vapor Pressure on the Water Vapor Permeability and Diffusion of Chitosan Films J.L. Wiles, P.J. Vergano, F.H. Barron, J.M. Bunn, and R.F. Testin

CONTENTS 15.1 Introduction 15.2 Materials and Methods 15.2.1 Water Vapor Permeability Coefﬁcients 15.2.2 Solubility Coefﬁcients 15.2.3 Diffusion Coefﬁcients 15.2.4 Statistical Analysis 15.3 Results and Discussion 15.4 Conclusions Nomenclature References

15.1 INTRODUCTION The mechanism for water vapor permeation through hydrophilic ﬁlms is extremely complex. The complexity is due to nonlinear water sorption isotherms and water content dependent diffusivities (Schwartzberg, 1986). Hydrophilic ﬁlms are usually used in applications where water vapor migration is not detrimental or water solubility is advantageous (Donhowe and Fennema, 1994). The water vapor transmission of hydrophilic ﬁlms varies nonlinearly with the water vapor partial pressure gradient. Since chitosan ﬁlms are cationic and strongly hydrophilic, water interacts with the polymer matrix and increases permeation for water vapor (Pascat, 1986).

© 2003 by CRC Press LLC

TABLE 15.1 Water Vapor Permeability from Prior Studies on Chitosan Films Water Vapor Permeability (g/m/sec/mmHg) 1.30 4.79 3.35 2.65 4.42

× × × × ×

−8

10 −9 10 −9 10 −8 −9 10 to 8.15 × 10 −9 −9 10 to 7.79 × 10

Reference

Conditions

Description of Film

Muzzarelli et al., 1974 Wong et al., 1992 Butler et al., 1996 Caner, et al., 1998 Park, 1998

38.7°C & 90% RH Ambient 25°C & 50% RH 25°C & 50% RH 25°C & 50% RH

Chitosan membranes Chitosan–lipid ﬁlms Chitosan–plasticizer Chitosan–plasticizer Chitosan–plasticizer

Most polymer plastic ﬁlms demonstrate ideal or Fickian permeability behavior because little or no interaction between the ﬁlm and the permeant occurs. Thus, Fick’s ﬁrst and Henry’s laws apply. Films that are hydrophilic in nature or react to organic vapors will demonstrate non-Fickian behavior because of the interaction between the permeant and the polymer ﬁlm. The ﬁlm’s thickness, moisture content, temperature, time, and pressure affect the water vapor permeation rate. For experimental purposes, most of these variables can be controlled during testing. Other inﬂuences on the permeation process include the nature of the polymer and the nature of the permeant (Pascat, 1986). Diffusion coefﬁcients (D) for hydrophilic ﬁlms such as chitosan ﬁlms may tend to increase with increasing water vapor concentration. Diffusion measured in steady state is a mean value over the range of concentration with ﬂux still being constant through the ﬁlm. Since D is concentration dependent, the concentration gradient is not linearly dependent on distance through the ﬁlm (Crank, 1975). Table 15.1 shows the water vapor permeability coefﬁcients of chitosan ﬁlms from previous work with this biopolymer. The hygroscopicity of chitin and chitosan is comparable to that of cellulose derivatives, but chitin’s surface is less active and permeable to water (Muzzarelli, 1977). Due to chitin’s insolubility in water, it is chemically treated to increase water solubility. As a result of this treatment, ﬁlms made with chitosan have signiﬁcant uptake of water and water vapor. At the present, no research has studied the permeability characteristics of chitosan ﬁlms over a wide range of relative humidity (RH) conditions. The water vapor permeability (WVP) characteristic of chitosan ﬁlm’s dependency on water concentration is important because of the magnitude of its effects. Hauser and McLaren (1948) developed a model to predict the WVP of hydrophilic ﬁlms under any RH gradient. Models are used to predict WVP over a large range of relative humidity conditions. McHugh and Krochta (1994) used the Hauser and McLaren method to predict WVPs of whey protein isolate and glycerin ﬁlms. They concluded that RH had an exponential effect on the WVP of whey protein ﬁlms. They recommended that all researchers who study edible ﬁlms should consider this method. The objective of this study was to determine the water vapor permeability, solubility, and diffusion coefﬁcients of chitosan ﬁlms over a wide range of relative humidity conditions at 25°C. Previously measured water vapor transmission rates

© 2003 by CRC Press LLC

TABLE 15.2 Measured WVTR, Thickness, and Water Concentration at Various Relative ο Humidity Conditions at 25 C for Chitosan Films % Relative Humidity

LSMEANS of 2 WVTR (g/m /day)

11 23 33 43 53 69 75 84

6.65 14.2 36.5 126 278 504 719 1140

LSMEANS of thickness (m) 3.98 3.93 3.98 3.92 3.98 4.42 4.85 5.93

× × × × × × × ×

−5

10 −5 10 −5 10 −5 10 −5 10 −5 10 −5 10 −5 10

LSMEANS of concentration 3 (g/m ) 4.64 6.36 8.36 1.09 1.38 1.99 2.28 2.76

× × × × × × × ×

4

10 4 10 4 10 5 10 5 10 5 10 5 10 5 10

WVTR × Thickness (g/m/day) 2.64 5.58 1.45 4.95 1.11 2.23 3.48 6.76

× × × × × × × ×

−4

10 −4 10 −3 10 −3 10 −2 10 −2 10 −2 10 −2 10

(WVTR) and thickness changes due to water vapor sorption, which are given in Table 15.2, were used to determine the WVP of chitosan ﬁlms (Wiles, 2000; Wiles et al., 2000). Before determining the permeability characteristics of chitosan ﬁlms, changes in thickness due to swelling by water vapor sorption were measured (Wiles, 2000) and applied to this study.

15.2 MATERIALS AND METHODS Chitosan ﬁlms of three levels of deacetylation (91.7%, 84.0%, 73.0%) were prepared by casting a 2% chitosan solution onto a level glass plate. Water sorption isotherms were determined using the method of discontinuous registration of weight changes in a static system (Labuza, 1984). Two standard test methods were used to determine WVTR of chitosan ﬁlms (Wiles et al., 2000). All ﬁlm samples were conditioned for 2 weeks at their speciﬁed relative humidity and 25°C. Chitosan ﬁlms were tested according to ASTM E96–80 (ASTM, 1980), the Desiccant Method, and ASTM F 1249–90 (ASTM, 1990) on the Permatran W600 (MOCON, Minneapolis, MN).

15.2.1 WATER VAPOR PERMEABILITY COEFFICIENTS 2

Equation (15.1) expresses water vapor permeability coefﬁcients in units of g⋅m/m / day/mmHg, achieved by measuring the WVTR, multiplying it by the thickness, and dividing by the water vapor partial pressure difference. Thickness measurement takes swelling into account. A mathematical model was used to describe swelling as a function of ambient water vapor pressure (Wiles, 2000). The model was based on data obtained by using the scanning electron microscopy (SEM) and optical microscope to measure swelling. The thickness model was ﬁtted with a polynomial curve 2 with a R of 1.00. WVP = WVTR l/(p1 − p1)

© 2003 by CRC Press LLC

(15.1)

WVP is deﬁned as the steady amount of water vapor ﬂow in unit time through unit area of a ﬁlm of unit thickness driven by water vapor pressure difference across the ﬁlm’s parallel surfaces under speciﬁed temperature and RH conditions (ASTM, 1980).

15.2.2 SOLUBILITY COEFFICIENTS Solubility coefﬁcient (S) can be derived from the moisture sorption isotherm. From the measurement for determining the moisture sorption isotherm, the amount of water (grams) per unit of water vapor pressure (mmHg) is measured in a volume 3 (m ). The volume measurement takes swelling into account.

15.2.3 DIFFUSION COEFFICIENTS Diffusion coefﬁcients are calculated at each water vapor pressure by using the measured value of WVP and dividing it by the measured value of S at the same water vapor pressure. D=

WVP S

g m 2 m ⋅ sec⋅ mmHg = g sec 3 m ⋅ mmHg

(15.2)

If ﬂux (WVTR) and concentrations are known, another method uses the equation: D = F(l)/∆C

(15.3)

F is WVTR, l is the ﬁlm’s thickness, and ∆C is the change in water concentration in the ﬁlm across the gradient. In the calculation of D, some assumptions are made about the permeation process in chitosan ﬁlms. Diffusion and swelling are limited to one dimension, i.e., perpendicular to the ﬁlm’s surface, which is parallel to thickness. It is assumed that the water vapor pressure gradient is linear across the ﬁlm in the range where a particular value of D is calculated.

15.2.4 STATISTICAL ANALYSIS The experimental design used was a randomized block design performed in three replications with 290 permeation and 682 sorption data measurements. Least-squares means (LSMEANS) were calculated for thickness, permeability, diffusion, and solubility coefﬁcients using the General Linear Models (GLM) of SAS (SAS, 1996). It was determined that no signiﬁcant difference existed in water vapor permeability characteristics among the types of chitosan ﬁlms made using 91.7%, 84.0%, and 73.0% deacetylated chitosan. Therefore, the data points are all compiled together in this study for further statistical analysis. LSMEANS of measured values were analyzed

© 2003 by CRC Press LLC

and ﬁtted with curves using a nonlinear (NLIN) procedure in SAS. The NLIN procedure uses the Gauss–Newton iterative method to regress the residuals onto the partial derivatives of the model until the parameter estimates converge. These models were used to express the relationships of permeability and diffusion in chitosan ﬁlms.

15.3 RESULTS AND DISCUSSION

2

(g m /m /day)

WVTR x thickness

In all cases except for solubility of the chitosan ﬁlms (Figure 15.1), the values increased with an increase in water vapor pressure. Exponential curves were ﬁtted to the LSMEANS of the measured values and plotted using NLIN procedure in SAS. Figures 15.2 and 15.3 show the exponential relationship of WVP and D with increases in water vapor pressure. Water vapor permeability and diffusion coefﬁcients are not constant but vary with water vapor partial pressure and concentration (Figures 15.2 and 15.3). Concentration of sorbed penetrant (water vapor) and temperature are the two main factors affecting polymer chain segmental motion. Temperature was controlled at 25°C for this study. The presence of water increases the free volume of the chitosan ﬁlm, therefore increasing permeability and diffusion (Rogers, 1985). Deviations from 8.00E-02 7.00E-02 6.00E-02 5.00E-02 4.00E-02 3.00E-02 2.00E-02 1.00E-02 0.00E+00

3.0E+05

2.5E+05

2.0E+05

1.5E+05

1.0E+05

5.0E+04

0.0E+00

3

Water Concentration (g/m )

FIGURE 15.1 A plot of WVTR × thickness vs. concentration can be used as an estimate of the dependence of diffusion on concentration from the slope.

Water Vapor Permeability (g/m/sec/mmHg)

Exponential LSMEANS

5.00E-08 4.00E-08 3.00E-08 2.00E-08 1.00E-08 0.00E+00 0

5 10 15 20 Water Vapor Pressure (mmHg)

25

FIGURE 15.2 The relationship between water vapor permeability of chitosan ﬁlms and water vapor pressure at 25°C.

© 2003 by CRC Press LLC

Exponential

Water Vapor Diffusion (m2/s)

LSMEANS

4.00E-12 3.00E-12 2.00E-12 1.00E-12 0.00E+00 0

5

10

15

20

25

Water Vapor Pressure (mmHg)

FIGURE 15.3 The relationship between water vapor diffusion of chitosan ﬁlms and water vapor pressure at 25°C.

typical Fickian behavior are associated with the ﬁnite rates at which the polymer structure may change in response to the sorption or desorption of penetrant molecules (Crank, 1975). Chitosan ﬁlms exhibit non-Fickian diffusion behavior. A plot of WVTR times thickness vs. water concentration of the ﬁlm quantiﬁes and displays this nonideal behavior (Figure 15.1). The initial dry thicknesses were adjusted according to the change in thickness (swelling) due to water vapor sorption at the higher water vapor pressures (Table 15.2). The average percentages of increase in thickness were 11% from 16.3 (69% RH) to 17.8 (75% RH) mmHg of water vapor pressure and 22% from 17.8 (75% RH) to 19.9 (84% RH) mmHg of water vapor pressure. Frisch (1957) obtained an expression for the time lag in linear diffusion through a membrane with a concentration dependent diffusion coefﬁcient without solving the diffusion equation. Frisch’s method determined the relationship between diffuβC sion and concentration in the form of D = D0 e . Stern and Saxena (1980) also assumed that the concentration dependent diffusion coefﬁcient was an exponential function of concentration. Zhou and Stern (1989) stated that this exponential expression for the dependency of concentration by diffusion describes the overall effect of water concentration on the diffusivity in glassy polymer but cannot explain the individual components of the sorption separately. Systems such as hydrophilic chitosan ﬁlms have strong interaction between water vapor and the ﬁlm itself, which deviates from ideal behavior by the swelling and plasticizing effects that vary with water vapor partial pressure. Figure 15.3 agrees with Frisch and others, showing that D is an exponential function of water concentration. Water vapor solubility of chitosan ﬁlms showed a slight decrease from the initial solubility at intermediate water vapor pressures, with a gradual increase at higher water vapor pressures. This gave a U-shaped curve (Figure 15.4). Water concentration inside the ﬁlm also increased substantially with an increase in water vapor pressure (Table 15.2). Here again, the effect of water vapor pressure on water concentration in chitosan ﬁlms increased exponentially. Permeability measurements were made at eight levels of water vapor partial pressure. The concentration gradient was, in every case, 0 mmHg on one side of the chitosan ﬁlm, with the other having the prescribed test water vapor pressure. By using the equation for determining the permeability constant of a multilayer ﬁlm or laminate (Equation (15.4)), the individual permeability in each range of water vapor

© 2003 by CRC Press LLC

3

Solubility (g/m /mmHg)

1.80E+04 1.60E+04 1.40E+04 1.20E+04 1.00E+04 8.00E+03 6.00E+03 4.00E+03 2.00E+03 0.00E+00 0

5

10

15

20

25

Water Vapor Pressure (mmHg)

FIGURE 15.4 The relationship between water vapor solubility in chitosan ﬁlms and water vapor pressure at 25°C. 5.00E-08 4.00E-08

Permeability per Layer (g/m/sec/mmHg)

3.00E-08 2.00E-08 1.00E-08

17.84–19.99

16.32–17.84

12.54–16.32

7.77–10.23

10.23–12.54

5.34–7.77

2.68–5.34

0.00–2.68

0.00E+00

Water Vapor Pressure Range (mmHg)

FIGURE 15.5 The water vapor ranges represent the eight different layers of permeability in the chitosan ﬁlm.

pressure can be calculated (Figure 15.5) and the range of the possible thicknesses of this layer can be determined. In this case, the multilayer ﬁlm consists of eight layers, which are the eight different water vapor pressure ranges shown in Figure 15.5. This information, which is calculated and not measured, can be used to give some insight into the concentration gradient inside the chitosan ﬁlm at various levels of water vapor pressure. It is important to keep the layers in order of low to high water vapor pressures arranged in the direction of diffusion through the ﬁlm. If layers are rearranged, then the calculation of permeability per layer is not possible because of the water vapor pressure dependence of diffusion. Using the data in Figure 15.5, the calculated permeability of each layer can be plotted over a possible range of layer thickness. The equation to calculate the permeability of a laminate or multilayer ﬁlm was used to determine the permeability

© 2003 by CRC Press LLC

at each layer according to its water vapor partial pressure range. If the individual thickness (xn) and permeability coefﬁcient (Pn) are known for each layer, the permeability of the layered ﬁlm (PT) can be calculated from the following equations if individual P values are independent of pressure (Crank, 1975; Rogers et al., 1957). PT =

xT x1 x 2 xn + + ⋅⋅⋅ + P1 P 2 Pn

(15.4)

Water Concentration (g/m3)

The thickness range limits are then used to plot the steady state water concentration gradient in the chitosan ﬁlms at various %RH. Figures 15.6–15.12 graphically represent the steady state concentration gradients across chitosan ﬁlms at various water vapor partial pressures or %RH at 25°C. From the concentration–distance curves, it can be determined that the pattern of concentration inside the ﬁlm has a consistent pattern with increasing relative humidity. Water vapor diffusion occurs in the direction from high concentration to low concentration of water vapor. These plots show graphically that when chitosan ﬁlms reach steady state diffusion, the majority of the concentration distance through

7.00E+04 6.00E+04 5.00E+04 4.00E+04 3.00E+04 2.00E+04 1.00E+04 0.00E+00 0

0.2

0.4

0.6

0.8

1

Distance (Dimensionless)

Water Concentration (g/m3)

FIGURE 15.6 The steady-state concentration distributions across the chitosan ﬁlm when D = 0 β(c) D e from 23 to 0% relative humidity at 25°C.

1.00E+05 8.00E+04 6.00E+04 4.00E+04 2.00E+04 0.00E+00 0

0.2

0.4

0.6

0.8

1

Distance (Dimensionless)

FIGURE 15.7 The steady-state concentration distributions across the chitosan ﬁlm when D = 0 β(c) D e from 33 to 0% relative humidity at 25°C.

© 2003 by CRC Press LLC

Water Concentration (g/m3)

1.20E+05 1.00E+05 8.00E+04 6.00E+04 4.00E+04 2.00E+04 0.00E+00 0

0.2

0.4

0.6

0.8

1

Distance (Dimensionless)

FIGURE 15.8 The steady-state concentration distributions across the chitosan ﬁlm when D = 0 β(c) D e from 43 to 0% relative humidity at 25°C.

Water Concentration (g/m3)

1.60E+05 1.40E+05 1.20E+05 1.00E+05 8.00E+04 6.00E+04 4.00E+04 2.00E+04 0.00E+00 0

0.2

0.4

0.6

0.8

1

Distance (Dimensionless)

3

Water Concentration (g/m )

FIGURE 15.9 The steady-state concentration distributions across the chitosan ﬁlm when D = 0 β(c) D e from 54 to 0% relative humidity at 25°C. 2.50E+05 2.00E+05 1.50E+05 1.00E+05 5.00E+04 0.00E+00 0

0.2

0.4

0.6

0.8

1

Distance (Dimensionless)

FIGURE 15.10 The steady-state concentration distributions across the chitosan ﬁlm when D = 0 β(c) D e from 68 to 0% relative humidity at 25°C.

the ﬁlm is at the higher concentration with a sharp decrease in concentration toward the low concentration end of the curve. This is not typical of most polymer plastic ﬁlms, but it is the norm for hydrophilic chitosan ﬁlms. This pattern may be found in other types of hydrophilic ﬁlms.

© 2003 by CRC Press LLC

3

Water Concentration (g/m )

2.50E+05 2.00E+05 1.50E+05 1.00E+05 5.00E+04 0.00E+00 0

0.2

0.4

0.6

0.8

1

Distance (Dimensionless)

Water Concentration (g/m3)

FIGURE 15.11 The steady-state concentration distributions across the chitosan ﬁlm when D = 0 β(c) D e from 75 to 0% relative humidity at 25°C.

3.00E+05 2.50E+05 2.00E+05 1.50E+05 1.00E+05 5.00E+04 0.00E+00 0

0.2

0.4

0.6

0.8

1

Distance (Dimensionless)

FIGURE 15.12 The steady-state concentration distributions across the chitosan ﬁlm when D = 0 β(c) D e from 86 to 0% relative humidity at 25°C.

15.4 CONCLUSIONS Water vapor partial pressure and concentration have a positive effect on the WVP and D of chitosan ﬁlms. These dependencies are non-Fickian in behavior and can be expressed exponentially except for S. Sorption and diffusion of water vapor are dependent on the sorbed concentration of water. Water vapor swells and plasticizes the chitosan ﬁlm’s polymer structure to increase the mobilities of both the chitosan polymer segments and water penetrant molecules. Deviations from Fickian behavior are the results of increased penetrant–polymer and penetrant–penetrant interaction. From the permeation models and results, there is an indication of two modes of diffusion in the permeation process from 2.68 to 19.99 mmHg of water vapor partial pressure. The ﬁrst mode, from 2.68 to 7.77 mmHg of pressure, is linear in behavior. At water vapor pressures above 7.77 mmHg pressure, the mode of diffusion is exponential in behavior. This study has shown the importance of reporting the actual water vapor partial pressure gradient parameters because of changes that occur in the chitosan ﬁlm’s polymer structure due to the plasticizing effect of water vapor. This concept also applies to most biopolymer ﬁlms. For example, stating a water vapor pressure gradient of 50% instead of the water vapor partial pressure range is not adequate because of the deviations from ideal sorption or diffusion behavior due to the dependency on the

© 2003 by CRC Press LLC

water concentration in the ﬁlm, which changes with water vapor pressure. The permeability measured from 0 to 50% RH is different from that measured from 50 to 100% RH due to microstructural changes in the ﬁlm due to water at different water concentrations, although the apparent pressure gradient is the same. From the graphical representation of the steady state concentration–distance curves, the concentration gradient through the chitosan ﬁlm is not ideal through the ﬁlm and therefore does not obey Henry’s law. The concentration–diffusion curves of chitosan ﬁlms demonstrate the merit of using the saturation/differential method (Demorest and Mayer, 1996) for measuring the steady state permeation of chitosan ﬁlms. By conditioning ﬁlms to equilibrium moisture content or water concentration, these ﬁlms reach steady state diffusion faster than if they were initially void of permeant. This occurs because of the lesser change needed in the concentration gradient, as shown in the concentration–distance curves. Chitosan ﬁlms that are fully conditioned have fewer stresses in them from the relaxation and swelling of the polymer chains of the ﬁlm as compared to a ﬁlm that is dry or void of water vapor. This occurs because the ﬁlm has already been exposed to water vapor in order to reach equilibrium. Chitosan ﬁlms that are nearer equilibrium moisture conditions before testing resulted in more precise WVP measurements.

NOMENCLATURE WVP WVTR l p1 p2 p1 − p2 D S F ∆C D0 e β c PT xT xn Pn

Water vapor permeability coefﬁcient (g/m/sec/mmHg) 2 Water vapor transmission rate (g/m /d) Film’s thickness (m) Water vapor partial pressure at ﬁlm’s surface outside the cup (mmHg) Water vapor partial pressure at the underside of the ﬁlm towards the desiccant (mmHg) Water vapor partial pressure difference (mmHg) 2 Diffusion coefﬁcient (m /sec) 2 Solubility coefﬁcient (g/m /mmHg) 2 Flux (g/m /d) 3 Change in water concentration across the ﬁlm (g/m ) 2 Diffusion coefﬁcient when concentration is zero (m /sec) The base of natural logarithms (2.71828) Constant characterizing the concentration dependency 3 Concentration of water in ﬁlm (g/m ) Permeability coefﬁcient of a multilayer ﬁlm (g/m/sec/mmHg) Total thickness of multilayer ﬁlm (m) Layer thickness (m) Layer permeability coefﬁcient (g/m/sec/mmHg)

REFERENCES ASTM, Standard test method for water vapor transmission of materials, in ASTM Book of Standards, E96–80, American Society for Testing and Materials, Philadelphia, 1980. ASTM, Standard test method for water vapor transmission rate through plastic ﬁlm and sheeting using a modulated infrared sensor, in ASTM Book of Standards, F1249, American Society for Testing and Materials, Philadelphia, 1990.

© 2003 by CRC Press LLC

Butler, B.L., Vergano, P.J., Testin R.F., Bunn, J.M., and Wiles, J.L., Mechanical and barrier properties of edible chitosan ﬁlms as affected by composition and storage, J. Food Sci., 61, 952–955, 1996. Caner, C., Vergano, P.J., and Wiles, J.L., Chitosan ﬁlm mechanical and permeation properties as affected by acid, plasticizer, and storage, J. Food Sci., 63, 1049–1053, 1998. Crank, J., The Mathematics of Diffusion, Clarendon Press, Oxford, 1975, pp. 1–10, 44–68, 254–265. Demorest, R.L. and Mayer D.W., Advanced measuring methods enhanced WVTR testing. Part II, J. Packag. Technol. Eng., 5, 20–24, 1996. Donhowe, G. and Fennema, O., Edible ﬁlms and coating: characteristics, formation, deﬁnitions, and testing methods, in Edible Coating and Films to Improve Food Quality, Krochta, J.M., Baldwin, E.A., and Nisperos-Carriedo, M.O., Eds., Technomic, Lancaster, PA, 1994, pp. 1–63. Frisch, H.L., The time lag in diffusion, J. Phys. Chem., 61, 93–95, 1957. Hauser, P.M. and McLaren, A.D., Permeation through and sorption of water vapor by high polymers, Ind. Eng. Chem., 40, 112–117, 1948. Labuza, T.P., Moisture Sorption: Practical Aspects of Isotherm Measurement and Use, American Association of Cereal Chemists, St. Paul, MN, 1984. McHugh, T.H. and Krochta, J.M., Permeability properties of edible ﬁlms, in Edible Coating and Films to Improve Food Quality, Krochta, J.M., Baldwin, E.A., and NisperosCarriedo, M.O., Eds., Technomic, Lancaster, PA, 1994, pp. 140–149. Muzzarelli, R.A.A., Chitin, Pergamon Press, Oxford, 1977. Muzzarelli, R.A.A., Isolati, A., and Ferrero A., Chitosan Membranes: Ion Exchange and Membranes, Vol. 1, Gordon and Breach Science Publishers, London, 1974, pp. 193–196. Park, S., Barrier and Mechanical Properties of Acetylated Chitosan Films, thesis, Clemson University, 1998. Pascat, B., Study of some factors affecting permeability, in Food Packaging and Preservation: Theory and Practice, Mathlouthi, M., Ed., Elsevier Applied Science, London, 1986, p. 7. Rogers, C.E., Permeation of gases and vapours in polymers, in Polymer Permeability, Comyn, J., Ed., Elsevier Science, New York, 1985, pp. 11–69. Rogers, C.E., Stannett, V., and Szwarc, M., Permeability of gases and vapors through composite membranes, Ind. Eng. Chem., 49, 1933–1936, 1957. SAS, release 6.12 TS020, SAS Institute, Inc. Cary, NC, 1996. Schwartzberg, H.G., Modeling of gas and vapour transport through hydrophilic ﬁlms, in Food Packaging and Preservation: Theory and Practice, Mathlouthi, M., Ed., Elsevier Applied Science, London, 1986, pp. 115–135. Stern, S.A. and Saxena, V., J. Membr. Sci., 7, 47, 1980. Wiles, J.L., The Effect of Relative Humidity on the Steady State Water Vapor Permeability of Chitosan Films, dissertation, Clemson University, 2000. Wiles, J.L., Vergano, P.J., Barron, F.H., Bunn, J.M., and Testin, R.F., Water vapor transmission rates and sorption behavior of chitosan ﬁlms, J. Food Sci., 65, 1175–1179, 2000. Wong, D.W., Gastineau, F.A., Gregorski, K.S., Tillin, S.J., and Pavlath, A.E., Chitosan–lipid ﬁlms: Microstructure and surface energy, J. Agric. Food Chem., 40, 540–544, 1992. Zhou, S. and Stern, S.A., The effect of plasticization on the transport of gases in and through glassy polymers, J. Polym. Sci. B Polym. Phys., 27, 205–222, 1989.

© 2003 by CRC Press LLC

16

Water Vapor Permeability, Water Solubility, and Microstructure of Emulsiﬁed Starch–Alginate–Fatty Acid Composite Films Y. Wu, C.L. Weller, F. Hamouz, S.L. Cuppett, and M. Schnepf

CONTENTS 16.1 Introduction 16.2 Materials and Methods 16.2.1 Materials 16.2.2 Preparation of Films 16.2.3 Thickness 16.2.4 Conditioning 16.2.5 Water Vapor Permeability (WVP) 16.2.6 Water Solubility (WS) 16.2.7 Scanning Electron Microscopy (SEM) 16.2.8 Statistical Analysis 16.3 Results and Discussion 16.3.1 Water Vapor Permeability 16.3.2 Water Solubility 16.3.3 Microstructure of Starch–Alginate–Fatty Acid Composite Films 16.4 Conclusions Nomenclature Acknowledgments References

© 2003 by CRC Press LLC

16.1 INTRODUCTION In the formation of edible ﬁlms, polysaccharides and proteins are generally used for their ability to establish polymer interactions and create a continuous network responsible for the mechanical properties of the ﬁlms (Krochta, 1992; Callegarin et al., 1997). Edible ﬁlms produced from polysaccharides and proteins, however, are highly sensitive to water and provide limited resistance to moisture transmission due to the substantial inherent hydrophilicity of the ﬁlm-forming substances and to the considerable amount of hydrophilic plasticizers incorporated into the ﬁlms (Guilbert, 1986; Krochta, 1992; Gennadios et al., 1994b; Guilbert et al., 1996; Callegarin et al., 1997). In contrast, lipids, such as neutral lipids of glycerides, long-chain fatty acids, waxes, resins, and oils, provide their moisture transfer barrier property for the ﬁlm because of their hydrophobic nature (Hernandez, 1994; Callegarin et al., 1997), but ﬁlms made from lipids alone are usually too brittle (Kester and Fennema, 1986; Guilbert, 1986; Krochta, 1992). Composite ﬁlms of polysaccharide–lipid (Kamper and Fennema, 1984a, b, 1985; Kester and Fennema, 1989; Greener and Fennema, 1989; Hagenmaier and Shaw, 1990; Koelsch and Labuza, 1992; Wong et al., 1992; Debeaufort et al., 1993; Park et al., 1994; Sapru and Labuza, 1994; Callegarin et al., 1997) or protein–lipid (AvenaBustillos and Krochta, 1993; Gennadios et al., 1993; McHugh and Krochta, 1994a, b; Gontard et al., 1994, 1995; Saravia, 1995; Shellhammer and Krochta, 1997b; Rhim et al., 1999), in laminated or emulsion forms, have been developed and have shown increased moisture resistance and improved functionality for edible packaging application. Starch–alginate coatings have been applied on precooked pork chops (Handley et al., 1996; Hargens-Madsen et al., 1995) and ground beef patties (Ma-Edmonds et al., 1995) to inhibit lipid oxidation and the formation of warmed-over ﬂavor. However, the poor moisture barrier property of starch–alginate ﬁlms hinders them from being used to control moisture loss in precooked meat products. When freestanding starch–alginate ﬁlms were applied on precooked meat products in a previous study, moisture absorption and ﬁlm swelling were observed on these ﬁlms and the packaged meat became dry over time (unpublished data). Mechanical properties and other barrier properties can be lost upon the hydration of the swollen ﬁlms. Incorporation of fatty acids into starch–alginate ﬁlms, therefore, may provide hydrophobicity and increase ﬁlm resistance to water transmission. In this study, the effect of fatty acids (lauric, palmitic, and stearic acids) on the moisture barrier property of starch–alginate ﬁlms was evaluated in terms of water vapor permeability and water solubility. Microstructure examination was performed to help elucidate the structure–function relation of starch–alginate–fatty acid composite ﬁlms.

16.2 MATERIALS AND METHODS 16.2.1 MATERIALS CstarEmCap 0637, a lipophilic modiﬁed starch, was obtained from Cerestar USA Inc. (Hommond, IN). Sodium alginate was provided by Kelco Division of Merck and Co. (Rahway, NJ). Glycerin was purchased from Mallinckrodt Baker Chemical (Phillipsburg, NJ). Lauric acid (LA), palmitic acid (PA), and stearic acid (SA) were

© 2003 by CRC Press LLC

purchased from Sigma Chemical Co. (St. Louis, MO). Lecithin (Lecigran 5750), an emulsiﬁer, was provided by Riceland Foods Inc. (Little Rock, AK). Ethyl alcohol (USP dehydrated, absolute-200 proof) was purchased from McCormick Distilling Co., Inc. (Weston, MO).

16.2.2 PREPARATION

OF

FILMS

A control (0% fatty acid) starch–alginate ﬁlm solution was prepared by slowly dissolving 5 g starch and 2 g alginate in a constantly stirred mixture of distilled water (127.3 ml), ethanol (63.6 ml), and glycerin (2.1 g). Additionally, three other starch–alginate–fatty acid ﬁlm solutions were prepared using LA, PA, and SA. For each starch–alginate–fatty acid ﬁlm, four levels of each fatty acid (10, 20, 30, or 40% w/w of starch and alginate) were used. An emulsion with each fatty acid was prepared by adding a portion of the fatty acid into the 200 ml starch–alginate ﬁlm solution with 30% (w/w of fatty acid) of lecithin. The solution was then heated to o boiling (78 C) with stirring to completely melt the fatty acid. All added fatty acids had melting points lower than the boiling point of the ﬁlm solution. Each boiled solution was homogenized using an Ultra-Turrax T25 homogenizer (Janke & Kunkel GMBH & Co. KG, Staufen, Germany) at 9500 r/min for 2 min, strained through eight-layered cheesecloth (grade 40, Fisher Scientiﬁc), and poured onto a leveled Teﬂon coated glass plate (21 cm × 35 cm). Film thickness was controlled by casting volumes of solutions having the same amount of solids (8.82 g) onto each plate. Films were allowed to dry at ambient conditions for about 24 h. Then they were peeled from the plate, and samples for property testing were cut. Water vapor permeability (WVP) and water solubility testing samples were squares of 7 × 7 and 2 × 2 cm, respectively.

16.2.3 THICKNESS Film thickness was measured to the nearest 2.54 µm (0.1 mil) with a hand-held micrometer (B.C. Ames Co., Waltham, MA). Five thickness measurements were taken on each WVP sample, one at the center and four around the perimeter, and the mean values were used in WVP calculations.

16.2.4 CONDITIONING All ﬁlm samples for WVP and WS were conditioned for 2 d in an environmental chamber (Model RC-5492, PGC Parameter Generation & Control, Inc., Black Mountain, NC) set at 50% RH and 25°C before testing (ASTM Standard Method D 618-61, ASTM, 1995a).

16.2.5 WATER VAPOR PERMEABILITY (WVP) .

2

WVP (g mm/m ⋅ h ⋅ KPa) was calculated as: WVP = (WVTR ⋅ L)/ ∆p

© 2003 by CRC Press LLC

(16.1)

WVTR was determined gravimetrically using a modiﬁed ASTM Method E 96-95 (ASTM, 1995b). Film specimens were mounted on poly(methyl methacrylate) cups ﬁlled with distilled water up to 1 cm from the ﬁlm underside. The cups were placed in an environmental chamber set at 25°C and 50% RH. A fan was operated within the chamber, creating an air velocity of 198 m/min over the surface of the cups to remove permeating water vapors. Weights of the cups were recorded every h for a period of 8 h. Steady state was reached after about 1 h. Slopes of the steady state (linear) portion of weight loss vs. time curves were determined by linear regression 2 to estimate WVTR. Coefﬁcient of determination (R ) for all reported data was 0.99 or greater. In calculating WVP, the effect of resistance of the stagnant air layer between the ﬁlm undersides and the surface of water in cups was corrected for (McHugh et al., 1993; Gennadios et al., 1994b). For each type of ﬁlm, WVP measurements were replicated three times.

16.2.6 WATER SOLUBILITY (WS) WS was calculated as the percentage of soluble matter to initial dry matter in each ﬁlm sample using the method of Gontard et al. (1992), with some modiﬁcations. Three randomly selected samples from each type of ﬁlm were ﬁrst dried at 105°C for 24 h to determine initial dry matter. After drying, ﬁlms were immersed in 30 ml of distilled water in a 50 ml beaker. Beakers were covered with Paraﬁlm “M” wrap (American National Can, Greenwich, CT) and stored in an environmental chamber at 25°C for 12 h with occasional gentle stirring. Since all ﬁlm samples disintegrated into small pieces after soaking in water, the sample solutions were set for another 10 min to allow the undissolved sample pieces to deposit on the bottom of the beakers. The supernatant of the solution (water) was then discarded and the deposited undissolved sample was poured into an aluminum drying dish with the water residue and oven dried at 105°C for 24 h. The weight of solubilized matter was calculated by subtracting the weight of undissolved dry matter from the weight of initial dry matter and expressed as a percentage of the initial dry matter content. Film samples were weighed to the nearest 0.0001 g before and after drying. WS was determined in triplicate for each type of ﬁlm.

16.2.7 SCANNING ELECTRON MICROSCOPY (SEM) Microstructural characteristics of starch–alginate ﬁlm samples were examined using an AMRAY 1000A electronic microscope (AMRAY Inc., Bedford, MA), while those of starch–alginate–fatty acid composite ﬁlm samples were examined using a JSM6100 scanning microscope (JEOL, Tokyo, Japan). All ﬁlm samples were prepared using the same methods as for preparing ﬁlms for WVP and WS testing, but without adding glycerin. Samples were mounted on an aluminum stub with copper tape, ﬁrst coated with carbon by vacuum evaporation on a Denton DV-502 vacuum evaporator (Denton Inc., Cherry Hill, NJ) and then sputter coated with gold–palladium alloy with a EBTEC sputter coater (EBTEC Co., Agawam, MA). Samples were examined using an accelerating voltage of 20 kV. Images were recorded on Polaroid ﬁlm (Type o 665) and photographed at a tilt angle of 60 to the electron beam for views in the cross section.

© 2003 by CRC Press LLC

16.2.8 STATISTICAL ANALYSIS Means and standard deviations on a completely randomized design with three replications were determined using the Genera Linear Models procedure in the SAS program (SAS Institute Inc., 1990). Fisher’s protected least signiﬁcant differences (Fisher’s protected LSD) were calculated to indicate differences among mean values. Signiﬁcance was accepted at a level of P < 0.05.

16.3 RESULTS AND DISCUSSION 16.3.1 WATER VAPOR PERMEABILITY The WVP values, along with the thickness values and actual RH conditions at the undersides of ﬁlms during testing, of control starch–alginate ﬁlm and emulsiﬁed composite starch–alginate–fatty acid ﬁlms are presented in Table 16.1. The WVP of . 2 the control starch–alginate ﬁlm was 5.14 g mm/m ⋅ h⋅KPa. This value was of the 2 same order of magnitude as mean WVP values of 2.20 g⋅ mm/m ⋅h ⋅ KPa and . 2 2.99–8.78 g mm/m ⋅ h⋅ KPa previously reported for polysaccharide ﬁlms made from methyl cellulose (Gennadios et al., 1994a) and chitosan (Rhim et al., 1998), respectively, which were tested with the same method and same conditions, i.e., 25°C and 100/50% RH gradient, as in the present study. TABLE 16.1 Water Vapor Permeability (WVP) and Water Solubility (WS) of Starch–Alginate Films with Lauric Acid (LA), Palmitic Acid (PA), or Stearic Acid (SA) Fatty Acid in Film (% of Starch–Alginate) Control LA

PA

SA

0 10 20 30 40 10 20 30 40 10 20 30 40

a

Thickness (µm)

RH Inside Cup (%)

106 148 128 127 126 101 96 103 109 90 106 116 111

77.1 ± 1.06 f 84.4 ± 1.20 de 88.9 ± 1.16 cde 89.9 ± 1.78 bcd 90.5 ± 1.28 f 85.2 ± 0.52 f 84.8 ± 1.22 f 85.5 ± 0.25 ef 87.3 ± 3.80 f 85.0 ± 2.35 de 89.7 ± 2.44 b 93.3 ± 0.46 bc 92.6 ± 1.08

g

a

a

WVP 2 · (g·mm / m · h·KPa) b

5.14 ± 0.05 b 4.74 ± 1.11 cde 2.52 ± 0.07 cde 2.22 ± 0.47 efg 2.04 ± 0.31 c 2.91 ± 0.19 cd 2.86 ± 0.24 c 2.91 ± 0.18 cde 2.60 ± 0.92 cde 2.69 ± 0.58 def 2.07 ± 0.25 g 1.25 ± 0.10 fg 1.30 ± 0.11

a

WS (%) 54.53 52.78 52.84 47.60 46.29 51.40 47.89 44.74 45.47 47.26 43.51 38.09 35.80

± ± ± ± ± ± ± ± ± ± ± ± ±

b

2.62 bc 1.84 bc 0.93 d 0.57 de 2.87 c 0.61 d 0.53 ef 0.92 def 1.11 de 0.98 f 2.52 g 0.32 g 1.70

Mean of three replicates ± standard deviation. Measured at 25°C and 100/50% RH gradient. RH at ﬁlm undersides inside cups and WVP were corrected to account for resistance of stagnant air layer between ﬁlm underside and water surface (Gennadios et al., 1994b). b–g Means within a column are signiﬁcantly (P < 0.05) different.

© 2003 by CRC Press LLC

With the exception of ﬁlms with 10% LA, WVP of starch–alginate ﬁlms was 2 signiﬁcantly reduced by incorporation of LA, PA, or SA to as low as 1.25 g⋅ mm/m ⋅ h⋅ KPa for ﬁlms with 30% SA. Decreases in WVP of starch–alginate ﬁlms may be attributed to the increased hydrophobicity and the structural complexity imparted into starch–alginate ﬁlms by the fatty acids, which is further discussed in the SEM result section in this work. Fatty acids have been successfully used to reduce WVP of emulsiﬁed cellulose ether ﬁlms (Kamper and Fennema, 1984a,b; Hagenmaier and Shaw, 1990; Koelsch and Labuza, 1992; Sapru and Labuza, 1994) and chitosan ﬁlms (Wong et al., 1992). The reduction of WVP has also been observed with addition of fatty acids into wheat gluten ﬁlms (Gontard et al., 1994; Derksen et al., 1995), whey protein ﬁlms (McHugh and Krochta, 1994b), and soy protein isolate ﬁlms (Rhim et al., 1999) using emulsion technique. Generally, with increasing length of the lipid hydrocarbon chain, as well as concentration of the lipid, resistance of a lipid ﬁlm to water vapor transmission increases (Fennema et al., 1993; Callegarin et al., 1997; Shellhammer and Krochta, 1997a). As shown in Table 16.1, the effect of chain length on WVP was mainly shown by the signiﬁcant differences in WVP values found between SA ﬁlms and LA and PA ﬁlms in the present study. In general, incorporation of SA into starch–alginate ﬁlms resulted in the lowest WVP values at all levels when compared with the incorporation of LA and PA. The WVP values of ﬁlms with PA and LA were similar, except at the level of 10%, where PA was more effective than LA in reducing WVP. WVP decreased signiﬁcantly as fatty acid concentration increased in ﬁlms with LA and SA. However, increasing PA concentration did not signiﬁcantly reduce WVP. For ﬁlms with LA and PA, a fatty acid content of 40% resulted in the lowest WVP, while the lowest WVP was obtained in ﬁlms with 30% of SA. The overall WVP change pattern in this study suggests that there is an optimum concentration of fatty acid at which WVP can be lowered most effectively. According to Kamper and Fennema (1984a), increasing the stearic acid concentration in emulsiﬁed hydroxypropyl methylcellulose–fatty acid ﬁlms decreased their WVP until an optimum was reached. Hagenmaier and Shaw (1990) found that hydroxypropyl methylcellulose–fatty acid emulsion ﬁlms had decreased WVP as the fatty acid concentration increased from 23 to 45%. However, an increase in permeability occurred above a volume fraction of stearic acid of 46%. Similar results have been reported by Sapru and Labuza (1994) in methyl cellulose–stearic acid composite ﬁlms, by Gontard et al. (1994) in wheat gluten–lipid composite ﬁlms, and by Rhim et al. (1999) in soy protein isolate ﬁlms composed with LA and PA. Sapru and Labuza (1994) found that when the stearic acid volume was above 22%, the increase in WVP was attributed to inadequate ﬁlling of the void volume within the stearic acid crystallites by the methyl cellulose–polyethylene glycol matrix.

16.3.2 WATER SOLUBILITY Similar to WVP, WS is an indication of the hydrophilicity of a ﬁlm. Moreover, WS is affected by the chemical nature and the structural integrity of ﬁlms. As shown in Table 16.1, incorporation of fatty acids signiﬁcantly reduced WS of starch–alginate ﬁlms by as much as 34% with 40% stearic acid. The overall WS decreased as the

© 2003 by CRC Press LLC

chain length of fatty acid increased, as indicated by signiﬁcant differences between ﬁlm types. WS reduction was more pronounced at increasing levels of fatty acid in the ﬁlms. It was also observed that ﬁlms, with or without fatty acids, disintegrated easily after 12 h of soaking. WS, apparently, is more affected by the hydrophilic nature of ﬁlms rather than by their structural integrity. WS (total soluble matter) of soy protein–fatty acid ﬁlms has been reported to be less than that of soy protein ﬁlms without fatty acids (Gennadios et al., 1997). Lai et al. (1997) determined water absorption rate, another property related to hydrophilicity of zein–fatty acid sheets, and reported that the amount of water absorbed deceased as fatty acid levels increased in the sheets. However, a sharp increase in WS beyond a threshold lipid material content has been observed in wheat gluten–lipid composite ﬁlms (Gontard et al., 1994) and soy protein–fatty acid composite ﬁlms (Rhim et al., 1999). These discrepancies may be attributed to the types of matrix materials used for ﬁlm formation, the types and amounts of emulsiﬁers added into the ﬁlms, and the differences in ﬁlm homogeneity and structure.

16.3.3 MICROSTRUCTURE OF STARCH–ALGINATE–FATTY ACID COMPOSITE FILMS To better understand the structure–function relation existing in starch–fatty acid composite ﬁlms, scanning electron microscopic examination was performed on the control starch–alginate ﬁlm and ﬁlms with 30% fatty acids. Variations in microstructure among these ﬁlms were evident from a comparison of the SEM photomicrographs, as shown in Figure 16.1. The structure of starch–alginate ﬁlm without the addition of fatty acid was compact and dense, and the ﬁlm surface had a smooth contour free from pores and cracks (Figure 16.1A). One of the basic physical properties of carbohydrates is that they attract water. Hydrophilicity is expected due to their numerous hydroxyl groups, which form hydrogen bonds with water molecules (Whistler and Daniel, 1985). It is also believed that water molecules can interact with the matrix and increase the permeation rate when they penetrate hydrophilic materials (Pascat, 1986). The hydrophilic nature of the starch–alginate ﬁlm, therefore, accounts for the water permeability value obtained in the present study (Table 16.1). When fatty acids were incorporated into the starch–alginate ﬁlm, the ﬁlm microstructure was changed dramatically (Figure 16.1B, C, and D). This change in the ﬁlm structure may play a key role in the barrier properties of the composite ﬁlms, as evidenced by the reduction in WVP and WS of the ﬁlms. For all fatty acid composite ﬁlms, there was no obvious migration of the fatty acid to the air–ﬁlm surface, as noted by other authors using methylcellulose derivatives as the base component (Greener and Fennema, 1989; Vojdani and Torres, 1989, 1990). Microstructures in the cross sections of these ﬁlms showed some differences. A stratiﬁed ﬂaky structure was found in the starch–alginate–LA ﬁlm (Figure 16.1B). This layer structure could be easily observed visually. A similar, but more compact, stacking layer structure has been noted in a chitosan–LA ﬁlm (Wong et al., 1992). The arrangement of ﬂaky layers of starch–alginate ﬁlms provided an extended network of channels lined with hydrophobic molecules. The lower WVP of starch–alginate–LA ﬁlms

© 2003 by CRC Press LLC

© 2003 by CRC Press LLC

(a)

(b)

(c)

(d)

FIGURE 16.1 Photomicrographs taken by scanning electron microscopy of starch–alginate–fatty acid composite ﬁlms (fatty acid = 30% starch–alginate, w/w). A: Pure starch–alginate ﬁlm; B: Starch–alginate–lauric acid ﬁlm; C: Starch–alginate–palmitic acid ﬁlm; D: Starch–alginate– stearic acid ﬁlm (bar = 20.8 µm).

(Table 16.1) suggests that this network hindered the penetration of water molecules through the ﬁlms. The structure of starch–alginate–PA showed a nonhomogeneous or irregular layered sponge-like structure (Figure 16.1C). Although the network of this structure is more complicated than that of ﬁlms with LA, which may have contributed to the lower WS in ﬁlms with PA, the nonhomogeneous distribution of PA may account for a WVP that did not signiﬁcantly differ from that of ﬁlms with different contents of PA and from that of LA ﬁlms. PA has been incorporated into zein sheets by Lai et al. (1997). They reported that layered structures were progressively formed, and that the structures became more compact when the concentration of PA was increased from 0 to 50% of corn zein protein in zein sheets. This change in structure was shown to coincide with the decreased water absorption of the zein sheets. In starch–alginate–SA ﬁlms, the structure was somewhat similar to that shown by PA ﬁlms (Figure 16.1D). However, the layered sponge-like structure of SA ﬁlms was highly channeled, and SA was evenly distributed in the continuous starch–alginate matrix, which may set up a more tortuous path or increased path length for diffusing water molecules than those found in the other ﬁlms. Consequently, ﬁlms with SA exhibited the lowest WVP and WS values among all composite ﬁlms. It is believed that a ﬁne particle size and even distribution of lipids are important to the effectiveness of an emulsion ﬁlm (Wong et al., 1992; McHugh and Krochta, 1994a; Debeaufort and Voilley, 1995). The existence of stearic hindrance and tortuosity in the ﬁlm structure also inﬂuences the permeability of ﬁlms (Holton et al., 1994). According to Koelsch (1994), the high degree of inherent tortuosity that resulted from an even interlocking network within methylcellulose–SA emulsiﬁed composite ﬁlms was responsible for the low WVP values of the ﬁlms. In these ﬁlms, the interlocking network of SA chains within the support matrix reached a maximum (i.e., maximum tortuosity) at about 30% SA, a concentration similar to our optimum SA level for starch–alginate–fatty acid ﬁlms. Besides the dispersion of fatty acids in the base matrix, complex formation between starch amylose/amylopectin fractions and fatty acids may also account for the changed microstructures, and thus the lowered WVP and WS values for the fatty acid composite ﬁlms. Fatty acids can form inclusion complexes with helical amylose and possibly with the longer outer chains of amylopectin. Such complexes resist entry of water (Whistler and Daniel, 1985). Gray and Schoch (1962) demonstrated that the presence of fatty acids decreased the swelling and solubilization of starch by forming a fatty acid–amylopectin complex. Lagendijk and Pennings (1970) found that the amount of fatty acid complexed with amylopectin increased linearly with increasing fatty acid chain length.

16.4 CONCLUSIONS Moisture barrier properties of starch–alginate ﬁlms can be improved substantially by incorporation of LA, PA, and SA. The reduction in WVP and WS of starch–alginate ﬁlms was more pronounced as the fatty acid chain length increased and at increasing levels of fatty acids in general. The tortuous network formed by the interaction of fatty acids and the starch–alginate matrix may contribute improved barrier properties.

© 2003 by CRC Press LLC

The more uniform the distribution of the fatty acid molecules, and the higher degree of the tortuosity of the network formed by the fatty acids in the ﬁlm’s microstructure, the better the moisture barrier property of the ﬁlm.

NOMENCLATURE WVP WVPR L ∆p

2

Water vapor permeability (g⋅mm/m ⋅ h⋅ KPa) 2 Measured water vapor transmission rate through a ﬁlm (g/m ⋅ h) Film thickness (m) Partial water vapor pressure difference across the two sides of a ﬁlm (Pa)

ACKNOWLEDGMENTS We express special appreciation to Tom Bargar in the Department of Veterinary and Biomedical Sciences at the University of Nebraska–Lincoln for assistance in scanning electron microscopy.

REFERENCES ASTM, Standard practice of conditioning plastics and electrical insulating materials for testing (D618-61), in Annual Book of ASTM Standards, Vol. 80, American Society for Testing and Materials, Philadelphia, 1995a, 37–39. ASTM, Standard test methods for water vapor transmission of materials (E 96–95), in Annual Book of ASTM Standards, Vol. 4.06, American Society for Testing and Materials, Philadelphia, 1995b, 697–704. Avena-Bustillos, R.J. and Krochta, J.M., Water vapor permeability of caseinate-based edible ﬁlms as affected by pH, calcium crosslinking and lipid content, J. Food Sci., 58, 904–907, 1993. Callegarin, F., Gallo, J.-A.Q., Debeaufort, F., and Voilley, A., Lipids and biopackaging, J. Am. Oil Chem. Soc., 74, 1183–1192, 1997. Debeaufort, F., Martin-Polo, M., and Voilley, A., Polarity, homogeneity and structure affect water vapor permeability of model edible ﬁlms, J. Food Sci., 58, 426–434, 1993. Debeaufort, F. and Voilley, A., Effect of surfactants and drying rate on barrier properties of emulsiﬁed edible ﬁlms, Int. J. Food Sci. Technol., 30, 183–190, 1995. Derksen, J.T.P., Cuperus, F.P., and Kolster, P., Paints and coatings from renewable resources, Industr. Crop. Prod., 3, 225–236, 1995. Fennema, O., Donhowe, I.G., and Kester, J.J., Edible ﬁlms: barriers to moisture migration in frozen foods, Food Austr., 45, 521–525, 1993. Gennadios, A., McHugh, T.H., Weller, C.L., and Krochta, J.M., Edible coatings and ﬁlms based on proteins, in Edible Coatings and Films to Improve Food Quality, Krochta, J.M., Baldwin, E.A., and Nisperos-Carriedo, M., Eds., Technomic, Lancaster, PA, 1994a, pp. 201–278. Gennadios, A., Weller, C.L., and Gooding, C.H., Measurement errors in water vapor permeability of highly permeable, hydrophilic edible ﬁlms, J. Food Eng., 21, 395–409, 1994b. Gennadios, A., Weller, C.L., and Hanna, M.A., Soy protein/fatty acids ﬁlms and coatings, Inform., 8(622), 624, 1997.

© 2003 by CRC Press LLC

Gennadios, A., Weller, C.L., and Testin, R.F., Modiﬁcation of physical and barrier properties of edible wheat gluten-based ﬁlms, Cereal Chem., 70, 426–429, 1993. Gontard, N., Duchez, C., Cuq, J-L., and Guilbert, S., Edible composite ﬁlms of wheat gluten and lipids: water vapor permeability and other physical properties, Int. J. Food Sci. Technol., 29, 39–50, 1994. Gontard, N., Duchez, C., Cuq, J-L., and Guilbert, S., Water vapor permeability of edible bilayer ﬁlms of wheat gluten and lipids, Int. J. Food Sci. Technol., 30, 49–56, 1995. Gontard, N., Guilbert, S., and Cuq, J-L., Edible wheat gluten ﬁlms: inﬂuence of the main process variables on ﬁlm properties using response surface methodology, J. Food Sci., 57, 190–195, 199, 1992. Gray, V.M. and Schoch, T.J., Effects of surfactants and fatty adjuncts on the swelling and solubilization of granular starches, Starch, 14, 239–246, 1962. Greener, I.K. and Fennema, O., Evaluation of edible, bilayer ﬁlms for use as moisture barriers for food, J. Food Sci., 54, 1400–1406, 1989. Guilbert, S., Technology and application of edible protective ﬁlms, in Food Packaging and Preservation Theory and Practice, Mathlouthi, M., Ed., Elsevier Applied Science, New York, 1986, pp. 371–394. Guilbert, S., Gontard. N., and Gorris, L.G.M., Prolongation of the shelf-life of perishable food products using biodegradable ﬁlms and coatings, Lebensm.-Wiss. Technol., 29, 10–17, 1996. Hagenmaier, R.D. and Shaw, P.E., Moisture permeability of edible ﬁlms made with fatty acid and (hydroxypropyl) methylcellulose, J. Agric. Food Chem., 38, 1799–1803, 1990. Handley, D., Ma-Edmonds, M., Hamouz, F., Cuppett, S., Mandigo, R., and Schenpf, M., Controlling oxidation and warmed-over ﬂavor in precooked pork chops with rosemary oleoresin and edible ﬁlm, in Natural Antioxidants: Chemistry, Health Effect, and Application, Shahidi, F., Ed., AOCS Press, Champaign, IL, 1996, pp. 311–318. Hargens-Madsen, M., Schnepf, M., Hamouz, F., Weller, C., and Roy, S., Use of edible ﬁlms and tocopherols in the control of warmed-over ﬂavor, J. Am. Diet. Assoc., 95, A-41, 1995. Hernandez, E., Edible coatings from lipids and resins, in Edible Coatings and Films to Improve Food Quality, Krochta, J.M., Baldwin, E.A., and Nisperos-Carriedo, M., Eds., Technomic, Lancaster, PA, 1994, pp. 279–303. Holton, E.E., Asp, E.H., and Zottola, E.A., Corn-starch-containing polyethylene ﬁlm used as food packaging, Cereal Foods World, 39, 237–241, 1994. Kamper, S.L. and Fennema, O., Water vapor permeability of an edible, fatty acid, bilayer ﬁlm, J. Food Sci., 49, 1482–1484, 1984a. Kamper, S.L. and Fennema, O., Water vapor permeability of edible bilayer ﬁlms, J. Food Sci., 49, 1478–1481, 1984b. Kamper, S.L., and Fennema, O., Use of an edible ﬁlm to maintain water vapor gradients in foods, J. Food Sci., 50, 382–384, 1985. Kester, J.J. and Fennema, O., Edible ﬁlms and coatings: a review, Food Technol., 40, 47–49, 1986. Kester, J.J. and Fennema, O., An edible ﬁlm of lipids and cellulose ethers: barrier properties to moisture vapor transmission and structural evaluation, J. Food Sci., 54, 1383–1389, 1989. Koelsch, C., Edible water vapor barrier: properties and promise, Trends Food Sci. Technol., 51, 76–81, 1994. Koelsch, C.M. and Labuza T.P., Functional, physical and morphological properties of methyl cellulose and fatty acid-based edible barriers, Lebensm.-Wiss. Technol., 25, 404–411, 1992. Krochta, J.M., Control of mass transfer in foods with edible coatings and ﬁlms, in Advances in Food Engineering, Singh, R.P. and Wifakaratakusumah, M.A., Eds., CRC Press, Boca Raton, FL, 1992, pp. 517–538.

© 2003 by CRC Press LLC

Lagendijk, J. and Pennings, H.J., Relation between complex formation of starch with monoglycerides and the ﬁrmness of bread, Cereal Sci. Today, 15, 354–356, 365, 1970. Lai, H-M., Padua, G.W., and Wei, L.S., Properties and microstructure of zein sheets plasticized with palmitic and stearic acids, Cereal Chem., 74, 83–90, 1997. Ma-Edmonds, M., Hamouz, F., Cuppett, S., Mandigo, R., and Schnepf, M., Use of rosemary oleoresin and edible ﬁlm to control warmed-over ﬂavor in precooked beef patties, abstract, in Book of Abstracts, Institute of Food Technologists, Chicago, 1995, pp. 139. McHugh, T.H., Avena-Bustillos, R., and Krochta, J.M., Hydrophilic edible ﬁlms: modiﬁed procedure for water vapor permeability and explanation of thickness effects, J. Food Sci., 58, 899–903, 1993. McHugh, T.H. and Krochta, J.M., Dispersed phase particle size effects on water vapor permeability of whey protein beeswax edible emulsion ﬁlms, J. Food Process. Preserv., 18, 173–188, 1994a. McHugh, T.H. and Krochta, J.M., Water vapor permeability properties of edible whey protein–lipid emulsion ﬁlms, J. Am. Oil Chem. Soc., 71, 307–312, 1994b. Park, J.W., Testin, R.F., Park, H.J., Vergano, P.J., and Weller, C.L., Fatty acid concentration effect on tensile strength, elongation, and water vapor permeability of laminated edible ﬁlms, J. Food Sci., 59, 916–919, 1994. Pascat, B., Study of some factors affecting permeability, in Food Packaging and Preservation: Theory and Practice, Mathlouthi, M., Ed., Elsevier Applied Science, London, 1986, pp. 7–24. Rhim, J-W, Weller, C.L., and Ham, K-S., Characteristics of chitosan ﬁlms as affected by the type of solvent, Food. Sci. Biotechnol., 7, 263–268, 1998. Rhim, J-W, Wu, Y., Weller, C.L., and Schnepf, M., Physical characteristics of emulsiﬁed soy protein–fatty acid composite ﬁlms, Sci. Aliment., 19, 57–71, 1999. Sapru, V. and Labuza, T.P., Dispersed phase concentration effect on water vapor permeability in composite methyl cellulose stearic acid edible ﬁlms, J. Food Process. Preserv., 18, 359–368, 1994. Saravia, R.A., Sorghum wax and selected applications, thesis, University of Nebraska, Lincoln, 1995. SAS Institute, Inc., SAS User Guide, version 6.0, SAS Institute Inc., Cary, NC, 1990. Shellhammer, T.H. and Krochta, J.M., Edible coatings and ﬁlm barriers, in Lipid Technologies and Applications, Gunstone, F.D. and Padley, F.B., Eds., Marcel Dekker, Inc., New York, 1997a, pp. 453–479. Shellhammer, T.H. and Krochta, J.M., Whey protein emulsion ﬁlm performance as affected by lipid type and amount, J. Food Sci., 62, 390–394, 1997b. Vojdani, F. and Torres, A., Potassium sorbate permeability of methylcellulose and hydroxypropyl methylcellulose multi-layer ﬁlms, J. Food Process. Preserv., 13, 417–430, 1989. Vojdani, F. and Torres, A., Potassium sorbate permeability of methylcellulose and hydroxypropyl methylcellulose coatings: effect of fatty acids, J. Food Sci., 55, 841–846, 1990. Whistler, R.L. and Daniel, J.R., Carbohydrates, in Food Chemistry, Fennema, O.R., Ed., Marcel Dekker, Inc., New York, 1985, pp. 69–137. Wong, D.W.S., Gastineau, F.A., Gregorski, K.S., Tillin, S.J., and Pavlath, A.E., Chitosan-lipid ﬁlms: microstructure and surface energy, J. Agric. Food Chem., 40, 540–544, 1992.

© 2003 by CRC Press LLC

17

Mass Transport Phenomena during the Recovery of Volatile Compounds by Pervaporation T. Schäfer and J.G. Crespo

CONTENTS 17.1 Introduction 17.2 The Principles of Pervaporation 17.2.1 Nonideal Transport Phenomena at the Membrane Surfaces: Concentration Polarization 17.2.2 Nonideal Transport Phenomena in the Membrane Polymer: Swelling and Flux Coupling 17.3 Technical Aspects of Pervaporation 17.4 Advantages and Applications of Pervaporation in the Food Industry 17.4.1 Hydrophilic Pervaporation 17.4.2 Organophilic Pervaporation 17.5 Conclusions References

17.1 INTRODUCTION This chapter presents pervaporation as a membrane separation process for the selective removal and recovery of dilute compounds from a bulk liquid. First, the principle of pervaporation will be described, followed by a discussion of its main transport phenomena and a mathematical description of ideal conditions. Pervaporation is, at ﬁrst sight, not a complicated process. It is, however, rather versatile. This is on the one hand an advantage, because pervaporation can be adapted and integrated in process lines with considerable ﬂexibility. On the other hand, this versatility has led to an abundance of different individual applications that cannot readily be compared. Recently, attempts have been made in the literature to search for empirical rules on

© 2003 by CRC Press LLC

pervaporation in individual situations. It is, however, the authors’ opinion that instead of empirical rules, a concise but comprehensive understanding of the scientiﬁc background of pervaporation fosters the creativity necessary for a ﬂexible and appropriate process design. The essentials of this background will be presented for ideal conditions in the ﬁrst section, “The Principles of Pervaporation,” in conjunction with a discussion of the most relevant nonideal phenomena. The second part of this chapter, “Technical Aspects of Pervaporation,” will demonstrate how the theory is put into practice. The ﬁnal section will illustrate the theoretical information provided by selected case studies with special regard to applications in the food industry. The potential, as well as the limits, of pervaporation will be discussed in comparison with other separation techniques, and it will be shown how careful process design allows the application of pervaporation to diverse separation problems.

17.2 THE PRINCIPLES OF PERVAPORATION Pervaporation is a membrane separation process that employs dense, nonporous membranes for the selective separation of dilute solutes from a liquid bulk solvent (Néel, 1991). The separation concept of pervaporation is based on the molecular interaction between the feed components and the dense membrane polymer. This differs from pressure-driven membrane separation processes involving porous membranes, such as microﬁltration, where the general separation concept is primarily based on molecular size exclusion. Pervaporation is a process very similar to vapor permeation, the only difference being that in the latter the feed is not liquid, but a vapor. It should, however, be clearly distinguished from membrane distillation (Luque de Castro and GámizGarcía, 2000), in which a porous membrane is in contact with a liquid feed, and feed components evaporate through the membrane pores. In this case, the membrane polymer does not have any selective impact on the solute transport, but merely serves as a mechanical barrier (Lawson and Lloyd, 1997). The principle of pervaporation is illustrated in Figure 17.1. A nonporous membrane separates a liquid feed, commonly close to atmospheric pressure, from a downstream compartment in which a vacuum is applied. When the feed contacts the membrane, the solutes (denoted i in Figure 17.1) sorb in the membrane surface due to solute–polymer interactions (Figure 17.1, bottom, I). These solute–polymer interactions imply that the solvating power of the polymer is higher with regard to some solutes than that of the bulk solvent. Under ideal conditions, a thermodynamic equilibrium will be reached when the chemical potential of the solute i is equal in the membrane surface and the liquid phase adjacent to it. The sorption of these solutes at the membrane surface creates a solute concentration gradient across the membrane, resulting in a diffusive net ﬂux of solute across the membrane polymer (Figure 17.1, bottom, II). In pervaporation, any solute that has diffused toward the membrane downstream surface is ideally instantaneously desorbed and subsequently removed by a vacuum applied on the downstream side of the membrane (Figure 17.1, bottom, III). As a consequence, the solute concentration on the membrane downstream surface remains practically zero, and a maximum concentration gradient between the two membrane surfaces is maintained. As a result, the diffusive net ﬂux across the membrane is maximal.

© 2003 by CRC Press LLC

µi feed

liquid phase

>>

µi permeate

vapor phase (vacuum)

(ambient pressure)

i i

i

pfeed

pperm

i

i

i i highly porous support

selective, nonporous membrane

I

II

i

i i i

i i

i

i

i

i i

i

i

i

i

i

i

i

i i

i

i

i

i

i i

i

III

i i

i

i

i

i

i i

i

i

i

ii i i

vacuum

FIGURE 17.1 The principle of solute transport across the membrane in pervaporation.

If the vacuum is not sufﬁciently low to desorb all of the solutes reaching the membrane downstream surface, the concentration of solute i at the membrane downstream surface will not be equal to zero. As a consequence, the concentration gradient will decrease and so will the diffusive net ﬂux across the membrane. The driving force in pervaporation is thus the gradient of the concentration, or more precisely of the chemical potential, of a solute across the selective membrane. It should be noted that the role of the vacuum in pervaporation is merely the efﬁcient desorption and removal of solutes from the membrane downstream surface, hence maintaining the driving force of the process. The pressure difference between the two sides of the membrane does not directly affect the transport of an individual component i within the membrane polymer, as is the case in pressure-driven processes involving porous membranes. Ideally, the molecular motion of a component i within the membrane polymer is purely diffusive and thus independent of any operating conditions beyond the membrane surfaces. Of course, these operating conditions contribute to determining the concentration of component i on the membrane surfaces, according to which, in turn, a certain diffusive net ﬂux of this component across the membrane results. To ensure the maximal concentration gradient, the downstream pressure must be low enough to remove any solute at the membrane downstream face. Because the solute i leaves the membrane downstream surface due to the vacuum in the vapor

© 2003 by CRC Press LLC

state, the downstream concentration of solute i is more conveniently expressed in terms of its partial pressure, according to Dalton’s law: p ip = y i ⋅ p p

(17.1)

p

where pi is the partial pressure of i in the permeate, yi is the molar fraction of I, p and p is the total downstream pressure. The solute feed concentration can be expressed in terms of its partial pressure in the feed by p if = x i ⋅ γ i ⋅ p 0i

(17.2) f

Equation (17.2) is a modiﬁed Raoult’s law where pi is the partial pressure of a compound i in the feed (Pa), xi is the molar fraction of I, and γi is the activity coefﬁcient of i in the feed. The saturated vapor pressure of i (Pa) at a given 0 temperature is denoted by pi . The activity coefﬁcient γi accounts for nonideal behavior of the solute in the feed solution as, for example, in the case of aqueous salt solutions (increased activity coefﬁcient of the solute due to the salting-out effect) or aqueous ethanol solutions (decreased activity coefﬁcient of the solute due to a co-solvent effect of ethanol). For the partial pressure gradient of solute i across the membrane, it hence follows: ∆p i = p if − p ip = x i ⋅ γ i ⋅ p 0i − y i ⋅ p p

(17.3)

Rearranging Equation (17.3) gives the minimum total downstream pressure p f necessary for ensuring ﬂux of a deﬁned solute i across the membrane, i.e., pi < pi: pp <

x i ⋅ γ i ⋅ p 0i yi

(17.4)

As long as Equation (17.4) is fulﬁlled, any compound possessing at least some volatility may be recovered from a liquid feed by pervaporation. Some aspects of Equation (17.4) should be emphasized and will be referred to later: 0

1. A low volatile compound (low pi ) might still be very well recovered by pervaporation if its activity coefﬁcient γi in the feed solution is high. 2. The driving force can be high either by a low total downstream pressure or by a high saturated vapor pressure of the solute, for example through heating of the feed solution. 3. Increasing the total upstream pressure does not effectively increase ﬂuxes because the bulk feed is liquid and thus of low compressibility. Assuming a constant solute feed concentration and instantaneous removal of any solute on the membrane downstream face, the selective transport of the solute i from the bulk feed to the downstream (vacuum) compartment can hence ideally be described by successive steps as:

© 2003 by CRC Press LLC

f c mem, i

µ

l, bulk i

f µmem, i

p µmem, i

p c mem, i

c l,i bulk

c

p i

µpi

FIGURE 17.2 The ideal proﬁle of the concentration and chemical potential of a solute i in the membrane polymer according to the equations derived in the text.

1. An equilibrium partitioning (sorption) of the solute i between the liquid bulk feed and the membrane upstream surface 2. A diffusion of solute i across the membrane polymer toward the membrane downstream surface 3. An equilibrium partitioning (desorption) of the solute i between the membrane downstream surface and the permeate vapor, as shown in Figure 17.2 For the equilibrium partitioning in steps 1 and 3, it follows that: cimem, f c mem, p = Si = i p l ,bulk ci ci mem,f,

l,bulk

mem,p

(17.5)

p

where ci ci , ci , and ci are the concentration of i in the membrane at the upstream interface, in the bulk liquid, in the membrane at the downstream interface, and in the permeate, respectively, and Si is the sorption (partitioning) coefﬁcient of i in the homogenous membrane polymer. For the ideal diffusion of solute i across the membrane polymer toward the membrane downstream surface, Fick’s First Law applies: J i = Dimem ⋅

c mem, f − cimem, p dc mem = Dimem ⋅ i dz z

(17.6)

where Ji is the ﬂux of solute i across the membrane, z is the selective membrane mem thickness, and Di is the diffusion coefﬁcient of i in the selective membrane polymer. Combining Equations (17.5) and (17.6) yields the transport model most applied in pervaporation, the so-called solution–diffusion model (Lee, 1975). This −2 −1 model gives the overall solute ﬂux across the membrane Ji (kg·m ·sec ) as

J i = Si ⋅ Dimem ⋅ 2

−1

∆ci (c l, bulk − cip ) = Pi ⋅ i z z

(17.7)

Pi (m ·sec ) is the so-called permeability of i in the membrane and a product of the solubility and the diffusivity of the solute i in the membrane. Because the

© 2003 by CRC Press LLC

solute concentration is related to the solute partial pressure, the driving force can also be expressed as a partial pressure gradient of the solute i across the membrane yielding J i = Si ⋅ Dimem ⋅

∆p i ( p f − p ip ) = Pi′⋅ i z z −1

−1

(17.8)

−1

with the permeability coefﬁcient Pi′ in (kg·m ·sec ·Pa ). It has been observed that the permeability Pi of solute i in a membrane can be described by an Arrhenius-type equation. Equation (17.4) can be rearranged to γ i ⋅ p i0 y i > = βimol pp xi

(17.9)

mol

where βi is deﬁned as the molar enrichment factor of i. If an enrichment of mol compound i is desired in the permeate, βi has to be greater than unity, and hence has the quotient yi/xi. An enrichment of compound i in the permeate is thus obtained by a low downstream pressure, a high saturated vapor pressure of compound i, or its high and positive activity coefﬁcient in the feed solution. It is common to use the enrichment factor βi as the ratio of the mass concentration of i in the permeate, −3 −3 p f ci (kg·m ), to the mass concentration of i in the feed, ci (kg·m ), rather than the mol molar enrichment factor βi : cip = βi cif

(17.10)

The ratio of the enrichment factors of a compound i and a compound j indicates the selectivity αij that a membrane has for compound i in comparison with compound j: cip

βi cf = p i = α ij βj cj c fj

(17.11)

For a given separation problem of a solute i from a bulk solvent j, the partial ﬂux Ji, or more generally the permeability Pi, the enrichment βi, and the selectivity αij, are the parameters that characterize the separation performance of a pervaporation process. When deriving the equations mentioned above, some assumptions were implicitly made with regard to the ideal transport of solute to, across, and away from the membrane. In pervaporation, nonideal transport phenomena can occur in the feed liquid phase adjacent to the membrane upstream surface, within the membrane polymer, and in the vapor phase adjacent to the membrane downstream face. All of these phenomena will be discussed in the following sections.

© 2003 by CRC Press LLC

17.2.1 NONIDEAL TRANSPORT PHENOMENA AT THE MEMBRANE SURFACES: CONCENTRATION POLARIZATION In Equations (17.7) and (17.8), perfect mixing of the feed bulk liquid and instant removal of solutes leaving the membrane downstream face were assumed. If these assumptions are not valid, boundary layers will develop on both sides of the membrane, affecting the solute transport to and away from the respective membrane surface. When feed components sorb in the membrane, a local concentration gradient develops in the liquid phase adjacent to the membrane upstream face. Due to this gradient, transport of components from the bulk liquid into the liquid–membrane interface occurs, replenishing the components sorbed in the membrane. This transport of components across the liquid phase adjacent to the membrane can be either convective or diffusive, depending on the hydrodynamic conditions over the membrane surface. If the ﬂux of a solute i across the liquid phase toward the membrane is lower than that across the membrane, solute i will be depleted in the liquid phase over the membrane upstream surface, resulting in a liquid solute concentration lower than that in the bulk feed (Figure 17.3A). Because the partitioning of the solute into the membrane is determined by the solute concentration in the liquid at the membrane upstream surface, the concentration of i in the membrane upstream surface, Equation (17.5), will be lower than expected according to its bulk feed concentration, as will the concentration gradient over the membrane and hence the trans-membrane ﬂux. This phenomenon is denoted concentration polarization and affects mainly the ﬂuxes of compounds of high sorption coefﬁcient, even under turbulent hydrodynamic conditions over the membrane, as will be shown. Under poor hydrodynamic conditions, a stagnant boundary layer forms over the membrane in which the solute transport is purely diffusive. Similar to the mass transport equation developed above for the solute transport across the membrane,

c mem,f i

c mem,f i c

mem,bl i

c mem,p i

c l,bulk i

c mem,p i

c l,bulk i

c ip

c ip

c l,bl i concentration boundary layer thickness δf

c mem,pbl i

membrane thickness z

(a)

membrane thickness z

concentration boundary layer thickness δp

(b)

FIGURE 17.3 The ideal concentration proﬁle of a solute i in the concentration boundary layer and in the membrane for the case of concentration polarization on (A) the membrane upstream side and (B) the membrane downstream side. The dotted line indicates the ideal concentration proﬁle without any concentration polarization.

© 2003 by CRC Press LLC

the diffusive solute ﬂux across this boundary layer can be described as

J i = Dif ⋅ f

c f − cil,bl dc bl = Dif ⋅ i δ dz

(17.12) l,bl

where ci is the bulk liquid feed concentration of solute i, ci is the concentration of f solute i in the liquid adjacent to the membrane surface, Di is the diffusion coefﬁcient of i in the liquid boundary layer, and δ is the concentration boundary layer thickness. Equation (17.12) implies that no solute–solute interactions occur in the boundary layer and is therefore only valid for dilute solutions. A similar phenomenon as described above can be found on the membrane downstream face. Because in pervaporation one aims at employing selective membranes as thin as possible for obtaining high ﬂuxes (see Equation 17.6), most membranes are composites consisting of a thin selective membrane and a macroporous support for mechanical stability and easier handling. The macroporous support faces the downstream compartment (Figure 17.1) and ideally should not interact with the solutes. During pervaporation, however, the narrow pores of the support constitute a mass transport resistance to the vacuum. This resistance results in a hindered transport of solutes away from the membrane downstream surface, causing an accumulation of solute in the pores of the support and hence a local increase of the solute concentration and thus downstream pressure. Assuming thermodynamic equilibrium at the membrane downstream face, this will cause the solute concentration to increase in the membrane downstream surface (see Equation 17.5), resulting in a lower concentration gradient and hence a reduced ﬂux across the membrane. Especially if the solute possesses a low partial pressure, the pressure drop in the macroporous support can cause the transmembrane ﬂux to cease totally.

17.2.2 NONIDEAL TRANSPORT PHENOMENA IN THE MEMBRANE POLYMER: SWELLING AND FLUX COUPLING In Equation (17.5), a Henry-type sorption of the solute in the membrane polymer was assumed, i.e., the sorption coefﬁcient was assumed linearly dependent on the solute concentration. When sorbing in the membrane polymer, the solutes cause a membrane swelling, which is the more pronounced the higher the degree of solute–polymer interaction or the higher the solute concentration in the feed. At high solute feed concentrations, the membrane polymer can swell to such an extent that its intrinsic properties are signiﬁcantly altered and strong nonideal interactions occur. These interactions and the swelling of the polymer can be described for complex mixtures by the Flory–Huggins theory (Flory, 1953; Mulder, 1991) and for binary mixtures by the solubility parameter theory if the feed components are hydrophobic (Hildebrand and Scott, 1949; Mulder, 1991). Even if the swelling of the membrane is less pronounced, it can affect the transport of solute across the membrane. Because a vacuum is applied for the removal of the solutes on the membrane downstream face, this side of the membrane is ideally “dry” in comparison to the more swollen and hence more ﬂexible membrane

© 2003 by CRC Press LLC

upstream face resulting from the solute uptake. This anisotropy of the membrane results in a nonuniform diffusivity of solute within the membrane, or in other words, mem Di will be concentration dependent and not constant across the membrane. One way to account for this phenomenon empirically is the relationship Dimem = Dimem,0 ⋅ e

π i ⋅φ

(17.13)

mem,0

where Di is the diffusion coefﬁcient of i in the membrane at zero concentration (under ideal conditions), πi is the so-called plasticizing constant, which is an empirical parameter for the degree of swelling of the membrane polymer caused by the solute, and φI is the volume fraction of solute in the membrane polymer. Equation (17.13) is merely empirical. A more phenomenological approach that considers the mobility of the permeating solute as a function of the free space available within the membrane polymer network is the free volume theory (Fujita, 1961; Fels and Huang, 1971), which has been discussed elsewhere (Huang and Rhim, 1991). In Equations (17.5) through (17.8) and (17.12) it is assumed that only solute– polymer and no solute–solute interactions occur. This excludes the possibility of synergistic effects between membrane permeants, such as ﬂux coupling. Flux coupling takes place when a permeant of low diffusivity (“slower” permeant) is dragged through the membrane polymer by a permeant of higher diffusivity (“faster” permeant), resulting in higher ﬂuxes of the slower permeant than expected. The opposite might also happen, i.e., the slowing down of the diffusion of the faster permeant by the slower one. The Maxwell–Stefan approach is capable of describing such nonideal phenomena (Wesselingh and Krishna, 1990). This theory assumes that the driving force for a solute i within a multicomponent mixture equals the sum of frictional resistances between solutes resulting from their relative motion while diffusing through the membrane polymer, as expressed by: 1 dµ i ⋅ = RT dz

n

∑x⋅ j

j=1

v j − vi D0ji

(17.14)

where dµi/dz is the local chemical potential gradient of i; xj is the mole fraction of solutes j = 1…n, vj is the local velocities of components j = 1…n, vi is the local 0 0 velocity of i, Dji is the Maxwell–Stefan interaction parameter, with 1/Dji indicating a friction coefﬁcient between components j and i, R is the universal gas constant, and T is the absolute temperature. Equation (17.14) represents the general Maxwell–Stefan equation. Applied to the special case of solute ﬂux across a polymer, Equation (17.14) needs to be adapted, which is accounted for in detail elsewhere (Heintz and Stephan, 1994). The Maxwell–Stefan approach is recommended for cases in which a strong nonideal behavior is observed because it is mathematically far more demanding than the equations presented above. It should be stressed, however, that for nonideal systems the Maxwell–Stefan approach might be the most elegant and efﬁcient way to describe the transport phenomena.

© 2003 by CRC Press LLC

The fundamentals of pervaporation were outlined above in the most simpliﬁed way, based on the mass conservation principle and Fick’s ﬁrst law, and discussed with regard to nonideal phenomena that may arise. Nonideal phenomena in pervaporation can be very complex and may demand individual solutions, which explains why until now no general mass transport model has been developed for pervaporation. To describe the mass transport across the dense membrane in a given situation, it might therefore be best to start with the simplest approach assuming Fickian diffusion. If, under the operating conditions of interest, nonideal mass transport phenomena are observed, a choice can still be made between an empirical adjustment of the ideal model or the use of a more complex structured model such as the ones mentioned above. In the latter case, one should be aware that most of the structured models still employ one or more empirical parameters that must be adjusted to experimental data. In addition, the experimental effort of determining all model parameters usually exceeds that needed for empirical models. An empirical model, on the other hand, will only be valid within the range of operating conditions studied and does not allow any extrapolation of the data.

17.3 TECHNICAL ASPECTS OF PERVAPORATION A typical pervaporation set-up is depicted in Figure 17.4. The liquid feed solution is recirculated continuously between the feed reservoir (1) and the pervaporation module (2). Pervaporation modules can be conﬁgured in a plate-and-frame, hollow ﬁber, or spiral wound mode (Rautenbach et al., 1991; Mulder, 1997; Fleming and Slater, 1992). The solutes permeating through the membrane leave the membrane downstream face as a vapor due to the vacuum that is established initially by the vacuum pump (4). The phase transition of the permeating solutes from the liquid to the vapor state goes along with heat consumption. This heat is taken up from the environment, 5

retentate F

P

T

2 feed P

1

T

4

T

permeate

3 fraction 2

fraction 1

FIGURE 17.4 A schematic standard pervaporation set-up. 1: feed tank; 2: pervaporation module; 3: condensation unit; 4: vacuum pump; 5: heat exchanger; F: ﬂow control; P: pressure indicator/ control; T: temperature control.

© 2003 by CRC Press LLC

namely the bulk feed, which consequently cools. In modules with a large membrane area, this causes a temperature drop between the feed and the retentate and must be compensated for. On the industrial scale, heat exchangers (5) are therefore implemented in the feed circuit. In laboratory units, this temperature drop may be neglected because the membrane area is commonly small in comparison to the recirculation rate of the feed, which is maintained at a controlled temperature. Instead of using a vacuum for maintaining the driving force, an inert gas can be swept over the membrane downstream surface for the removal of the permeate solutes (sweeping gas pervaporation). However, this mode of operation is less efﬁcient for maintaining the driving force, and it renders the condensation of the permeate solutes from the sweeping gas stream more difﬁcult. The permeate vapor is recovered in condensers at a temperature that allows a quantitative condensation of the vapor. The condensation can optionally be carried out in a series of condensation stages at different temperatures in order to achieve a permeate fractionation and increased enrichment of target compounds (3). As will be illustrated, a careful design of the condensation strategy is indispensable and most important in pervaporation. Once the vacuum is established, the vacuum pump (4) is shut off and ideally the condensation unit alone maintains the vacuum. Only if noncondensable gases permeate the membrane and enter the downstream compartment is continuous operation of the vacuum pump required for removal of these noncondensable gases, which otherwise would lead to an increased downstream pressure. Theoretically, scaling up is straightforward in pervaporation, and the ﬂuxes obtained on a laboratory scale can serve as a basis for the plant design on the larger scale. However, because it is common and easy to design laboratory-scale experiments close to ideal conditions, which on the larger scale would be uneconomical, care must be taken when up-scaling laboratory experiments with regard to the hydrodynamic conditions, the vacuum pressure, and the condensation strategy. Industrial size plate-and-frame modules, for example, consist of a stack of tightly packed membranes over which the feed solution is recirculated (Mulder, 1997). The membranes are separated by spacers and the permeate withdrawn optionally by a central permeate pipe (Stürken, 1994). Pressure losses on both the feed and the permeate sides of the packed membranes occur and need to be accounted for in the module design. On the feed side, the hydrodynamic conditions over the membrane will be less uniform than on the laboratory scale, resulting in more pronounced concentration polarization. On the permeate side, the packed conﬁguration of the membranes may constitute a mass transport resistance to the vacuum, resulting in a downstream pressure locally higher than that measured in the main vacuum duct. Both aspects may cause solute ﬂuxes lower than expected and a possible shift in selectivities. On the laboratory scale, the permeate vapor is commonly condensed at about 77°K using liquid nitrogen. For economic reasons, the condensation temperature on the industrial scale should be considerably higher. Because condensation efﬁciency is determined by both the condenser temperature and the residence time of the permeate vapor in the condenser, careful design of the condensation unit becomes crucial. It should be noted that a lower downstream pressure, desirable for high solute ﬂuxes, goes along with a higher permeate vapor velocity in the downstream

© 2003 by CRC Press LLC

compartment, and hence a lower residence time in the condenser. As a consequence, either the heat exchange area or the condenser temperature must be adjusted accordingly. A fractionated condensation at different condensation temperatures can signiﬁcantly increase the process performance, if the permeate composition allows (Brüschke et al., 1992; Baudot and Marin, 1997), as it enables further product enrichment and a more ﬂexible and deﬁned condensation of the permeate vapor. In the case of coupling a pervaporation unit to an active fermentation, special attention must be paid to noncondensable fermentation off-gases, such as carbon dioxide from a yeast fermentation, which can permeate through the membrane in large quantities. Using liquid nitrogen on the laboratory scale, most of these gases are condensed. On the industrial scale, however, these gases may pass the condensation unit virtually unaffected, lowering both the partial pressure and residence time of other permeants in the condenser. The consequence can be a strongly decreased condenser efﬁciency resulting in considerable loss of the more volatile permeate vapor compounds. The technical aspects of pervaporation as outlined above illustrate that for process optimization all process parameters must be considered, since they strongly affect each other. It should also be pointed out that although pervaporation is in principle a membrane separation process, its selectivity and effectiveness may be signiﬁcantly determined by mass and heat transport phenomena occurring beyond the membrane surfaces.

17.4 ADVANTAGES AND APPLICATIONS OF PERVAPORATION IN THE FOOD INDUSTRY As can be seen from the brief description of the pervaporation separation principle, in comparison to mere evaporative techniques the membrane constitutes an additional transport resistance; however, it allows a far more selective recovery of solutes due to solute–polymer interactions. Membrane polymers can be widely tailor made for individual applications. One membrane polymer is barely applicable to every imaginable separation problem, as will be shown in the following section.

17.4.1 HYDROPHILIC PERVAPORATION The most successful application of pervaporation on the industrial scale has been the dehydration of ethanol. Distillations of ethanol/water mixtures reach an azeotropic point at about 95.6 wt% of ethanol. The azeotrope can only be broken and the remaining water removed by adding entrainers such as benzene to the ethanol/water mixture. Entrainers constitute an environmental problem as well as requiring additional downstream processing for their subsequent removal from the ﬁnal product. Using hydrophilic polyvinylalcohol (PVA) membranes, pervaporation has been successfully coupled to distillation for water removal, yielding a ﬁnal purity of ethanol of about 99.95 wt% without the need to employ entrainers. PVA is a crystalline or so-called glassy polymer, with the polymer chains constituting a rigid network of little ﬂexibility (Mulder, 1997). Both ethanol and water sorb in PVA; however, due to its larger molecular size, the diffusivity of ethanol through the rigid

© 2003 by CRC Press LLC

PVA network is strongly hindered in comparison to water. Because the use of glassy polymers has been restricted so far mainly because of the selective removal of water from organic solvents, such as dichloroethylene, isopropylalcohol, and tetrahydrofuran, this separation has been widely referred to as hydrophilic pervaporation.

17.4.2 ORGANOPHILIC PERVAPORATION The removal of organic compounds from aqueous solutions, also called organophilic pervaporation, requires the use of a more ﬂexible polymer structure. Almost all organic compounds are of a larger molecular size than water, and their diffusivity is hindered in glassy structures. Membranes used for the separation of organic compounds from water are therefore of a rubbery nature, with a more ﬂexible polymeric network. Evidently, an eased diffusivity for the organic compounds goes along with that of water, resulting in a considerable loss of membrane selectivity. Therefore, special attention is given to modiﬁcation of rubbery polymers so that strong solute–polymer interactions are promoted, greatly enhancing the sorption of the organic solute in the membrane polymer in comparison with water. For example, using a silicon rubber membrane, a toluene/water separation factor of about 970 has been reported (Baker et al., 1997). Using an ethylene-propylene 1,4-hexadiene copolymer (EPDM) of similar thickness, these researchers obtained a separation factor of 33,400. This illustrates the importance of selecting or developing the appropriate membrane for the individual separation task. Glassy and rubbery membranes differ strongly with regard to the ﬂexibility of their polymeric structure. Within the more rigid polymeric network of a glassy membrane, the diffusivity of components will be strongly related to their molecular volume, whereas in the more ﬂexible structure of a rubbery membrane, it is less the diffusivity that differs strongly for different components, but far more the solute–polymer interaction. This is why the selectivity of glassy membranes is more diffusion controlled, while the selectivity of rubbery membranes is more sorption controlled. In food technology, the main interest in applying pervaporation is in separating organic compounds from an aqueous solution, i.e., the recovery of aroma compounds (so-called bioﬂavors) formed by microbial fermentations and biotransformations. Bioﬂavors are preferable to chemically synthesized ones due to their better public acceptance. In addition, bioﬂavors often exhibit a greater aromatic diversity than their chemically synthesized counterparts, as is the case, for example, with vanillin (Berger, 1995). Aroma concentrates are widely used as food additives to enhance the overall ﬂavor of foods or to compensate for the loss of aromas during food processing. They must hence represent the organoleptic characteristics of the aroma origin as well as be free of any harmful chemical contamination resulting from the aroma recovery process. Traditional aroma recovery processes such as distillation, adsorption, and solvent extraction often are discouraged because they operate at an elevated temperature that deteriorates the aroma quality, are not environmentally friendly due to high energy consumption and the use of toxic solvents, or involve elaborate puriﬁcation steps to remove solvent residues from the ﬁnal food product (Fleming, 1992; Schreiber et al., 1997). As a consequence, in recent years separation processes operating at gentler temperatures and avoiding harmful extraction aids have been investigated. These include

© 2003 by CRC Press LLC

steam distillation, air stripping (Le Thanh et al., 1993), the spinning cone column (Wright and Pyle, 1996), supercritical carbon dioxide extraction (Jolly, 1981), and membrane separation processes (Baudot and Marin, 1997). Bioﬂavors consist of aroma compounds of very differing physicochemical properties (Berger, 1995). Hence, the in situ recovery of these aromas from a microbial fermentation broth requires a process capable of simultaneously extracting aroma compounds of differing chemical nature. In addition, disturbing of or interfering with the ongoing bioconversion process should also be avoided. Thus, the recovery process should be efﬁcient at the bioconversion temperature, usually close to ambient, as well as recover, for example, low and high volatile compounds equally well. Pervaporation can be operated continuously at low temperature, does not require any extraction aid, and does not exert high stress on the active biocatalyst (Schäfer and Crespo, 2000). It is a membrane separation process that has been extensively studied on the laboratory scale for the recovery of ﬂavor compounds (Baudot and Marin, 1997; Karlsson and Träghård, 1993). Membrane fouling is a minor problem in pervaporation because the membranes used are nonporous. Organophilic pervaporation linked to a bioconversion process has until now solely been studied for the recovery of individual aroma compounds or inhibiting metabolic products (Böddeker, 1994; Lamer et al., 1996; Rajagopalan et al., 1994). Most research on aroma recovery by organophilic pervaporation has been conducted using aqueous aroma model solutions (Börjesson et al., 1996; Baudot and Marin, 1997), with the emphasis on the engineering aspects of pervaporation. An evaluation of the actual organoleptic value of an aroma concentrate obtained by pervaporation has only been reported recently (Schäfer et al., 1999). A few examples are presented to illustrate the separation principles outlined above, as well as to demonstrate the potential of pervaporation to respond to very diverse aroma separation problems under well-deﬁned operating conditions. Based on Equation (17.4), it was mentioned that low volatile compounds can still be recovered by pervaporation, given that their activity coefﬁcient in the feed solution is sufﬁciently high. Two examples of such low volatile compounds are γ-decalactone (boiling point 554°K) and vanillin (boiling point 515°K). Both compounds possess a saturated vapor pressure below 1 Pa at ambient temperature but a high activity in aqueous solution due to their hydrophobicity. TM Using a PDMS GFT 1060 membrane, a silicon membrane supported by a macroporous support, γ-decalactone was successfully recovered by pervaporation from −1 an aqueous feed solution with an initial concentration of 100 mg·kg (Baudot et al., 1999). However, a strong dependence of the γ-decalactone ﬂux on the total downstream pressure was observed (Figure 17.5). While the water ﬂux decreased linearly with increasing downstream pressure, the γ-decalactone ﬂux decreased exponentially. This observation can be explained by the differing capacity of the vacuum to remove both the water and γ-decalactone solutes that have diffused toward the membrane down0 stream surface. Because γ-decalactone is very slightly volatile (Pi of γ-decalactone at 303.15°K is 0.65 Pa while that of water is 4200 Pa), a slight increase of the total downstream pressure can cause an accumulation of γ-decalactone solutes in the macroporous support on the membrane downstream side, and concentration polarization occurs, resulting in a lower γ-decalactone ﬂux. On the contrary, the decrease in

© 2003 by CRC Press LLC

100

1.0

50

0.5

–2

water flux [ g·m ·h

–1

–2

]

–1

1.5

γ-decalactone flux [ g·m ·h ]

150

0

0

500

1000

1500

2000

0.0

total permeate pressure [ Pa ]

FIGURE 17.5 The ﬂux of water (䊊) and γ-decalactone (䊉) as a function of the total downstream pressure (Data from Baudot et al., J. Membrane Sci., 158(1–2), 167, 1999).

water ﬂux with increasing total downstream pressure is solely due to a decreased driving force within the premeate pressure range depicted. The recovery of vanillin (Böddeker et al., 1997) by a homogeneous polyether– block–polyamide membrane is unique in that vanillin crystallizes at ambient temperature in the downstream compartment due to its high melting point, without any need for condensation. Any other more volatile solutes permeating the membrane pass the crystallized vanillin and can either be subsequently condensed or discarded. It should be noted that for such a demanding separation problem composite membranes cannot be used, as the pressure loss within the macroporous support can be sufﬁcient to cause the condensation of vanillin at the membrane downstream face. While most applications of pervaporation deal with the removal of single aroma compounds, little has been reported on the recovery of a distinct aroma proﬁle. An example of such an aroma proﬁle is that of a muscatel wine formed during the viniﬁcation process. The aroma produced by yeast during wine must fermentation comprises up to 800 aroma compounds (Rapp, 1990), which makes it a challenge to recover aromas without altering their organoleptic quality. Using a polyoctylmethylsiloxane–polyetherimide (POMS–PEI) composite membrane, a muscatel wine must aroma concentrate can be obtained that is faithful to its origin and of high organoleptic value according to sensory panel evaluation (Schäfer et al., 1999). With the aroma proﬁle of muscatel wine must consisting of a subtle balance among individual aroma compounds of varying physicochemical properties, it is not obvious that their transport across the membrane polymer results in an aroma concentrate organoleptically faithful to the aroma of the feed solution. In fact, it has been observed that concentration polarization phenomena on the feed side strongly affect the permeate composition (Figure 17.6). Based on the equations presented above, the water-free mass fraction of four representative aroma compounds in the permeate, ethyl acetate, ethyl butanoate, ethyl hexanoate and linalool, was simulated as a

© 2003 by CRC Press LLC

permeate mass fraction [ % ]

60

40

20

0

0.01

0.1

1

10

ratio boundary layer/membrane thickness [ ]

FIGURE 17.6 The permeate mass fraction in wt% as a function of the ratio boundary layer/ membrane thickness. The permeate composition is calculated on a water-free basis for a dilute aqueous feed solution of ethyl acetate (solid), ethyl butanoate (dotted), ethyl hexanoate (long dash), and linalool (short dash).

function of the hydrodynamic boundary layer/membrane thickness on the basis of their sorption coefﬁcient Si, as well as their diffusion coefﬁcients in water and the membrane. Of the compounds investigated, ethyl hexanoate showed the highest afﬁnity for the membrane polymer and ethyl acetate the lowest. Diffusion coefﬁcients varied slightly among the compounds, however, to a much lesser extent than their respective sorption coefﬁcients. As can be seen in Figure 17.6, only below a boundary layer/membrane thickness ratio of about 0.01 does the permeate mass fraction remain constant. In other words, if a membrane of 20 µm thickness is used during pervaporation, the hydrodynamic boundary layer thickness should be less than 0.20 µm in order to avoid any shift in the permeate mass fraction due to concentration polarization. Highly turbulent conditions are hence required over the membrane. Less turbulent conditions will lead to a thicker hydrodynamic boundary layer, resulting in a shift in the permeate mass fraction, as is indicated by the dotted vertical lines in Figure 17.6.

17.5 CONCLUSIONS The principles of pervaporation and its advantages for the recovery of volatile compounds from bioconversions in particular have been presented and discussed. It has been shown that pervaporation is a versatile process that should be understood as a whole, and the process components of which can be adapted to individual separation problems. This versatility allows the invention of novel, tailor-made process strategies differing from the standard process design as depicted in Figure 17.4. One might, for example, think of alternative methods for capturing aroma compounds in the vapor permeate. The vapor permeate does not necessarily have to be condensed before the vacuum pump. Using liquid ring vacuum pumps, it may be condensed in the pump itself. Using dry vacuum pumps, it may be captured after the pump under a higher pressure than that of the vacuum. This opens the possibility of conceiving

© 2003 by CRC Press LLC

various alternatives for capturing aromas, such as the recovery of the aromas in an adsorptive matrix resulting immediately in a ﬁnal product, as for example for applications of controlled release. Likewise, other steps during the pervaporation process may be optimized and adapted for an individual separation problem.

REFERENCES Baker, R.W., Wijmans, J.G., Athayde, A.L., Daniels, R., Ly, J.H., and Le, M., The effect of concentration polarization on the separation of volatile organic compounds from water by pervaporation, J. Membrane Sci., 137, 159–172, 1997. Baudot, A. and Marin, M., Pervaporation of aroma compounds: comparison of membrane performances with vapor–liquid equilibria and engineering aspects of process improvement, Trans. IChemE., 75C, 117–142, 1997. Baudot, A., Souchon, I., and Marin, M., Total permeate pressure inﬂuence on the selectivity of the pervaporation of aroma compounds, J. Membrane Sci., 158, 167–185, 1999. Berger, R.G., Aroma Biotechnology, Springer, Berlin, 1995. Böddeker, K.W., Recovery of volatile bioproducts by pervaporation, in Membrane Processes in Separation and Puriﬁcation, Crespo, J.G. and Böddeker, K.W., Eds., Kluwer, Dordrecht, The Netherlands, 1994, pp. 195–207. Böddeker, K.W., Gatﬁeld, I.L., Jähnig, J., and Schorm, C., Pervaporation at the vapor pressure limit: vanillin, J. Membrane Sci., 137, 155–158, 1997. Börjesson, J., Karlsson, H.O.E., and Trägårdh, G., Pervaporation of a model apple juice solution: comparison of membrane performance, J. Membrane Sci., 119, 229–239, 1996. Brüschke, H.E.A., Schneider, W., and Tusel, G.F., Patent DE 3804236C2, 1992. Fels, M. and Huang, R.Y.M., Theoretical interpretation of the effect of mixture composition on separation of liquids in polymers, in Permselective Membranes, Rogers, C.E., Ed., Dellke Inc., New York, 1971, pp. 89–97. Fleming, H.L., Consider membrane pervaporation, Chem. Eng. Proc., 7, 46–52, 1992. Fleming, H.L. and Slater, C.S., Pervaporation: design, in Membrane Handbook, Ho, W.S. and Sirkar, K.K., Eds., Chapman and Hall, New York, 1992. Flory, P.J., Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953. Fujita, H., Diffusion in polymer–diluent systems, Fortschr. Hochpolym. Forschung, 3, 1–47, 1961. Heintz, A. and Stephan, W., A generalized solution–diffusion model of the pervaporation process through composite membranes, Part II. Concentration polarization, coupled diffusion and the inﬂuence of the porous support layer, J. Membrane Sci., 89, 153–169, 1994. Hildebrand, J.H. and Scott, R.L., The Solubility of Non-Electrolytes, Plenum Press, New York, 1949. Huang, R.Y.M. and Rhim, J.W., Separation characteristics of pervaporation membrane separation processes, in Pervaporation Membrane Separation Processes, Huang, R.Y.M, Ed., Elsevier, Amsterdam, 1991, pp. 111–180. Jolly, D.R.P., Wine Flavour Extraction with Liquid Carbon Dioxide, Process Biochem., Aug/Sept 1981, pp. 36–40. Karlsson, H.O.E., and Träghård, G., Pervaporation of dilute organic–water mixtures. a literature review on modelling studies and applications to aroma compound recovery, J. Membrane Sci., 76, 121–146, 1993.

© 2003 by CRC Press LLC

Lamer, T., Spinnler, H.E., Souchon, I., and Voilley, A., Extraction of benzaldehyde from fermentation broth by pervaporation, Process Biochem., 31, 533–542, 1996. Lawson, K.W. and Lloyd, D.R., Membrane distillation, J. Membrane Sci., 124, 1–25, 1997. Le Thanh, M., Voilley, A., and Tanluu, R.P., The inﬂuence of the composition of model liquid culture medium on vapor liquid partition coefﬁcient of aroma substances, Sci. Aliment., 13, 699, 1993. Lee, C.H., Theory of reverse osmosis and some other membrane permeation operations, J. Appl. Polym. Sci., 19, 83–95, 1975. Luque de Castro, M.D. and Gámiz-García, L., Analytical pervaporation: an advantageous alternative to headspace and purge-and-trap techniques, Chromatographia, 52, 265–272, 2000. Mulder, M., Basic Principles of Membrane Technology, Kluwer, Dordrecht, 1997. Mulder, M.H.V., Introduction to pervaporation, in Pervaporation Membrane Separation Processes, Huang, R.Y.M., Ed., Elsevier, Amsterdam, 1991, pp. 1–86. Néel, J., Thermodynamic principles of pervaporation, in Pervaporation Membrane Separation Processes, Huang, R.Y.M., Ed., Elsevier, Amsterdam, 1991, pp. 225–251. Rajagopalan, N., Cheryan, M., and Matsuura, T., Recovery of diacetyl by pervaporation, Biotechnol. Tech., 8, 869–872, 1994. Rapp, A., Natural ﬂavours of wine: correlation between instrumental analysis and sensory perception, Fresenius J. Anal. Chem., 337, 777–785, 1990. Rautenbach, R., Herion, C., and Meyer-Blumenroth, U., Engineering aspects of pervaporation: calculation of transport resistances, module optimization and plant design, in Pervaporation Membrane Separation Processes, Huang, R.Y.M., Ed., Elsevier, Amsterdam, 1991, pp. 225–251. Schäfer, T., Bengtson, G., Pingel, H., Böddeker, K.W., and Crespo, J.P.S.G., The recovery of aroma compounds from a wine-must fermentation by organophilic pervaporation, Biotechnol. Bioeng., 62, 412–421, 1999. Schäfer, T. and Crespo, J.G., Extraction of aromas from active fermentation reactors by pervaporation, in Integration of Membrane Processes into Bioconversions, BélaﬁBakó, K., Gubicza, L. and Mulder, M., Eds., Kluwer Academic/Plenum Publishers, New York, 2000, pp. 177–186. Schreiber, W.L., Scharpf, L.G., Jr., and Katz, I., Flavors and fragrances: the chemistry challenges, Chemtech, 3, 58–62, 1997. Stürken, K., Organophile Pervaporation: Ein Membranverfahren zur Aufarbeitung verdünnter wäßrig-organischer Lösungen, dissertation, GKSS Forschungszentrum Geesthacht GmbH, 1994. Wesselingh, J.A. and Krishna, R., Mass Transfer, Ellis Horwood, New York, 1990. Wright, A.J. and Pyle, D.L., An investigation into the use of the spinning cone column for in situ ethanol removal from a yeast broth, Process Biochem., 31, 651–658, 1996.

© 2003 by CRC Press LLC

18

Ultrasonic Mass Transfer Enhancement in Food Processing A. Mulet, J. Cárcel, J. Benedito, C. Rosselló, and S. Simal

CONTENTS 18.1 Introduction 18.2 Generation Methods of Power Ultrasound 18.3 Applications 18.3.1 Gas–Solid Mass Transfer Process 18.4 Liquid–Solid Mass Transfer Process 18.4.1 Inﬂuence of the Material Treated 18.4.2 Inﬂuence of Ultrasound Intensity 18.5 Conclusions Nomenclature References

18.1 INTRODUCTION High intensity ultrasound produces a variety of effects, such as radiation pressure, streaming, cavitation, and interface instabilities. These effects can inﬂuence mass transfer processes by producing changes in concentration gradients, diffusion coefﬁcients, or boundary layer (Liang, 1993). Heating produced by absorption of ultrasonic energy (thermoacoustic effect) can also affect mass diffusion. The transducers most commonly used to generate high intensity ultrasound are piezoelectric (Mason, 1998). Based on this technique, ultrasonic cleaning baths are the commercial systems where most experimental results have been obtained and published in the literature. Ultrasonic probe systems with mechanical ampliﬁers are also used when it is necessary to concentrate the generated acoustic energy. These two methods used to produce ultrasound are suitable for treatments in a liquid environment. Another arrangement of transducers is required for applications in gaseous media, due to their low density, and is responsible for their low speciﬁc acoustic impedance.

© 2003 by CRC Press LLC

In order to control a process, it is necessary to measure the main parameters. In ultrasonic applications, the amount and characteristics of the energy applied need to be known. The measurement of power and frequency enables not only a correct evaluation of the importance of these factors in the process, but also the appropriate process control. The use of high intensity ultrasound has been considered to enhance mass transfer for different products and processes such as brining of meat (Sajas and Gorbatow, 1978) and cheese (Sánchez et al., 1999), drying of rice (Muralidhara et al., 1985) and carrots (Gallego-Juárez et al., 1999), osmotic dehydration of apples (Floros and Liang, 1994; Simal et al., 1998), and extraction processes of several products such as pectin from apples (Panchev et al., 1988), chymosin from the fourth stomach of milk-fed calves to manufacture cheese (Kim and Zayas, 1991), bioactive principles from plant materials (Vinaturo et al., 1997), and even extractions with supercritical ﬂuids (Jun et al., 1997). The aim of this work is to examine the application of high intensity ultrasound to mass transfer processes. Four cases are analyzed to show the inﬂuence of transmission medium and the material considered. Three are applications in a liquid medium and the fourth is in a gaseous medium. The cases in a liquid medium are: a structured material, microscopically isotropic and with a large quantity of air-ﬁlled pores (osmotic dehydration of apple); a low structured, macroscopically isotropic material with a large quantity of liquid-ﬁlled pores (pressed cheese curd in brine, an intermediate product in some cheese manufacturing processes); and a highly structured, anisotropic material with low porosity (pork loin in brine). For the mass transfer process in a gaseous medium, a structured vegetal, nonisotropic material with partially air-ﬁlled pores will be considered (carrot dried with hot air).

18.2 GENERATION METHODS OF POWER ULTRASOUND Piezoelectric transducers convert a high frequency alternating current into mechanical vibrations. The most common applications of power ultrasound in mass transfer processes take place between a solid and a liquid medium. For these cases, ultrasonic cleaning baths are the most commonly used commercial equipment. In ultrasonic baths, the transducers are attached to the bottom of the bath. When they start to oscillate, vibrations are transmitted into the liquid. Standing waves are created by reﬂection of the emitted sound waves at the liquid/air interface. High and low intensities are obtained at ﬁxed levels (half wavelength) throughout the bath depth. As a consequence, the ultrasonic ﬁeld formed inside a bath is irregular and inﬂuenced by liquid height and the introduced loading (Figure 18.1). The technology of ultrasonic probe systems is also based on piezoelectric transducers. A “horn” is attached to a piezoelectric sandwich transducer in order to amplify the generated acoustic energy. The length of the horn is generally a half wavelength (or a multiple). The horn shape makes it possible to concentrate the ultrasonic energy. The gain for a given form of the horn is deﬁned by a speciﬁc ratio of the diameter of the two faces of the horn. If D is the driven face and d is the emitting face for an exponential horn, the ratio is D/d. This means that for a

© 2003 by CRC Press LLC

2.8 Hydrophone

Transducers

2.6

Acoustic pressure (bar)

2.4

Out

2.2 2.0 1.8 1.6 1.4

Water surface

1.2 1.0 0

5

10

15

20

Distance from the bottom (cm)

FIGURE 18.1 Example of the acoustic pressure variation vs. the distance from the bottom in an ultrasonic bath.

uniform cylinder there is no gain in wave amplitude, but rather the horn acts as an extender for the transference of the acoustic energy. For a stepped horn, the gain 2 is (D/d) . Horns are generally made of titanium due to the high resistance of this material to fatigue and erosion. The erosion of the transmitter surface causes a fall in the power. Variation in horn length can affect the frequency. For applications of power ultrasound in gaseous media, the most important problems are related to the efﬁcient generation and transmission of ultrasonic energy. It is necessary to achieve ultrasonic generators that meet the following requirements: good impedance matching with the air, large amplitude of vibration, high directional radiation, and high power capacity. In addition, for large-scale industrial applications, extensive radiating area would be required in the transducers. Presently, no commercial transducers meeting all the aforementioned conditions are available. A new type of ultrasonic generator has recently been developed (Gallego-Juárez et al., 1989). It is comprised of a transducer with a stepped-plate radiator and an electronic unit for driving the transducer (Figure 18.2). The design of the stepped proﬁle of the radiating plate allows control of the vibration and radiation pattern, thus permitting distribution of the vibration amplitude and, consequently, the acoustic ﬁeld, according to the needs of the speciﬁc application. The signal frequency can slide during operation in association with changes in the mechanical load. Keeping the voltage and current signals in the transducer in phase, a speciﬁcally designed electronic circuit can automatically correct the frequency of the generated signal so that the electronic system drives the transducer by producing a signal within the very narrow band corresponding to the resonance frequency of the transducer.

© 2003 by CRC Press LLC

Radiating plate

Piezoelectric ceramics

Mechanical amplifier

Sandwich

FIGURE 18.2 Structure of the stepped-plate transducer. (From Gallego-Juárez, J.A. et al., Drying Technol., 17, 597–608, 1999, courtesy of Marcel Dekker.)

One important point in the use of high intensity ultrasound is the power measurement. Due to problems of sonic wave reﬂections and the wearing out of transmitters, the power and frequency applied to samples may be modiﬁed. Hydrophones can supply local information on the acoustic pressure and frequency (Pugin and Turner, 1990). The signal created by a hydrophone may be captured and treated through an oscilloscope. This allows characterization of the acoustic ﬁeld and identiﬁcation of standing waves, high and low intensity zones, etc. A calorimetric method is another way to measure the input of the acoustic power into a medium. The method consists of the measurement of the temperature rise against the time in adiabatic conditions when ultrasound is applied (Margulis and Maximenco, 1990). The average power absorbed is: P = mC p

dT dt

where m is the liquid mass treated, Cp is the heat capacity and dT/dt is the variation of temperature T with time t that can be approximated by ∆T/∆t. As can be seen in Figure 18.3, there is a linear temperature increase. These unpublished data correspond to the results of experiments performed by the authors. A good correlation between acoustic pressure measured by a hydrophone and power estimated through the rate of the temperature increase was found (Figure 18.4). The measurements were carried out in a 600 ml glass beaker with 400 ml saturated brine. The starting temperature was the same in all cases (3°C).

18.3 APPLICATIONS 18.3.1 GAS–SOLID MASS TRANSFER PROCESS Drying carrots is an example of mass transfer from a solid medium to a gas medium. Gallego-Juárez et al. (1989) carried out experiments drying carrots with and without application of airborne ultrasound. A special generator unit and a stepped plate were

© 2003 by CRC Press LLC

Temperature of the medium (°C)

6 5 4 3 Start of the ultrasound application

2 1 0 0

50

100

150

200

250

Time (sec)

FIGURE 18.3 Temperature increase with application of ultrasound with a sound probe system.

Calorimetric measurement (W/cm2)

20 18 16 14 12 10 8 y = 33.922x – 18.22

6

R2 = 0.9958

4 2 0.5

0.7

0.9

1.1

1.3

Hydrophone pressure (bar)

FIGURE 18.4 Correlation between power ultrasound estimation by a calorimetric method and measurement of the acoustic pressure with a hydrophone.

used (Gallego-Juárez, et al. 1989). The experimental tests mainly consisted of measuring the water content of food samples after different times of application of highintensity ultrasonic ﬁelds in combination with forced air at various temperatures and ﬂow velocities. In all experiments, the frequency was kept constant at about 20 kHz while different sound pressure levels were applied. The experimental set-up can be seen in Figure 18.5. Different drying temperatures, air velocities, and power ultrasound were used. From data published by Gallego-Juárez et al. (1998), it is possible to calculate an

© 2003 by CRC Press LLC

TABLE 18.1 Diffusivities Calculated for Dehydration with and without Airborne Ultrasound Diffusivity × 10

Experiment T T T T T

= 60°C; Without ultrasound = 60°C; With ultrasound = 90°C; Without ultrasound = 90°C; With ultrasound = 115°C; With and without ultrasound

−6

2

(m /h)

2.67 4.86 6.22 7.74 11.35

Source: Data from Gallego-Juárez et al. (1998). Air velocity (V) = 1.3 m/sec; carrot samples 14 mm × 2 mm

Transducer Electronic generator

Hot air generator

Vibrating plate

Sample

Support plate FIGURE 18.5 Experimental set-up for forced air drying assisted by airborne ultrasound. (From Gallego-Juárez, J.A. et al., Drying Technol., 17, 597–608, 1999, courtesy of Marcel Dekker.)

effective diffusivity of water. For that purpose, a diffusive model for carrots proposed by Mulet (1994) was used. The less complex model was chosen for its simplicity. It was assumed that the solid temperature was constant and equal to drying air temperature and that the diffusivity was constant during drying experiments; the shrinkage was not considered. The model is valid if external resistance to mass transfer is negligible. Mulet et al. (1987) indicated that the air ﬂow had no inﬂuence 2 on carrot drying rate when greater than 6000 kg/hm (≈1.29 m/sec). Mitchell and 2 Potts (1958) ﬁxed this ﬂux limit at 4200 kg/hm (≈0.9 m/sec). The analyzed experiments were carried out at constant air velocity of 1.3 m/sec, hence the process was controlled by internal resistance. The diffusivities were calculated from GallegoJuárez et al.’s results and are shown in Table 18.1. The values are similar to those −6 found in the literature. Mulet (1994) reported an effective diffusivity of 6.3 × 10 2 2 m /h for carrot cubes using an air ﬂow of 8000 kg/hm at 60°C through drying. The obtained values showed that under similar conditions the carrot diffusivity in experiments carried out with ultrasound was higher than in experiments without

© 2003 by CRC Press LLC

Transducer Electronic generator Hot air generator

Samples

Vibrating plate

Suction system

Support plate Drain channels Static pressure

FIGURE 18.6 Experimental set-up for dehydration by directly coupled ultrasonic vibration. (From Gallego-Juárez, J.A. et al., Drying Technol., 17, 597–608, 1999, courtesy of Marcel Dekker.)

ultrasound. When the drying air temperature increased, the relative inﬂuence of ultrasound decreased. For an air temperature of 115°C, Gallego-Juárez (1998) did not ﬁnd differences between applying and not applying ultrasound. The ultrasound pressure levels used by these authors were 155 and 163 dB. No important differences in sample water content were found between samples dehydrated under these acoustic pressures. Signiﬁcant differences were found only in the fast-drying zone (i.e., the ﬁrst 10 min). The main difﬁculty in dehydration by airborne ultrasonic radiation is the low penetration of the acoustic energy into the food material due to the mismatch between acoustic impedances. Acoustic impedance is deﬁned as the product of density and sound speed in the material. When ultrasonic waves arrive at the air–material interface, a high percentage of their energy is reﬂected due to impedance differences between gas and solid. In order to avoid this problem, Gallego-Juárez et al. (1999) carried out another kind of experiment. A stepped-plate transducer was applied to the product directly, and static pressure was simultaneously exerted on the samples (Figure 18.6). To facilitate water removal, an air ﬂow of 1 m/sec at 22°C was applied. Assuming again that internal resistance controls the process, an effective diffusivity using the afore−6 2 mentioned model can be calculated. The result was 21.92 × 10 m /h. This diffusivity was higher than that found in 115°C drying air temperature experiments. In fact, the drying process is more powerful, since the ﬁnal moisture of the samples could be less than 1% (Gallego-Juárez et al., 1999). These results show that this procedure may be useful for food products with components sensitive to high temperature. The main mechanism involved may be the “sponge effect.” Ultrasound produces contractions and expansions of the material, and water is forced to exit from the vegetal matrix. Additionally, the acoustic stress may create microchannels that assist the water evacuation.

© 2003 by CRC Press LLC

18.4 LIQUID–SOLID MASS TRANSFER PROCESS 18.4.1 INFLUENCE

OF THE

MATERIAL TREATED

In ultrasound application in liquid media, an important parameter that should be kept in mind is the viscosity of the liquid. If this is high, the ultrasonic energy may be absorbed within a few centimeters from the emitters (Mason and Cordemans, 1996). The surface tension is another important factor, since it can prevent the appearance of cavitation phenomena. The solid material processed (in a liquid) is another factor to be considered when examining the effects produced by ultrasound. Simal et al. (1998) studied ultrasound inﬂuence (0.81 ± 0.17 bar; 40 kHz) in osmotic dehydration of apples at different temperatures. Water loss and sucrose gain were measured in apple cube samples at different times during the osmotic process. The results showed an acceleration of water loss and sugar gain rate when ultrasound was applied. In Figure 18.7, the differences between experiments with agitation of osmotic solution and with ultrasound are shown. The difference in water content after 3 h of treatment was approximately 25% lower in the ultrasonic experiment. The increase of dry matter in ultrasonic treatment relative to agitation experiments was about 40% at 50°C and 15% at 70°C after 3 h. Simal et al. (1998) found that the solute gain was more important at 40°C with ultrasonic application than at 70°C with agitation. Sánchez et al. (1999) carried out experiments on pressed cheese curd brining, an intermediate process in some types of cheese manufacture. Three kinds of brining

Difference (%) between ultrasonic and agitation brining

100 80 60 40 20 0 -20 -40 0

2000

4000

6000

8000

10000

12000

Time (sec)

FIGURE 18.7 Difference (% d.m.) in water content and solute content between ultrasonic and agitation experience for apple osmotic dehydration. 50°C, solute content; 70°C, solute content; 50°C, water content; 70°C, water content. Difference = 100 × (content with ultrasound − content with agitation)/content with ultrasound.

© 2003 by CRC Press LLC

Difference (%) between ultrasonic and static brining

30 25 20 15 10 5 0 -5

-10 -15 -20 0

2000

4000

6000

8000

10000

12000

Time (sec)

FIGURE 18.8 Difference (% d.m.) in water content and solute content between ultrasonic and static brining of pressed cheese curd. 5°C, solute content; 10°C, solute content; 5°C, water content; 10°C, water content. Difference = 100 × (content with ultrasound– content in static conditions)/content with ultrasound.

were tested: with brine agitation (dynamic conditions); without brine agitation (static conditions); and with applications of ultrasound. An ultrasonic cleaning bath was used as an ultrasonic generator (1.7 ± 0.22 bar; 30 kHz). The difference between ultrasonic and static conditions in 5 and 10°C experiments are shown in Figure 18.8. In this case, the decrease in water content was more important than the increase of solute content. Both processes (osmotic dehydration of apples and pressed cheese curd brining), with and without ultrasonic applications, ﬁtted well to a diffusional model (Simal et al., 1998; Sánchez et al., 1999), thus an effective diffusivity can be calculated. The Arrhenius equation was adequate to model temperature inﬂuence on diffusivity in all cases except for solute gain in osmotic dehydration of apple. The fact that apple cubes osmotically treated at different temperatures gained similar amounts of sucrose during the drying process could indicate that the main mechanism involved in sucrose transfer from the osmotic solution into the solid when sonication was used was not of a diffusional nature. A different mechanism for solute gain should be explored. As can be seen in Figures 18.7 and 18.8, the difference of solute and water between ultrasonic and nonultrasonic experiments had distinct behavior. Apple is a porous product with partially air-ﬁlled pores. Pressed curd is also a porous product, but its pores are ﬁlled with liquid. In osmotic dehydration of apple, the sponge effect, produced by ultrasound, forces the occluded air in the pores to exit. Then the osmotic solution enters the pores. Ultrasound produces a pressure assisted osmotic dehydration. Positive and negative pressures occur with the same frequency as the ultrasound is applied. The entry of solution into the apple matrix

© 2003 by CRC Press LLC

produces an important increase of sugar in ultrasonic assisted osmotic dehydration according to a mechanism other than diffusion. Similar results were obtained by Shi and Fito (1993). These authors found that although an increase in the solution temperature had a favorable effect on the rate of water diffusion, no signiﬁcant inﬂuence of temperature on sugar gain could be observed in apricot and pineapple samples treated through vacuum osmotic dehydration. This could explain the lack of inﬂuence of temperature on the sugar gain process. The proportion of air in cheese pores is lower than that in apple pores. Thus, the inﬂuence of ultrasonic compressions and expansions is less important. In the ﬁrst stages of brining, the pore air is “liberated” by ultrasound. Then the differences with regard to static conditions of brining are important. When there is no air in the pores, the effect of ultrasound decreases. Chiralt and Fito (1996) found in vacuum impregnation of Manchego cheese that during vacuum treatment the outﬂow of gas involved a residual whey release as well, because it was interchanged with brine during the inﬂow of the external liquid step when atmospheric pressure was restored. This could be the reason that the difference in salt content between ultrasonic and nonultrasonic experiments remains after the ﬁrst stage of brining in the time span considered. Another factor that may explain the different behavior between apple and cheese could be their different structure. The rigid structure of apples makes them a better ultrasonic vibration conductor than cheese, which presents a “rubbery” structure where the ultrasound waves are more easily absorbed. In both cases, apple and cheese, the water content decreased in experiments with ultrasound more quickly than in experiments without ultrasound. For the time spans considered, the difference in water content between ultrasonic and nonultrasonic experiments increased with the time of treatment. The ultrasonic waves could produce microcurrents in the solid–liquid interface that cause an increase of diffusion coefﬁcients and a decrease of the boundary layer of diffusion. Therefore, the water loss process may be inﬂuenced by ultrasound waves due to their effect on external resistance or/and internal resistance.

18.4.2 INFLUENCE

OF

ULTRASOUND INTENSITY

The effects produced by ultrasound in mass transfer processes are inﬂuenced by the intensity applied. Several authors have described the existence of an intensity threshold; for lower intensities no ultrasound effects were observed. Arkhangel’skii and Statnikov (1973) found that this threshold in acoustic evaporation was about 140 dB. The effect of acoustic streaming becomes greater than the inﬂuence of natural convection. High intensity produces high acoustic vibration, more violent cavitation, and greater microstreaming; thus the inﬂuence of ultrasound is intensiﬁed. In order to show ultrasound intensity effects, Cárcel et al. (1999) carried out several brining experiments using pork. Loin pork was brined in a NaCl-saturated brine for 45 min. Experiments were performed with and without ultrasound application. In the case of ultrasonic brining, nonexternal agitation was applied to the brine. In nonultrasonic brining, the experiments were carried out with and without brine agitation. For ultrasonic experiments, two types of generators were used: an

© 2003 by CRC Press LLC

TABLE 18.2 Mean Values and Conﬁdence Intervals (95%) for Salt Gain in Pork Loin after 45 Minutes of Brining Experiment Nonultrasonic without agitation Nonultrasonic with agitation Ultrasonic bath Sound probe system

g NaCl/g Initial Dry Matter 0.16 0.18 0.18 0.38

± ± ± ±

0.08 0.08 0.06 0.08

ultrasonic cleaning bath and a probe system. The acoustic pressures applied with the bath and with the probe system were 0.81 ± 0.05 bar (40 kHz) and 1.07 ± 0.20 bar (20 kHz), respectively. During brining, the temperature of the brine was maintained at a constant 2.0 ± 0.5°C. Final moisture and salt gain were measured. For every type of salting, at least three replications were carried out. In experiments with brine agitation, a strong stirring was used to create negligible external resistance to mass transfer. An ANOVA was performed on the ﬁnal moisture and NaCl gain of samples in the different experiments. Four groups of experiments were considered (nonultrasonic and nonagitation, nonultrasonic and agitation, using an ultrasonic bath, and using a sonic probe system treatment). For ﬁnal moisture content, at a 95% level of conﬁdence, no differences between different brining groups were observed. However, the experiments carried out with a probe system showed a higher ﬁnal moisture, and at the 90% level of conﬁdence, this group was signiﬁcantly different. On the other hand, signiﬁcant differences were found for salt gain between groups (95%), as can be seen in Table 18.2. The samples treated with the sound probe system gained more NaCl than the others. No differences were found between agitation, nonagitation brine, and ultrasound applied by means of the ultrasonic bath. Treatments in an ultrasonic bath consisted of the application of an ultrasonic energy in a volume of liquid. The fact is that all carcasses vibrate to produce an ultrasonic ﬁeld more or less irregular in all quantities of liquid contained. The sound probe system can generate a high intensity ﬁeld in a small zone and then produce an ultrasonic ﬁeld when focused. Just below the probe tip, the maximum ultrasonic power is generated. If a sample is placed at this point, it receives a large amount of the acoustic pressure emitted. Pork loin is not a porous material, so the effects of ultrasound are less important than for other foods. According to the literature, when the intensity of ultrasound is above the threshold, the salt gain should be increased with respect to the nonultrasonic brining. In that case, the effects created by ultrasound become important when the intensity is sufﬁcient. Only then, microstreaming, contractions and expansions of material, cavitation, etc., force the entry of salt into the meat matrix. However, this high intensity seems to affect the exit of water from the pork loin, an effect different from the one found in apple and cheese osmotic dehydration, where an increase in water loss was observed.

© 2003 by CRC Press LLC

18.5 CONCLUSIONS High intensity ultrasound enhances the mass transfer process, affecting internal as well as external resistance to mass transfer. The propagating medium, material treated, and intensity applied can inﬂuence the effects produced by ultrasound. Different technologies are needed for applications in gas and liquid media. Stepped-plate transducers generate the intensity to accelerate the drying of carrots with air. The decrease of the boundary layer and successive contractions and expansions produced by ultrasound aid water exit from carrot matrix. In liquid applications, mass transfer is also improved. Water loss in osmotic dehydration of apple and cheese brining is increased by applications of ultrasound. The material structure also affects the inﬂuence of ultrasound. The removal of air from apple pores is assisted by ultrasound, and the air is replaced by osmotic solution. Thus, solute increase in a solid matrix is very important. Cheese pores have less air occluded and, as a consequence, the inﬂuence of ultrasound on solute gain is less important. Additionally, apple structure better transmits ultrasound than does cheese. Pork loin has no large pores, and therefore mass transfer is difﬁcult. Nonsigniﬁcant differences appear between applications of ultrasound by means of a commercial cleaning bath and agitation or nonagitation brine experiments. Higher ultrasonic intensity generated by a probe system accelerated salt gain. This shows the existence of a threshold where the inﬂuence of ultrasound appears. Commercial baths do not usually reach this threshold for some products, and no differences appear, as reported in the literature. High intensities applied to meat increase salt gain and make water loss difﬁcult. These effects could lead to an increase in the process efﬁciency.

NOMENCLATURE D d P m Cp T t

Diameter of driven face of a transductor; m Diameter of emitting face of a transductor; m Power; W Mass; kg Heat capacity; J/kg°C Temperature; °C Time; sec

REFERENCES Arkhangel’skii, M.E. and Statnikov, Y.G., The action of ultrasonic vibrations on diffusion, in Physical Principles of Ultrasonic Technology, Vol. 2, Rozenberg, L.D., Ed., Plenum Press, New York, 1973. Cárcel, J.A., Benedito, J., Llull, P., Clemente, G., and Mulet, A., Inﬂuence of Ultrasound in Meat Brining, Proceedings of AICHE-CoFE 99, Dallas, November 2–5, 1999, pp. 163–170. Chiralt, A. and Fito, P., Salting of Manchego-type cheese by vacuum impregnation, in Food Engineering 2000, Chapman and Hall, New York, 1996, pp. 215–230. Floros, J.D. and Liang, H., Acoustically assisted diffusion through membranes and biomaterials, Food Technol., December 1994, pp. 79–84.

© 2003 by CRC Press LLC

Gallego-Juárez, J.A., Some applications of air-borne power ultrasound to food processing, in Ultrasound in Food Processing, Povey, M.J.W. and Mason, T.J., Eds., Blackie, Glasgow, 1998, pp. 127–143. Gallego-Juárez, J.A., Rodriguez-Corral, G., Gálvez-Moraleda, J.C., and Yang, T.S., A new high-intensity ultrasonic technology for food dehydration, Drying Technol., 17, 597–608, 1999. Gallego-Juárez, J.A., Rodríguez-Corral, G., San Emetano, J.L., and Montoya-Vitini, F., Electroacoustic unit for generating high sonic and ultrasonic intensities in gases and interphases, Spanish patent 8903371, 1989; European patent No. EP 450.030.A1, 1991; U.S. patent No. 5,299,175, 1994. Jun, C., Kedie, Y., Shulai, C., Adschiri, T., and Arai, K., Effects of Ultrasound on Mass Transfer in Supercritical Extraction, The 4th International Symposium on Supercritical Fluids, Sendai, Japan, May 11–14, 1997, pp. 707–710. Kim, S.M. and Zayas, J.K., Effects of ultrasound treatment on the properties of chymosin, J. Food Sci., 56, 926–930, 1991. Liang, H., Modelling of ultrasound assisted and osmotically induced diffusion in plant tissue, thesis, Purdue University, Lafayette, IN, 1993. Margulis, M.A. and Maximenco, N.A., Appendix: measurement of ultrasound-absorbed power (calorimetric methods), in Advances in Sonochemistry, Vol. 2, Mason, T.J., Ed., JAI Press, London, 1990, pp. 288–289. Mason, T.J., Power ultrasound in food processing: the way forward, in Ultrasound in Food Processing, Povey, M.J.W. and Mason, T.J., Eds., Blackie, Glasgow, 1998, pp. 105– 126. Mason, T.J. and Cordemans, E.D., Ultrasonic intensiﬁcation of chemical processing and related operations: a review, Trans. IchemE., 74, 511–516, 1996. Mitchell, T.J. and Potts, C.S., Through-circulation drying of vegetables. III. Carrots, J. Sci. Food Agric., 9, 93–98, 1958. Mulet, A., Drying modelling and water diffusivity in carrots and potatoes, J. Food Eng., 22, 329–348, 1994. Mulet, A., Berna, A., Borrás, M., and Piñaga, F., Effect of air ﬂow rate on carrot drying, Drying Technol., 5, 245–258, 1987. Muralidhara, H.S., Ensminger, D., and Putnam, A., Acoustic dewatering and drying (low and high frequency): state of the art review, Drying Technol., 3, 529–566, 1985. Panchev, I., Kirchev, N., and Kratchanov, C., Improving pectin technology. II. Extraction using ultrasonic treatment, Int. J. Food Sci. Technol., 23, 337–341, 1988. Pugin, B. and Turner, A.T., Inﬂuence of ultrasound on reaction with metals, in Advances in Sonochemistry, Vol. 1, Mason, T.J., Ed., JAI Press, London, 1990, pp. 81–118. Sajas, J.F. and Gorbatow, W.M., Use of ultrasound in meat technology, Fleischwirtschaft, 58, 1009–1021, 1978. Sánchez, E.S., Simal, S., Femenia, A., Benedito, J., and Rosselló C., Inﬂuence of ultrasound on mass transport during cheese brining, Eur. Food Res. Technol., 209, 215–219, 1999. Shi, Q.S. and Fito, P. 1993. Vacuum osmotic dehydration of fruits, Drying Technol., 11, 1432–1442, 1993. Simal, S., Benedito, J., Sánchez, E.S., and Rosselló, C., Use of ultrasound to increase mass transport rates during osmotic dehydration, J. Food Eng., 36, 323–336, 1998. Vinatoru, M., Toma, M., Radu, O., Filip, P.I., Lazurca, D., and Mason T.J., The use of ultrasound for the extraction of bioactive principles from plant materials, Ultrason. Sonochem., 4, 135–139, 1997.

© 2003 by CRC Press LLC

19

Mass Transfer and Residence Time Studies in Spinning Cone Columns M.E. Vargas-Ugalde, K. Niranjan, D.L. Pyle, and G.F. Gutiérrez-López

CONTENTS 19.1 Introduction 19.2 Background 19.2.1 Flavor Recovery Technology 19.2.2 The Spinning Cone Column 19.2.3 Mass Transfer Coefﬁcients 19.2.4 Mean Residence Time 19.3 Materials and Methods 19.3.1 Equipment 19.3.1.1 SCC 1000 Flavourtech 19.3.1.2 SCC Perspex Laboratory Model 19.3.2 Methods 19.3.2.1 Determination of Overall Volumetric Mass Transfer Coefﬁcients (KLa) 19.3.2.2 Evaluation of the Mean Residence Time 19.4 Results and Discussion 19.4.1 Mass Transfer 19.4.2 Mean Residence Time 19.5 Conclusions Nomenclature Acknowledgments References

19.1 INTRODUCTION The Spinning Cone Column (SCC) is a multistage liquid–gas contacting unit with increasing applications in food processing. SCC is a type of distillation equipment that operates under vacuum pressures. It presents many advantages because of its mass transfer efﬁciency, the short processing times involved, and its ability to handle

© 2003 by CRC Press LLC

highly viscous and non-Newtonian liquids under reduced pressure. An understanding of some of the mechanisms of simultaneous transfer of momentum, heat, and mass in this equipment is necessary to save energy and to improve not only the separation efﬁciency, but also the basis for selection, design, and control of columns and processes involved. Despite the extensive use of this technology, few studies have been conducted concerning the performance and mathematical modeling of this equipment. To study the mass transfer and the residence time distribution in this device, a Perspex model geometrically similar to the pilot plant SCC 1000 Flavourtech Europe LTD installed at the University of Reading, U.K., was employed. This model uses air to simulate the steam current. For these experiments, two spinning and two stationary cones were employed; residence time experiments were also performed in the pilot equipment.

19.2 BACKGROUND 19.2.1 FLAVOR RECOVERY TECHNOLOGY The main objective when processing foods is preservation; the processes used include evaporation, pasteurization, high temperature–short time pasteurization, distillation, drying, and other operations. By applying these processes, it is possible to extend the shelf life of many food materials. However, in most heat treatment procedures, the operating conditions may change the original properties of a product. The use of low temperature and vacuum pressure is a popular way of maintaining ﬂavor and aroma characteristics. In most cases, compounds responsible for ﬂavor and aroma are present in products in small amounts; they are highly volatile and extremely sensitive to heat damage. To minimize losses of aroma and ﬂavor when processing foods, ﬂavor/ aroma recovery technology is widely used. Basically, this technology consists of removing and collecting volatiles before the main process and reincorporating them into the ﬁnal product at the last stage of processing. In this way, the original sensory characteristics are maintained (Schobinger, 1999). Flavor recovery technique was initially applied to process juice fruits around 1940. There exist different kinds of equipment to perform the separation of volatiles; the use of a particular one depends on the product characteristics, the process costs, and the ﬁnal quality to be obtained.

19.2.2 THE SPINNING CONE COLUMN Among the uses of the SCC in the food industry are (Menzi and Emch, 1989; Flavourtech, 1998): • • • • • •

Aroma recovery from fruit and vegetable juices, botanicals, herbs and spices Dealcoholization of drinks Desulﬁting of grape juice Removal of tannins Coffee, tea, and citrus byproduct processing Removal of off-odors from dairy products

© 2003 by CRC Press LLC

In fruit juice processing, the SCC is employed just before the product enters the concentrator. Through the use of SCC, a substantial aroma recovery can be achieved with a low evaporation rate (from 0.5 to 2.0% depending on the fruit) (Craig, 1987; Schobinger, 1999). The SCC resembles a combination of centrifuge–distillation units, and it is classiﬁed in the same group of equipment as the packed, bubble-cap, and plate columns (Menzi and Emch, 1989; Shah, 1995). In this equipment, the inert stripping gas—nitrogen or steam at low temperatures — removes a vapor stream of volatile compounds from liquids or slurries. Internally, the column contains two series of inverted cones. A series of ﬁxed cones is attached to the inside wall of the column; another series of cones, parallel to those ﬁxed, is attached to a rotating shaft. The stationary and rotating cones alternate vertically. The product comes in to the top of the column, ﬂows down the upper surface of the ﬁrst ﬁxed cone, and drops onto the ﬁrst rotating cone due to gravity. Then, due to centrifugal force, the liquid is spun into a turbulent thin ﬁlm that is forced upward to the top of the spinning cone, dropping onto the next stationary cone. The product then goes from cone to cone to the bottom of the column, following a spiral trajectory. The gas for stripping comes into the bottom of the column and ﬂows upward, passing across the surface of the thin ﬁlm of liquid and collecting volatile compounds along its path. On the underside of the rotating cones are bafﬂes that create a high degree of turbulence in the rising vapor stream. The vapor ﬂows out of the top of the column and passes through a condensing system, which captures the volatile compounds in a concentrated liquid form. The remaining liquid or slurry is pumped out of the bottom of the column (Flavourtech, 1991).

19.2.3 MASS TRANSFER COEFFICIENTS In chemical and food engineering, empirical correlations are commonly used in many situations because real systems exhibit a different behavior from ideal, and it is not easy to determine the contribution of each of the variables involved in a particular case. Although these correlations cannot be applied to general cases, they are useful to predict the behavior of a given phenomenon within the range of conditions studied. The rates of mass transfer between gas and liquid phases are strongly affected by the solubility of the gaseous components in the liquid. Oxygen is among the sparingly soluble gases in aqueous solutions. The solubility of a gas in a liquid depends on the temperature, the equilibrium partial pressure of the solute gas in the gas phase, and the concentration of the solute gas in the liquid phase (Aiba et al., 1973). The total pressure on the system also affects the solubility, but when the value of this parameter is lower than 5 atm, the solubility of gases can be considered independent of the total pressure. In those cases where the concentration of dissolved gas is small and the temperature and pressure are far from the critical temperature and pressure of the gas, Henry’s law can express the solubility of a gas in a liquid: p=Hx

© 2003 by CRC Press LLC

(19.1)

Henry’s constant (H) is affected by temperature, concentration of dissolved salts, and pH. For a sparingly soluble gas, such as oxygen, the overall gas transfer rate (R) is given by the ﬂux equation: *

R = KLa (c − c)

(19.2)

Volumetric R and a are evaluated considering the total liquid volume, since the gas hold-up is considered negligible for calculation purposes. Concentration patterns in the SCC are not those of a perfectly mixed tank, but they resemble those of plug ﬂow. Then, the log mean oxygen concentration applies, and it is possible to calculate KLa from a mass balance, assuming the oxygen concentration in the liquid phase is equal to zero: (V KLa) ∆clm = L ∆c

(19.3)

For cylinders and disks rotating in an inﬁnite ﬂuid, several equations have been developed to predict mass transfer rates. In Sherwood et al. (1975) the following relationship for cylinders is reported: 2/3

0.664

JD = St Sc = (kc/U) Sc

(19.4)

The same authors reported the following equation for oxygen transport to a 5 6 rotating disk in salt water for values of Re between 6 × 10 and 2 × 10 and Sc numbers between 120 and 1200. k cd = 5.6 Re1.1 Sc0.333 D

(19.5)

They reported a semitheoretical relationship for the turbulent region: k cd = α Re 0.4 Sc0.25 D

(19.6)

They also described electrochemical studies by Bagotskaya, who found values of kc proportional to the ﬁrst power of rotational speed in the case of turbulent ﬂow on a rotating disk. Blanch and Clark (1996) have reported α and β values (see Equation 19.7) to obtain kLa in bubble columns and airlift contactors as a function of the superﬁcial gas velocity and liquid properties for low liquid viscosities. In these systems, α values from 0.4 to 1.09 and β values from 0.89 to 1.23 were reported. β

kLa = α vs

(19.7)

Blanch and Clark (1996) also reported on correlations for kLa in stirred tanks for inviscid systems as follows:

© 2003 by CRC Press LLC

For coalescing (clean) dispersions: −2

0.4

−3

0.7

0.5

(19.8)

0.2

(19.9)

kLa = 2.6 × 10 (Po/V) vs For noncoalescing (dirty) dispersions: kLa = 2.0 × 10 (Po/V)

vs

−3

These equations were obtained for power inputs from 500 to 10,000 watt m and small vessels of up to several thousand liters (Blanch and Clark, 1996) Zivdar (1997) reported results on mass transfer characteristics of structured packed columns 0.1 m in diameter were evaluated for humidiﬁcation of air and oxygen desorption from water. Gas and liquid transfer mass coefﬁcients were dependent on the corresponding ﬂow rates, and gas phase mass transfer was also inﬂuenced by change of liquid hold-up due to gas ﬂow.

19.2.4 MEAN RESIDENCE TIME The measurement of residence time distributions (RTD) is useful to estimate the performance of process equipment or to ﬁnd how much it deviates from the ideal behavior. Even when the overall ﬂow rate may have no detectable variation, not all particles passing through the system stay there for the same length of time. For a single system, there is a spread of residence times, which can be caused by channelling, recycling, or creation of stagnant regions of ﬂuid in the vessel. The residence time distribution function, E(t), is deﬁned considering that the fraction of product in the outlet stream that has been in the system for a length of time between t and t + dt is equal to Edt (Denbig and Turner, 1984), so that:

∫

∞

E( t )dt = 1

(19.10)

0

The average time spent by a product ﬂowing at ﬂow rate v through a vessel volume V is equal to V/v. If the density of the ﬂowing stream does not change as it passes through the system and for a no-back-mixing situation, the mean residence time (MRT) is equal to V/v and: MRT =

∫

∞

tE( t )dt

(19.11)

0

19.3 MATERIALS AND METHODS Two types of spinning cone columns were used in this work: a pilot plant SCC1000 model (Flavourtech LTD, Europe), and a Perspex laboratory model. To determine the dissolved oxygen concentration in the laboratory column, a JENWAY 9071 dissolved oxygen meter was used. Compressed nitrogen was the degassing agent used to eliminate oxygen from deionized water during the measurements.

© 2003 by CRC Press LLC

An injection gun (APV Co. Ltd.) and a spectrophotometer (CECIL 1000 Series, CE1021 model) were used for the residence time distribution (RTD) studies with cochineal red A spec Pure 70 BAYER AG as a tracer. The carboxymethylcellulose (CMC) working solutions were prepared with Blanose CMC 7HF Sodium Carboxymethylcellulose Aqualon, Hercules Inc.

19.3.1 EQUIPMENT 19.3.1.1 SCC 1000 Flavourtech The SCC column 1000 is composed of a vertical stainless steel cylinder 2.0 m in height and 0.33 m in diameter, with 40 cones and a capacity range of 100–1000 −1 −1 l h . The rotating speed varies from 26 to 160 sec ; nitrogen or low temperature steam can be used as the stripping medium, and the column usually operates at vacuum pressures (Flavourtech, 1991). 19.3.1.2 SCC Perspex Laboratory Model To get information about the performance of the SCC, a Perspex model geometrically similar to the pilot plant column was employed in this research. The model is 0.2 m in height and 0.37 m in diameter; it has three stationary and two spinning cones. It works at atmospheric pressure, and air is used instead of steam or nitrogen for hydrodynamic purposes. The model has a shaft 50 mm in radius, and the column inner radius is 185 mm. Both the spinning and the stationary cones have inner and outer radii of 50 and 145 mm, respectively. Four pressure taps are also available, and it is possible to change shaft velocity, number of cones, and liquid and air ﬂow rates. A diagram of this column is presented in Figure 19.1.

Perspex Column

air

cin

pt Oxygen probe

cones pt

tank

solution

shaft

motor

Recirculation or drain tube

cout

pump water pool pt = pressure tappings

FIGURE 19.1 Schematic diagram of the SCC laboratory Perspex model.

© 2003 by CRC Press LLC

N2

TABLE 19.1 Conditions for Mass Transfer Experiments Water Flow Rate 3 −1 5 (m sec × 10 )

Nitrogen Flow Rate 3 −1 4 (m sec × 10 )

Cone Velocity (sec )

4.2, 5.8, 11.7

8, 1.2, 1.6, 2.0

26, 47, 79, 131

−1

For the RTD determinations, several experiments were performed using the pilot plant SCC.

19.3.2 METHODS 19.3.2.1 Determination of Overall Volumetric Mass Transfer Coefﬁcients (KLa) KLa were calculated by measuring the dissolved oxygen concentration in deionized water at the bottom of the column until the condition of equilibrium was reached, employing a deoxygenating method using nitrogen as the displacing gas (Heineken, 1971; Atkinson and Mavituna, 1991), based on the factorial experimental design presented in Table 19.1. 19.3.2.2 Evaluation of the Mean Residence Time Water and carboxymethylcellulose (CMC) at 0.5 and 1% w/w were used, employing different conditions in both the Perspex model and the pilot plant SCC, as presented in Table 19.2. Mean residence time (MRT) was measured by a pulse method (Levenspiel, −3 1972) using cochineal red dye as a tracer (0.15 g cm for the laboratory model and −3 0.3 g cm for the pilot column) and measuring the concentration as a function of time by reading the absorbance of the samples at the exit of the equipment in a spectrophotometer CECIL 1021 and by applying Equation (19.11).

19.4 RESULTS AND DISCUSSION 19.4.1 MASS TRANSFER KLa values for the conditions presented in Table 19.1 were calculated by applying 3 Equation (19.3) for a tank volume (V) of 0.0215 m . Oxygen concentration values at −3 the inlet of the system (cin) fell within 0.007 to 0.008 kg m for most of the trials. The equilibrium oxygen concentration (cout) was measured with an oxygen probe immersed in the water pool formed at the bottom of the column. Equilibrium was considered to have been reached when no change of this measured value was registered by the probe (see Figure 19.1). In Figure 19.2, calculated KLa values as a function of angular velocity of the −4 3 −1 cones and gas ﬂow rate for a liquid ﬂow rate of 4.2 × 10 m sec are presented. In Figure 19.3, calculated KLa values as a function of gas ﬂow rate and liquid ﬂow

© 2003 by CRC Press LLC

TABLE 19.2 Conditions for Determination of Mean Residence Time Experiments

Water

CMC

Water

CMC 0.5%

SCC Perspex Model −1 Cone velocity (sec ) 3 −1 5 Liquid ﬂow rate (m sec ) × 10 3 −1 4 Gas ﬂow rate (m sec ) × 10 Concentration (%) 3 −1 5 Liquid ﬂow rate (m sec ) × 10 3 −1 4 Gas ﬂow rate (m sec ) × 10 −1 Cone velocity (sec )

26, 47, 79, 131 3.3, 6.7 0, 18.33 0.5 1.6, 3.3 0 79, 47, 131

SCC Pilot Plant −1 Cone velocity (sec ) 3 −1 5 Liquid ﬂow rate (m sec ) × 10 3 −1 Gas ﬂow rate (m sec ) −1 Cone velocity (sec )

26, 61 5.6, 11.1 0 26, 61

3

−1

Liquid ﬂow rate (m sec ) × 10 3 −1 Gas ﬂow rate (m sec )

5

1.0 0.8 0 79

2.8, 5.6 0

0.007

KLa sec-1

0.006 0.005 0.004 0.003

131

0.002

79

0.001

47

0

26 7.88

11.81

15.83

Angular velocity sec-1

19.67

Gas flow rate m3sec-1 × 10-4 −4

3

−1

FIGURE 19.2 KLa for oxygen in water. Liquid ﬂow rate = 4.2 × 10 m sec .

© 2003 by CRC Press LLC

0.009 0.008

KLa sec

-1

0.007 0.006 0.005 0.004

11.67

0.003 0.002

5.83

Liquid flow rate 3 -1 -5 4.17 m sec × 10

0.001 0 7.88

11.81

15.83

19.67

Gas flow rate m3 sec -1 × 10-4

−1

FIGURE 19.3 KLa for oxygen in water. Angular velocity = 47 sec . −1

rate for an angular velocity of 47 sec are presented. From Figures 19.2 and 19.3, it is possible to observe that KLa increases with gas and liquid ﬂow rates and angular velocity; this agrees with ﬁndings made by Zivdar (1997) for structured packed columns. Empirical correlations reported in the literature for mass transfer descriptions for rotating disks, cylinders (Sherwood et al., 1975), bubble columns, and stirred tanks (Blanch and Clark, 1996) showed that the dimensionless mass transfer number 0.5 depends on the value of (Re) . An empirical correlation (Equation 19.12) of KLa values and ω, L, and G was obtained by means of the S.A.S. statistical program (S.A.S. Institute, 1989) using an iterative nonlinear least squares methodology based on the Gauss–Newton method. 0.489

KLa = 2.254

(19.12)

It is possible to observe that KLa depends on the dynamic parameters with an exponent close to 0.5. This may indicate that mass transfer in the SCC follows a similar trend as in other situations reported in the literature (Sherwood et al., 1975; Blanch and Clark, 1996; Zivdar, 1997).

19.4.2 MEAN RESIDENCE TIME An example of the E curves obtained using the Perspex laboratory model is presented in Figure 19.4. From Figure 19.4, a plug ﬂow pattern can be observed. Similar ﬁndings have been reported by other authors when working with a SCC (Shah, 1995; Menzi and Emch, 1989).

© 2003 by CRC Press LLC

0.09 0.08 0.07

E value

0.06

Fluid: Water Angular velocity = 79 sec-1 Air flow rate = 6.7 x 10-5 m3sec-1 Liquid flow rate= 18.33 x 10-4 m3sec-1

0.05 0.04 0.03 0.02 0.01 0 0

100

200

300

400

time

sec

FIGURE 19.4 Example of an E curve.

TABLE 19.3 Mean Residence Time (MRT) for Water in the SCC Perspex Laboratory Model Conditions Cone Velocity (sec )

Liquid Flow Rate 3 −1 5 (m sec × 10 )

Air Flow Rate 3 −1 (m sec )

MRT (sec)

26 26 26 26 47 47 47 47 79 79 79 79 131 131 131 131

3.3 3.3 6.7 6.7 3.3 3.3 6.7 6.7 3.3 3.3 6.7 6.7 3.3 3.3 6.7 6.7

0 18.33 0 18.33 0 18.33 0 18.33 0 18.33 0 18.33 0 18.33 0 18.33

16 20 13 17 13 16 16 13 14 15 12 12 29 29 18 14

−1

Mean residence times (MRT) for water and CMC were calculated from these E curves (Figure 19.4). Values of MRT for water and CMC are presented in Tables 19.3 and 19.4, respectively. For the conditions studied in the Perspex laboratory model, residence

© 2003 by CRC Press LLC

TABLE 19.4 Mean Residence Time (MRT) for CMC in the SCC Perspex Laboratory Model Conditions Cone Velocity (sec )

Liquid Flow 3 –1 5 (m sec × 10 )

Air Flow 3 –1 (m sec )

Concentration (%)

MRT (sec)

79 79 79 47 131

0.8 3.3 1.6 3.3 3.3

0 0 0 0 0

1.0 0.5 0.5 0.5 0.5

199 30 71 29 35

Mean Residence Time (MRT)

−1

300 Code [ letter] / [value ] / [value] on x-axis represents: [product (W = water, C = CMC0.5%)] / [liquid flow rate m3sec-1 x 10-5] / [cone velocity sec-1]

250 200 150 100 50 0

8/

2.

C

26

8/

C

2.

61

6/

C

5.

26

6

6

W

5.

/2

6/

61

1/

W

5.

W

. 11

26

1/

61

. 11

W

FIGURE 19.5 Mean residence time for water and CMC (0.5%) in the SCC pilot plant.

time for water was not inﬂuenced by air nor by liquid ﬂow rate, nor even by cone rotating velocity. The average MRT obtained for this equipment was about 17 seconds. In the case of experiments using 1% CMC solution (apparent viscosity: 960 cP −1 at 10 sec at T = 25°C), MRT was about 11.7 times greater than the average MRT −1 for water. When using 0.5% CMC solution (apparent viscosity: 200 cP at 10 sec ο at T = 25 C), MRT was 1.8 to 4.2 times greater than values for water. The inﬂuence of liquid ﬂow rate on MRT was determined using 0.5% CMC solu−5 3 −1 tions. At 3.3 × 10 m sec , the MRT was 2.4 times lower than at a ﬂow rate of 1.6 × −5 3 −1 −1 10 m sec . There was no inﬂuence of cone velocity on MRT for 79 and 47 sec . The −1 time for 131 sec was longer; this can be explained by ﬂooding conditions in the ﬁrst spinning cone (Shah, 1995). Results for the experiments in the SCC pilot plant are presented in Figure 19.5. It is possible to observe that MRT for water depends on ﬂow rate as well as on cone velocity, becoming shorter at higher values of both variables, as expected. The effect of viscosity on MRT can be observed from the experiments with CMC 0.5% at the

© 2003 by CRC Press LLC

same conditions. MRT for CMC is 1.62 times greater than MRT for water. In the −5 3 −1 experiments with water at 5.6 × 10 m sec , MRT is 1.28 times greater for a cone −1 −5 3 −1 speed of 26 than 61 sec . From experiments at a ﬂow rate of 11.1 × 10 m sec −1 and rotating velocity of 26 sec , MRT is 1.14 times greater than that obtained at a −1 rotating speed of 61 sec . In Figure 19.5, the effect of the liquid ﬂow rate using water on MRT is shown, −1 comparing results at a constant angular speed. At 26 sec , MRT is 1.67 times greater −5 3 −1 −5 3 −1 −1 for a ﬂow rate of 5.6 × 10 m sec than for 11.1 × 10 m sec . At 61 sec , MRT −5 3 −1 −5 3 is 1.49 times greater for a ﬂow rate of 5.6 × 10 m sec than for 11.1 × 10 m −1 sec . The effect of liquid ﬂow rate using CMC solution (0.5%) is shown comparing −1 −5 3 −1 data for a constant speed. MRT at 26 sec and 2.8 × 10 m sec is 1.72 times −5 3 −1 greater than MRT for 5.6 × 10 m sec . With a ﬂow rate of CMC solution (0.5%) −5 3 −1 −1 of 2.8 × 10 m sec , MRT obtained at an angular velocity of 26 sec is 1.05 times −1 greater than MRT at 61 sec .

19.5 CONCLUSIONS Mass transfer into the spinning cone column depends on angular cone velocity and liquid and gas ﬂow rate; it is higher at higher values for these variables; their inﬂuence can be represented by a power equation. Mean residence time is affected by liquid ﬂow rate, cone speed, and viscosity of the product; the inﬂuence of liquid ﬂow rate is greater than the inﬂuence of cone speed. The combined effect of high mass transfer rates and short mean residence times for the product into the column brings an advantage for the recovery of aromas and ﬂavors in foods, since it diminishes the damage caused by heat and processing time to these volatile compounds. However, the evidence of a long tail in the residence time distribution must be considered, since this means that some of the volatiles are still present after the mean process and may be affected by having longer processing times. The information given in this work may be used for ﬁnding appropriate operating conditions for a particular product, aiming to obtain as much mass transfer as possible within the economic limits of power requirements for pumping the liquid and for rotating the cones so as to obtain low MRT.

NOMENCLATURE a c c* ∆c ∆clm

2

−3

Bubble surface area per unit volume; (m m ) −3 Dissolved oxygen concentration in the bulk liquid; (kg m ) −3 Solubility of oxygen in equilibrium with pG (c* = pG/H); (kg m ) Concentration difference between the inlet and the outlet of the system; (cin − cout) Logarithmic mean of concentration difference between the inlet and the    (c − c )  outlet of the system  inc out  in  ln cout 

© 2003 by CRC Press LLC

D d E(t) G H JD kc

2

−1

Diffusivity coefﬁcient; (cm sec ) Disk diameter; (m) Residence time distribution function 3 −1 Gas ﬂow rate; (m sec ) −1 Henry’s law constant; (atm mole fraction ) Mass transfer dimensionless group Individual mass transfer coefﬁcient in Equations (19.4), (19.5) and −1 (19.6); (cm sec ) −1 KLa Overall volumetric mass transfer coefﬁcient based on the liquid phase; (sec ) −1 kLa Individual volumetric mass transfer coefﬁcient based on the liquid phase; (s ) 3 −1 L Liquid ﬂow rate; (m sec ) l Characteristic length; (cm) MRT Mean residence time; (sec) p Partial pressure of the solute in the gas phase; (atm) pG Gas pressure; (atm) −3 Po/V Gassed power per volume; (watt m ) −3 −1 R Overall oxygen transfer rate; (kg m sec ) Re Reynolds number based on diameter and peripheral velocity of disk in Equation (19.5); (d U ρ/µ) RTD Residence time distribution Sc Schmidt number; (µ/ρ D) Sh Sherwood number; (kc l/D) St Stanton number; (Sh/Re Sc) t Time; (sec) −1 U Peripheral velocity of cylinder in Equation (19.4); (m sec ) 3 V Reactor volume; (m ) −1 v Material ﬂow rate in a reactor; (m sec ) −1 −1 vs Superﬁcial velocity; (cm sec in Equation (19.7); m sec in Equations (19.8) and (19.9)) x Mole fraction of the solute in the liquid phase (molar concentration of the dissolved gas for sparingly soluble gases) α Coefﬁcient in Equation (19.7) β Exponent in Equation (19.7) −1 −1 µ Viscosity; (g cm sec ) −3 ρ Density (g cm ) −1 ω Angular velocity of the cone; (sec )

ACKNOWLEDGMENTS The authors thank the ALFA Network: Food Quality in Food Engineering, coordinated by the University of Reading, U.K., EU Contract Number ALR/B 7–3011/ 94.04–5.0130.9; Flavourtech Europe Ltd. for allowing the use of the Spinning Cone Column model 1000; FES Cuautitlán-UNAM, ENCB-IPN, and CYTED project Xl.13.

© 2003 by CRC Press LLC

REFERENCES Aiba, S., Humphrey, S., and Millis, F., Biochemical Engineering, 2nd ed., Academic Press, New York, 1973, pp. 163–194. Atkinson B. and Mavituna, F., Gas–liquid mass transfer and mixing, in Biochemical Engineering and Biotechnology Handbook, Macmillan Pub. Ltd., U.K., 1991, pp. 703–731. Blanch, H.W. and Clark, D.S., Biochemical Engineering, Marcel Dekker, New York, 1996, pp. 388–392. Craig, A.J.M., Flavor recovery by the Flavortech Recovery System, Food Technol. Aust., 39, 102–104, 1987. Denbig, K.G. and Turner, J.C.R., Chemical Reactor Theory: An Introduction, 3rd ed., Cambridge University Press, Cambridge, 1984. Flavourtech, Ltd., SCC Treatment of UHT Milk, SCC Technical Bulletin TB, February 21, 1998. Flavourtech Ltd., Finally: Processed and Packaged Foods and Beverages Can Taste as Good as the Originals, Commercial Bulletin, 1991. Heineken, F.G., Oxygen mass transfer and oxygen respiration rate measurements utilising fast response oxygen electrodes, Biotech. Bioeng., 13, 599–618, 1971. Levenspiel, O., Chemical Reaction Engineering, 2nd ed., John Wiley and Sons, New York, 1972, pp. 253–325. Menzi, H. and Emch, F., The spinning cone column: An efﬁcient separator of aroma volatiles from a liquid, Lebensmit. Wiss. Technical., 22, 324–328, 1989. S.A.S. Institute Inc., The S.A.S. System for Microsoft Windows, Release 6.10, Cary, N.C., 1989. Schobinger, U., Progress in fruit juice technology during the last 50 years — A survey, Fruit Process., 7, 275–281, 1999. Shah, N.A., Study of the Fluid Dynamics in the Spinning Cone Column, thesis, University of Reading, 1995. Sherwood, T.K., Pigford, R.I., and Wilke, C.H.R., Mass Transfer, McGraw-Hill, New York, 1975, pp. 236–241. Zivdar, M., Distillation for Food Flavour Separations, seminar, July 4, 1997, Department of Chemical Engineering, University of Sydney, Australia, http://www.chem.eng.usyd. edu.au.

© 2003 by CRC Press LLC

Part III Heat Transfer

© 2003 by CRC Press LLC

20

Transport Phenomena during Double-Sided Cooking of Meat Patties S.E. Zorrilla, S. Wichchukit, and R.P. Singh

CONTENTS 20.1 Introduction 20.2 Mathematical Model 20.2.1 The Basic Equation 20.2.2 The Melting Moving Boundary 20.2.3 The Evaporating Moving Boundary 20.3 Thermal Properties 20.3.1 Contact Heat Transfer Coefﬁcient 20.4 Simulation and Model Validation 20.5 Future Considerations 20.6 Conclusions Nomenclature References

20.1 INTRODUCTION In 1998, 5.5 billion hamburgers or cheeseburgers were served in commercial restaurants in the United States (NCBA, 1998). Unfortunately, since 1982 several outbreaks caused by Escherichia coli O157:H7 have been linked to the consumption of beef patties (D’Sa et al., 2000). Consequently, the U.S. Department of Agriculture (USDA) and U.S. Food and Drug Administration (FDA) have recommended cooking ground beef products to 71°C for home preparation and 68°C for 15 sec for food service, respectively (USDA, 1998; FDA, 1997). However, suitable procedures for measuring internal temperature in beef patties are difﬁcult, especially at food service establishments. As a result, patties may be overcooked with undesirable textural and sensory characteristics or undercooked and microbiologically unsafe. Therefore, a fundamental understanding of the heat transfer process is necessary to design equipment and sensors that ensure the desired safety and quality goals during beef patty cooking. One widely used beef patty cooking method in restaurants involves placing frozen patties between two heated plates with the plate surface temperatures generally

© 2003 by CRC Press LLC

greater than 160°C. As heat penetrates the patty, a thawing process begins. As heating continues, higher temperatures cause protein denaturation and considerable lowering in water holding capacity (Lawrie, 1991). Water and fat may be partially squeezed out because of meat shrinkage and external pressure. Near the patty surface, browning reactions occur, and a combination of dehydration and high temperature lead to the formation of a crust (Dagerskog and Bengtsson, 1974). In a simpliﬁed model, as heat penetrates the frozen patty, two moving boundaries can be distinguished: the thawing and the evaporation boundaries (Singh, 2000). Predictive mathematical models based on classical transport phenomena equations can be a useful tool to represent this process.

20.2 MATHEMATICAL MODEL Different mathematical models for studying the contact cooking process in hamburger patties have been developed (Dagerskog, 1979a, b; Ikediala et al., 1996; Pan et al., 2000; Zorrilla and Singh, 2000a, b). Dagerskog (1979a) proposed a model of heat transfer based on the heat conduction equation. Internal mass transfer was based on an empirical relation between water retaining capacity and temperature. Dagerskog (1979b) modiﬁed this original model for use with the frozen state. In both cases, the models were solved by ﬁnite difference methods. However, experimental and theoretical values did not agree well. Ikediala et al. (1996) modeled the heat transfer in unfrozen meat patties during single-sided pan frying with and without turn-over. The main assumptions were that heat was transferred inside the patty by conduction with no heat generation and negligible meat patty shrinkage or swelling. These authors considered cylindrical geometry and incorporated the heat removed due to moisture loss, which was experimentally determined. The model was solved by a ﬁnite element method. Pan et al. (2000) developed a model for cooking a frozen hamburger patty based on the enthalpy formulation, considering the effect of mass transfer and variable heating temperature and heat transfer coefﬁcient. Water and fat losses were obtained experimentally and were found to affect the thermal properties. The mathematical prediction taking into account mass transfer did not signiﬁcantly improve the prediction results. Zorrilla and Singh (2000a) developed a simpliﬁed one-dimensional model to predict temperature proﬁles in a frozen meat patty during double-sided cooking. Conduction was considered the main mechanism for heat transfer, and enthalpy formulation was used to avoid the discontinuity problem of the phase change during melting. The mathematical formulation considered different top and bottom heating temperatures and was validated by comparing predicted and experimental temperature proﬁles obtained at 163 and 204°C for the bottom plate and 177 and 221°C for the top plate, respectively. Zorrilla and Singh (2000b) extended the model to a twodimensional cylindrical geometry. The results showed no signiﬁcant difference when a cylindrical geometry or radial shrinkage was considered to predict the temperature at the geometric center of a patty under normal conditions of hamburger cooking. However, the two-dimensional model provides a description of temperature in regions close to the circumferential edge of the patty, which is not possible with the one-dimensional model.

© 2003 by CRC Press LLC

20.2.1 THE BASIC EQUATION The heat conduction equation for a homogeneous, isotropic solid in a cylindrical coordinate system is (Ozisik, 1993): ∂T 1 ∂  ∂T  1 ∂  ∂T  ∂  ∂T   kr  +  k  +  k  + g = ρC p ∂t r ∂r  ∂r  r 2 ∂φ  ∂φ  ∂z  ∂z 

(20.1)

where T is the temperature in the solid; t is the time; r, φ, and z are the cylindrical coordinates; g is the heat generation term; k is the thermal conductivity; ρ is the density; and Cp is the speciﬁc heat. When no heat is generated and temperature has no φ dependence, Equation (20.1) becomes: 1 ∂  ∂T  ∂  ∂T  ∂T  kr  +  k  = ρC p r ∂r  ∂r  ∂z  ∂z  ∂t

(20.2)

A meat patty is not a homogeneous solid. However, if the thermal properties are considered as effective properties, and assuming local thermal equilibrium among the different phases present such as ice, fat, and nonfat solids, Equation (20.2) is still valid (Farkas et al., 1996). During cooking of a frozen beef patty, ice melts and water partially evaporates, while solid fat melts. Assuming that the energy involved in fat melting is negligible, only two moving boundaries need to be considered.

20.2.2 THE MELTING MOVING BOUNDARY In problems involving melting or solidiﬁcation, the location of the moving solid– liquid interface is not known a priori, and it has to be determined as part of the solution (Ozisik, 1994). As a result, phase change boundary problems are nonlinear and their analytical solution is difﬁcult. The situation is more complex when the material is nonhomogeneous. The actual phase change takes place over a wide range of temperatures at which food properties change considerably. Mannapperuma and Singh (1988) proposed a method using the approach of enthalpy formulation to solve this heat conduction problem involving gradual phase change. Therefore, Equation (20.2) can be written in terms of enthalpy (H) as: 1 ∂ ∂T(H)  ∂  ∂T(H)  ∂H  rk(H)  +  k(H) = r ∂r  ∂r  ∂z  ∂z  ∂t

(20.3)

valid for the region where the thawing process takes place.

20.2.3 THE EVAPORATING MOVING BOUNDARY The water boiling at an interface separates two regions of different thermal properties. In immersion frying of potatoes, these regions are core and crust (Farkas et al., 1996).

© 2003 by CRC Press LLC

In cooking of hamburger patties, these regions are better deﬁned as core and sear layer. There are different methods to consider this boundary. Farkas et al. (1996) considered two regions and solved coupled heat and mass transfer equations for each one. Because the crust thickness is thin compared with core dimensions for the usual cooking times, a linear temperature change in the crust region can be assumed (Vijayan and Singh, 1997). Table 20.1 shows the boundary and initial conditions to complete the mathematical formulation.

TABLE 20.1 Summary of Boundary and Initial Conditions to Complete the Mathematical Formulation during Double-Sided Cooking of Meat Patties Heat Transfer in the Core Boundary Conditions T = Tb ∂T =0 ∂r

z = S1(r,t), S2(r,t); 0 < r < a(t); t > 0

(20.4)

r = 0; S1(r,t) < z < S2(r,t); t > 0

(20.5)

∂T = h c (T − Ta ) ∂r T = Tb

r = a(t); S1(r,t) < z < S2(r,t); t > 0

(20.6a)

r = R(z,t); S1(r,t) < z < S2(r,t); t > 0

(20.6b)

Initial Condition T = T0

t = 0; S1(r,t) < z < S2(r,t); 0 < r < a(t)

(20.7)

−k

Heat Balances at Interfaces between Core and Crust − k crust

∂S ( r, t ) ∂T ∂T +k = λ vρx w i ∂t ∂z ∂z

z = Si(r,t); i = 1, 2; t > 0

(20.8)

− k crust

∂R(z, t ) ∂T ∂T +k = λ vρx w ∂t ∂r ∂r

r = R(z,t); t > 0

(20.9)

− k crust

∂T = h(Tp1 ( t ) − T) ∂z

Heat Balances and Approximations at Surface

∂T Tb − T = ∂z S1 ( r, t ) − k crust

∂T = h(T − Tp 2 (t )) ∂z

Tb − T ∂T = ∂z L − S2 ( r, t ) − k crust

∂T = h c (T − Ta ) ∂r

Tb − T ∂T = ∂r a( t ) − R(z, t )

© 2003 by CRC Press LLC

z = 0; t > 0

(20.10)

z = 0; t > 0

(20.11)

z = L; t > 0

(20.12)

z = L; t > 0

(20.13)

r = a(t); t > 0

(20.14)

r = a(t); t > 0

(20.15)

Equations (20.6b), (20.9), (20.14), and (20.15) are valid when the boiling temperature is reached in the radial direction.

20.3 THERMAL PROPERTIES Thermal properties are important to complete the mathematical description. However, while information about the thermal properties of frozen and unfrozen foods at ambient temperature is widely available, data at higher temperatures are scarce. Urbicain and Lozano (1997), Cleland and Valentas (1997), Rahman (1995), and Sweat (1994) reported predictive equations, correlations, and experimental values for thermal properties considering different composition and temperature ranges. Their equations can be used to estimate the properties at lower and ambient temperatures. In Table 20.2, experimental values and correlations for thermal properties of ground beef products during cooking conditions are given.

20.3.1 CONTACT HEAT TRANSFER COEFFICIENT The contact heat transfer coefﬁcient appears between two solids that are not perfectly in contact. In this case, the contact depends on the grill and patty surface characteristics and the characteristics of any other medium between them. Because juice is released as the cooking process takes place, that medium is a thin layer of fat/air/moisture. Generally, a constant value of this coefﬁcient is assumed for

TABLE 20.2 Thermal Properties of Meat Patties during Cooking Property

Source

3

Density (kg/m ) ρ = 1300 − 300 x w − 400 x f − (0.4 x w + 0.7 x f )T 1.025 (30–75°C)

a b

Apparent Speciﬁc Heat (J/kg°C) C p = 1600 − 2600 x w + 15T x f

a

Thermal Conductivity (W/m°C) k = 0.5 − 0.92 x f + 0.0024T

a

k = 0.001(668.4 − 704 x f − 305 x w + 1.35T)

c

0.35 to 0.41 (5–70°C)

b

Note: xw = water content in decimal fraction; xf = fat content in decimal fraction; T = temperature in °C. a

Dagerskog, M., Lebensm.-Wiss. Technol., 12, 217–224, 1979. Pan, Z., thesis, University of California, Davis, 1998. c Baghe-Khandan, M.S., Okos, M.R., and Sweat, V.E., Trans. ASAE, 25, 1118–1122, 1982. b

© 2003 by CRC Press LLC

calculations (Dagerskog, 1979a; Ikediala et al., 1996). Most research papers address contact between metals under steady state conditions (Madhusudana, 1996), but little information is available on contact heat transfer coefﬁcient values for solid foods. Houˇsová and Topinka (1985) have shown experimentally that the contact heat transfer coefﬁcient depends on product type, contact plate temperature, contact pressure, and stage in the heat treatment. The heat transfer coefﬁcients measured were in the 2 range of 200 to 1200 W/m °C. Dagerskog and Sörenfors (1978) found contact heat transfer coefﬁcient values for cooking of minced meat patty in the range of 260 ± 2 2 50 W/m °C during contact cooking and 90 ± 20 W/m °C during cooking in a convection oven. Dagerskog (1979a) obtained contact heat transfer coefﬁcient values 2 in the range of 425 ± 33 W/m °C during double-sided contact frying of meat patties. Pan (1998) experimentally determined values of this coefﬁcient by measuring the heat ﬂux involved and the temperatures of the heating surface and the patty surface. The 2 contact heat transfer coefﬁcients obtained were in the range of 200 to 1200 W/m °C. Wichchukit et al. (2000) obtained contact heat transfer coefﬁcient values, h, under various cooking conditions and determined the changes in heat transfer coefﬁcient during the cooking process and the inﬂuence of factors for each cooking condition on heat transfer coefﬁcient. Contact heat transfer coefﬁcient values were calculated using Newton’s law of cooling and measuring the heat ﬂux transferring from the grill plate to a hamburger patty, the grill plate temperature, and the patty surface temperature. Different temperatures (177, 191, 204°C), different gap thicknesses between plates (10.0, 10.5, 11.0 mm) and top or bottom plate were considered in a split–split plot design to study the inﬂuence of these operating variables. Average h values for the conditions studied are shown in Figure 20.1. The h 2 values varied with cooking time and were in the range of 250 to 650 W/m °C. A maximum value of h was observed in the beginning, and later it reached an asymptotic value. At the beginning of the cooking process, the solid frozen patty offers more resistance to the deformation caused by compression from the top plate, resulting in an increase of the contact area. The decrease in the heat transfer after about 60 sec may be related to the fact that at this point the hamburger is almost completely thawed. Therefore, the hamburger is easily compressed, and the interfacial contact forces and contact area may decrease. When the gap thickness between plates decreases, the patty is more compressed, the contact area increases, and the heat transfer may increase. However, under compression the fat and water discharge also increases, changing the composition of the layer between the hamburger and the plate, thus affecting the heat transfer. A higher peak of h was observed for a 10.5 mm gap thickness compared with the value for a 11.0 mm gap thickness (P < 0.05). The maximum values for h involving the bottom plate were higher than those involving the top plate (P < 0.05). The grill has top heating plates covered with Teﬂon release sheets to prevent the material from sticking to the plate. Some experiments were carried out placing the release sheet on the bottom plate, and a similar trend as with the top plate was observed. Therefore, it may be concluded that the release sheet offered resistance to heat transfer to the hamburger patties during cooking. The asymptotic values for h involving the bottom plate were also higher than those involving the top plate (P < 0.05). When the plate temperature increased, the

© 2003 by CRC Press LLC

Bottom plate

Top plate

800

600

600

h (W/m2°C)

h (W/m2°C)

Gap thickness = 10.0 mm 800

400

400

200

200

0

0 0

20

40

60

80

100

0

120

20

40

60

80

100

120

Time (sec)

Time (sec)

800

600

600

h (W/m2°C)

800

2

h (W/m °C)

Gap thickness = 10.5 mm

400

200

400

200

0

0

0

20

40

60

80

100

120

0

20

40

Time (sec)

60

80

100

120

100

120

Time (sec)

600

600 2

h (W/m °C)

800

2

h (W/m °C)

Gap thickness = 11.0 mm 800

400

200

400

200

0

0 0

20

40

60

80

Time (sec)

100

120

0

20

40

60

80

Time (sec)

FIGURE 20.1 Average contact heat transfer coefﬁcients involving top and bottom plates for different gap thicknesses and set grill temperatures: (—) 177°C, (—) 191°C, (- - -) 204°C.

asymptotic value of h decreased (P < 0.05). The asymptotic values for 177 and 191 2 or 204°C were 350 and 250 W/m °C, respectively. At high temperatures, more dehydration near the patty surface occurs, increasing the cohesive forces of the protein matrix. Therefore, adhesion to the grill surface may decrease, decreasing the contact area and the contact heat transfer coefﬁcient.

© 2003 by CRC Press LLC

20.4 SIMULATION AND MODEL VALIDATION The solution of the system comprised of Equations (20.3–20.15) was obtained numerically using ﬁnite difference methods (Zorrilla and Singh, 2000a, b). A computer program was written in Fortran (Digital Visual Fortran Version 5.0). The input data included gap thickness between plates, radius of the patty, product composition, unfreezable water content, initial freezing point, initial temperature of the product, plate temperature history, surrounding air temperature, contact heat transfer coefﬁcient, combined radiation and convection heat transfer coefﬁcient at the circumferential surface, and total cooking time. The gap thickness, radius of the patty, product composition, initial temperature of product, plate temperature history, and total cooking time were measured during the experiment. Thermal properties varying with temperature were calculated using the procedure developed by Mannapperuma (1988) based on composition, thermal properties for the unfrozen state, unfreezable water content, and initial freezing point. Thermal properties for the unfrozen state were estimated using correlations based on the composition (24% fat content, 60% w.b. moisture, 16% protein content), and 3 the following values were obtained: density, 1026.7 kg/m ; apparent speciﬁc heat, 3268 J/kg°C; thermal conductivity, 0.416 W/m°C; unfreezable water, 4%, and initial freezing point, –1°C (Cleland and Valentas, 1997). 2 An average contact heat transfer coefﬁcient of 900 W/m °C, a combined radiation and convection heat transfer coefﬁcient at the circumferential surface of the patty 2 of 60 W/m °C (Geankoplis, 1993), and the average value of the plate temperatures as a surrounding air temperature were assumed. The last assumption was veriﬁed experimentally. Typical simulated temperature distributions in two dimensions (radial and axial) are plotted in Figures 20.2 and 20.3 for 50 and 124 sec of cooking time. It is evident that temperature changes in the circumferential region of the patty (region near r = a) are different from the changes in the central region (region near r = 0). Preliminary results showed that this difference affects texture parameters. A one-dimensional model would not be able to ﬁnd such differences in temperature proﬁles. The experimental validation is not easy because of the difﬁculty of appropriately placing the thermocouples. Although thermocouples are placed carefully at the beginning, when the cooking starts, it is possible for them to change position because of the softening of the material. Validation is generally carried out by measuring the temperature at the geometric center of the patty. Typical experimental and predicted temperatures at the patty center are shown in Figure 20.4 (Zorrilla and Singh, 2000a). The predicted values correspond to a simulation for the one-dimensional model. However, Zorrilla and Singh (2000b) observed that the two-dimensional model has no signiﬁcant effect on the prediction of temperature at the geometric center. For simulation, a constant contact heat transfer coefﬁcient was used. If the experimental h values were used, a lower center temperature would have been predicted because the h values measured are in the range of 2 250–650 W/m °C and are lower than the value assumed for simulations (900 2 W/m °C). However, the calculations carried out with the experimental h values will lead to safer cooking times.

© 2003 by CRC Press LLC

220

Temperature (°C)

180

140

100

60 58.4 46.7 35.1 Radial distance 23.4 from center, r, mm 11.7

20

Distance from top patty surface, z, mm

0.0

11.0

8.8

9.9

7.7

5.5

6.6

3.3

4.4

2.2

0.0

1.1

-20

FIGURE 20.2 Temperature distribution in a hamburger patty at 50 sec of cooking time (L = 2 2 11 mm; a = 58 mm; Tp1 = 221°C; Tp2 = 204°C; h = 900 W/m °C; Ta = 212°C; hc = 60 W/m °C).

220

Temperature (°C)

180

140

100

60 58.4 46.7 35.1 Radial distance 23.4 from center, r, mm 11.7

20

9.9

Distance from top patty surface, z, mm

0.0 11.0

8.8

6.6

7.7

5.5

3.3

4.4

2.2

0.0

1.1

-20

FIGURE 20.3 Temperature distribution in a hamburger patty at 124 sec of cooking time (L = 2 2 11 mm; a = 58 mm; Tp1 = 221°C; Tp2 = 204°C; h = 900 W/m °C; Ta = 212°C; hc = 60 W/m °C).

© 2003 by CRC Press LLC

250 Set top plate temperature = 221°C

200

Temperature (°C)

Set bottom plate temperature = 204°C

150

100

50

0

-50 0

25

50

75

100

125

Time (sec)

FIGURE 20.4 Experimental (ⵧ) and predicted (—) temperatures at patty center (L = 11 mm; 2 h = 900 W/m °C).

20.5 FUTURE CONSIDERATIONS The mathematical model is the ﬁrst step of an optimization process (Banga et al., 1991, 1997). The results of predictive heat transfer models help to address food safety issues associated with the survival of pathogens. On the other hand, the optimization procedure must take into account information related not only to microbial destruction, but also to textural and sensory characteristics. In recent years, texture has become an important attribute indicative of hamburger patty quality (Berry, 1994; Bigner-George and Berry, 2000; Dreeling et al., 2000; Ju and Mittal, 1999, 2000). Moreover, instrumental methods for textural properties have been successfully correlated with sensory data and are often more precise and reproducible (Beilken et al., 1991). Zorrilla et al. (2000) related the textural and cooking parameters with the plate temperature and gap thickness between plates during double-sided cooking of meat patties as an attempt to relate physical results to any change in the heat transfer mechanism. For correlations, the volume averaged temperature, T, was used:

∫∫∫ T(z, t) dV ∫ T= = dV ∫∫∫ V

L

T(z, t ) dz

0

L

(20.16)

V

where T(z,t) is the temperature proﬁle inside the patty for a one-dimensional model, and L is the gap thickness between plates. An example of the regression surfaces obtained is shown in Figure 20.5. In this case, cooking loss is one of the cooking parameters studied.

© 2003 by CRC Press LLC

Cooking loss (%)

38

34

34

30

30

26

26

22 90

22

11

75

Gap th

0.5

1

icknes s

10

(mm)

65

9.5

70

80

d ge

e tur era

85

Cooking loss (%)

38

) (°C

p

tem

era -av

e lum

Vo

FIGURE 20.5 Cooking loss values correlated with volume averaged temperature and gap thickness between plates.

The optimization problem can be formulated as follows: Find the heating policy of a hamburger contact cooking process in order to obtain minimum cooking loss while ensuring the mandatory level of microbiological destruction and ﬁnal temperature at the coldest point. At present, the optimization process is a subject of current study.

20.6 CONCLUSIONS Mathematical models based on classical transport phenomena equations satisfactorily predicted the temperature proﬁles inside hamburger patties during double-sided contact cooking. A model considering a one-dimensional geometry appropriately predicts temperature proﬁles at the geometric center, while a model for a twodimensional cylindrical geometry provides a temperature history at regions close to the circumferential edge of the patty, which is not possible with a one-dimensional model. The contact heat transfer coefﬁcient is one of the parameters needed to complete the mathematical formulation. Since little information is available on heat transfer coefﬁcient values for solid foods, a detailed discussion was included. The contact heat transfer coefﬁcient changes during the cooking process. The small gap thickness enhances the contact between a patty and the grill surfaces. A Teﬂon release sheet offers ﬁnite resistance to heat transfer to the hamburger patties during cooking. Higher heat transfer coefﬁcient values after reaching maximum value were found with the low set grill temperature and may result from the adhesion phenomenon occurring between the patty surface and the grill surfaces.

NOMENCLATURE a Cp

Radius of the patty, m Apparent speciﬁc heat, J/kg°C

© 2003 by CRC Press LLC

3

g h hc H k kcrust L r R S1, S2 t T T

Ta Tb Tp1, Tp2 T0 xf xw z

Heat generation term, J/m sec 2 Contact heat transfer coefﬁcient, W/m °C 2 Combined radiation and convection heat transfer coefﬁcient, W/m °C 3 Enthalpy, J/m Thermal conductivity in the core, W/m°C Crust thermal conductivity, W/m°C Gap thickness, m Cylindrical coordinate, m Position of moving boundary that separates the crust region from the core region in the radial direction, m Positions of moving boundary that separate the crust region from the core region in the axial direction, m Time, sec Temperature, °C Volume averaged temperature, °C Surrounding air temperature, °C Boiling temperature, °C Plate temperatures, °C Initial temperature, °C Fat content, decimal fraction Water content, decimal fraction Cylindrical coordinate, m

GREEK SYMBOLS λv ρ φ

Latent heat of water vaporization, J/kg 3 Hamburger density, kg/m Cylindrical coordinate

REFERENCES Baghe-Khandan, M.S., Okos, M.R., and Sweat, V.E., The thermal conductivity of beef as affected by temperature and composition, Trans. ASAE, 25, 1118–1122, 1982. Banga, J.R., Alonso, A.A., and Singh, R.P., Stochastic dynamic optimization of batch and semi-continuous bioprocesses, Biotechnol. Prog., 13, 326–335, 1997. Banga, J.R., Perez-Martin, R.I., Gallardo, J.M., and Casares, J.J., Optimization of the thermal processing of conduction-heated canned foods: study of several objective functions, J. Food Eng., 14, 25–51, 1991. Beilken, S.L., Eadie, L.M., Grifﬁths, I., Jones, P.N., and Harris, P.V., Assessment of the textural quality of meat patties: correlation of instrumental and sensory attributes, J. Food Sci., 56, 1465–1469, 1991. Berry, B.W., Fat level, high temperature cooking and degree of doneness affect sensory, chemical and physical properties of beef patties, J. Food Sci., 59, 10–14, 1994. Bigner-George, M.E. and Berry, B.W., Thawing prior to cooking affects sensory, shear force, and cooking properties of beef patties, J. Food Sci., 65, 2–8, 2000.

© 2003 by CRC Press LLC

Cleland, D.J. and Valentas, K.J., Prediction of freezing time and design of food freezers, in Handbook of Food Engineering Practice, Valentas, K.J., Rotstein, E., and Singh, R.P., Eds., CRC Press LLC, Boca Raton, FL, 1997, pp. 71–123. Dagerskog, M., Pan frying of meat patties I. A study of heat and mass transfer, Lebensm.Wiss. Technol., 12, 217–224, 1979a. Dagerskog, M., Pan frying of meat patties II. Inﬂuence of processing conditions on heat transfer, crust color formation, cooking losses and sensory quality, Lebensm.-Wiss. Technol., 12, 225–230, 1979b. Dagerskog, M. and Bengtsson, N.E., Pan frying of meat patties: relationship among crust formation, yield, composition, and processing conditions, Lebensm.-Wiss. Technol., 7, 202–207, 1974. Dagerskog, M. and Sörenfors, P., A comparison between four different methods of frying meat patties I. Heat transfer, yield and crust formation, Lebensm.-Wiss. Technol., 11, 306–311, 1978. Dreeling, N., Allen, P., and Butler, F., Effect of cooking method on sensory and instrumental texture attributes of low-fat beefburgers, Lebensm.-Wiss. Technol., 33, 234–238, 2000. D’Sa, E.M., Harrrison, M.A., Williams, S.E., and Broccoli, M.H., Effectiveness of two cooking systems in destroying Escherichia coli O157:H7 and Listeria monocytogenes in ground beef patties, J. Food Protection, 63, 894–899, 2000. Farkas, B.E., Singh, R.P., and Rumsey, T.R., Modeling heat and mass transfer in immersion frying. I. Model development, J. Food Eng., 29, 211–226, 1996. FDA, Food Code, chapter 3, 3–401.11. http://vm.cfsan.fda.gov/~dms/fc-3.html, 1997. Geankoplis, C.J., Transport Processes and Unit Operation, 3rd ed., Prentice Hall, Englewood Cliffs, NJ, 1993. Houˇsová, J. and Topinka, P., Heat transfer during contact cooking of minced meat patties, J. Food Eng., 4, 169–188, 1985. Ikediala, J.N., Correia, L.R., Fenton, G.A., and Ben-Abdallah, N., Finite element modeling of heat transfer in meat patties during single-sided pan-frying, J. Food Sci., 61, 796–802, 1996. Ju, J. and Mittal, G.S., Effects of fat-substitutes, fat levels and cooking methods on the quality of beef patties, J. Food Process. Preserv., 23, 87–107, 1999. Ju, J. and Mittal, G.S., Relationships of physical properties of fat-substitutes, cooking methods and fat levels with quality of ground beef patties, J. Food Process. Preserv., 24, 125–142, 2000. Lawrie, R.A., Meat Science, 5th ed., Pergamon Press, Oxford, 1991. Madhusudana, C.V., Thermal Contact Conductance, Springer-Verlag, New York, 1996. Mannapperuma, J.D., Thawing of foods in humid air, dissertation, University of California, Davis, 1988. Mannapperuma, J.D. and Singh, R.P., Prediction of freezing and thawing times of foods using a numerical method based on enthalpy formulation, J. Food Sci., 53, 626–630, 1988. NCBA, (National Cattlemen’s Beef Association) on the Internet at: http://www. beeffood service.com/working/fs.dll?beef, 1998. Ozisik, M.N., Heat Conduction, John Wiley & Sons, New York, 1993. Ozisik, M.N., Finite Difference Methods in Heat Transfer, CRC Press, Boca Raton, FL, 1994. Pan, Z., Predictive modeling and optimization of hamburger patty contact-cooking process, dissertation, University of California, Davis, 1998. Pan, Z., Singh, R.P., and Rumsey, T.R., Predictive modeling of contact-heating process for cooking a hamburger patty, J. Food Eng., 46, 9–19, 2000. Rahman, S., Food Properties Handbook, CRC Press LLC, Boca Raton, FL, 1995. Singh, R.P., Moving boundaries in food engineering, Food Technol., 54, 44–53, 2000.

© 2003 by CRC Press LLC

Sweat, V.E., Thermal properties of foods, in Engineering Properties of Foods, Rao, M.A. and Rizvi, S.S.H., Eds., Marcel Dekker, New York, 1994, pp. 99–138. Urbicain, M.J. and Lozano, J.E., Thermal and rheological properties of foodstuffs, in Handbook of Food Engineering Practice, Valentas, K.J., Rotstein, E., and Singh, R.P., Eds., CRC Press LLC, Boca Raton, FL, 1997, pp. 425–486. USDA, USDA urges consumers to use food thermometer when cooking ground beef patties, Food Safety and Inspection Service, United States Department of Agriculture, Washington, DC http://www.fsis.usda.gov/OA/news/colorpr.htm, 1998. Vijayan, J. and Singh, R.P., Heat transfer during immersion frying of frozen foods, J. Food Eng., 34, 293–314, 1997. Wichchukit, S., Zorrilla, S.E., and Singh, R.P., Heat transfer coefﬁcients in contact cooking of meat patties as inﬂuenced by process conditions, presented at the Institute of Food Technologists Annual Meeting, Dallas, 2000. Zorrilla, S.E., Rovedo, C.O., and Singh, R.P., A new approach to correlate textural and cooking parameters with operating conditions during double-sided cooking of meat patties, J. Texture Stud., 31, 499–523, 2000. Zorrilla, S.E. and Singh, R.P., Heat transfer in meat patties during double-sided cooking, Food Sci. Technol. Res., 6, 130–135, 2000a. Zorrilla, S.E. and Singh, R.P., Heat transfer in double-sided cooking of meat patties considering two-dimensional geometry and radial shrinkage, presented at the Institute of Food Technologists Annual Meeting, Dallas, 2000b.

© 2003 by CRC Press LLC

21

Thermal Processing of Particulate Foods by Steam Injection. Part 1. Heating Rate Index for Diced Vegetables K.S. Pannu, F. Castaigne, and J. Arul

CONTENTS 21.1 Introduction 21.2 Theoretical Considerations 21.3 Materials and Methods 21.3.1 Equipment Design 21.3.2 Data Acquisition 21.3.3 Equipment Operation 21.3.4 Food Samples and Test Sensor Preparation 21.3.5 Data Analysis 21.4 Results and Discussion 21.4.1 Time–Temperature Data 21.4.1.1 Regression for fh and jh Values 21.4.1.2 Temperature at the Food Surface 21.4.2 Heating Rate Index (fh) and the Lag Factor (jh) 21.4.2.1 fhc Values 21.4.2.2 Lag Factor and j Values 21.4.2.3 Errors Associated with fh and jh Values 21.4.2.4 Particle-to-Particle Interaction 21.4.2.5 Steam Flow Direction 21.4.2.6 SMFR and Steam Temperature 21.4.3 Heat Transfer Coefﬁcient (h) and the Biot Number (Bi) 21.4.4 Product Quality 21.4.5 Moisture Loss 21.4.6 Process Implications on Product Blanching/Sterilization

© 2003 by CRC Press LLC

21.5 Conclusions Nomenclature References

21.1 INTRODUCTION Although steam is commercially employed to sterilize and blanch food products, there is a lack of readily available data that can be used with conﬁdence to simulate packed bed heating of diced vegetables by steam injection. Basic parameters and properties required are the food product thermal diffusivity at temperatures over 100°C and the convective surface heat transfer coefﬁcient (h value) for steam. Data on h values for food processing applications range from 400 (Zhang and Cavalieri, 2 2 1991) to 12,000 W/m °C (Tung et al., 1990). An h value of about 5000 W/m °C is commonly employed (Skjöldebrand and Ohlsson, 1993) for steam heating, but for a 12-mm food cube this provides a Biot number (Bi) of about 50, indicating inﬁnite resistance to surface heat transfer. This may not be so in light of data presented by Rumsey et al. (1980), Pannu et al. (1990) and Zhang and Cavalieri (1991), which show that 0.1 ≤ Bi ≤ 40. Also, very little work has been documented in the area of packed bed processing of moist food solids with steam. Thus, the objectives of this study were to investigate the steam injection packed bed heating of potato and carrot cubes/slices. Food center and surface temperatures were measured under a variety of process conditions. The speciﬁc objective was to assess the inﬂuence of steam temperature, ﬂow rate, ﬂow direction (upward and downward), food particle size/shape, and particle-to-particle interaction on product 1 temperature and the food particle heating rate (fh) during packed bed heating.

21.2 THEORETICAL CONSIDERATIONS The transient heat transfer equation for an object of simple shape, initially at a uniform temperature Ti, exposed to a step-change immersion into a heating medium at temperature Ts, can be expressed as follows (Luikov, 1968): θ object =

Ts − T( x,t ) Ts − Ti

∞

=

∑A B e n

n

− β n2 Fo

(21.1)

n =1

Values for An, Bn, and βn are dependent on object shape (inﬁnite slab, sphere, or inﬁnite cylinder), and T(x,t) (or T without a subscript) represents the time-dependent temperature at a ﬁxed location x within the solid. The Fourier number is deﬁned as 2 Fo = αt/R , with α being the thermal diffusivity, t the time, and R the half thickness. Furthermore, the inﬁnite summation can be approximated by only the ﬁrst term (n = 1), provided Fo > 0.2 (Heisler, 1947; Singh, 1982). Using ﬁrst term approximation and by taking logarithms of both sides, Equation (21.1) simpliﬁes to Equation (21.2). 1

The f and j values deﬁned and used here are the true “lumped” form of the analytical transient heat conduction equation, with f as the exponential component and j the ﬁrst two terms (A and B) of Equation (21.1). The f and j values are used for comparison of products and thermocouple location.

© 2003 by CRC Press LLC

For inﬁnite slabs and cubes, the time-temperature data can be analyzed by making the appropriate substitutions from Equations (21.4) and (21.5), respectively, into Equation (21.2).  Τ − Τi  t = fh ln jh s   Τs − Τ  A1 =

 β1 x  2sin β1 ; B1 = cos  and β1tan β1 = Bi β1 + sin β1cos β1  R 

(21.2)

(21.3)

Inﬁnite slab: R2 and jh = A1B1 (β1 )2 α

(21.4)

R2 and jh = (A1B1 )3 3(β1 )2 α

(21.5)

fh = Cube: fh =

Equation (21.2) is extensively used for evaluating the straight line segment of the heating curve, with fh and jh representing the negative inverse slope (heating rate index) and the intercept, respectively, obtained from a semilogarithmic plot of the 2 temperature ratio at the center (θc) vs. time. A second set of subscripts, c and s, representing the center or surface, respectively, are added to fh and jh. Thus, fhc and fhs represent the f value at the center and at the surface layer, respectively. Equations (21.4) and (21.5) show that f values are position independent (fhc = fhs), but j values are not (jhc ≠ jhs) because B1 is location dependent (Figure 21.1). Care has to be taken in computing the jhs value of a cube because it is location sensitive. However, at the geometric center, jhc = A1, as B1 = 1 since x = 0.

21.3 MATERIALS AND METHODS 21.3.1 EQUIPMENT DESIGN Details of the test apparatus are presented in Figure 21.2. Steam enters from the bottom into the annular jacket, which is equipped with a steam trap and an electric heating coil. A three-way valve is used to direct good quality (dry) steam exiting from the top of the annular jacket into the processing chamber for product treatment. Two three-way valves are required (Figure 21.2, top) to ensure continuous steam ﬂow through the processing chamber or to redirect steam ﬂow via the bypass line. Steam exits as water after passing through a steam condensation unit. Flexible hoses 2

Note that a factor of 2.303 is used with the decimal logarithm scale (log 10). For the log 10 scale: fh = 2.303⋅fh. The natural logarithm (ln) scale was used in this study.

© 2003 by CRC Press LLC

Case 1 Center of X-Y plane Surface of Z plane

-X Food Cube

Case 2 Surface of Y & Z planes Off-center on X plane

-Z

Y

Case 3 Surface of all 3 planes X, Y and Z

Case 4 Surface of Y plane Off-center on X & Z planes

FIGURE 21.1 Location inﬂuence for estimating j values.

(hose-1 and hose-2) were used to redirect steam ﬂow through the processing chamber via the three-way valves. Thus, steam ﬂow direction (upward or downward) into the processing chamber can be changed by switching the ﬂexible hoses at locations AA and B-B. Figure 21.2 depicts steam ﬂowing in the upward direction. Each of the four thermocouple locations, T1–T4, is equipped with two thermocouples and a pressure gauge. One thermocouple from each of the four points was connected to the data acquisition unit. The second thermocouple was connected to a digital display unit for visual veriﬁcation of pressure and temperature.

21.3.2 DATA ACQUISITION ®

The data acquisition system consisted of a Personal Computer (PC), MetraByte ® ® hardware (MetraByte Corporation, Taunton, MA), the Lotus 1–2–3 spreadsheet ® program (Lotus Development Corporation, Cambridge, MA) and Labtec Note® book (Laboratory Technologies Corporation, Wilmington, MA) software packages. ® The MetraByte hardware package included a DASH-8 eight-channel 12-bit high® speed A/D converter and timer/counter board and an EXP-16 expansion board with 16 pairs of screw terminals for the attachment of thermocouple wires. The software package provided real time graphic display of the heating process.

21.3.3 EQUIPMENT OPERATION The pressure was regulated using a Taylor Lin-E-Aire valve (Taylor Instrument Company, Broadview Heights, OH) and controlled pneumatically by an Electromax digital process controller (Leeds and Northrup, North Wales, PA). For system startup, approximate system pressure and temperature were achieved in the bypass mode with the digital process controller. Steam mass ﬂow rate (SMFR) was determined by collecting condensate discharge for 120 sec (Figure 21.2, top). Condensing steam to water is the most reliable method for obtaining data on steam ﬂow rate. Depending on

© 2003 by CRC Press LLC

Personal Computer

Hose-1 T-4 B-B T-2

Food Container

Bypass Line 3-Way Valve

Processing Chamber Needle Valve

Annular Jacket

T-1

PRV: Pressure Regulating Valve

Steam Supply

Cold Water

A-A T-3

Hose-2 Steam Condensation for Mass Flow Rate Measurement

Temp. Pressure Measurement

Steam to Water

Steam Out Cover Plate Thermocouples

Dimensions & Details

Rubber Seals

Process Simulator Electric Heating Element

Material: Aluminum Height = 21 cm I D = 15.2 cm Annular space = 2.5 cm

6-Thermocouple Probe Food Container

Condensation Unit Material: Copper tubing Tube Dia. = 1.9 cm Coil height = 40 cm Coil dia. = 20 cm # of turns = 12

Annular Jacket (Steam Heating) Processing Chamber Steam In

A.C. Supply

Pressure: 275 – 550 kPa Quality: Unknown

Steam Trap Steam from Jacket to Processing Chamber

Steam Supply

Processing Chamber Pressure Release Valve

FIGURE 21.2 Schematics of the laboratory apparatus for heating diced vegetables in steam.

the desired SMFR, ﬂow conditions were established by manually adjusting the needle valve (#SS-1RS8; Whitey Co., Highland Heights, OH) located prior to the condensation unit (Figure 21.2), by restricting steam discharge. The annular jacket performs four tasks: 1. It acts as a buffer tank. 2. It removes condensed water through the steam trap.

© 2003 by CRC Press LLC

3. It acts as a thermal jacket for the processing chamber. 4. It performs steam superheating. For all experiments, a few degrees of superheat (5–15°C) were provided. Detailed information about the equipment and its operation has been presented elsewhere (Pannu, 1992). All test containers were ﬂanged to facilitate their installation into the heating chamber. The container ﬂange ﬁts into a recessed slot with thermocouple wires sandwiched between two silicone rubber rings. This ensures good sealing; no leakage of steam was observed. For each test, the food batch was weighed and transferred to the test container in layers to facilitate positioning of the test sensors and thermocouple wires. Two screws were inserted from the bottom of the ﬂange to attach the test container with the two rubber rings and thermocouple wires to the cover plate. The assembly was placed next to the simulator to facilitate the connection of thermocouple wires to the data logger. Subsequently, the cover plate/food container assembly was installed in place and tightly secured with four butterﬂy nuts. After commencing data acquisition, steam was diverted to the processing chamber via the three-way valve. The data acquisition system provided real time graphic display of the heating process. Temperatures were recorded until the center temperature of food particles reached that of the heating medium; the steam supply to the processing chamber was then cut off. The product was cooled to 100°C by slow depressurization of the heating chamber. Data acquisition was terminated when the product had cooled to 100°C. The food container was then removed, product quality visually inspected, and thermocouple location/placement veriﬁed. SMFR was measured before and during the test and after termination of heating. Temperature data from the steam inlet/exit, preheating chamber, heating chamber, food surface, and center and other locations were used to evaluate the performance of the equipment under selected processing conditions. Time-temperature data were recorded at 1 sec intervals with strategically located ﬁne wire (36-gauge) copper-constantan thermocouples. Special test sensors were fabricated by positioning two thermocouples into the food pieces (Figure 21.3a). These were embedded in the food material to register the temperature history of 36-gauge type-T thermocouple wire

1/2 cube thickness

Food Cube

Wooden toothpick diameter = 1.2 mm

(a)

Fine cord

(b)

FIGURE 21.3 (a) Placement of thermocouple probe in the food cube. (b) Details of the thermocouple probe.

© 2003 by CRC Press LLC

individual solids. Heating time of the food particulates was continually monitored and manually controlled. Steam supply was shut off and redirected through the bypass line when the food particle center temperature reached that of steam. The steam ﬂowing through the processor was condensed to liquid water for determining the system steam mass ﬂow rate (SMFR). Since process come-up time was very short (~5 sec), stable processing conditions were achieved, and heat losses were negligible with a steam jacket surrounding the food treatment chamber.

21.3.4 FOOD SAMPLES

AND

TEST SENSOR PREPARATION

Food cubes were prepared by cutting peeled potatoes and carrots into slices and then passing the slices through a french fry cutter. The material was sorted, washed, surface dried with paper towels, sealed in plastic containers, and set aside for 2 h to allow the product to attain a uniform initial temperature (Ti). Temperatures at the center and the surface layer of a food particle were measured by installing special thermocouple probes into selected food pieces (Figure 21.3b). The probes were constructed with thermocouple junctions positioned half the food piece thickness apart and were secured on opposite sides (180° apart) of a wooden toothpick with a ﬁne cotton thread. A 1.2-mm hole was drilled into the test sample to facilitate the correct positioning of the thermocouples and to prevent particle shape distortion (Figure 21.3a). The wooden toothpick assembly was soaked in water for about 2 h prior to installation into the test piece to avoid migration of water from food to wood and to minimize the thermal insulation effects of wood. Only food cubes of uniform size (measured with a digital caliper) and shape were selected for the construction of the test sensors. Three food sensors were positioned at the top, bottom, and center of the food bed. The top and bottom sensors were placed one food layer away from the top layer and bottom layer of the food bed, respectively. Experiments were conducted with approximately 180 g of food and in a container that resembled a 300 × 400 can (Pannu, 1992). Potato and carrot pieces were processed in two shapes (cubes and slices) and two sizes. Moisture content was determined by vacuum drying in a laboratory oven at 70°C for 48 h. Quality and physical structure of the processed food cubes were examined visually.

21.3.5 DATA ANALYSIS Interactive Lotus 1-2-3 macro programs were developed (Pannu, 1992) to analyze the data and obtain temperature–time graphs. The linear segment of the heating curve was used to obtain an estimate of ƒh and the corresponding intercept jh.

21.4 RESULTS AND DISCUSSION 21.4.1 TIME–TEMPERATURE DATA Typical time–temperature data for steam ﬂowing downward at a rate of 3.8 g/sec through a bed of large (12 mm) potato cubes are shown in Table 21.1. Temperatures of steam from the supply line to the processor are in column 2, and those of steam exiting from the superheater (annular jacket) in column 3. Data for steam entering/exiting

© 2003 by CRC Press LLC

TABLE 21.1 a Typical Time–Temperature Data for Steam Flowing Downward at a Rate of 3.8 g/sec through a Bed of Potato Cubes (12 mm) Sensor Location in the Food Bed 1

2 1

Time V sup (sec) (°C)

3

4

5

6 7 Bottom

8 9 Center

10

11

12

Top

V aj (°C)

V top V bot (°C) (°C)

Fc (°C)

Fs (°C)

Fc (°C)

Fs (°C)

Fc (°C)

Fs (°C)

V pc (°C)

20.0 20.0 20.0 20.0 20.0 19.7 20.0 21.8 24.2 26.8 28.9 34.2 38.6 43.7 50.3 57.4 64.9 71.8 78.7 84.9 90.2 94.7 98.9

17.2 17.2 17.6 17.2 17.6 17.6 61.9 89.9 107.3 114.0 118.6 121.4 121.9 122.1 122.3 122.4 122.5 122.6 122.8 122.9 123.2 123.2 123.2

18.2 17.9 17.9 18.2 18.2 18.2 18.8 21.5 23.6 25.9 26.8 31.0 35.4 40.9 48.3 55.7 63.0 70.2 75.9 81.9 87.3 91.5 95.3

18.2 18.2 18.2 18.2 18.2 18.5 34.8 74.3 85.9 93.4 99.5 109.4 113.7 114.8 116.8 117.3 118.4 118.6 118.6 119.4 119.6 120.2 120.5

20.0 20.0 20.0 20.0 20.3 20.6 21.2 23.0 24.7 25.9 26.8 30.1 33.6 39.4 46.3 54.3 62.4 70.2 77.0 83.5 89.2 94.2 98.4

28.9 29.2 29.2 29.5 29.5 30.1 75.4 103.4 114.3 117.8 120.4 121.7 121.9 122.1 122.2 122.4 122.6 122.4 122.8 123.1 122.9 123.2 123.4

63.0 63.0 63.0 63.3 63.3 63.3 63.0 93.7 110.1 116.3 121.9 122.9 122.7 123.2 123.7 123.9 123.9 123.9 123.9 124.2 123.9 123.9 124.2

122.2 122.2 122.2 121.9 120.6 118.6 101.0 99.5

120.1 120.1 120.4 120.4 120.1 119.1 101.8 100.5

122.4 122.2 121.9 121.7 120.1 118.6 101.3 100.0

123.9 123.4 122.9 122.4 120.6 118.4 101.3 100.0

–4 –3 –2 –1 0 1 2 3 4 5 6 10 15 20 25 30 35 40 45 50 55 60 65

124.2 124.5 124.5 124.2 124.7 125.7 125.2 123.9 123.4 123.9 123.9 125.0 123.9 123.9 123.9 124.2 123.9 123.9 124.2 124.2 124.4 124.2 124.2

132.7 132.7 132.7 132.7 131.2 134.2 131.2 122.2 123.7 126.7 129.2 130.2 130.5 130.7 131.2 131.5 131.7 131.7 131.7 131.7 131.7 132.0 131.7

28.3 28.6 28.6 28.3 28.3 42.9 102.1 115.3 121.7 122.9 123.7 122.4 122.2 122.2 122.7 122.7 123.2 123.2 123.2 123.2 123.2 123.2 123.4

133 134 135 136 138 140 155 160

124.2 124.5 124.2 124.5 124.5 124.5 124.2 124.2

132.5 132.5 132.5 132.5 132.7 132.2 132.2 132.2

122.4 121.9 121.9 121.7 118.9 116.8 103.2 102.9

32.4 32.4 32.4 32.4 32.4 33.0 36.5 115.5 122.2 123.2 123.9 122.7 122.2 122.4 122.7 122.7 123.2 123.2 123.3 123.4 123.4 123.4 123.2

Cooling by Depressurization 122.7 120.1 123.2 118.6 122.2 120.4 122.9 118.9 121.4 120.1 122.4 119.1 120.6 120.4 121.9 119.1 119.4 120.1 119.9 119.1 117.6 119.1 118.1 119.1 100.7 101.5 100.5 101.8 100.5 100.5 99.5 100.2

Note: V: vapor; sup: steam supply; aj: exit at annular jacket; bot: bottom location; pc: processing chamber; Fc: food center; Fs: food surface. a

Time–temperature data recorded at 1 sec intervals have been abbreviated for presentation.

© 2003 by CRC Press LLC

at the top and bottom of the processing chamber, respectively, are in columns 4 and 5. Column 12 provides steam temperatures inside the chamber; the data in columns 6 through 11 are from food sensors. The time scale in column 1 was corrected to reﬂect the true time zero; this was accomplished by comparing temperature data in columns 4 or 5. A sudden jump in temperature indicated the time when steam ﬁrst entered the processing chamber and was assigned the value of t = 1 sec. 21.4.1.1 Regression for fh and jh Values Results for fh and jh can vary depending on the values of Ts and Ti and the range selected for regression (Larkin, 1989). To overcome this problem and eliminate bias, Lotus macros were used to carry out the regression analysis. Ts was computed as an average of 93 temperature readings recorded in columns 4, 5, and 12 (Table 21.1). Ti for each food sensor was computed as an average of the food center temperature between t = –5 and 0 sec. The time period selected for the regression analysis was t = 50 to 100 sec for f and j values at the center of the large cube and from 15 to 35 sec for surface temperature data. For the small cubes, the range selected was between 40 and 80 sec for center temperature data and between 10 and 25 sec for surface temperature data. −7 The regression range was selected by calculating te with αpotato = 1.6 × 10 2 m /sec (Kostaropoulos et al., 1975) for Fo = 0.2. An estimate for the isothermal heating time (te), at which the curvilinear portion of a heating curve terminates, can also be obtained with Equation (21.6) (Hayakawa, 1982). For a cube, jhc ≈ 2.0; by assuming that fhc = 35 × 2.303 (log 10 scale), te ≈ 55 sec. A te value of 45 sec was obtained by using Fo = 0.2. Thus, the time periods selected for regression were justiﬁable. However, these methods cannot be applied for surface temperature data. te = 0.7fh( jh – 1)

(21.6)

Semilogarithmic plots obtained from temperatures registered at the food center and surface layer are presented in Figure 21.4. A value for fhs is only possible 0.5

Temperature Ratio (in-scale)

0

Temp. Ratio (Ta – T)(Ta – Ti)

-0.5 -1 -1.5 -2 -2.5 -3 -3.5

Food center Food surface

-4 -4.5 0

20

40

60

80

100

120

Heating Time (sec)

FIGURE 21.4 Semilogarithmic plots from packed bed heating of large (11.5-mm) carrot cubes at 126°C with steam.

© 2003 by CRC Press LLC

130

130

120

120

Temperature (C)

110

110

(A-1)

100

100

90

90

80

80

70

70

60

60 50

50 Steam F-top F-cen F-bot

40 30 20

Steam F-top F-cen F-bot

40 30 20 10

10 -10

Temperature Ratio (in-scale)

(B-1)

10

30

50 70 90 Heating time (sec)

110

-10

130

10

30

50 70 90 Heating time (sec)

110

130

0.0

0.0 -0.2 -0.4 -0.6

-0.2 Temp Ratio = (Ta – T)/(Ta – Ti)

(A-2)

Temp Ratio = (Ta – T)/(Ta – Ti)

-0.4

(B-2)

-0.6

-0.8 -1.0 -1.2 -1.4 -1.6

-0.8 -1.0 -1.2 -1.4

-1.8 -2.0 -2.2 -2.4

-1.6

Upward Flow

Downward Flow

-1.8

F-top F-cen F-bot

F-top F-cen F-bot

-2.0 -2.2

-2.6

-2.4 0

20

40 60 Heating time (sec)

80

100

0

20

40 60 Heating time (sec)

80

100

FIGURE 21.5 Comparing temperature proﬁles for upward (A) and downward (B) ﬂow steam trough a bed of 11.7-mm potato cubes processed at 125°C with steam. Bottom plots (A-2 and B-2) compare f values at food bed top, center, and bottom locations.

provided the surface temperature is lower than that of the heating medium. Data 2 for regression analysis provided R values of 0.97 or better for fhc, as opposed to 0.92 or better for fhs. Typical temperature data and the dimensionless temperature ratio results (ln scale) obtained from food cubes placed at the top, center, and bottom locations within the food bed are presented in Figure 21.5. The two cases presented here show steam ﬂow in the upward (A1) and downward (B1) directions through a bed of large (11.7 mm length) potato cubes. Data in plots A2 and B2 were used to obtain the heating rate index (slope: fh) and the intercept (jh). SMFR and steam temperatures for these experiments were approximately 5 g/sec and 124°C, respectively. Figure 21.5 and Tables 21.1 and 21.2 show that the food sensors registered nearly the same initial temperature, but the temperatures changed rapidly as steam was injected into the processing chamber, indicating that food was heated uniformly throughout the bed since the transducers located at the top, center, and bottom positions registered similar temperature increases.

© 2003 by CRC Press LLC

21.4.1.2 Temperature at the Food Surface Food surface temperatures (Figure 21.4) were obtained from a 12-mm carrot cube located at the center of the food bed and processed at 126°C with steam ﬂowing upwards. Temperature recorded at the food surface is highlighted in Table 21.1. These data show that food surface temperatures rose rapidly but took approximately 20–40 sec to reach steam temperature. The fact that temperatures measured at the food surface were slightly lower than the temperature of the steam indicated that Bi was less than 40, suggesting that high temperature short time (HTST) processing of diced vegetables involves ﬁnite resistance to surface heat transfer. The h value data evaluated in this work also show that Bi was less than 40.

21.4.2 HEATING RATE INDEX (fh)

AND THE

LAG FACTOR (jh)

21.4.2.1 fhc Values Tables 21.2 and 21.3 provide results for fhc at the top, center, and bottom locations of the food bed and for fhs, jhc and jhs. Data for the latter three are lumped as an average of the data obtained at the top, center, and bottom locations. Additional experimental runs were carried out with the large potato cubes to study the inﬂuence of SMFR and steam temperature on product heating. The initiation of the linear heating segment after approximately 45 sec (center) and 10 sec (surface) showed that the previously deﬁned ranges for regression analysis are correct (Figure 21.4). In general, the experimental values for fhc and fhs obtained from the heating of potato cubes varied between 31 and 35 sec for the larger cubes and between 23 and 26 sec for the smaller cubes. Carrot samples provided slightly lower f values, ranging between 28 and 30 sec for the larger cubes and between 21 and 23 sec for the smaller cubes. Carrot cubes heated faster because they have a higher thermal diffusivity. The data also show that f values at the cube surface were similar to those at the food cube center. However, in some instances, larger than general values (underscored) for fhc were obtained. This issue, together with j values, is discussed later. Potatoes and carrots were also processed in the form of cylindrical slices/slabs. The diameter to thickness ratio indicated in Tables 21.2 and 21.3 refers to the fact that the thin slices were cylindrical. Results show that even for a cylinder thickness to diameter ratio of 1:5, a criterion for an inﬁnite slab was not satisﬁed, since fh slab < 3fh cube. For a ratio of 1:5, the lateral surface of the cylinder represents 30% of its total surface area. Thus, f values for slabs should be less than three times those of cubes of equivalent thickness. It is interesting to note that a 1:5 ratio provided an fh value 2.3 times larger, whereas a 1:4 ratio provided an fh value twice as large as that of a cube of the same thickness. 21.4.2.2 Lag Factor and j Values The jhc values obtained for food cubes were lower than the theoretical value of 2.0. Since j values are location sensitive, small directional errors at the center of food cubes were probably ampliﬁed. Average jhc values of 1.69 and 1.63 were obtained for the

© 2003 by CRC Press LLC

TABLE 21.2 fh and jh for Steam-Injection Heating of Diced Potato Samples in Packed Beds f Value at Particle a

Run No.

Steam Temp °C

Center Flow Direction

SMFR (g/sec)

Bottom (sec)

Center (sec)

Surface Top (sec)

j Values at Particle

(sec)

Center

Surface

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16

126.5 124.2 118.2 123.3 124.1 123.9 123.7 131.6 131.5 124.4 118.2 119.0 124.1 123.8 123.8 130.5

Up Up Up Up Up Up Up Up Up Down Down Down Down Down Down Down

Large Cubes (Length = 11.7 mm) 1.15 34.0 34.9 32.4 c c 45.0 32.0 1.32 40.5 1.97 31.5 32.1 31.6 2.33 32.2 33.7 33.3 2.53 34.3 34.9 33.6 3.88 34.5 34.9 34.5 5.25 33.5 33.8 32.7 7.05 35.0 34.7 34.1 c 31.5 7.27 33.3 49.5 1.27 31.0 34.2 31.9 1.95 31.8 32.3 30.7 1.97 32.8 34.2 30.9 2.55 33.8 38.0 32.4 3.83 32.5 37.8 31.8 5.28 34.8 37.0 34.5 7.32 32.1 37.4 32.3

32.9 31.8 33.2 33.1 31.3 34.0 32.2 32.1 34.0 33.3 32.3 32.8 31.6 34.8 31.7 32.6

1.688 1.557 1.747 1.903 1.726 1.765 1.663 1.474 1.845 1.830 1.645 1.552 1.663 1.711 1.651 1.619

0.108 0.113 0.117 0.117 0.121 0.101 0.103 0.108 0.103 0.109 0.108 0.125 0.106 0.117 0.119 0.110

2.1 2.2 2.3 2.4

125.6 123.8 124.1 130.4

Up Up Down Down

Small Cubes (Length = 9.9 mm) 1.32 24.4 25.7 24.1 2.50 24.5 25.9 23.8 1.22 24.0 24.2 23.9 c 2.58 22.7 33.9 23.9

24.4 24.2 23.8 22.8

1.683 1.693 1.487 1.639

0.115 0.118 0.123 0.124

Up Up Down Down

Potato Slabs (Thickness = 1.30 56.1 59.2 2.40 55.8 57.6 1.32 59.0 63.8 c 2.53 58.3 101.2

55.4 53.2 57.2 58.1

1.119 1.158 1.116 1.131

0.096 0.051 0.077 0.081

b

3.2 3.1 3.4 3.3

124.9 124.6 125.2 124.6

9.9 mm) 59.3 52.6 53.2 56.7

Note: SMFR, steam mass ﬂow rate. a b c

f values at particle center are at bed locations: bottom, center, and top. The length to thickness ratio of the slabs was greater than 5. Data out of range.

large and small potato cubes and 1.90 and 1.58 for carrot cubes, respectively. The experimental average jhs values for large/small potato and carrot cubes obtained from the data (Tables 21.2 and 21.3) were 0.112, 0.12, 0.111 and 0.114, respectively, which compare favorably with the theoretical value of 0.15 (1.26 * 1.26 * 0.095 = 0.15).

© 2003 by CRC Press LLC

TABLE 21.3 fh and jh for Steam-Injection Heating of Diced Carrot Samples in Packed Beds f Value at Particle a

Center

Surface

Steam Temp. °C

Flow Direction

1.1 1.2 1.3 1.4 1.5 1.6

126.1 118.6 126.7 117.9 125.9 126.7

Up Up Up Down Down Down

2.1 2.2 2.3 2.4

125.3 125.2 117.6 124.0

Up Up Down Down

126.0 126.6 124.2 125.0 125.4

Large Cylindrical Carrot Slabs (Thickness = 11.5 mm) d Up 1.83 64.0 108.5 63.4 62.6 Up 2.40 60.2 71.2 74.3 68.9 Up 2.53 — 56.7 — 52.2 Up 2.55 68.7 74.3 56.7 70.9 Down 2.47 58.9 56.2 56.4 58.4

118.4 125.5 124.2 125.7 124.2

Cylindrical Potato Slabs Up 1.83 43.6 Up 2.47 45.5 Up 2.53 — Down 1.33 47.6 Down 2.50 43.1

Run No.

SMFR (g/sec)

Bottom (sec)

Center (sec)

Top (sec)

(sec)

j Values at Particle Center

Surface

Large Carrot Cubes (Length = 11.5 mm) 1.32 29.7 28.9 29.7 27.6 1.85 28.5 29.6 28.8 28.3 2.55 29.2 29.3 28.9 29.1 1.92 29.1 32.7 28.6 28.7 2.02 30.2 29.7 29.1 29.4 2.58 29.6 30.2 29.4 28.6

1.841 2.058 1.857 1.908 1.839 1.783

0.117 0.108 0.121 0.111 0.105 0.103

Small Carrot Cubes (Length = 9.8 mm) 1.32 20.3 21.8 21.4 2.53 21.1 21.5 20.9 1.87 21.8 22.5 20.5 2.60 22.5 22.9 22.9

1.823 1.261 1.794 1.441

0.121 0.109 0.111 0.115

1.121 1.163 1.134 1.212 1.115

0.113 0.112 0.101 0.104 0.099

1.218 1.161 1.118 1.213 1.141

0.097 0.118 0.114 0.109 0.102

20.9 20.7 22.2 21.1

b

3.1 3.2 3.3 3.4 3.5

4.1 4.2 4.3 4.4 4.5

c

(Thickness = 9.8 mm) 50.9 40.9 43.1 43.8 39.4 46.1 42.9 — 43.8 44.0 46.7 39.9 43.9 41.1 43.5

Note: SMFR, steam mass ﬂow rate. a b c d

f values at particle center are at bed locations: bottom, center, and top. The diameter to thickness ratio of the cylindrical carrot slabs was between 3:1 and 3.5:1. The diameter to thickness ratio of the cylindrical potato slabs was between 3.5:1 and 4:1. Datum out of range.

21.4.2.3 Errors Associated with fh and jh Values In analyzing the sources of error associated with f and j values, it was observed that a ±1°C change in Ts (steam temperature) altered fhc by less than 5%. However, this was not so for jhc, fhs, and jhs values. The inﬂuence of small changes in Ts on f and j values is shown in Figure 21.6, using the surface temperature data with Ts − 1 deﬁned as error 1 and Ts + 1 as error 2. This was done because the temperature ratio (θs)

© 2003 by CRC Press LLC

1

Temperature Ratio (in-scale)

0 Food center -1 -2 -3

ERROR 2

-4 CORRECTED -5 Food surface

-6

ERROR 1

-7 0

20

40 60 Heating Time (sec)

80

100

FIGURE 21.6 Inﬂuence of error 1 (Ts – 1) and error 2 (Ts + 1) on the experimental fhs value.

at the surface layer is very sensitive to changes in Ts. Results show that fhs increased with increases in Ts. Furthermore, the value of jhc could be related to that of fhc. During the course of this study, a small increase in steam temperature over time was observed (Figure 21.4). Thus, the use of a slightly lower Ts value would result in a steeper slope. Although such a change had negligible inﬂuence on the fhc value, the impact on j value was large since the data were plotted on a logarithmic scale. An in-depth analysis of fhc variations due to factors such as environment and computation procedure was not carried out. 21.4.2.4 Particle-to-Particle Interaction Deviations from general fhc values, presented in Tables 21.2 and 21.3, are due to particle-to-particle interaction. It was indicated earlier that some adhesion of potato cubes was observed due to gelatinization of starch. Particle adhesion resulted in a larger particle mass, and hence the f value increased. However, small variations in the value of fh can be attributed to: (1) edge contacts and (2) experimental errors associated with variability in particle size. Furthermore, a closer inspection of Table 21.2 shows that slightly higher f values were obtained at the center of the food bed. This effect was not as pronounced for carrot cubes (Table 21.3) as for potato cubes. The slightly higher f value for potato cubes, at the center location of the bed, is possibly a result of condensate build-up, which may have slightly depressed the heating rate. 21.4.2.5 Steam Flow Direction It is difﬁcult to deﬁne which ﬂow direction is superior from temperature and f value data. However, data recorded on food bed heights showed that 180 g of large potato cubes provided an average bed height of 73 mm before processing. This reduced to 64 and 68 mm after treatment due to bed settling, for downward and upward steam

© 2003 by CRC Press LLC

ﬂow, respectively. Since these data are speciﬁc to the simulator used in this study, no general conclusions could be drawn. 21.4.2.6 SMFR and Steam Temperature Steam velocity (SMFR) and processing temperature did not have any inﬂuence on particle heating rate within the range tested. The data for large potato cubes show that similar f values were obtained with steam processing temperatures of 118 and 131°C. An increase in temperature of 9°C (from 118 to 127°C) also produced similar results for carrot cubes. Data also show that a sixfold increase in SMFR did not inﬂuence the particle heating rate. It can thus be concluded that the steam process temperature and SMFR have negligible inﬂuence on the product heating rate.

21.4.3 HEAT TRANSFER COEFFICIENT (h) AND THE BIOT NUMBER (Bi) It was indicated earlier that a ﬁnite surface resistance to heat transfer occurs during packed bed HTST processing of diced vegetables in steam. In cases where 0.1 < Bi < 100, the internal dissipation of heat, although slow, maintains its capacity to keep the surface temperature lower than that of the heating medium, as observed. The system h value and the Biot number can be estimated with Equations (21.3) and (21.5), and by using thermal property data (thermal diffusivity, α, and thermal conductivity, k). From results reported by Kostaropoulos et al. (1975) and Pannu −7 2 et al. (1990), the following data are available: αpotato = 1.6 * 10 m /sec, kpotato = −7 2 0.62 W/m°C, αcarrot = 1.7 * 10 m /sec and kcarrot = 0.66 W/m°C. From the data presented in Tables 21.2 and 21.3, we obtain: fpotato = 33.1 sec, fcarrot = 29.3 sec, Rpotato = 1.17/200 m and Rcarrot = 1.15/200 m. For large cubes, the following results were obtained by using Equations (21.2) and (21.5): β1 potato = 1.47, Bipotato = 14.2, 2 2 hpotato = 1500 W/m °C, β1 carrot = 1.49, Bicarrot = 17.8 and hcarrot = 2000 W/m °C. Similar h values were obtained by using f value data for the smaller (9.9 mm) 2 food cubes. These results are higher than the value of 1100 W/m °C reported by 2 Ling et al. (1974) but in the range of 1900–2500 W/m °C reported by Pannu et al. (1990). The latter study was conducted using single particles. However, the above results for the system heat transfer coefﬁcients are lower than the minimum value 2 of 5000 W/m °C for condensing water vapor, as reported by Holman (1976), for processing of food containers and pouches with steam. Thus, there is need for additional work in this area.

21.4.4 PRODUCT QUALITY Product handling and particle identity were observed by placing processed products on a plate. Potato cubes processed at ≤125°C retained their shape and identity. However, potato cubes processed at 130°C were fragile and overcooked, and there was evidence of particle breakup. In a few instances, it was noticed that potato cubes adhered to each other as well as to the processing container wall. On the other hand, carrot cubes showed no clumping, and the particles maintained their shape and

© 2003 by CRC Press LLC

TABLE 21.4 Moisture Content of Raw and Processed Food Particulates and Visual Observations

Batch No.

Treatment

Initial Mass (g)

Final Mass (g)

Moisture Content (%)

1.1

Uncooked

8.28

1.2

Uncooked

8.54

1.71

79.98

1.3 1.4 1.5

Cooked Cooked Cooked

8.34 8.14 8.44

1.58 1.52 1.61

81.06 81.33 80.92

1.6

Cooked

8.12

1.52

81.28

2.1

Uncooked

7.72

2.2

Uncooked

8.47

0.89

89.49

2.3 2.4 2.5 2.6

Cooked Cooked Cooked Cooked

7.25 6.92 7.11 6.31

0.91 0.84 0.85 0.80

87.45 87.86 88.05 87.32

Visual Observation

Potato Cubes 1.65 80.07

Good shape Good, some adhesion Some adhesion to the container Good shape

Carrot Cubes 0.78 89.90

Good, Good, Good, Good,

no no no no

adhesion adhesion adhesion adhesion

integrity. Processed carrots were more intense in color than the raw product and did not adhere to the container wall.

21.4.5 MOISTURE LOSS Table 21.4 shows that there was no signiﬁcant gain or loss in food moisture content during the processing of potato and carrot cubes in steam. The small increase in moisture of processed potato samples is attributable to higher moisture retention of gelatinized starch. On the other hand, moisture loss by processed carrots probably takes place due to collapse of cellular structure.

21.4.6 PROCESS IMPLICATIONS

ON

PRODUCT BLANCHING/STERILIZATION

To achieve commercial sterility, it is necessary for the center of the food particle to undergo heat treatment to achieve a lethality of 3 min or more (Heldman and Hartel, 1997). The thermal resistance kinetic parameters for Clostridium botulinum are D121 of 0.26 minutes and a z value of 10°C (Perkins et al., 1975). For a 12D process, the particle needs to be held at 121°C for 3 min. Problems such as these need to be resolved through a biological validation study. Furthermore, the deﬁnition of the cold point “in the can” may also need to be redeﬁned for packed bed processing.

© 2003 by CRC Press LLC

In this work, it was shown that there was no cold spot in the food container (processing “can”) after 5 to 10 sec of heating during steam injection heating of diced particles. The cold spot effectively is the particle center point, dispersed throughout the “can.” It is generally recognized that HTST processing will provide a product of superior quality in the case of blanching (Heldman and Hartel, 1997). Thus, the role of steam injection heating in providing optimally processed vegetables for readyto-eat meal packages also needs to be evaluated. As blanching/pasteurization requirements are less severe, packed bed heating of particles in batches by steam injection can provide adequate processing. Listeria monocytogenes, which has been of great concern in recent times, has D70 = 0.14 to 0.27 min and a z value between 6 and 7.5°C (Gaze et al., 1989). As other microorganisms of interest present similar trends, using this microorganism as reference and the temperature data presented in Table 21.4, it can be shown that pasteurization requirements for large potato cubes (11.7 mm) are satisﬁed after approximately 80 sec of steam heating at 125°C. Thus, the data presented in this study can be used to determine thermal process adequacy for various microorganisms of interest.

21.5 CONCLUSIONS The concept of processing food particles in preweighed lots seems promising, and its potential in aseptic processing warrants further investigation. The results of this study show that batch heating of carrot and potato cubes in packed beds with steam provides a processed product that retains shape, identity, and color. Furthermore, steam heating prevents physical losses due to leaching, and under proper conditions the product heats uniformly with negligible gain or loss of moisture. Sensitivity of the temperature data can be appreciated from the fact that carrot and potato cubes produced noticeably different fh values, indicating different heating rates. SMFR (velocity) and steam temperature have only minimal inﬂuence on product heating rate. This study also conﬁrms that ﬁnite resistance to surface heat transfer occurs during packed bed heating of food particles by steam injection. By using literature values for food thermal properties, the apparent surface heat transfer coefﬁcient 2 value was found to range from 1500 to 2000 W/m °C with Bi on the order of 14–17 for 1.2-cm food cubes. There is need for additional work on h values associated with steam processing, as well as a sensitivity analysis of the inﬂuence of process temperature on fh. Process validation, product cook quality, process optimization, and means to aseptically cool the product are areas that need further attention.

NOMENCLATURE α β q Bi Fo

2

−1

Thermal diffusivity (m sec ) Characteristic root, Equation (21.1) Unaccomplished temperature ratio, Equation (21.1) Biot number (= hR/k) 2 Fourier number (= αt/R )

© 2003 by CRC Press LLC

fh H Jh K R T Ts Ti T(x,t)

Heating rate index; negative inverse slope in Equations (21.2), (21.4) and (21.5) (sec) 2 Convective heat transfer coefﬁcient (W/m °C) Thermal lag factor/intercept, Equation (21.2) Thermal conductivity (W/m°C) Characteristic length (m); 1 2 thickness of cube or slice Time (sec) Steam temperature (°C) Initial (food) temperature (°C) Variable internal (particulate) temperature (°C)

REFERENCES Gaze, J.E., Brown, G.D., Gaskell, D.E., and Banks, J.G., Heat resistance of Listeria monocytogenes in homogenates of chicken, beef steak, and carrot, Food Microbiol., 6, 251, 1989. Hayakawa, K.I., Empirical formula for estimating nonlinear survivor curves of thermal vulnerable factors, Can. Inst. Food Sci. Technol., 32, 59, 1982. Heisler, M.P., Temperature charts for induction and constant temperature heating, Trans. ASME, 69, 227, 1947. Heldman, D.R. and Hartel, R.W., Principles of Food Processing, Thomson Publishers, New York, 1997. Holman, J.P., Heat Transfer, 4th ed., McGraw-Hill, New York, 1976. Kostaropoulous, A.E., Spiess, W.E.L., and Wolf, W., Reference values for thermal diffusivity of foodstuffs, Lebensm.-Wiss. Technol., 8, 108, 1975. Larkin, J.W., Use of modiﬁed Ball’s formula method to evaluate aseptic processing of foods containing particulates, Food Technol., 43, 124, 1989. Ling, C.C.A., Bomben, J.L., Farakas, D.F., and King, C.J., Heat transfer from condensing steam to vegetable pieces, J. Food Sci., 39, 692, 1974. Luikov, A.V., Analytical Heat Diffusion Theory, Academic Press, New York, 1968. Pannu, K.S., High Temperature Transient Heating of Vegetables by Steam Injection, thesis, Laval University, Ste-Foy, Quebec, 1992. Pannu, K.S., Castaigne, F., Ramaswamy, H., Arul, J., Audet, P., and Desilets, D., Rapid Sterilization of Particulate Food by Steam Injection: Evaluation of Thermal Parameters, ASAE paper #90–6527, presented at the 1990 ASAE winter meeting, Chicago, 1990. Perkins, W.E., Ashton, D.S., and Evancho, G.M., Inﬂuence of the z value of Clostridium botulinum on the accuracy of process calculation, J. Food Sci., 40, 1189, 1975. Rumsey, T., Farakas, D.F., and Hudson, J.S., Measuring steam heat transfer coefﬁcient of vegetables, Trans. ASAE, 24, 1048, 1980. Singh, R.P., Thermal diffusivity in food processing, Food Technol., 36, 87, 1982. Skjöldebrand, C. and Ohlsson, T., A computer simulation program for evaluation of the continuous heat treatment of particulate food products. Part 2: Utilization, J. Food Eng., 20, 167–181, 1993. Tung, M.A., Britt, I.J., and Ramaswamy, H.S., Food sterilization in steam/air retorts, Food Technol., 44, 105, 1990. Zhang, Q. and Cavalieri, R.P., Thermal model for steam blanching of green beans and determination of surface heat transfer coefﬁcient, Trans. ASAE, 34, 182, 1991.

© 2003 by CRC Press LLC

22

Thermal Processing of Particulate Foods by Steam Injection. Part 2. Convective Surface Heat Transfer Coefﬁcient for Steam K.S. Pannu, F. Castaigne, and J. Arul

CONTENTS 22.1 Introduction 22.2 Materials and Methods 22.2.1 Computational 22.2.2 Equipment and Experimental 22.2.3 Data Analysis 22.3 Results and Discussion 22.3.1 Temperature Proﬁles 22.3.2 Impact of Flow Direction 22.3.3 Transducer Location in the Food Bed 22.3.4 Inﬂuence of Steam Mass Flow Rate (SMFR) 22.3.5 Steam Temperature Effects 22.3.6 Inﬂuence of Particle Size 22.3.7 Inert Material vs. Food 22.3.8 h Values of Food vs. Metal 22.4 Conclusions References

22.1 INTRODUCTION Batch heating of solid foods by steam injection was investigated to determine feasibility and process requirements. This method has potential for high temperature short time (HTST) processing conditions, which are favorable for minimizing nutrient

© 2003 by CRC Press LLC

loss and improving quality of the processed product. Furthermore, product sterilization by steam processing is desirable from the standpoint of minimization of efﬂuent (wastewater) discharge (Poulsen, 1986). The basic premise of this process is that a preweighed quantity of food particulates would be held in specially designed containers and batch heated by ﬂowing steam, which allows HTST processing, with the product ﬂowing continuously. Construction of a laboratory processor and determination of the heating rate of food particulates in a packed bed with steam are described elsewhere (Pannu et al., Chap. 21, this volume). This chapter describes the determination of the surface convective heat transfer coefﬁcient (h value) obtained during packed bed heating with steam. Heat process development involves not only the determination of processing conditions, but also the prediction of product heating time. Basic information requirements are thermal and physical property data for food, thermal property data for steam, steam ﬂow conditions, and the mode of heat transfer. Batch heating of diced carrots and potato cubes showed that the resistance to heat transfer at the food surface was not negligible and that the Biot number was less than 40 when food pieces were heated with steam (Pannu et al., Chap. 21, this volume). These results are in agreement with those reported by Rumsey et al. (1980) and Pannu et al. (1990). In addition, 2 surface heat transfer coefﬁcient values of approximately 2000 W/m °C were obtained with food cubes (Pannu et al., Chap. 21, this volume). These are inferior to the 2 minimum h value of 5000 W/m °C associated with condensing steam (Holman, 1976). This disparity of results requires explanation. To obtain reliable estimates for product heating time, it is imperative to correctly deﬁne h and the associated Biot (Bi) number. An assumption that Bi > 40 is valid for the processing of metal cans and pouches in condensing steam because these objects have a characteristically large size. However, heating time estimates of 113 and 103 sec were obtained for steam processing of 12-mm potato and carrot cubes, respectively, where steam temperature was 125°C and the product initial and ﬁnal temperatures were 25 and 121°C, respectively. Calculations used the ﬁrst term approximation for the transient heat conduction in the equation of Luikov (1968), assuming inﬁnite Biot −7 number (Bi > 40). The normally accepted thermal diffusivity values of 1.6 × 10 and −7 2 1.7 × 10 m /sec (Kostaropoulos et al., 1975) were used for potato and carrot, respectively. However, with Bi ≈ 15, the heating time increased to 130 and 115 sec for the potato and carrot cubes, respectively. The latter values for product heating time are in agreement with our experimental data (Pannu et al., Chap. 21, this volume) and provide 2 h value estimates for steam on the order of 1500 to 2000 W/m °C. The most common explanation for decrease in h value is the presence of air in the steam. Tung et al. (1990) reported that even a small amount of air present in steam could dramatically decrease the h value. Othmer (1929) reported h values of 2 steam with an air content of 0, 1, and 2% to be 15,900, 7900 and 5200 W/m °C, respectively. On the other hand, Pﬂug (1964) found that the h value decreased to 2 2 1300 W/m °C (from about 5000 W/m °C) with 10% air in the steam. Tung et al. (1984) obtained h values higher than those of Pﬂug (1964), but their data support the hypothesis that h values decrease with increasing air content. In addition, they showed that h values were higher during downward steam ﬂow but were not dependent on steam temperature. These differences in results obtained by various researchers

© 2003 by CRC Press LLC

can, at least in part, be attributed to the variations in “come-up time” and/or the “ﬂush time” in different retorts. A second explanation for h value depression, speciﬁc to the food processing situation, is the phenomenon described as “gassing out,” where gases present in fruit and vegetable tissue are released during heating. Brown (1974), Ling et al. (1974), and Zhang and Cavalieri (1991) reported that h values decreased to 400–1100 2 W/m °C during the processing of vegetables in condensing steam because of the “gassing out” effect, leading to the formation of a layer of noncondensable gases at the boundary layer of the food particle. Despite its importance, the h value for steam relating to food processing has not 2 been speciﬁed by application but is generally said to range from 400 to 16,000 W/m °C (Tung et al., 1984). Holman (1976) indicated that the h value for condensing steam 2 2 could range from 5000 to 100,000 W/m °C. The estimate of 5000 W/m °C reported by Pﬂug (1964) has gained acceptance in the food industry and is also the value suggested by Skjöldebrand and Ohlsson (1993) as the condensing steam to wall h value. This 2 2 value of 5000 W/m °C is superior to the values of 850 –1700 W/m °C reported by 2 Rumsey et al. (1980) and 1800 –2500 W/m °C reported by Pannu et al. (1990). Thus, it is imperative to understand the factors contributing to the reduction in h value. Packed bed heating with steam injection was investigated primarily to evaluate the h value for steam under a variety of heating conditions and, secondly, to gain an understanding of how steam ﬂow and condensation effect could affect packed bed heating. The convective surface heat transfer coefﬁcient was determined with temperature measurements obtained from metal cubes placed in the bed of food pieces and inert material. The h values were reported for steam heating of packed beds as affected by process variables such as steam ﬂow direction, ﬂow rate, and temperature, as well as bed characteristics such as particle size and bed composition (food vs. inert material).

22.2 MATERIALS AND METHODS 22.2.1 COMPUTATIONAL The internal resistance to heat transfer is small in metal cubes, and hence the lumped heat capacity method is appropriate for estimation of h values, provided the Biot number is small (Bi ≈ 0.1 or lower). Equation (22.1) was used to compute h values from temperatures registered at the geometric center of metal cubes. Ts − T( t ) −(hA/ρCpV)t = θsolid = e Ts − Ti

(22.1)

The terms A, ρ, Cp, V, and L represent the solid surface area, density, speciﬁc heat, volume, and characteristic length, respectively. Subscripts for temperature (T), listed as s, i, and t, denote steam, initial (metal cube), and time t (metal cube), respectively. The density and speciﬁc heat data are from Holman (1976). ρ and Cp 3 3 for steel are 7830 kg/m and 465 J/kg°C, and those for aluminum are 2707 kg/m and 896 J/kg°C, respectively.

© 2003 by CRC Press LLC

22.2.2 EQUIPMENT

AND

EXPERIMENTAL

Details on apparatus construction and operation have been described elsewhere (Pannu et al., Chap. 21, this volume). The test apparatus had steam superheating capability to provide dry saturated steam to the central treatment chamber. Experiments were conducted with good quality saturated steam, as the outer annular jacket (steam superheater) was always maintained at a slightly higher temperature than the interior treatment chamber, such that heat losses in the central treatment zone were negligible (Pannu, 1992). Two three-way valves and ﬂexible hoses were used for the process setup and to control the steam ﬂow direction through the particle bed. The test apparatus also had provision for regulating the steam velocity through the chamber. Steam was condensed to liquid water, and the condensate collected at intervals was used to determine steam mass ﬂow rate (SMFR). A test container with a diameter of 7.5 cm and a height of 10.3 cm was ﬁlled with glass beads of diameter 6 or 14 mm or with rehydrated chickpeas (diameter ≈ 11 mm), to a bed height of 9 cm. For all experiments, three metal cubes (transducers) were positioned in the particle bed at the top, center, and bottom locations to obtain the desired time–temperature data. The top and bottom transducers were positioned approximately 1 cm below and above the bed extremities, respectively. Thermocouples and pressure gauges were also positioned at strategic locations to allow observation and control of steam pressure and the temperature of the process (Pannu et al., Chap. 21, this volume). The metal transducers were fabricated by positioning a ﬁne-wire copper constantan (36 gauge, type-T) thermocouple at the geometric center of each metal cube. To accomplish this task, a 0.7-mm hole was drilled into each metal cube at the central axis up to a depth equivalent to half the cube dimension. An epoxy cement with high heat resistance and high thermal conductivity was used to bond the thermocouples in place (Omegabond 200, Omega Engineering Inc., Stamford, CT). The cube-shaped metal (aluminum and steel) transducers were constructed in three sizes (9.5, 11.1 and 12.7 mm). Most of the experiments were conducted using the 11.1-mm aluminum cubes. The metal transducers and other thermocouples recorded temperatures at 1 reading/sec for 30 sec, followed by 5 readings/sec (fast test cycle) for the next 60 sec. Thereafter, the data logger recorded the temperatures at 1 reading/2 sec until shutdown. Steam was injected into the central processing chamber once the data logger commenced recording data at the fast test cycle.

22.2.3 DATA ANALYSIS Abbreviated time–temperature data acquired for a typical run are given in Table 22.1. This experiment was carried out with steam at a temperature of approximately 140°C at a ﬂow rate of 3.37 g/sec, ﬂowing downwards through a bed of rehydrated chickpeas. Steam temperatures were monitored at three locations (columns 4 to 6). The reference thermocouple (Ref, column 4) was located 2 cm below the test container and measured the temperature of steam inside the processing chamber. Locations Top (column 5) and Bottom (column 6) measured steam temperatures at the entry and exit positions, respectively, of the apparatus. Temperature data from these three

© 2003 by CRC Press LLC

TABLE 22.1 a Abbreviated Time–Temperature Data for a Typical Run 1

2

3 Time (sec)

1 2 3 4 5 6 7 8 9 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 29 31 34

4

5

6

Steam Temperature (°C)

7

8

9

Transducer Temperature (°C)

Actual

Corrected

Ref

Top

Bot

Bot

Cen

Top

0.0 10.0 20.0 30.0 31.0 31.2 31.4 31.6 31.8 32.0 32.2 32.4 32.6 32.8 33.0 33.2 33.4 33.6 33.8 34.0 34.2 34.4 34.6 34.8 35.0 37.0 39.0 42.0

–32.0 –22.0 –12.0 –2.0 –1.0 –0.8 –0.6 –0.4 –0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 5.0 7.0 10.0

22.5 22.7 23.1 23.1 23.1 23.4 23.1 23.4 23.4 23.4 89.8 122.5 126.3 131.1 135.1 136.6 138.0 138.5 138.8 139.3 139.3 139.3 139.8 138.3 138.3 139.3 139.3 139.5

51.0 50.7 50.1 50.1 50.4 49.9 49.9 100.6 107.4 114.1 120.2 124.3 129.3 132.8 136.3 138.0 138.8 140.0 140.3 140.8 140.8 140.8 141.5 140.5 140.0 140.8 141.3 141.3

45.9 45.9 45.6 45.6 45.3 45.3 45.3 45.9 45.6 46.1 46.7 48.7 57.2 84.4 111.0 124.5 130.8 134.8 137.5 138.0 138.8 138.8 137.8 138.0 136.3 139.8 140.3 140.3

23.1 23.4 23.4 23.6 23.4 23.4 23.4 23.6 23.6 27.2 38.4 52.7 64.7 79.0 87.9 96.4 103.2 107.9 112.5 116.6 119.5 121.7 123.8 125.3 127.4 137.8 138.3 139.0

22.8 23.1 22.8 23.1 23.1 22.8 23.1 23.4 25.7 33.1 48.1 64.5 79.8 91.6 101.4 109.7 116.6 122.2 126.3 129.6 131.8 133.8 135.3 136.6 137.0 139.5 139.5 140.0

22.8 22.8 22.5 23.1 22.5 22.5 22.8 23.4 29.6 47.6 65.3 80.4 92.1 102.2 110.0 116.1 121.5 125.0 128.1 130.6 132.1 133.8 134.6 135.3 136.1 139.0 139.3 139.8

Note: Ref, Bot, Cen: Reference, Bottom, and Center, respectively. a

Downward ﬂow of steam (140°C), at the rate of 3.4 g/sec, through a bed of rehydrated chickpeas.

locations facilitated the adjustment of real time (column 3) and calculation of the steam temperature (Ts). The dimensionless temperature ratios (θ) were calculated for each of the metal transducers, and their natural logarithms [ln(θ)] were plotted against heating time. The h value was computed for each metal cube by determining the slope (X coefﬁcient, Table 22.2) of the linear region of the semilogarithmic plot, using standard regression analysis.

© 2003 by CRC Press LLC

TABLE 22.2 Basic Information and Standard Regression Analysis to Determine h Value Material: Mass: Steam Mass Flow Rate: Processing Temperature:

Chickpeas 240 g 3.37 g/m 140.1°C

Transducer: Location Material: Size: 1 (cm) 3 Density: ρ (kg/m ) Speciﬁc heat: Cp (J/kg°C)

Bottom Steel 1.111 7830 465

Center Aluminum 1.111 2707 896

Top Aluminum 1.270 2707 896

Regression Analysis: Number of data points Degrees of freedom X coefﬁcient Standard error of coefﬁcient 2 R 2 Estimated h values (W/m °C) Estimated Biot Number (–)

21 19 –0.662 0.0066 99.9 4465 0.459

21 19 –1.214 0.0127 99.8 5455 0.148

21 19 –1.120 0.0070 99.9 5748 0.176

22.3 RESULTS AND DISCUSSION 22.3.1 TEMPERATURE PROFILES Typical temperature proﬁles obtained from metal transducers under upward and downward steam ﬂow conditions are shown in Figures 22.1a and 22.1b. They indicate that an instant rise in temperature was evident when steam was injected into the processing chamber, and that all metal transducers had a uniform and constant initial temperature just prior to heat treatment. Furthermore, the lower transducer was ﬁrst to register temperature rise when the ﬂow of steam was upward, and the inverse was true during downward ﬂow. The semilogarithmic plots indicated that linearization was possible after a very short lag period. Biot number values of 0.459 and 0.15 for the 11-mm steel and aluminum test transducers were obtained with the data presented in Table 22.2. The Biot criterion (of Bi ≤ 0.1) was not satisﬁed by the steel transducer. For this reason, most of the investigation was conducted with aluminum transducers.

22.3.2 IMPACT

OF

FLOW DIRECTION

The h values obtained with steam ﬂowing through a bed of rehydrated chickpeas are presented in Figures 22.2 to 22.4. Comparative data for food and glass beads are presented in Figure 22.5. Figure 22.2 shows the transducer locations and h values

© 2003 by CRC Press LLC

Small glass beads

Upward Flow SMFR = 5.5 g/s Top Center Bottom Steam

0

1

2

3

4

5

6

Large glass beads

130 120 110 100 90 80 70 60 50 40 30 -1

Temperature (°C)

Temperature (°C)

120 110 100 90 80 70 60 50 40 30 20 -1

7

Downward Flow SMFR = 2.1 g/s Top Center Bottom Steam

0

Heating Time (sec)

1

2

3

4

5

Heating Time (sec)

(a)

(b)

FIGURE 22.1 Temperatures registered by the metal cubes in beds of 6 mm (a) and 14 mm (b) glass beads. DOWNWARD

6000

h-value (W/m2°C)

SMFR 5500

DOWNWARD

5.67 g/s

1.58 g/s

7.67 g/s

1.50 g/s

9 cm 8 cm

0 cm 1 cm

5000 4.5 cm

4.5 cm UPWARD

4500

1 cm 0 cm

8 cm 9 cm

4000 0

2

4

6

8

Distance (cm): Bed height = 9 cm

10 UPWARD

FIGURE 22.2 The inﬂuence of steam ﬂow rate (SMRF), ﬂow direction, bed height, and location on h values. Experiments were conducted at 120°C with rehydrated chickpeas.

obtained with steam temperatures of ≈120°C in a bed of rehydrated chickpeas under different steam ﬂow rates, with upward and downward ﬂow of steam. In general, all these plots show that h values were higher during downward ﬂow of steam, and the results are in agreement with the general trend reported by Tung et al. (1984). However, the inﬂuence of ﬂow direction vanished when live steam at 100°C (atmospheric pressure) was injected (Figure 22.3), and h values were found to be 2 between 4300 and 4500 W/m °C. The h values remained nearly the same for down2 ward ﬂow but decreased to about 4000 W/m °C for upward ﬂow with pressurized steam at 110°C. Although this may appear to be an anomaly, it can be understood when the contribution of phase change or condensation of steam to heat transfer is taken into consideration. With live steam, a quasi-total condensation is expected, whereas it is partial with pressurized steam. At 100°C, the h value is not signiﬁcantly affected by steam ﬂow direction, presumably because the level of condensation in both directions is nearly the same. With an increase in steam temperature, the h value increases but with a constant disparity between ﬂow directions. This difference has

© 2003 by CRC Press LLC

6000 OPEN HEATING AT 100°C

h-value (W/m2°C)

5500

DOWNWARD

5000 UPWARD 4500 4000 3500 3000 100

110

120

130

140

150

Temperature (°C) FIGURE 22.3 The inﬂuence of steam ﬂow direction and temperature on h values. Steam ﬂowed at a rate of ∼3.4 g/sec through a bed of rehydrated chickpeas. 6000

h-value (W/m2°C)

DOWNWARD

Steam Flow Direction

Top Center Bottom

5500

UPWARD DOWNWARD

5000

4500

4000 1

2

3

4

5

6

Steam Mass Flow Rate (g/sec) FIGURE 22.4 The inﬂuence of steam ﬂow rate, direction, and location on h at temperature of ∼115°C in a bed of rehydrated chickpeas.

to do with the degree of condensation and/or thickness of the condensate ﬁlm, which can play a role in the resistance to heat transfer. The results indicate that with downward ﬂow, a higher level of condensation occurs and/or condensate is ﬂushed out more effectively. The results also indicate that there is a lesser degree of condensation with pressurized steam compared with live steam, and that condensation behavior of pressurized steam is affected by its ﬂow direction. Condensation of steam occurs because of temperature and pressure drops through the particulate bed. It is conceivable that

© 2003 by CRC Press LLC

5500

h-value (W/m2°C)

Large glass beads Chickpeas Small glass beads 5000

4500

Steam Flow Direction UPWARD DOWNWARD 4000 0

2

4

6

8

10

Steam Mass Flow Rate (g/sec)

FIGURE 22.5 The inﬂuence of bed composition, particle size, steam ﬂow rate, and ﬂow direction at a temperature of ∼120°C on h values in beds of 6 mm and 14 mm glass beads and rehydrated chickpeas. The h values were pooled from all three locations.

the drop in steam temperature due to sensible heat exchange may not be signiﬁcantly different between the ﬂow directions. But the drop in steam pressure can be different because downward ﬂow tends to compact the packed bed, while upward ﬂow tends to expand it. Consequently, higher pressure drop and reduced void bed volume would take place during downward ﬂow, while the reverse would be true for upward ﬂow. Reduced void space would facilitate retention of a smaller quantity of condensate. Thus, enhanced condensation (latent heat transfer) and reduced condensate ﬁlm (heat transfer resistance) should lead to a higher h value during downward ﬂow than upward ﬂow under similar heating conditions. Because condensation plays a role, the boundary layer formed by the condensate (liquid water) should be a consideration in heat transfer. Luikov (1968) showed that h is related to the boundary layer thickness (δ) and k, the thermal conductivity of the condensate layer, by equations (2a) and (2b):

h(Ts – Tps) = kf

or δ =

(Ts − Tps ) δ kf h

(22.2a)

(22.2b)

where Ts and Tps are the steam and particle surface temperatures, respectively. An estimate of δ from Equation (22.2b) yields values of 0.3 mm for food materials and 0.12 mm for metal cubes. Larger boundary layer thicknesses increase the resistance to heat transfer and reduce h value.

© 2003 by CRC Press LLC

22.3.3 TRANSDUCER LOCATION

IN THE

FOOD BED

The h values were location sensitive, and more so with steam ﬂowing downward than upward (Figures 22.2 and 22.4). In downward ﬂow, the h values at the uppermost location were highest, and they decreased with bed height; i.e., h values were highest at the point of steam entry into the bed and lowest at the exit end. This was also evident in time–temperature plots for glass beads because the metal transducer at the top location had a steeper slope. In upward steam ﬂow, slightly higher h values were obtained at the top location (Figure 22.2); this is contrary to downward ﬂow, as h values were higher at the exit. Overall, h values were more uniform in upward ﬂow but slightly lower at the bed center.

22.3.4 INFLUENCE

OF

STEAM MASS FLOW RATE (SMFR)

The effect of steam mass ﬂow rate on the value of h is depicted in Figures 22.4 and 22.5. Figure 22.4 shows the changes in h value registered by metal cubes placed in rehydrated chickpeas at steam temperature of 115°C for both ﬂow directions. Figure 22.5 shows the changes in h value for glass beads of diameter 6 and 14 mm and rehydrated chickpeas at 120°C, with steam ﬂow in both upward and downward directions. In the range of SMFR, 1.2 to 5.8 g/sec and Ts ≈ 115°C, (Figure 22.4), h values registered in a bed of chickpeas showed small increases with increase in SMFR at all locations with downward ﬂow. The h values increased at the top, center, and bottom of the food bed 2 2 by about 8% (5000 to 5400 W/m °C), 5% (4650 to 4900 W/m °C), and 14% (4300 to 2 4900 W/m °C), respectively, during downward ﬂow (Figure 22.4). However, the change in h value was negligible when the direction of the steam ﬂow was upward. The pooled data (average for all three locations) presented in Figure 22.5 show that at 120°C the metal transducers experienced small increases in h values, in beds of large glass beads as well as for chickpeas, for both upward and downward ﬂow of steam. However, the increase in h value was negligible for small glass beads for both directions of steam ﬂow (Figure 22.6). Overall, the effect of SMFR on h value was small; the ﬂow direction of steam, as well as particle location, had stronger inﬂuences. Nonetheless, the inﬂuence of SMFR was noticeable for packed beds with larger void spaces, such as large glass beads or chickpeas. The effect waned when the void volumes became small, as in the case of small glass beads.

22.3.5 STEAM TEMPERATURE EFFECTS The effect of steam temperature on h values for rehydrated chickpeas at SMFR of 3.4 g/sec in both the upward and downward ﬂow of steam is shown in Figure 22.3, pooling data for the three locations. To compare the inﬂuence of temperature effects (Figure 22.6) in the three different beds, glass beads of two different sizes and chickpeas, h value data for similar temperatures but different SMFR were pooled for both ﬂow directions and location to provide average values. Whatever the direction or particle size of the bed, h increased with temperature at nearly the same rate. A high h value recorded at 100°C can be attributed to a very high level of condensation of live steam. As steam temperature or pressure was increased, h value remained the same or decreased up to 110°C, depending on steam ﬂow direction; above this

© 2003 by CRC Press LLC

6000

h-value (W/m2°C)

5500 5000 4500 4000 3500

Large glass beads (φ = 14 mm) Chickpeas (φ = 11 mm) Small glass beads (φ = 6 mm)

OPEN HEATING AT 100°C

3000 100

110

120

130

140

Temperature (°C) FIGURE 22.6 The inﬂuence of temperature on h in beds of 6 mm and 14 mm glass beads and ∼11 mm rehydrated chickpeas. Data for similar temperatures but different ﬂow rates were pooled for both ﬂow directions and location to obtain mean values.

temperature, h value increased steadily (Figure 22.3). This suggests that the condensation effect is reduced with pressurized steam. However, the temperature effect compensates for the contribution of condensation to heat transfer and hence, the h value increases above 110°C. In effect, quasi-total steam condensation is achieved with pressurized steam at ~108°C in a downward ﬂow and at ~125°C with upward ﬂow (Figure 22.3). The effects of steam ﬂow direction, SMFR, and temperature on h value can also be understood through the condensation effect. When dry steam ﬁrst enters the packed bed and makes contact with the cold particles, partial condensation occurs and a ﬁlm of water is deposited on the particle surface, and some of the free void space is ﬁlled with the condensate. Since smaller size particles provide more resistance to ﬂuid ﬂow and also have smaller open spaces, it is probable that slightly more water is entrapped because of capillary edge effects, and this increases the boundary layer and consequently reduces the h value. Because condensate is tightly held between the small beads, SMFR and ﬂow direction do not appear to inﬂuence the h value (Figure 22.5). However, as particle diameter increases, void spaces are larger, and as the bed opens up, resulting in better condensate ﬂushing and ﬂuid ﬂow, the effects of SMFR and ﬂow direction come into play (Figures 22.4 and 22.5). Furthermore, heat transfer involves not only sensible heat, but also latent heat effects due to condensation. Hence, the differences in h value ultimately depend on the degree of condensation, ﬂuid ﬂow through the bed, and locations depending on the direction of steam ﬂow. In addition, the dry steam provided for heating can, and most likely does, exit as wet steam. The amount of free water that can be readily carried away by the exiting wet steam is probably related to bed restrictions, SMFR, and temperature. Thus, as temperature increases, effects related to the degree of wetness of exiting steam become important, and the h value increases as the condensate boundary layer shrinks.

© 2003 by CRC Press LLC

22.3.6 INFLUENCE

OF

PARTICLE SIZE

The inﬂuence of particle size on h value is shown in Figures 22.5 and 22.6. Figure 22.5 shows the effect of particle size on h value at various SMFR, while Figure 22.6 provides data on h values at various temperatures. It is clear from these data that h values are dependent on the particle size of the bed. The value of h is higher in packed beds of larger particle size, attributable to larger void spaces within the bed.

22.3.7 INERT MATERIAL

VS.

FOOD

Figure 22.6 indicates that glass beads (inert) and chickpeas display similar trends in the proﬁle of h value with temperature of steam. Large glass beads (diameter 14 mm) show higher h values at all steam temperatures, and small glass beads (diameter 6 mm) show lower values than chickpeas (~diameter 11 mm), which are intermediate in size. Furthermore, assuming chickpeas to be spheres, and ignoring the end effects, the porosity of all three beds is similar. Hence, differences in h value data are attributable to the void spaces between particles rather than to their composition or to the gassing-out effect, which is a possibility since rehydrated chickpeas contain air dissolved in the rehydrated tissue.

22.3.8 h VALUES

OF

FOOD

VS.

METAL

Pannu et al. (Chap. 21, this volume) determined h values for steam processing of 12-mm potato and carrot cubes. Potato and carrot cubes produced h values of about 2 1500 and 2000 W/m °C, respectively; in comparison, similar size metal cubes 2 produced h values ranging between 4300 and 5500 W/m °C (Figures 22.2 to 22.6). 2 The value of about 5000 W/m °C is in agreement with h values for condensing steam reported by Pﬂug (1964) and Skjöldebrand and Ohlsson (1993). The results of this study and previous results (Pannu et al., 1990) show that food particles do not produce h values similar to those obtained with metal transducers. The h values obtained with food pieces were about 40% lower than those obtained with metal cubes under similar process conditions. The obvious differences between these two materials are thermal diffusivity and boundary layer thickness of condensed water. The thermal diffusivity of metals is far higher than that of food −5 2 −7 2 materials (~8.4 × 10 m /sec for aluminum vs. ~1.6 and 1.7 × 10 m /sec for potato and carrot, respectively). Furthermore, the water ﬁlm thickness on metals should be lower because water does not adhere well to metal surfaces, whereas the hydration layer around food facilitates the formation of a thicker boundary layer.

22.4 CONCLUSIONS The h values provided by metal cubes embedded in particle beds heated with steam 2 were closer to the value of 5000 W/m °C of h reported by Pﬂug (1964). These h values 2 are signiﬁcantly higher than the value of 2000 W/m °C obtained for food cubes 2 (Pannu et al., Chap. 21, this volume), but lower than the value of 12,000 W/m °C reported by Tung et al. (1984). The h values were not appreciably affected by SMFR over the range tested. Higher h values were obtained by downward steam ﬂow and

© 2003 by CRC Press LLC

higher steam temperature and in beds of larger size particles. It appears that the gassing-out phenomenon is not involved in the reduction of h values, nor in altering the heat transfer characteristics of steam. Excessive condensation of the heating ﬂuid in the particle bed increases the boundary layer thickness and enhances the resistance to heat transfer. The h values obtained from metal cubes during steam heating were about 2.5-fold higher than those obtained from food of similar size and shape. These differences are attributable to thermal diffusivity and the boundary layer thickness of the condensate. Thus, good quality dry steam is necessary for efﬁcient and uniform heating of food beds to avoid build-up of condensate.

REFERENCES Brown, G.E., Importance of surface heat transfer during steam heat and heat/hold processes, J. Food Sci., 39, 1066, 1974. Holman, J.P., Heat Transfer, 4th ed., McGraw-Hill, New York, 1976. Kostaropoulous, A.E., Spiess, W.E.L., and Wolf, W., Reference values for thermal diffusivity of foodstuffs, Lebensm.-Wiss. Technol., 8, 108, 1975. Ling, C.C.A., Bomben, J.L., Farakas, D.F., and King, C.J., Heat transfer from condensing steam to vegetable pieces, J. Food Sci., 39, 692, 1974. Luikov, A.V., Analytical Heat Diffusion Theory, Academic Press, New York, 1968. Othmer, D.F., The condensation of steam, Ind. Eng. Chem., 21, 576, 1929. Pannu, K.S., High Temperature Transient Heating of Vegetables by Steam Injection. Ph.D. thesis, Laval University, Ste-Foy, Quebec, 1992. Pannu, K.S., Castaigne, F., and Arul, J., Chap. 21, this volume. Pannu, K.S., Castaigne, F., Ramaswamy, H., Arul, J., Audet, P., and Desilets, D., Rapid Sterilization of Particulate Food by Steam Injection: Evaluation of Thermal Parameters, ASAE paper # 90–6527, Presented at the 1990 ASAE winter meeting, Chicago, 1990. Pﬂug, I.J., Evaluation of heating media for processing food in ﬂexible packages. Phase I. Final report, contract DA19-AMC-145(N), U.S. Army Natick Laboratories, Natick, MA, 1964. Poulsen, K.P., Optimization of vegetable blanching, Food Technol., 40, 122–129, 1986. Rumsey, T., Farakas, D.F., and Hudson, J.S., Measuring steam heat transfer coefﬁcient to vegetables, Trans. ASAE, 24, 1048, 1980. Skjöldebrand, C. and Ohlsson, T., A computer simulation program for evaluation of the continuous heat treatment of particulate food products. Part 2: Utilization, J. Food Eng., 20, 167–181, 1993. Tung, M.A., Britt, I.J., and Ramaswamy, H.S., Food sterilization in steam/air retorts, Food Technol., 44, 105, 1990. Tung, M.A., Ramaswamy, H.S., Smith, T., and Stark, R., Surface heat transfer coefﬁcients for steam/air mixtures in two pilot scale retorts, J. Food Sci., 49, 939, 1984. Zhang, Q. and Cavalieri, R.P., Thermal model for steam blanching of green beans and determination of surface heat transfer coefﬁcient, Trans. ASAE, 34, 182, 1991.

© 2003 by CRC Press LLC

23

Modeling of Heat Conduction in Elliptical Cross Sections (Oval Shapes) Using Numerical Finite Difference Models ˇ F. Erdogdu, M.O. Balaban, and K.V. Chau

CONTENTS 23.1 Introduction 23.2 Materials and Methods 23.2.1 Power Curves Method 23.2.2 An Alternate Flexible Method 23.3 Results and Discussion 23.4 Conclusions and Suggestions Nomenclature References

23.1 INTRODUCTION Heat transfer is an important part of several unit operations in food processing. Foods commonly have irregular shapes, and heat transfer analysis is usually avoided because of the difﬁcult mathematical treatment and numerical solutions (Erdoˇgdu et al., 1998b). There has been a wealth of studies, programs and accumulated knowledge of heat transfer in circular cylinders. This is not the case for elliptical cross sections. There have been several studies regarding heat transfer in elliptical cross sections (Erdoˇgdu, 1996). McLahlan (1945) was the ﬁrst to publish analytical equations governing the heat transfer in an inﬁnite elliptical cylinder with a uniform initial temperature and subjected to an inﬁnite convective heat transfer coefﬁcient. The numerical solution for

© 2003 by CRC Press LLC

McLahlan’s equation was provided by Kirkpatrick and Stokey (1959) for ellipses having eccentricities of 0.6, 0.7, 0.8, and 0.9 against Fourier numbers of 0.1, 0.2, 0.5, and 1.0 at certain locations of the geometry. Manson et al. (1974) predicted the transient temperatures in conduction heating of pear-shaped objects using a ﬁnite difference model. Simpson et al. (1989) evaluated thermal processes of foods in oval-shaped containers using a ﬁnite difference approximation of the differential equation for transient heat conduction in three dimensions. Eshleman (1976), Califano and Zaritzky (1993), Sheen et al. (1993), Akterian and Fikiin (1994), and Kim and Teixeira (1997) developed ﬁnite difference methods for simulating heat conduction in irregularly shaped foods. Erdoˇgdu et al. (1998b) developed a volume element based approach on ﬁnite difference models for heat transfer in elliptical cross sections by using power curves. They also reported that the use of power curves, assuming heat transfer is along the curve, can be considered a favored method for heat transfer problems in elliptical cross sections since it reduces the three-dimensional problem into two dimensions in ﬁnite cylinders and the two-dimensional problem into one dimension in inﬁnite cylinders. It was also possible to accurately predict the center temperatures in conductively heated elliptical cylinders by substituting them with a right circular cylinder with equal ratio of surface area to volume when the eccentricity of the ellipse was lower than 0.9. However, neither of these methods was ﬂexible enough to accept different boundary conditions at the surface or inside the surface (e.g., different convective heat transfer coefﬁcient and surface temperatures at the different parts of the surface or nonhomogeneous thermophysical properties inside the geometry). Thus, the development of a ﬂexible alternate ﬁnite difference solution to heat transfer problems in elliptical cross sections to eliminate the previous methods’ deﬁciencies would be valuable. Therefore, the objectives of this study were to review the power curves method, to develop an alternate ﬂexible volume element based approach to accept different boundary conditions at the surface and nonhomogeneous thermophysical properties inside, and to compare these methods.

23.2 MATERIALS AND METHODS 23.2.1 POWER CURVES METHOD As explained by Erdoˇgdu (1996) and Erdoˇgdu et al. (1998b), the following procedure was used to generate the numerical network by the power curves method. The equations representing the power curves and an ellipse with half-major axis “a” and half-minor axis “b” (and also elliptical isotherms) are shown in Equations (23.1) and (23.2).

© 2003 by CRC Press LLC

y = c ⋅ xn

(23.1)

x2 y2 + =1 a 2 b2

(23.2)

Since the power curves are orthogonal to the elliptic isotherms, the product of the slope of the power curves and ellipses must be equal to –1 at their intersection. Equidistant points (the number of power curves) on the perimeter of the ellipse with known values of “a” and “b” were found. These points are at the intersections between the ellipse and the power curves, and the arc length of an ellipse between the horizontal axis and angle 2 was given by: θ

p = a⋅

∫

1 − Sin 2 θ ⋅ dθ

(23.3)

0

where e is the eccentricity (the measure of the roundness of ellipse) and is given by: a 2 − b2 a

e=

(23.4)

The arc length between two intersection points was: perimeter/(number of power curves + 1). Equation (23.3) was used to determine the angle necessary for a given arc length; a bisection method was applied to ﬁnd the intersection point xint, yint. Then, knowing the “a,” “b,” “xint,” and “yint” values, the coefﬁcients of the power curves were calculated using the orthogonality requirement between the ellipse and power curves: n=

y int sp ⋅ x int

(23.5)

n −1 where sp ( = c ⋅ n ⋅ x int ) is the slope of the power curve at the intersection point. Then, the concentric ellipses with major and minor axes decreasing at the same proportions were drawn. The intersection points between the power curves and the concentric ellipses were determined by solving Equation (23.6) using the Newton–Raphson method (Erdoˇgdu, 1996; Erdoˇgdu et al., 1998b).

f=

x 2int c2 ⋅ x 2intn + −1 a2 b2

(23.6)

For an elliptical cross section of a given thickness, a volume element was deﬁned as the volume between two consecutive ellipses and power curves (Figure 23.1). The area bounded by the minor axis and any heat ﬂow line was given by Equation (23.7), and the area of a given volume element was obtained by successive subtraction of areas (Erdoˇgdu, 1996; Erdoˇgdu et al., 1998b). The volume of each element was calculated by multiplying its area by its thickness approximating the curved surfaces by planar surfaces.

A=

© 2003 by CRC Press LLC

x int

x2 b⋅ 1− 2 a

0

c⋅x n

∫ ∫

dy ⋅ dx

(23.7)

a

a a

b

b

a

b b

b

b b

a b

b b

c c

b

b

b b

cc

a

b

b b

b b b b

b b

b b

b

b

a

FIGURE 23.1 Representation of volume element network in an elliptical cross section for the power curves method. (Adapted from Erdoˇgdu, F., Balaban, M.O., and Chau, K.V., J. Food Eng., 38, 223–239, 1998.)

Then, the ﬁnite difference equations were generated by writing energy balance equations for each volume element. The outer surface nodes were treated as noncapacitance surface nodes (NCSN) (Chau and Gaffney, 1990; Welt et al., 1997; Erdoˇgdu, 1996; Erdoˇgdu et al., 1998b). The equations generated for an inﬁnite elliptical cylinder (Figure 23.1) are given below for surface volume elements (a), volume elements between surface and center along the heat ﬂow lines (b), and center volume elements (c), respectively. Volume element type a:   k⋅A  ∆t 1 i , j−1 n +1 n n −1 n n   Ti, j = Ti, j + ⋅ ⋅ (Ti, j − Ti, j ) + ⋅ ( T∞ − Ti, j ) ∆ri, j 1  ρ ⋅ c p ⋅ Vi, j  ∆ri, j−1 +   h ⋅ A i, j k ⋅ A i, j  

(23.8)

Volume element type b:

Tin, j+1 = Tin, j +

  k ⋅ A i, j−1 k ⋅ A i, j ∆t ⋅ ⋅ (Tin, j−1 − Tin, j ) + ⋅ (Tin, j+1 − Tin, j ) ρ ⋅ c p ⋅ Vi, j  ∆ri, j−1 ∆ri, j 

(23.9)

Volume element type c:

Tin, j+1 =

∆t ρ ⋅ c p ⋅ Vi, j

  k ⋅ A i, j−1 ⋅ ⋅ (Tin, j−1 − Tin, j )  ∆ri, j−1 

(23.10)

In the case of ﬁnite elliptical cylinders, where heat ﬂow is assumed to be in the longitudinal direction and along the heat ﬂow line, nine ﬁnite difference equations

© 2003 by CRC Press LLC

were needed. A detailed description for the generation of these equations was given by Erdoˇgdu (1996) and Erdoˇgdu et al. (1998b). An explicit method was used to solve the ﬁnite difference equations. At the end of each time step, there were slightly different temperatures for the center volume elements. Therefore, the overall volume average temperature of the center elements was calculated. For the next time step, the initial temperature of all the center volume elements was taken as the average temperature. The computer program to solve these equations was written in Visual Basic V. 6.0 (Microsoft, 1994). The details of the program are given in Erdoˇgdu (1996) and Erdoˇgdu et al. (1998b).

23.2.2 AN ALTERNATE FLEXIBLE METHOD The following procedure was used to generate the numerical network for the alternate ﬂexible method for the numerical evaluation of conduction heat transfer in elliptical cylinders. By using Equations (23.1), (23.2), and (23.3), the equidistant points on the perimeter of the ellipse with known values of “a,” “b,” and “P” were found, and the θ angle values giving this equidistant arc length between the points (Equation (23.3)) were evaluated using a bisection method. The x and y values of the equidistant points were determined using a bisection method with the known θ value. The boundaries of the volume elements were formed by drawing lines parallel to the x and y axes from the equidistant points. The points where the lines parallel to the x axis intersected with the boundary were used as the starting point for the points parallel to the y axis, and all these were applied to the other three quadrants in a cross section (Figure 23.2). Type 5

Quadrant 4

d: Type 4 b e e c

b

Quadrant 1 b

Type 3

e

c

c

e

c

c

c

b

e

c

c

c

c

b: Type 2

g

g a: Type 1

Type 6

Type 7 f

Quadrant 3

g

g

g

Quadrant 2

FIGURE 23.2 Representation of volume element network in an elliptical cross section for the alternate ﬂexible approach.

© 2003 by CRC Press LLC

Vn

yn – 1 yn

xn – 1

xn

FIGURE 23.3 Representation of volume of a surface element in the volume element network for the alternate ﬂexible approach.

Surface volume elements were treated as capacitance surface nodes (CSN) (Welt et al., 1997). The volume and surface area of the volume elements were determined by using those of a rectangle for the inside nodes, and by integration for the surface nodes. The volume of a surface element for a known thickness (∆l) is given in Equation (23.11) (Figure 23.3):  xn  b Vn =  ⋅ a 2 − x 2 ⋅ dx − [( x n − x n −1 ) ⋅ ( y n − y n −1 )] ⋅ ∆ l   a  x n −1 

∫

(23.11)

The heat transfer area of the CSN was taken as the curve bordered by the equidistant points. It was the product of arc length and the given thickness. The ﬁnite difference equations were generated developing energy balance equations for each volume element. The thermal and physical properties of each volume element were independent of the others. Figure 23.4 shows the different types of volume elements in quadrant 1 of an elliptical cross section. Equations (23.12) to (23.18) are the generated ﬁnite difference equations for these volume elements. Volume element type 1:  k ⋅ YA q1,i, j+1  1  1 − ∆t ⋅ ⋅  q1,i, j (ρ ⋅ c p ⋅ V)q1,i, j  ∆x q1,i, j    Tqn1+1 (i, j) = Tqn1 (i, j) ⋅      + k q 2,i, j ⋅ XA q1,i, j+1 + h q1,i , j ⋅ YA q1,i , j    ∆y q1,i, j    ⋅ XA q1,i, j+1 n k   k q1,i, j ⋅ YA q1,i, j+1 n ⋅ Tq1 (i, j + 1) + q 2,i, j ⋅ Tq1 (i − 1, j + 1)  ∆x q1,i, j ∆y q1,i, j  + ∆t ⋅     + h q1,i, j ⋅ YA q1,i, j−1 ⋅ Tq∞1,n (i, j) (23.12)

© 2003 by CRC Press LLC

Type 3

Type 2

Volume element Type 1

h convection

(i+1,j-1)q1

h convection

(i,j)=(1,2) (i,j+1) q1

(i,j)q1

(i,j+1) q1

(i,j)q2

(i,j) q1

(i,j)q1

(i,j+1)q1

(i,j-1) q1

(i-1,j+1)q1

(i-1,j+1)q1

Type 5 (i+1,j-1)q1

Type 4 h convection (i,j)q4

(i,j)q1 (i,j)q4

(i,j)q1

(i,j-1)q1

(i-1,j+1)q1

(i-1,j+1)q1

Type 7

Type 6

(i+1,j-1) q1

(i+1,j-1) q1

(i,j)q4

(i,j)q1

(i,j)q2

(i,j-1)q1

(i,j+1) q1

(i,j) q1

(i,j-1) q1

(i,j) q2

FIGURE 23.4 Representation of different volume elements in quadrant 1 for the alternate ﬂexible approach (see Figure 23.1).

© 2003 by CRC Press LLC

Volume element type 2:    k q1, i, j + 1 ⋅ YA q1, i, j 1  1 − ∆t ⋅ ⋅ (ρ ⋅ c p ⋅ V) q1, i, j  ∆x q1, i, j    Tqn1+ 1 (i, j) = Tqn1 (i, j) ⋅      k q1, i − 1, j + 1 ⋅ XA q1, i − 1, j + 1 + h q1, i, j ⋅ YA q1, i, j − 1   + ∆y q1, i, j    k q 2, i, j ⋅ XA q1, i − 1, j + 1 n  k q1, i, j + 1 ⋅ YA q1, i, j n  ⋅ Tq1 (i, j + 1) + ⋅ Tq1 (i − 1, j + 1)  ∆ ∆ x y q1, i , j q1, i , j  + ∆t ⋅    + h q1, i, j ⋅ YA q1, i, j − 1 ⋅ Tq∞1, n (i, j)   

(23.13) Volume element type 3:    k q1,i, j+1 ⋅ YA q1,i, j 1  1 − ∆t ⋅ ⋅   (ρ ⋅ c p ⋅ V)q1,i, j  ∆x q1,i, j     k XA k XA ⋅ ⋅ q1,i +1, j−1  q1,i , j−1 Tqn1+1 (i, j) = Tqn1 (i, j) ⋅ + q1,i −1, j−1 + q1,i +1, j−1   ∆y q1,i +1, j−1 ∆y q1,i, j−1       k q1,i −1, j+1 ⋅ XA q1,i, j  +    ∆ y  q1,i , j   k ⋅ XA q1,i, j−1 n   k q1,i, j+1 ⋅ YA q1,i, j n ⋅ Tq1 (i, j + 1) + q1,i, j−1 ⋅ Tq1 (i, j − 1)   ∆x q1,i, j ∆y q1,i, j−1   + ∆t ⋅   k q1,i −1, j+1 ⋅ XA q1,i, j n   k q1,i +1, j−1 ⋅ XA q1,i +1, j−1 n ⋅ Tq1 (i + 1, j − 1) + ⋅ Tq1 (i − 1, j + 1) + ∆y q1,i +1, j−1 ∆y q1,i, j   (23.14) Volume element type 4:   k q 4, i, j ⋅ YA q1, i, j  1  1 − ∆t ⋅ ⋅ ∆x q1, i, j (ρ ⋅ c p ⋅ V) q1, i, j     Tqn1+ 1 (i, j) = Tqn1 (i, j) ⋅      k q1, i − 1, j + 1 ⋅ XA q1, i, j + h q1, i, j ⋅ YA q1, i, j   + ∆y q1, i, j    k q1, i − 1, j + 1 ⋅ XA q1, i, j n   k q 4, i, j ⋅ YA q1, i, j n ⋅ Tq 4 (i, j) + ⋅ Tq1 (i − 1, j + 1)  ∆ x ∆ y q1, i , j q1, i , j  + ∆t ⋅     + h q1, i, j ⋅ YA q1, i, j ⋅ Tq∞1, n (i, j)  

© 2003 by CRC Press LLC

(23.15)

Volume element type 5:  1 1 − ∆t ⋅ (ρ ⋅ c p ⋅ V) q1, i, j  Tqn1+ 1 (i, j) = Tqn1 (i, j) ⋅    k q1, i, j − 1 ⋅ YA q1, i, j − 1 +  ∆x q1, i, j − 1 

 k q 4, i, j ⋅ YA q1, i, j  ⋅ + ∆x q1, i, j     k q1, i − 1, j + 1 ⋅ XA q1, i, j    ∆y q1, i, j  

k q1, i, j − 1 ⋅ YA q1, i, j − 1 n   k q 4, i, j ⋅ YA q1, i, j n ⋅ Tq 4 (i, j) + ⋅ Tq1 (i, j − 1) +   ∆ ∆ x x q1, i , j q1, i , j − 1   + ∆t ⋅     k q1, i − 1, j + 1 ⋅ XA q1, i, j n ⋅ Tq1 (i − 1, j + 1)   ∆ y   q1, i , j

(23.16)

Volume element type 6:   k ⋅ YA q1,i, j 1  1 − ∆t ⋅ ⋅  q 4 ,i , j (ρ ⋅ c p ⋅ V)q1,i, j  ∆x q1,i, j    Tqn1+1 (i, j) = Tqn1 (i, j) ⋅     + k q 2,i, j ⋅ XA q1,i, j + k q1,i, j−1 ⋅ YA q1,i, j−1 + k q1,i +1, j−1 ⋅ XA q1,i +1, j−1    ∆y q1,i, j ∆x q1,i, j−1 ∆y q1,i +1, j−1   ⋅ XA q1,i, j n k  k q 4,i, j ⋅ YA q1,i, j n  ⋅ Tq 4 (i, j) + q 2,i, j ⋅ Tq 2 (i, j)   ∆x q1,i, j ∆yy q1,i, j   + ∆t ⋅   k q1,i +1, j−1 ⋅ XA q1,i +1, j−1 n  k q1,i, j−1 ⋅ YA q1,i, j−1 n  ⋅ Tq1 (i, j − 1) + ⋅ Tq1 (i + 1, j − 1) + x ∆ ∆ y q1,i , j−1 q1,i +1, j−1   (23.17) Volume element type 7:    k q1, i, j + 1 ⋅ YA q1, i, j 1  1 − ∆t ⋅ ⋅ ∆x q1, i, j (ρ ⋅ c p ⋅ V) q1, i, j     Tqn1+ 1 (i, j) = Tqn1 (i, j) ⋅     ⋅ k ⋅ YA k ⋅ XA k XA  q1, i, j − 1 q 2, i , j q1, i , j  q1, i , j − 1 q1, i + 1, j − 1 q1, i + 1, j − 1 + + +   ∆y q1, i + 1, j − 1 ∆y q1, i, j ∆x q1, i, j − 1    k q1, i, j − 1 ⋅ YA q1, i, j − 1 n   k q1, i, j ⋅ YA q1, i, j n ⋅ Tq1 (i, j + 1) + ⋅ Tq1 (i, j − 1)   ∆ ∆ x x q1, i , j q1, i , j − 1   + ∆t ⋅   k q 2, i, j ⋅ XA q1, i, j n   k q1, i + 1, j − 1 ⋅ XA q1, i + 1, j − 1 n ⋅ Tq1 (i + 1, j − 1) + ⋅ Tq 2 (i, j) + y y ∆ ∆   q1, i + 1, j − 1 q1, i , j

(23.18)

© 2003 by CRC Press LLC

An explicit method was used to solve these ﬁnite difference equations. All calculations were performed using a computer program written in Visual Basic V. 6.0 (Microsoft, 1994). The developed program calculated the temperature distribution in elliptical cross sections using the power curves method and alternate ﬂexible approach. The ﬂow diagram for the developed program for both approaches is given in Figure 23.5.

A. Volume element network generation Data Input: a: half-major, b: half-minor axis for elliptical cross-section for volume element network generation and all thermophysical properties Calculation of: eccentricity, perimeter, arc length between two intersection points and the coordinates of the intersection points using Eqs. 3.4.1 to 3.4.6

B. Calculation of the physical properties of the volume elements and generation of finite difference equations Defining the volume elements for power curves method of the alternate flexible approach Calculation of the area and volume of each volume element using Eqs. 3.4.7 to 3.4.11 and the distances between the volume elements in each direction

C. Generation of finite difference equations and the solution using an explicit procedure Generation of finite difference equations (using Eqs. 3.4.8 to 3.4.10 for the power curves method and Eqs. 3.4.12 to 3.4.18 for power curves method for the alternate flexible approach) by writing energy balances for each volume element, and using an explicit procedure to solve these equations knowing outside temperatures, product properties, and heat transfer conditions on the surface

FIGURE 23.5 Flow diagram of the developed program for the power curves method and the alternate ﬂexible approach.

© 2003 by CRC Press LLC

23.3 RESULTS AND DISCUSSION The NCSN and CSN volume element ﬁnite difference models developed for modeling of heat conduction in elliptical cross sections were validated by experiments. Long plexiglass elliptical cylinders with eccentricities of 0.63 (a = 2.2 cm, b = 1.7 cm, l = 15 cm) and 0.69 (a = 1.25 cm, b = 0.9 cm, l = 8 cm) were used for the validation studies. The thermal conductivity, heat capacity, and density of these 3 cylinders were 0.1875 W/m-K, 1465.4 J/kg-K, and 1190 kg/m , respectively (Polycast Technology, 1996). Heating experiments were performed in a well-agitated water bath (inﬁnite h), 2 and cooling was done in ice slush (h ≈200 W/m °K) (Erdoˇgdu et al., 1998a). Time–temperature data from the experiments were gathered using Type-T, 36 gauge thermocouples (Ecklund, Fort Myers, FL), inserted and stabilized in the cylinders, and a data acquisition system (DAS-TC, Kethley Metrabyte, Taunton, MA). The experimental data were compared with the model results. Ten experiments were conducted for the validation studies at temperatures of 75 and 85°C. Figures 23.6 and 23.7 show the comparison of two of the experimental and predicted temperatures (at center and off-center points) of “inﬁnite” elliptical cylinders of eccentricity of 0.69 and 0.63 by the alternate ﬂexible approach and the power curves method. In both approaches, the model predictions were close to the experimental results. Since a circular cross section can be described as an elliptical cross section with equal “a” and “b” values, both approaches can also be used for simulation studies in circular cylinders. The advantage of the power curves method is that it reduces the heat transfer problem from three- to two-dimensional in ﬁnite cylinders, and from two- to onedimensional in inﬁnite cylinders. However, the advantage of the second approach over the power curves method is that it allows simulations with different boundary conditions in different directions and different volume elements, as seen in Figure 23.8.

Temperature (°C)

100 80 60 40 20 0 5

0

10

15

20

25

30

35

Time (min) Model Center

Exp. Center

Exp. Off-center

Medium Temperature

Model Off-center

FIGURE 23.6 Comparison of experimental and model center temperatures in a long elliptical cylinder (a = 2.2 cm, b = 1.7 cm, l = 15 cm, e = 0.63; by alternate ﬂexible approach).

© 2003 by CRC Press LLC

Temperature (°C)

100 80 60 40 20 0 0

5

10

15

20

Time (min) Model Center

Exp. Center

Exp. off-center

Medium Temperature

Model off-center

FIGURE 23.7 Comparison of experimental and model center temperatures in a long elliptical cylinder (a = 1.25 cm, b = 0.9 cm, l = 8 cm, e = 0.69; by power curves method).

Quadrant 4 T1, h1

Quadrant 3 T2, h2

Quadrant 1 T1, h1

Quadrant 2 T2, h2

* Shaded areas show the volume elements with different thermophysical properties.

FIGURE 23.8 Representation of using the alternate ﬂexible approach for different boundary conditions and volume element properties.

© 2003 by CRC Press LLC

For example, the heat transfer problem for an elliptic–cylindrical shaped food with each half having different boundary conditions, such as one half in sauce and the other facing air, can be solved using the developed alternate ﬂexible approach. Since the power curves method assumes the heat transfer along the power curves, not between them, it becomes impossible to use this method for this kind of problem. Other examples showing the efﬁcacy of the second method include the following: Burfoot and James (1988) reported that the heat transfer coefﬁcient is location dependent for thawing and cooking of cylindrical shaped meats. Burfoot et al. (1990) compared the heating and cooling times of meat joints. The developed alternate ﬂexible approach can be easily used for both problems, taking into account the different thermophysical properties of meat joints and including the bones inside the meats. The ﬂexibility of the second method when applied to systems with nonhomogeneous initial temperature distribution can be given as another example of the efﬁcacy of this method.

23.4 CONCLUSIONS AND SUGGESTIONS Both power curves and the developed alternate ﬂexible approach were successfully applied to analyze the heat conduction in elliptical cross sections. Both of these methods can also be used to predict the temperature distribution in response to dynamic surface temperature history. The Windows-based software developed in this study calculated the temperature distribution in inﬁnite elliptical cylinders for both approaches at any given time, knowing outside temperature (constant or variable), product properties (homogeneous or heterogeneous), and heat transfer conditions at the surface (constant throughout the surface or variable). The validation of the second approach for different food systems and modiﬁcation to simulate the heat transfer in ﬁnite cylinders and ﬁnite slabs will result in a powerful tool which can be used for the analysis of thermal processing in food systems with nonhomogeneous thermal properties.

NOMENCLATURE a Ai,j b c cp cp qm,i,j ∆r ∆t ∆l e f h k

Half-major axis for ellipse, m 2 Surface area of the volume element i, j, m Half-minor axis for ellipse, m Constant Heat capacity, J/kg-K Heat capacity of volume element i, j in quadrant m, J/kg-K Distance between the volume elements along the heat ﬂow line, m Time step used in explicit solution method, sec Thickness for a volume element Eccentricity of an ellipse Function for the intersection points of ellipses and power curves 2 Convective heat transfer coefﬁcient, W/m -K Thermal conductivity, W/m-K

© 2003 by CRC Press LLC

kqm,i,j n p ρ ρqm,i,j se sp

Thermal conductivity of volume element i, j in quadrant m, W/m-K Constant Perimeter of an ellipse, m 3 Density, kg/m 3 Density of volume element i, j in quadrant m, kg/m Slope of a tangent line at any point on the ellipse Slope of a tangent line at any point on the power curve

Tin,j

Temperature of the volume element i, j at the time step n, °C

n +1 i, j n qm

T

Temperature of the volume element i, j at the next time step, °C

T (i, j)

Temperature of the volume element i, j at the time step n for quadrant m, °C Temperature of the volume element i, j at the next time step for quadrant m, °C Medium temperature of the volume element i, j at the next time step for quadrant m, °C The angle of the line connecting the center of an ellipse and a point on the ellipse circumference, radian 3 Volume of the volume element i, j, m Intersection points between a heat ﬂow line and an ellipse The surface area of the volume element i, j in quadrant m in y direction, ∫ m ∫ The surface area of the volume element i, j in quadrant m in x direction, m

n+1 Tqm (i, j) ∞,n Tqm (i, j)

θ Vi,j xint,yint XAqm,i,j YAqm,i,j

REFERENCES Akterian, S.G. and Fikiin, K.A., Numerical simulation of unsteady heat conduction in arbitrary shaped canned foods during sterilization processes, J. Food Eng., 21, 343–354, 1994. Burfoot, D. and James, S.J., The effects of spatial variations of heat transfer coefﬁcient on meat processing times, J. Food Eng., 7, 41–61, 1998. Burfoot, D., Self, K.P., Hudson, W.R., Wilkins, T.J., and James, S.J., Effect of cooking and cooling method on the processing times, mass losses and bacterial condition of large meat joints, Int. J. Food Sci. Technol., 25, 657–667, 1990. Califano, A.N. and Zaritzky, N.E., A numerical method for simulating heat transfer in heterogeneous and irregularly shaped foodstuffs, J. Food Process Eng., 16, 159–171, 1993. Chau, K.V. and Gaffney, J.J., A ﬁnite difference model for heat and mass transfer in products with internal heat generation and transpiration, J. Food Sci., 55, 484–487, 1990. Erdoˇgdu, F., Modeling of temperature distribution in shrimp, and measurement of its effect on texture, shrinkage and yield loss, thesis, University of Florida, Gainesville, 1996. Erdoˇgdu, F., Balaban, M.O., and Chau, K.V., Automation of heat transfer coefﬁcient determination: development of a Windows-based software tool, Food Technol. Turkey, 10, 66–75, 1998a Erdoˇgdu, F., Balaban, M.O., and Chau, K.V., Modeling of heat conduction in elliptical cross-section: I. Development and testing of the model, J. Food Eng., 38, 223–239, 1998b. Eshleman, W.D., A numerical method for predicting heat transfer in axi-symmetrical shaped solids, thesis, University of Florida, Gainesville, 1976.

© 2003 by CRC Press LLC

Kim, K.H. and Teixeira, A.A., Predicting internal temperature response to conduction-heating of odd-shaped solids, J. Food Process Eng., 20, 51–63, 1997. Kirkpatrick, E.T. and Stokey, W.F., Transient heat conduction in elliptical plates and cylinders, J. Heat Transfer, 80, 54–60, 1959. Manson, J.E., Stumbo, C.R., and Zahradnik, J.W., Evaluation of thermal process for conduction heating foods in pear-shaped containers, J. Food Sci., 39, 276–281, 1974. McLahlan, N.W., Heat conduction in elliptical cylinder and an analogous electromagnetic problem, Philosophical Magazine, 36, 600–609, 1945. Microsoft Corporation, Visual Basic Professional, Version 3.0, Microsoft, Redmond, WA, 1994. Polycast Technology, Thermal Property Data for Acrylic Plexiglass, Polycast, Westport, CT, 1996. Sheen, S., Tong, C.H., Fu, Y., and Lund, D.B., Lethality of thermal processes for food in anomalous-shaped plastic containers, J. Food Eng., 20, 199–213, 1993. Simpson, R., Aris, I., and Torres, J.A., Sterilization of conduction-heated foods in oval-shaped containers, J. Food Sci., 54, 1327–1331, 1363, 1989. Welt, B.A., Teixeira, A.A., Chau, K.V., Balaban, M.O., and Hintenlang, D.E., Explicit ﬁnite difference methods for heat transfer simulation and thermal process design, J. Food Sci., 62, 230–236, 1997.

© 2003 by CRC Press LLC

24

Heat Transfer Coefﬁcient for Model Cookies in a Turbulent Multiple Jet Impingement System N. Nitin and M.V. Karwe

CONTENTS 24.1 Introduction 24.1.1 Flow Field in a Submerged Turbulent Jet 24.1.1.1 Free Jet 24.1.1.2 Impinging Jet 24.1.1.3 Flow Field in Turbulent Multiple Submerged Jets 24.1.2 Heat Transfer Characteristics of a Single Impinging Jet 24.1.3 Heat Transfer Characteristics for Multiple Jet Conﬁgurations 24.2 Materials and Methods 24.2.1 Experiments (Stationary Mode) 24.2.2 Experiments (Rotational Mode) 24.3 Results and Discussion 24.3.1 Maximum Jet Velocity 24.3.2 Heat Transfer Coefﬁcient 24.4 Conclusions Nomenclature Acknowledgment References

24.1 INTRODUCTION Jet impingement technology is used in several industrial applications such as electronic cooling, cooling of hot metal plates and gas turbine blades, high performance low weight heat exchangers, and driers. In the food industry, jet impingement technology has been used in baking and freezing operations for faster and better processing due to high heat transfer rates with better quality retention. Jet impingement ovens are used to bake pizza

© 2003 by CRC Press LLC

shells, crackers, and cookies and to toast ready-to-eat cereals. Prior studies (Walker and Sparman, 1989) showed that jet impingement ovens could not only reduce the time of processing by a factor of about two, but also produce good quality products in terms of better moisture retention. However, little is known about the detailed transport phenomena associated with multiple jet impingement oven systems. Several researchers have experimentally investigated the heat transfer associated with impinging jets. The major studies in this area have been carried out to understand the ﬂuid ﬂow in a single and multiple jet system. A few studies have focused on heat transfer characteristics. Most of the heat transfer studies apply only to a narrow range of Reynolds numbers, with the major focus on cooling applications over a ﬂat surface. Jets can be broadly classiﬁed as submerged or nonsubmerged. When the medium of the jet is the same as the surrounding medium, it is classiﬁed as a submerged jet. Submerged jets can be further divided into two categories, free jets and impinging jets. The majority of industrial applications involve impinging jets. In impinging jets, a jet of liquid or gas comes from a nozzle and impinges on a desired surface, while in the case of free jets there is no target surface for impingement. Submerged impinging jets can be further classiﬁed as laminar or turbulent jets. When the Reynolds number based on the nozzle diameter of the jet exceeds 3000, it is generally classiﬁed as a turbulent jet. In this chapter, we focus on turbulent submerged jets because they are used in food processing operations. cvf(Van Dyke, 1982)

FIGURE 24.1 Laminar region near the nozzle in a turbulent free jet with Reynolds number Re = 30,000. (From Van Dyke, M., An Album of Fluid Motion, The Parabolic Press, Stanford, CA, 1982. With permission.)

© 2003 by CRC Press LLC

shows a typical turbulent jet (Re = 30,000) coming out of a tube of diameter 6.35 mm. It shows a laminar region near the nozzle before the jet becomes turbulent. Since the nature of the ﬂow depends upon the axial downstream distance, the heat transfer characteristic in jet impingement will depend upon the distance of the target plate from the nozzle.

24.1.1 FLOW FIELD

IN A

SUBMERGED TURBULENT JET

24.1.1.1 Free Jet Flow ﬁeld studies (Gardon and Akﬁrat, 1965) for a submerged single turbulent free jet have shown that as the jet comes out of a nozzle, there is a mixing of the jet air with the surrounding air with an increase in the width of the mixing region. This is shown schematically in Figure 24.2 (Gardon et al., 1965). In the initial region of about 4–5 nozzle diameters, the mixing of the jet air with surrounding air takes place only at jet boundaries. The mixing results in an exchange of momentum of the jet at the jet boundaries with the surrounding medium. This exchange of momentum decreases the jet velocity at the jet boundary, while the centerline velocity does not change signiﬁcantly over this initial region, characterized as a potential core region. Beyond this potential core region, the centerline velocity decreases as more and more of the surrounding ﬂuid is entrained. This results in an increase in the

@ Z/D= 2

@ Z/D= 12

@ Z/D= 6

U/ UE

0 0

U/ UE

0

U/ UE

1

1

1

VELOCITY VELOCITY

VELOCITY

TURBULENCE TURBULENCE TURBULENCE

MIXING REGION

0

0.2

U’/ UM

POTENTIAL CORE

0.2

0 U’/ UM

0.2

0 ’

U / UM

FIGURE 24.2 Schematic distribution of velocity and turbulence in an axis-symmetric jet. U = jet velocity; UE = jet exit velocity; UM = r.m.s. value of ﬂuctuating component of velocity; U′ = centerline velocity of jet; Z/D = ratio of axial distance to nozzle diameter. (Adapted from Gardon, R. and Akﬁrat, J.C., Int. J. Heat Mass Transfer, 8, 1261–1272, 1965.)

© 2003 by CRC Press LLC

D

FREE JET

STAGNATION ZONE

LATERAL SPREAD REGION

PLATE FIGURE 24.3 Schematic diagram of three zones in a single impinging jet.

width of the mixing region. The mixing of the surrounding air with the jet air generates turbulence in the free jet (Gardon and Akﬁrat, 1964; Gardon and Cobonpue, 1961). Figure 24.2 shows that the turbulence level increases with the increase in jet length. The peak of the turbulence shifts from the outer region of the jet to the center of the jet with downstream distance. 24.1.1.2 Impinging Jet Flow studies (Gardon and Akﬁrat, 1964; Martin, 1977) have indicated that ﬂow in a turbulent single impinging jet can be divided into three regions: the free jet region, the stagnation region, and the lateral spread region. Figure 24.3 shows these three regions in a single impinging jet. In the free jet region, the ﬂow behavior is the same as discussed above for the free submerged turbulent jet. The impinging jet behaves as free jet up to a distance of about 1–1.5 nozzle diameters from the impinging surface. After this, deceleration of the impinging jet begins as the jet enters into the stagnation region. In the stagnation region there is impingement and deﬂection of the jet. In this region, the jet experiences a deceleration (Gardon and Akﬁrat, 1965). The axial velocity decreases rapidly, and the static pressure rises. In the lateral spread region, the negative pressure gradient causes a rapid increase in the radial velocity near the deﬂection region, and it drops away to a region away from it. This drop in velocity is due to wider area available for the same mass of material to ﬂow and also due to the viscous losses at the wall. 24.1.1.3 Flow Field in Turbulent Multiple Submerged Jets The majority of studies in the ﬂow ﬁeld of multiple jets geometry for turbulent regime (Re ~ 25,000) have been done using nonsubmerged water jets (Viskanta and Huber, 1994b; Saripalli, 1983). Only a few studies on ﬂow ﬁeld have been reported using a submerged air jet system. One of the major ﬂow ﬁeld studies (Marcoft, 1999) using a submerged air multiple jets conﬁguration has been done using the technique of LDA (Laser Doppler Anemometry). It was used to map the velocity ﬁeld for three- and four-jet conﬁgurations. The results showed that the axial velocity contours for multiple submerged air jet conﬁgurations show similar trends in the

© 2003 by CRC Press LLC

60

Uz (m/sec)

Y(mm)

40

20

23.94 20.16 16.38 12.61 8.83 5.05 1.28 -2.50 -6.27 -10.05

Jet #3 Jet #2

0

Jet #1 -20

-40 -80

-60

-40

-20

0

20

X(mm) -X +Z

10 mm

FIGURE 24.4 Contours of constant axial (uz) velocity for three jets impinging on a ﬂat plate. Measurements made in a plane 10 mm from the ﬂat plate.

free mixing and stagnation region as discussed for single jet conﬁguration. Figure 24.4 and Figure 24.5 show the details of velocity contours at a distance of 10 mm from the impingement plate for three- and four-jet conﬁgurations, respectively. In addition to the characteristics of the velocity ﬁeld for a single jet, the measured velocity proﬁles also showed negative velocity regions in the lateral ﬂow regime. These negative velocity regions result because of the interaction between the adjacent jets, which causes ﬂow reversal in the lateral ﬂow regime of the multiple jets. This region has been shown to be of great importance in describing the heat transfer characteristics of multiple jets (Marcoft, 1999). For measurements made close to the ﬂat plate, the magnitude of maximum negative velocity in these regions was almost 50% of the maximum jet velocity measured near the nozzle exit. The range of this negative velocity depends on the nozzle-to-nozzle spacing, velocity of the jets, and nozzleto-plate spacing. Similar results of jet interaction resulting in reverse ﬂow have been shown (Viskanta and Huber, 1994b; Saripalli, 1981) using water jets. Both of these studies have shown the formation of an interaction fountain, i.e., the reverse ﬂow in between the adjacent impinging jets. Figure 24.6 shows the details of the reverse ﬂow in the form of an interaction fountain between the adjacent jets for water jets.

© 2003 by CRC Press LLC

Jet #3 40 Jet #4

20

Uz (m/sec) 21.49 18.18 14.87 11.56 8.25 4.94 1.62 -1.69 -5.00 -8.31

0 Jet #2

-20

Y (mm)

Jet #1 -40

-60

-80

-100 -80

-60

-40

-20

0

20

40

X (mm) -X +Z

10 mm

FIGURE 24.5 Contours of constant axial (uz) velocity for four jets impinging on a ﬂat plate. Measurements made in a plane 10 mm from the ﬂat plate.

INTERACTION FOUNTAIN

INTERACTION FOUNTAIN

FIGURE 24.6 Schematic diagram of reverse ﬂow (interaction fountain) in multiple jet conﬁgurations.

24.1.2 HEAT TRANSFER CHARACTERISTICS OF A SINGLE IMPINGING JET The heat transfer characteristics for a single jet impinging on a ﬂat surface show maxima in the magnitude of the heat transfer coefﬁcient in the stagnation region of the jet. The magnitude of these maxima is shown to be a function of the Reynolds number and nozzle-to-plate separation (Gardon and Akﬁrat, 1964; Martin, 1977). With an increase in Reynolds number and in nozzle-to-plate spacing up to 5–6 nozzle diameters, the magnitude of the maxima in heat transfer coefﬁcient increases (Gardon and Akﬁrat, 1965). Figure 24.7 (Gardon and Akﬁrat, 1965) shows the variation of heat transfer coefﬁcient at different nozzle-to-plate spacings. The increase in heat transfer coefﬁcient with the increase in nozzle-to-plate spacing is due to the increase

© 2003 by CRC Press LLC

LOCAL HEAT TRANSFER COEFFICIENT, h (Btu/h ft2 degF)

100

B = 1/8 in. Ree = 11000 8 6

80

B = 1/8 in. Ree = 11000

B = 1/8 in. Ree = 11000

8

5 16

2

zn / B

60

zn / B

zn / B = 1/3

32 2

40

5

6

8 8

16

32 80

80

20

(a) 2 ≤ zn / B ≤ 8 0 -20

-10

0

(b) 8 ≤ zn / B ≤ 80 10

20 -20

-10

0

(c) zn / B = 1/3 10

20 -20

-10

0

10

20

DISTANCE FROM STAGNATION POINT, x/B

FIGURE 24.7 Lateral variation of local heat transfer coefﬁcients between a plate and an impinging two-dimensional air jet at different nozzle-to-plate distances. (From Gardon, R. and Akﬁrat, J.C., Int. Heat Mass Transfer, 8, 1261–1272, 1965. With permission.)

in level of turbulence developed as a result of mixing of the surrounding air while the centerline velocity is nearly constant (Gardon and Akﬁrat, 1965). For nozzle-toplate spacing greater than eight nozzle diameters, a decrease in the magnitude of maxima for the heat transfer coefﬁcient around the stagnation region is observed, as shown in Figure 24.7. This has been explained by the decrease in the velocity of the jet with no appreciable increase in the turbulence level with an increase in the distance from the jet nozzle beyond seven nozzle diameters. This clearly shows that the magnitude of the maxima in heat transfer coefﬁcient in the stagnation region is due to two parameters, turbulence and jet velocity. The studies of small nozzle-to-plate spacing, i.e., between 0.25 and 1 nozzle diameters, have shown great potential for cooling applications in the electronic packaging industry (Viskanta and Huber, 1994a). This study showed that at a large Reynolds number (Re ~ 15,000) and small nozzle-to-plate spacing (0.25–1 nozzle diameters), the maximum in the heat transfer coefﬁcient is observed not at the stagnation point as for large nozzle-to-plate spacing (5–6 nozzle diameters), but at a distance away from the center. Figure 24.8 (Viskanta et al., 1994a) shows the variation of local heat transfer coefﬁcient (represented in terms of the dimensionless heat transfer number, Nusselt number (Nu)) for small nozzle-to-plate spacing. Similar trends were also observed by others (Goldstein and Seol, 1991; Ichimiya and Okuyama, 1980; Lytle and Webb, 1994; Saad et al., 1980). For nozzle-to-plate spacing of less than one nozzle diameter, the local heat transfer coefﬁcient in the stagnation region increases as the distance between the plate and the nozzle decreases. The existence of secondary maxima in the local heat transfer has also been indicated for small nozzle-to-plate spacing, whereas there is a monotonous

© 2003 by CRC Press LLC

(a)

Local Nusselt number NuD

120

0.25

100

1.0 80 60 40

H/D = 6.0 20 0

0

0.5

1

1.5

2

2.5

3

2.5

3

r/D (b)

Local Nusselt number NuD

140

0.25

120

1.0 100 80 60

H/D = 6.0

40 20 0

0

0.5

1

1.5

2

r/D

FIGURE 24.8 Effect of separation distance (H/D) on local Nusselt number distributions for Reynolds number (a) 10,300 and (b) 17,100. (From Huber, A.M. and Viskanta, R., ASME J. Heat Transfer, 116, 573, 1994a. With permission.)

decrease in heat transfer coefﬁcient in the lateral region for large nozzle-to-plate spacing. This difference in the variation of heat transfer coefﬁcient at very small nozzle-to-plate spacing (less than one nozzle diameter) has been attributed to the difference in the nature of the jet. For very small spacing the shear layer does not develop, as the jet does not get a chance to mix with the surrounding air. The existence of local maxima near the center of the jet has been attributed to the sudden acceleration of the ﬂuid after impinging on the plate (Viskanta and Huber, 1994a). In the lateral spread region of a single jet, the heat transfer coefﬁcient drops monotonously with the radial distance for nozzle-to-plate spacing greater than ﬁve nozzle diameters. For nozzle-to-plate spacing between two and ﬁve nozzle diameters, the heat transfer does not drop monotonously, as in the earlier case. There are small

© 2003 by CRC Press LLC

secondary maxima in the heat transfer coefﬁcient around the stagnation point. This point is illustrated in Figure 24.7. Beyond these small secondary maxima in the lateral region for the case of nozzle-to-plate spacing of between two and ﬁve nozzle diameters, the heat transfer coefﬁcient drops monotonously in the lateral spread region of the jet. The drop in the heat transfer coefﬁcient is steeper in the case of smaller nozzle-toplate spacing (Gardon and Akﬁrat, 1965; Martin, 1977). Thus, the magnitude of the heat transfer coefﬁcient is more uniform over a wider area for higher nozzle-to-plate spacing; however, the magnitude of the maxima at stagnation point decreases for large nozzle-to-plate spacing (greater than eight nozzle diameters). For nozzle-to-plate spacing of less than one nozzle diameter, there is a sharp increase in the magnitude of the secondary heat transfer coefﬁcient maxima in the lateral jet region (Figures 24.7 and 24.8). The location of these secondary maxima has been found to be a function of the Reynolds number and plate-to-jet spacing. Studies (Martin, 1977; Viskanta and Huber, 1994a) have shown that for smaller nozzle-to-plate spacing, the average heat transfer coefﬁcient is higher due to existence of these secondary maxima.

24.1.3 HEAT TRANSFER CHARACTERISTICS JET CONFIGURATIONS

FOR

MULTIPLE

Relatively few studies have been carried out to characterize heat transfer in multiple jet conﬁgurations. The heat transfer characteristics for multiple jets in the stagnation region are expected to be similar to those of a single jet. In the lateral spread region, some difference in heat transfer characteristics is expected due to interaction of adjacent jets. As described earlier, the ﬂuid ﬂow in the case of the multiple jet system shows an interaction between adjacent jets depending upon the spacing of adjacent jets. This interaction, which induces the reverse ﬂow, has been shown to signiﬁcantly increase the heat transfer for multiple jet conﬁgurations (Lytle and Webb, 1994; Viskanta and Huber, 1994b). The existence of secondary maxima in the lateral region due to jet interaction has also been shown in the study by Viskanta and Huber (1994b). The increase in the heat transfer coefﬁcient has been attributed to increased turbulence due to jet interaction. The objective of our study reported in this chapter was to determine the correlations for average surface heat transfer coefﬁcient for a cookie-shaped object in a pilot scale jet impingement oven. The variation of the heat transfer with position of the model object in the oven, size of the model object, rotation of the oven plate, air velocity, and air temperature was investigated.

24.2 MATERIALS AND METHODS During baking or cooking in a jet impingement oven, simultaneous heat and mass transfer occurs. The resistance to heat transfer in an actual baking operation lies both in the hot ﬂuid and the food material. Since our goal was to determine only the surface heat transfer characteristics, we chose a lumped mass approach. In this approach, the resistance offered by the material to heat transfer was kept negligible, which happens when the Biot number is less than 0.1. Aluminum disks were used as model cookies

© 2003 by CRC Press LLC

in this study. Aluminum has a high thermal conductivity value (200 W/mK). Therefore, the Biot number (=hH/ks) based on the thickness of the disk was expected to be much less than 0.1, where h is the average surface heat transfer coefﬁcient and it is supposed 2 <2000 W/m K, ks is the conductivity of the solid, and H is the thickness of the disk. This requirement was later veriﬁed from the experimental results. In jet impingement, forced convection heat transfer occurs, and in forced heat convection the h value depends only on the shape of the object and not on the thermal properties of the object. Selection of this approach also eliminates the mass transfer process in the system. So, from the transient heat transfer response of the system to step change in ambient temperature, h can be calculated from the response time τ of the system using Equation (24.1). For Bi < 0.1, the variation of temperature of the cookies with time is given by −t/τ

(Tt − To)/(Ti − To) = e

(24.1)

where Tt = temperature at the center of the cookie at any time t, Ti = initial temperature of the cookie, To = temperature of the heating medium, t = time, and τ = time constant of the cookie. τ = mcp/h A

(24.2)

where m = mass of the cookie, cp = heat capacity, h = average surface heat transfer coefﬁcient, and A = surface area of the cookie. The slope of the plot of ln (Tt − To)/(Ti – To) vs. time (t) will be –1/τ, from which h can be calculated. The study was carried out using a pilot plant scale jet impingement oven (Jetzone, Wolverine Corporation, Merrimac, MA). Figure 24.9 shows the schematic diagram of the multiple jets and test chamber and the position of the jet tubes. The impingement oven consisted of an air ﬁlter, three electric heaters, a blower, a plenum chamber, an electric motor, a rotating turntable, an aluminum bowl, and an exhaust fan. During processing, heated air was directed downward from the plenum chamber through 13 parallel jet tubes to impinge on a product in the bowl, which was placed on a rotary (maximum of 60 r/min) turntable. During operation, the bowl was lifted until it pressed against the glass canopy. A rubber bushing sealed the bowl with the glass canopy. The maximum pressure in the plenum chamber that could be maintained was 1200 Pa (ﬁve in water). Each jet tube was 420 mm long with an inner diameter of 17.6 mm. The maximum velocity in each jet was 50 m/sec. The temperature of the jets could be maintained between room temperature and 232°C. Aluminum disks of different diameters were selected to study the effect of variation of size of the model object on the heat transfer coefﬁcient. The sizes of different model aluminum cookies studied are listed in Table 24.1. The 50 and 35 mm cookies with thicknesses of 10 and 15 mm, respectively, were selected so that the cookies would have the same total surface area. The 8 mm diameter cookie with a thickness of 10 mm was selected to study the effect of variation of the local average heat transfer for cookies placed right under the jet, as the diameter of this cookie was smaller than the jet diameter.

© 2003 by CRC Press LLC

TABLE 24.1 Description of Dimensions of Model Cookies Geometry

Diameter (mm)

Thickness (mm)

Area/Mass Ratio 2 (mm /kg)

50 20 8 35

10 10 10 15

6.58E-04 1.73E-03 2.15E-03 6.58E-04

Disk Disk Disk Disk

Plenum Chamber Glass Canopy Jet Tubes (13) Rubber Bushing

Aluminum Bowl

Turntable (a)

5

1

3

53.4 mm

10

7

11

8

12

13

53.2 mm

4

6

18.6 mm

2

9

(b)

FIGURE 24.9 Schematic diagram of (a) the test chamber and (b) positions of the jet tubes.

© 2003 by CRC Press LLC

During the experiment, the aluminum cookies were placed on a wooden plate so that no heat transfer would take place from the bottom of the aluminum bowl due to conduction. To get the transient temperature response, a thermocouple was inserted at the center of the cookie from the bottom. To measure the cookie center temperature (Tt) and the jet air temperature (To), T-type thermocouples made using 30-gauge wires were used. The response time for these thermocouples in this system was on the order of 0.5 seconds. To measure the cookie center temperature, a hole was drilled up to half the thickness of the cookie, and a thermocouple supported on metal tubing was inserted. In order to ensure proper contact between the cookie and the thermocouple, the hole was ﬁlled with high conductivity Omegatherm paste (Omega Engineering, Inc., Stamford, CT). The variation of temperature with time in stationary mode of the turntable was recorded using Keithley Metrabyte data acquisition hardware and TestPoint software (Keithley Inc., Cleveland, OH). During the rotation mode of the turntable, the ACR data acquisition system (Webco Controls Inc., Ambler, PA) was used to record the temperature versus time. The ACR system consisted of a programmable data logger box, which could be attached to the rotating bowl. To develop heat transfer coefﬁcient correlations in terms of Reynolds number, experiments were carried out at different values of jet velocity, which was varied by varying the plenum pressure. The maximum jet velocity under each jet was measured using a pitot tube (Airﬂow Technical Products, Netcong, NJ).

24.2.1 EXPERIMENTS (STATIONARY MODE) Temperature measurement experiments were carried out without rotation of the turntable. The metal cookie was placed inside the aluminum bowl at different positions. The base of the metal bowl was insulated using a piece of wood of the same diameter as the bowl in order to eliminate any conduction heat transfer to the cookie from the base of the bowl. The experiments were carried out under jets #3, #7, and #11 and midway between jet #3 and jet #7 (see Figure 24.9). The jet temperatures were varied at four levels (65, 94, 121, and 148°C). The air pressure in the plenum chamber was varied at four levels (250, 500, 775, and 1050 Pa). Full factorial design was implemented with three replications. The same experimental design was carried out for all the different cookie sizes selected for the study.

24.2.2 EXPERIMENTS (ROTATIONAL MODE) Under this set-up, the major objective was to study the effect of rotation on the heat transfer coefﬁcient as compared to the stationary mode. The cookie was placed under the center of jet # 3, which was off-center with respect to the center of the bowl. The jet temperature was maintained at 107°C and the pressure was varied at 250 and 1050 Pa. The speeds of rotation of the turntable were 12 and 60 r/min. The experiments were designed to have all possible combinations of rotation speed and pressures with three replications of each data set. The data were collected using the ACR portable data logger. For analyzing the effect of rotation, the data were also collected in stationary mode under same conditions of temperature and pressures

© 2003 by CRC Press LLC

using the same data acquisition system. For the rotation mode, the experiments were carried out for the 50 mm diameter disk with 10 mm thickness and 20 mm diameter with 10 mm thickness.

24.3 RESULTS AND DISCUSSION 24.3.1 MAXIMUM JET VELOCITY Figure 24.10 shows variation of maximum jet velocity measured at 20 mm from the tube ends as a function of pressure in the plenum chamber for the three different jets under different conditions of temperature. The results showed an expected nonlinear increase in velocity with an increase in the jet air pressure. The results Jet #7 45

40

40

35 65¡C 30

94¡C 121¡C

25

148¡C

VELOCITY (m/sec)

VELOCITY (m/sec)

Jet #3 45

35 65¡C 30

94¡C 121¡C

25

148¡C

20

20

15

15 0

500

0

1000 1500

500

1000

1500

PRESSURE (Pa)

PRESSURE (Pa)

(a)

(b)

Jet #11

VELOCITY (m/sec)

45 40 35 65¡C

30

94¡C 25

121¡C 148¡C

20 15 0

500

1000

1500

PRESSURE (Pa)

(c)

FIGURE 24.10 Variation of maximum jet velocity with pressure in the plenum chamber: (a) jet #3, (b) jet #7, (c) jet #11.

© 2003 by CRC Press LLC

also indicated the increase in velocity with increase in temperature at a given pressure. This was expected, as the density of the air decreases with increase in temperature. The results of the velocity measurement experiments using the pitot tube indicated a fair amount of uniformity in the maximum velocity under different jets at same conditions of temperature and pressure. The velocity values ranged from 18 to 44 m/sec. The experimentally determined value of maximum velocity was used to calculate the Reynolds number values.

24.3.2 HEAT TRANSFER COEFFICIENT The results for the average heat transfer coefﬁcient (h), obtained from Equation (24.2.), are presented in terms of average Nusselt number (Nu), as a function of the Reynolds number (Re) and Prandtl number (Pr), deﬁned as follows: Nud = hD/ka

Re = ρVD/µ

Pr = Cp µ/ka

where h is calculated using Equation (24.2), ka is the thermal conductivity of air, ρ is the density of air, V is the maximum jet velocity, D is the jet tube inside diameter, and µ is the viscosity of air. All properties for air were evaluated at corresponding jet temperatures. Pr number was almost constant (0.65–0.70) over the entire range of experimental conditions. Hence, it was taken as constant. Figure 24.11 shows the variation of Nu with Re under different jets with the bowl stationary. The Nu values varied from 60 to 120, which correspond to a range 2 of heat transfer coefﬁcient (h) of 140–200 W/m K. The results indicate no signiﬁcant difference in the average heat transfer coefﬁcient for a 50 mm cookie placed under different jets. This indicates that the average value of the heat transfer coefﬁcient for a 50 mm diameter disk is uniform under different positions in the jet impingement oven. Similar results were obtained for the 35 mm diameter model cookie with 15 mm thickness.

NUSSELT NUMBER (Nu)

140 120 100 Jet #7

80

Jet #3

60

Between Jet #3 and Jet #7

40 20 0 0

10000

20000

30000

40000

REYNOLDS NUMBER (Re)

FIGURE 24.11 Variation of average Nusselt number (Nu) with Reynolds number (Re) at different positions in an oven for a 50 mm diameter cookie with 10 mm thickness.

© 2003 by CRC Press LLC

140

NUSSELT NUMBER (Nu)

120

100 #7 (35 mm)

80

Between #3 and #7 (35 mm) #3 (35 mm)

60

#7 (50 mm) #3 (50 mm)

40 Between #3 and #7 (50 mm)

20

0 0

5000

10000

15000

20000

25000

30000

35000

REYNOLDS NUMBER (Re)

FIGURE 24.12 Variation of average Nusselt number (Nu) with Reynolds number (Re) for 50 mm and 35 mm diameter aluminum cookies with 10 mm and 15 mm thickness, respectively.

Figure 24.12 shows the comparison of the results for the 35 mm diameter cookie with 15 mm thickness with that of the 50 mm cookie with 10 mm thickness. The results showed no signiﬁcant difference in the average heat transfer coefﬁcient for the two cookie-shaped disks with the same total surface area. The results for the 8 mm diameter cookie with 10 mm thickness showed a higher value of the heat transfer coefﬁcient. Earlier studies have shown that a local maximum exists in the heat transfer coefﬁcient right under the jet, i.e., in the stagnation region. Since this 8 mm cookie was just half the diameter of jet, it experienced a peak in local maxima with the result that the average heat transfer coefﬁcient over a small area showed a higher value as compared to the other two cookie sizes. To determine the importance of the operating parameters, jet air pressure and temperature, on the h values an analysis of variance (ANOVA) for the two-factor experiment was carried out. It showed that only pressure had a statistically signiﬁcant effect on the h value, while temperature did not have signiﬁcant effect on the heat transfer coefﬁcient. To determine the effect of bowl rotation, experiments were carried out with and without rotation of the bowl under jet #3. Figure 24.13 (a) and (b) shows the variation of h with bowl rotation at two different plenum pressures for two different sizes of model cookies. Based on the estimated systematic error in the experimental set-up, the error bars are drawn to compare the results of the heat transfer coefﬁcient experienced by a model cookie in a stationary mode with that of a cookie in a rotational mode. In the case of the 50 mm diameter cookies no effect of rotation was observed at both levels of rotation speed of the bowl and both levels of plenum pressure. In the case of the 20 mm diameter cookie, the effect of rotation was

© 2003 by CRC Press LLC

300

250

h ( W/m2 K)

200

Plenum Pressure = 250 Pa

150 Plenum Pressure = 1050 Pa 100

50

(a)

0 0

50

100

ROTATION SPEED (RPM)

250

200

h (W/m2K)

Plenum Pressure = 250 Pa 150 Plenum Pressure = 1050 Pa 100

50

(b) 0 0

50

100

ROTATION SPEED (RPM)

FIGURE 24.13 Effect of bowl rotation on average heat transfer coefﬁcient for (a) a model cookie with 20 mm diameter with 10 mm thickness; (b) a model cookie with 50 mm diameter with 10 mm thickness. The bars indicate the range of error.

© 2003 by CRC Press LLC

TABLE 24.2 Heat Transfer Correlations at Different Jet Positions for a 50 mm Aluminum Cookie Jet Number 3 7 Between 3 and 7 (off center) 11

Heat Transfer Correlation 0.595

Un = 0.227 Re 0.387 Un = 2.077 Re 0.609 Un = 0.210 Re 0.414 Un = 1.68 Re

R

2

0.942 0.906 0.938 0.978

observed at low plenum pressure (250 Pa) and low level of rotation speed (12 r/min). The value of the average heat transfer coefﬁcient experienced by the model cookie at low plenum pressure and low rotational speed was lower than the value observed without rotation for the same conditions. This result can be explained on the basis of the existence of local maxima right under the jet. As the larger diameter cookie spends a longer time under the jet as compared to the smaller cookie, h is not affected by rotation in the case of the larger diameter cookie. Another plausible explanation for this can be based on the response time of the model cookie. The smaller diameter cookie has a smaller response time to the changes in h as compared to the larger diameter cookie. Thus, the effect of rotation is observed in the smaller diameter cookie as compared to the larger diameter model cookie. The correlations for Nu as a function of Re were generated using SAS (SAS, Inc., Cary, NC). The correlations are shown in Table 24.2. The correlations show a power law dependence of Nu on Re with the exponent varying between 0.4 and 0.6. Similar correlations have been reported (Martin, 1977) for single and multiple jets impinging on a ﬂat surface for the Reynolds number in the range of 2,000 to 120,000. These correlations have a similar power law relation, and the range of the exponent of Reynolds number was between 0.55 and 0.7. Thus, the correlations developed for the cookie-shaped objects in a jet impingement oven were similar to those developed over a ﬂat surface.

24.4 CONCLUSIONS The measured values of the average heat transfer coefﬁcient were within the range of values reported in the literature. The results indicated that the variation of the average heat transfer coefﬁcient under and between different jets was small. However, a local maximum in heat transfer under each jet was observed. This indicates that a part of the cookie right under the jet will experience higher heat transfer than the rest of the cookie. So, for cookies placed on a moving belt in an industrial application, smaller cookies will experience more ﬂuctuation in the heat transfer coefﬁcient as compared to larger cookies, depending on the size of the nozzle and the spacing between the nozzles. This was conﬁrmed by the rotation experiment in which the smaller diameter cookie showed measurable variation in the h value as compared to the larger diameter cookie under the same set-up.

© 2003 by CRC Press LLC

NOMENCLATURE D Cp H To Ti Tt V h ka m r t uz z Nu Pr Re ρ µ

Diameter of the nozzle (m) Speciﬁc heat (J/kg K) Distance between the nozzle and the target plate (m) Temperature of the heating medium (K) Initial temperature of the model cookie (K) Temperature at the center of the cookie at any time t (K) Maximum jet velocity (m/sec) 2 Average heat transfer coefﬁcient (W/m K) Thermal conductivity of air (W/m K) Mass of the cookie (kg) Radial distance (m) Time (sec) Axial velocity (m/sec) Distance between the nozzle and target plate (m) Nusselt number (h D/ka) Prandtl number (Cp µ/ka) Reynolds number (DVρ/µ) 3 Density (kg/m ) Viscosity (Pa sec)

ACKNOWLEDGMENT This work was supported by a grant (#9801317) from the U.S. Department of Agriculture, under the National Research Initiative Competitive Grants Program.

REFERENCES Gardon, R. and Akﬁrat, J.C., Heat Transfer Characteristics of Impinging Two-dimensional Air Jets, ASME-HT-20, 1964. Gardon, R. and Akﬁrat, J.C., The role of turbulence in determining the heat transfer characteristics of impinging jets, Int. J. Heat Mass Transfer, 8, 1261–1272, 1965. Gardon, R. and Cobonpue, J., Heat Transfer Between a Flat Plate and Jets of Air Impinging on It, International Heat Transfer Conference, Part II, 1961, pp. 454–460. Goldstein, R.J. and Seol, W.S., Heat transfer to a row of impinging circular air jets including the effect of entrainment, Int. J. Heat Mass Transfer, 34, 2133–2147, 1991. Huber, A.M. and Viskanta, R., Convective heat transfer to a conﬁned impinging array of air jets with spent air exits, ASME J. Heat Transfer, 116, 573, 1994. Ichimiya, K. and Okuyama, K., Characteristics of Impingement Heat Transfer Caused by Circular Jets with Conﬁned Walls, Proceedings of the Third International Heat Transfer Conference, 1980, pp. 523–532. Lytle, D. and Webb, B.W., Air jet impingement heat transfer at low nozzle-plate spacings, Int. J. Heat Mass Transfer, 37, 1687–1697, 1994. Marcoft, H., Measurement of Velocity Distribution in a Jet Impingement Oven Using Laser Doppler Anemometry, thesis, Rutgers University, New Brunswick, NJ, 1999.

© 2003 by CRC Press LLC

Martin, H., Heat and mass transfer between impinging gas jets and solid surfaces, Adv. Heat Transfer, 13, 1–60, 1977. Saad, N.R., Mujumdar, A.S., and Douglas, W.J.M., Heat transfer under multiple turbulent slot jets impinging on a ﬂat plate, in Drying ’80: 1. Developments in Drying, Mujumdar, A.S., Ed., Hemisphere Publishing Corporation, New York, 1980, pp. 422–430. Saripalli, K.R., Visualization of multi-jet impingement ﬂow, AIAA/SAE/ASMA 17th Joint Propul. Conf., Colorado Springs, CO, July 27–29, 1981. Paper No. 81-1364. Van Dyke, M., An Album of Fluid Motion, The Parabolic Press, Stanford, CA, 1982. Viskanta, R. and Huber, A.M., Effect of interactions between adjoining rows of circular freesurface jets on local heat transfer from the impingement surface, ASME, 118, 88–95, 1994a. Walker, C.E. and Sparman, A.B., Impingement Oven Technology. Part II. Applications and Future, Technical Bulletin, American Institute of Baking, 11, 1, 1989.

© 2003 by CRC Press LLC

25

Flow Dynamics and Heat Transfer in Helical Heat Exchangers P. Coronel and K.P. Sandeep

CONTENTS 25.1 Introduction 25.1.1 Dean Effect, Factors Affecting It, and Means of Inducing Secondary Flow 25.1.2 Friction Factor 25.1.3 Laminar and Turbulent Flow 25.1.4 Residence Time Distribution (RTD) 25.1.5 Heat Transfer Coefﬁcients 25.2 Experiments 25.3 Concluding Remarks Nomenclature References

25.1 INTRODUCTION In an attempt to improve the rate of heat transfer and the uniformity of heating, many novel types of heat exchangers have been manufactured. One such category is helical heat exchangers (Figure 25.1). A variety of helical heat exchangers are in use in the food industry; however, the underlying principle and hence the design criteria are not well understood. This has resulted in much use of trial and error in ascertaining the appropriate combination of system and process parameters for the design of a process. Once we understand the principle of mixing occurring in a helical tube, we can design helical heat exchangers and holding tubes in a much more efﬁcient manner, which in turn will result in a much more uniform process from both a ﬂuid mechanics and a heat transfer standpoint. However, ﬂow in coiled tubes is much more complicated than in straight tubes, and hence the design of helical heat exchangers that operate at a high efﬁciency is not straightforward. Several basic theoretical, numerical, and experimental studies have been conducted in this area, and a summary of these studies is presented here.

© 2003 by CRC Press LLC

Inner Coil Outlet

Outer Coil Outlet

Hot Water Outlet Hot Water Inlet Outer Coil Inlet

Inner Coil Inlet

FIGURE 25.1 Schematic drawing of a helical heat exchanger.

25.1.1 DEAN EFFECT, FACTORS AFFECTING IT, OF INDUCING SECONDARY FLOW

AND

MEANS

Just as ﬂow and heat transfer in straight tubes are dependent on the Reynolds number, the Dean number ( N De = N Re r / R , where r is the radius of the tube and R is the radius of the helical coil) governs the type of ﬂow and rate of heat transfer in curved tubes. The Dean number is the ratio of the square root of the product of inertial and centrifugal forces to the viscous forces. Since secondary ﬂow is induced by centrifugal forces, the magnitude of the Dean number is a measure of the extent of secondary ﬂow. It is also important to note that no secondary ﬂow will be induced for an inviscid ﬂuid. The secondary ﬂow pattern arises due to the centrifugally induced pressure gradient (a small but ﬁnite pressure gradient is required to balance the centrifugal force), which is approximately uniform across the cross section, driving the slower

© 2003 by CRC Press LLC

moving ﬂuid near the wall inward and the faster moving ﬂuid at the core outward. The vortices are almost symmetrical and the stagnation points (or centers) are located less than halfway from the center to the periphery. The region of maximum velocity moves outward depending on the value of the Dean number. Beyond a certain value of the Dean number, the double helical streamlined ﬂow changes to turbulent ﬂow. For ﬂow in curved pipes, the pressure increases monotonically from the inner convex wall to the outer concave wall across any cross section due to the centrifugal forces existing because of the curvature in the tube. However, the centrifugal force ﬁrst increases and then decreases as we move from the inner to outer wall after attaining a maximum value along a line parallel to the horizontal axis. Figure 25.2a shows the ideal secondary ﬂow conditions in a helical tube. The secondary ﬂow ﬁeld consists of a relatively inviscid core and a viscous boundary layer.

Outside

Inside

(a)

Outside

Inside

(b)

FIGURE 25.2 Secondary ﬂow proﬁles in a helical tube showing (a) ideal and (b) free convection at a low Reynolds number.

© 2003 by CRC Press LLC

Outside

Inside

(a)

Outside

Inside

(b)

FIGURE 25.3 Axial velocity contours in a helical tube: (a) low Dean numbers; (b) high Dean numbers.

Figure 25.2b shows the secondary ﬂow in a helical tube at low Reynolds numbers where free convection is a dominant factor and gravity, aided by density difference, causes ﬂow in the vertical direction. Similarly, Figure 25.3a shows the axial velocity contour at low Dean numbers (where the contours are almost symmetrical), while Figure 25.3b shows the asymmetric axial velocity contours at high Dean numbers. The main factor affecting the extent of mixing taking place in a helical system is the ratio of tube diameter to coil diameter. Other effects include particle ﬂow rate and concentration. Several other techniques (and their beneﬁts) used by various manufacturers are also described, for example, corrugated tubes and use of bafﬂes.

© 2003 by CRC Press LLC

The secondary ﬂow phenomenon in curved pipes has received great attention after Dean’s (1927, 1928) analysis of the problem. Dean (1927, 1928) and Dean and Hurst (1959) investigated the ﬂow in helically coiled circular tubes and reported that a pair of symmetric vortices formed on the cross sectional plane due to centrifugal force. Dean also obtained, by solving the Navier–Stokes equations, the equations of motion for incompressible laminar ﬂow in the case of small curvature ratios. Taylor and Yarrow (1929) found that secondary ﬂow could stabilize laminar ﬂow, providing transition Reynolds numbers as high as 6000 to 8000 in a curved tube, as compared to 2100 in a straight tube, even when the inlet ﬂow was turbulent. Koutsky and Adler (1964) pointed out that the pressure drop in a tube formed into a helix can be up to four times as great as that in an identical straight tube. They also found that stable laminar ﬂow can be maintained in helices at Reynolds numbers up to 8000. Both of these facts imply the existence of strong secondary ﬂow in helices. Studies by Mori and Nakayama (1965), Patankar (1974), Kao (1987), and Futagami and Aoyama (1988) showed that the presence of secondary ﬂow could increase the rate of momentum and mass and heat transfer. For ﬂow in a helical tube of square cross section, the centrifugal force causes a secondary ﬂow with a pair of counter-rotating vortices. For values of the Dean number above the critical value, the secondary ﬂow pattern has an additional pair of vortices near the central outer region; this phenomenon is referred to as Dean’s instability, and is known to increase the friction factor. Studies by Bara et al. (1992), Cheng et al. (1976), and Kumar et al. (1989) reveal this phenomenon. This phenomenon is not, however, observed when the cross section of the pipe is inclined (Duh and Shih, 1989). The instability phenomenon was observed by Masliyah (1980) in semicircular tubes and by Nandakumar and Masliyah (1982) and Dennis and Ng (1982) in circular tubes. Studies by Choi et al. (1979) suggested that there could be several pairs of vortices in the entry section of a curved tube. It is known that for a given pressure gradient, the ﬂow rate in a coiled tube is lower than that in a straight tube. Berger et al. (1983) presented the following correlation to determine the nondimensional volumetric ﬂow rate in a curved pipe: 2 4 ˙  N 2De   N 2De  V c + = 1 − 0 . 0306 0 . 012     π R2 u  288   288 

(25.1)

where u is the average velocity in a straight pipe of the same radius under the same axial pressure gradient. The beneﬁcial effects of secondary ﬂow were made use of by Carlson (1991) to develop helical heat exchangers that resulted in uniform heating of viscous ﬂuids and foods containing particulates. In addition to making use of the secondary ﬂow, Carlson placed bafﬂes outside the pipes to increase the heat transfer coefﬁcient on the heating medium side by inducing turbulence. Muguercia et al. (1993) measured the primary and secondary ﬂow velocities of water in a curved pipe using the Laser Doppler Anemometry technique. Maximum secondary velocity was found to increase linearly with axial velocity. These researchers reported that the secondary ﬂow is created by the centrifugal force, forcing the

© 2003 by CRC Press LLC

ﬂuid to move toward the outer wall. The ﬂuid, after reaching the outer wall edges, turns to the top or the bottom of the tube, making its way to the inner wall through the region near the pipe wall. Also reported was that the two secondary ﬂow vortices were asymmetric due to the torsion effect of the coiled pipe geometry. Increasing the Reynolds number from 1000 to 2500 caused the maximum dimensionless axial velocity (ratio of maximum to mean axial velocity) to increase from 1.70 to 1.80. Fluid elements in the high axial velocity region appeared to be pushed toward the outer wall by centrifugal force. The effect of pitch on primary and secondary ﬂow in fully developed turbulent ﬂow through helically coiled pipes was studied numerically by Yang and Ebadian (1994, 1995). These researchers showed that the secondary ﬂow distorted the axial ﬂow and pushed the high axial ﬂow region toward the outer wall. For the same pitch and curvature ratio, torsion effect (a rotational force due to ﬁnite pitch) is much larger in laminar ﬂow than in turbulent ﬂow as a result of the dominating centrifugal force effect, due to much higher axial velocities in turbulent ﬂow. These authors observed that the two vortices formed across the pipe cross section were symmetric for zero pitch. However, for a ﬁnite pitch, the torsion effect resulted in the loss of symmetry of the two secondary ﬂow vortices. Fiedler (1997) presented a brief description of the effect of two consecutive bends oriented in different planes on inducing swirl in the ﬂuid ﬂow ﬁeld. Thomson et al. (1998) studied low Dean number convective heat transfer in helical ducts of rectangular cross section and found that torsion, which is known to increase friction factor, caused a decrease in the fully developed Nusselt number compared to that in a pure toroidal ﬂow Hence, they recommended that torsion be minimized to enhance heat transfer.

25.1.2 FRICTION FACTOR As a ﬂuid ﬂows through a tube, losses in energy (Ef) and pressure (Pf) due to friction occur, determined as follows: Ef =

∆ Pf u2 L = 2f ρ d

(25.2)

In the above equation, f is the friction factor, which varies with the type of pipe, ﬂow conditions, and system geometry. The friction factor for laminar ﬂow in a straight pipe is given by fs = 16/NRe and for turbulent ﬂow is usually determined from the Moody (1944) diagram. An alternative way to determine the friction factor is to use the following equation by Colebrook (1939) to perform an iterative analysis:  1 ε 1.255  1 = − 4 ln  +  f  3.7 d N Re f 

(25.3)

These are standard methods for determining friction factors in straight pipes. However, for curved pipes, many additional factors, such as coil diameter, pitch, and Dean number, come into play, and hence no standard formula or procedure is available. Manlapaz and Churchill (1980) published a list of studies conducted for

© 2003 by CRC Press LLC

the determination of friction factors in curved pipes. In the following section, a list of other correlations developed based on various studies in curved pipes is presented. White (1929) developed the following correlation to determine the friction factor under laminar ﬂow conditions: 0.45 2.2   fc    11.6    = 1 − 1 −  fs    N De       

−1

for 11.6 < NDe < 2000

(25.4)

White (1932) extended the laminar ﬂow study and developed the following correlation to determine the friction factor for the case of turbulent ﬂow: fc = 0.08 N −Re0.25 + 0.012( r / R )0.5

for 15,000 < NRe < 100,000

(25.5)

Several other correlations have been developed for different ﬂow conditions and different geometries of holding tubes. In correlations such as the one listed below (Yang and Chang, 1994) other parameters have been factored into the correlation: fc = 0.689 N 0De.0817 N 0Pr.0081 N 0Ra.0068 δ 0.084 fs

(25.6)

where δ = r/R, for 10 < NDe < 25,000, 0.7 < NPr < 100, 0 < NRa < 320, and 0.01 < δ < 0.8.

25.1.3 LAMINAR

AND

TURBULENT FLOW

The ﬂow behavior and heat transfer of ﬂuids and particulates in pipes depends largely on whether the ﬂow is laminar or turbulent. Turbulent ﬂow is generally associated with high heat transfer, but so is the presence of secondary ﬂow under laminar ﬂow conditions. Thus, it is important to characterize the type of ﬂow occurring in pipes under various situations. For ﬂow in a straight pipe, laminar conditions are said to prevail if the Reynolds number is less than 2100 or 2300. For curved pipes, the presence of secondary ﬂow stabilizes the ﬂow pattern, and turbulence is delayed. The results of some studies conducted to determine the critical value of the Reynolds number that separates laminar and turbulent ﬂow are given below. White (1929) conducted experiments with oil and water for different curvatures of helical tubes. For NRe > 100 and d/D = 1/50, a curved pipe had greater resistance than a straight pipe of the same diameter and length. The resistance to ﬂow was 2.9 times that in a straight pipe at NRe = 6000 (~NRe when ﬂow becomes turbulent). When d/D = 1/15, turbulent ﬂow was seen at NRe ~ 9000, and when d/D = 1/2050, turbulence was seen at NRe ~ 2250 to 3200. Several correlations (for example, Equation (7), developed by Kutateladze and Borishanskii (1966)) have been developed to determine the critical Reynolds number: N Rec = 2300 + 12930 ( r / R )0.3

© 2003 by CRC Press LLC

for 0.0417 < d/D < 0.166

(25.7)

25.1.4 RESIDENCE TIME DISTRIBUTION (RTD) Uniformity of heating is important when considering ﬂow in tubes in the chemical, food, pharmaceutical, and various other industries, as it relates to product quality, cost of production, and other factors. As a Newtonian ﬂuid ﬂows through a straight pipe under laminar ﬂow conditions, a parabolic velocity proﬁle develops. Thus, different ﬂuid elements take different times to pass through the pipe, and the distribution in the time spent by various ﬂuid elements in the pipe is referred to as the Residence Time Distribution (RTD). RTD becomes narrower or broader in a tube depending on the type of ﬂow and type of ﬂuid. In order to achieve uniform heating, a narrow RTD is desired. Some methods for narrowing RTD are to induce turbulence or to use helical pipes. The effect of helical pipes in narrowing RTD is described below. Taylor (1953) described the process by which axial dispersion of a solute in a helical tube was reduced by radial diffusion, which is now usually referred to as Taylor dispersion. Radial mixing due to molecular diffusion is complemented by convective secondary motions in a helical tube. Koutsky and Adler (1964) showed that axial dispersion could be greatly reduced as compared to a straight tube when the tube was formed into a helix. They found that this effect was more pronounced in the turbulent region. The study also indicated that in a laminar ﬂow regime, the ﬂuid elements on the secondary ﬂow streamlines of smaller perimeter moved downstream more rapidly than those on larger streamlines. More narrow and peaked tracer distributions were observed as a result of reduced axial dispersion, especially at high Reynolds numbers. These researchers reported that the transition to turbulent ﬂow (3000 < NRe < 7000) was more gradual and occurred at higher Reynolds numbers in helical tubes when compared to straight tubes. The strength of secondary ﬂow at low curvatures was diminished by the onset of turbulent ﬂow, whereas at high curvatures secondary ﬂow was shown to be still effective in reducing the axial dispersion even at higher Reynolds numbers. They also observed that the axial dispersion in helical tubes in the Reynolds number range of 7,000–40,000 was considerably less than that in laminar ﬂow. Saxena and Nigam (1984) studied the ﬂow inversion in helical coils and utilized the centrifugal force concept to develop secondary ﬂow in laminar ﬂow systems. They reported that a 90° bend located midway in the coiled tube was more effective when compared to 30, 45, and 60° bends in inducing secondary ﬂow, thus narrowing the RTD. They also found that increasing the number of bends (more than three) signiﬁcantly decreased the RTD. The study revealed that up to a Dean number (NDe) of 1.5, the secondary ﬂow was responsible for narrowing the RTD, whereas above 1.5, the change in the direction of centrifugal force caused RTD narrowing by mixing the ﬂuid elements. Mathematical modeling by Liu and Zuritz (1995) and Sandeep et al. (1995) indicated that RTD in helical tubes was always narrower than the RTD in straight tubes of similar lengths and diameters. Parametric analyses were conducted to ascertain the effects of various system and process parameters for the cases of single and two-phase ﬂows. Sandeep et al. (1997) found that the two counter-rotating vortices that developed in the radial direction in the case of helical ﬂow are responsible for mixing the ﬂuid

© 2003 by CRC Press LLC

elements and reducing the velocity gradient across the tube, which in turn results in a decrease in the RTD. Residence time distribution in a helically coiled tube and a chaotic system, where the tube was formed into an array of bends with the plane of curvature of each bend making a 90° angle with that of the adjacent one, was studied by Castelain et al. (1997) within the Reynolds number range of 800–13,500. These authors reported that for Reynolds numbers higher than 2500, a chaotic system was 20% more effective in minimizing the axial dispersion than a helically coiled tube having the same number of bends. They attributed this further improvement to the chaotic trajectories resulting from the change in the plane of Dean vortices due to the bends of the chaotic system. The two conﬁgurations were reported to be comparable in terms of their axial dispersion effect for Reynolds numbers less than 2500.

25.1.5 HEAT TRANSFER COEFFICIENTS Heat transfer for laminar ﬂow in a straight tube (heat exchanger or holding tube) is usually low since very little mixing in the radial direction occurs. However, ﬂow in a coiled tube is fully three-dimensional, and the rate of heat transfer can be much higher than that in a straight tube. This is due to the development of secondary ﬂow (in the directions normal to the main direction of ﬂow) due to the pressure gradient imposed as a result of the centrifugal forces present in the curved section. The secondary ﬂow serves as a means of redistributing ﬂuid elements in the radial direction, thereby transferring heat more efﬁciently between the bulk of the ﬂuid and the ﬂuid elements near the tube wall. Various studies have been conducted in helical tubes to determine Nusselt number correlations under different ﬂow and system conditions in helical tubes, and some of those correlations are shown below. Seban and McLaughlin (1963) developed the following equations to predict the heat transfer coefﬁcient under laminar and turbulent ﬂow conditions: Laminar ﬂow: f  N Nu = 0.13 N1Pr/3  c N 2Re  8  

1/ 3

with fc being determined from White’s (1929) correlation. Turbulent ﬂow: N Nu =

fc N N 0.4 8 Re Pr

with

fc = 0.023 N −Re0.15 ( r / R ) 0.01

2

for NRe (r/R) > 6 The ﬁrst order approximation for determination of the Nusselt number for ﬂow in a coiled tube developed by Mori and Nakayama (1965) is as follows: N Nuc N Nus

© 2003 by CRC Press LLC

=

0.1979 0.5 N De z

(25.8)

where z is the ratio of the thickness of the thermal and velocity boundary layer and is given by: 2   77  z = 1 + 1 +  11   4 N 2Pr  

0.5

  

for NPr ≥ 1

and (25.9)

z=

 1   10 2 +  2 − 1 5   N Pr  

0.5

  

for NPr ≤ 1

Ozisik and Topakoglu (1968) developed the following expression for Nusselt number in a curved pipe: N Nu

−1 ˙ 2  C1 r 2  48  V c = ˙  1 − R 2  11  V s

(25.10)

where C1 =

C2  C2  6.95513 N 2Pr    1  165.47 + 7 N Pr + −71.6 +  9.96576 +   264  112  2.8  1.1    2

C2 = NRe /36

and

˙  V r 2  1.541 C 22 c = 1 − + 1.1 C 2 − 1 2  ˙ 48 R  67.2 Vs 

(25.11)

˙ and V ˙ being the mass ﬂow rates in the curved and straight tubes, respectively. with V c s Dravid et al. (1971) conducted numerical studies for ﬂow in a helical tube for small aspect ratios and for the case where axial conduction is negligible in comparison with axial convection (NPe > 20). They developed the following correlation for heat transfer coefﬁcient at distances close to the inlet of the tube: N Nuc N Nus

= 0.447N1De/ 6

(25.12)

At NDe = 125, the heat transfer coefﬁcient in the helical tube is the same as that in the straight tube. It should not, however, be inferred that for lower values of the Dean number the heat transfer coefﬁcient is higher in the straight tube, since at short distances from the inlet the temperature ﬁeld does not signiﬁcantly penetrate the secondary ﬂow ﬁeld. Based on their experimental study, Dravid et al. (1971) developed the following correlation for the asymptotic Nusselt numbers applicable for 50 < NDe < 2000 and 5 < NPr < 175:

[

]

N Nu = 0.76 + 0.65 N De N 0Pr.175

© 2003 by CRC Press LLC

(25.13)

The asymptotic Nusselt numbers for the straight tube case are 3.66 for the case of constant wall temperature and 4.36 for the case of constant wall heat ﬂux. These values are signiﬁcantly higher for the helical tube case. Oliver and Asghar (1976) developed the following Nusselt number correlation for ﬂow in a helical coil: µ  N Nu  w   µb 

0.14

µ  N Nu  w   µb 

0.14

(

)

for 4 < NDe < 60

(25.14)

(

)

for 60 < NDe < 2000

(25.15)

0.13 = 1.75 N Gz 1 + 0.36 N 0De.25

0.13 = 1.75 N Gz 1 + 0.118 N 0De.5

Janssen and Hoogendoorn (1978) developed the following Nusselt number correlations for different ranges of Dean numbers:

(

)

(

)

N Nu = 1.7 N 2De N Pr N Nu = 0.9 N 2Re N Pr

1/ 6

1/ 6

(

for NDe < 20 and N 2De N Pr

)

0.5

> 100

for 20 < NDe < 100

N Nu = 0.7 N 0Re.43 N1Pr/6 ( r / R ) 0.07

(25.16)

(25.17)

for 100 < NDe < 8300

(25.18)

These researchers concluded that the effect of d/D can be neglected for Dean numbers less than 100 in the fully developed thermal region. They also found that for all cases with N 2De N Pr > 100, the Nusselt number in the fully developed thermal region was proportional to N1Pr/6 and that for the thermal entry region, the Nusselt number was proportional to N1Pr/3 . Abul-Hamayel and Bell (1979) conducted experimental studies of heating of ethylene glycol, distilled water, and butyl alcohol in a helical coil with D/d = 20.2 and developed the following Nusselt number correlation:

(

N Nu

)

3.94   N Gr   = 4.36 + 2.84 2   1 + 0.0276 N 0De.75 N 0Pr.197  N Re   

[

2.78 −1.33 N Gr   µ  0.14   N Gr  N 2De  b  × 1 + 0.9348 2  e   µ b    N De 

6

for 92 < NRe < 5500, 2.2 < NPr < 101, and 760 < NGr < 10 .

© 2003 by CRC Press LLC

] (25.19)

In the above equation, the quantities in the ﬁrst, second, third, and fourth brackets are the expressions for ﬂow in a straight tube, secondary ﬂow contribution, natural convection contribution, and viscosity correction factor, respectively. Yang and Chang (1994) developed the following Nusselt number correlation as a function of Dean number, Prandtl number, Rayleigh number, and curvature: N Nuc N Nus

= 0.42 N 0De.111 N 0Pr.21 N 0Ra.0513 δ − 0.0974

(25.20)

where δ = r/R, for 10 < NDe < 25,000, 0.7 < NPr < 100, 0 < NRa < 320, and 0.01 < δ < 0.8. Thus, it can be seen that different correlations have been developed for different ﬂow conditions and different tube geometries. It is thus important to look into the range of applicability of various correlations before applying them to different situations.

25.2 EXPERIMENTS In order to compare heat transfer coefﬁcients in straight and helical heat exchangers, we conducted studies using both conﬁgurations. The helical heat exchanger used was a Multicoil heat exchanger (VRC Co., Inc., Cedar Rapids, IA). The Multicoil heat exchanger (Figure 25.4) consists of a shell within which two coils of tubes (inner coil and outer coil) are situated. The heating medium (pressurized water) ﬂows in the shell at a very high ﬂow rate and recirculates through the system while the product ﬂows inside the coiled tube(s). Bafﬂes present outside the coils increase the turbulence of the heating medium and thus enhance the outside heat transfer coefﬁcient. Either one or both of the coils can be used, and they can be connected in a series or parallel conﬁguration. A shell and tube heat exchanger that utilizes steam and has an automatic control system to maintain a desired temperature is used to provide the hot water to heat the product. The temperature and pressure of both the product and heating medium are monitored at various locations within the system. The outer shell of the Multicoil heat exchanger is insulated to minimize heat loss to the surroundings. City water was used as the test ﬂuid, and the properties of water (thermal conductivity, density, and speciﬁc heat) were calculated using correlations (Popiel and Wojtkowiak, 1998). The ﬁrst set of experiments involved pumping the product using a piston pump (Model 629A, Marlen Research Corp., Overland Park, KS) through the system (Multicoil heat exchanger, holding tube, and four tubular coolers) at different ﬂow rates (0.19–0.63 kg/sec) and at different set point temperatures (100–150°C). The ﬁrst two tubular cooling units utilized city water as the cooling medium, while the third and fourth coolers utilized a 30% propylene glycol solution. Temperatures of the product and heating medium were monitored at various locations within the system using type-T thermocouples and recorded in a data acquisition system using the software PC208W (Model CR10, Campbell Scientiﬁc, Inc., Logan, UT). The volumetric ﬂow rate of the heating medium was measured using an external ﬂowmeter (Model 1010WP1, Controlotron, Inc, Hauppauge, NY), and the volumetric ﬂow rate of the product was determined by noting the time taken by the product to ﬁll a

© 2003 by CRC Press LLC

FIGURE 25.4 Schematic representation of the Multicoil heat exchanger.

container of known volume. The speciﬁcations of the experimental set-up are given in Table 25.1. The holding tube and tubular cooling units did not have any insulation on the outside. The Multicoil heat exchanger is similar to a countercurrent heat exchanger and was modeled as a countercurrent heat exchanger for calculation purposes. Based on the

© 2003 by CRC Press LLC

TABLE 25.1 Speciﬁcations of the Experimental Set-Up Multicoil Heat Exchanger Total length of outer coil of Multicoil heat exchanger = 39.6 m Diameter of outer coil of Multicoil heat exchanger = 0.3 m a I.D. of pipe of Multicoil heat exchanger = 0.01 m b O.D. of pipe of Multicoil heat exchanger = 0.013 m Thermal conductivity of the material of the pipe = 16 W/m-K Holding Tube Length of holding tube = 48.8 m a I.D. of holding tube = 0.023 Tubular Coolers Length of each of the four coolers = 6.1 m a I.D. of the inner pipe = 0.023 m b O.D. of the inner pipe = 0.025 m a I.D. of the outer pipe = 0.048 m b O.D. of the outer pipe = 0.05 m Thermal conductivity of the material of the pipe = 16 W/m-K a b

I.D. = inside dimension. O.D. = outside dimension.

recorded temperatures and ﬂow rates, the overall heat transfer coefﬁcient in the Multicoil heat exchanger and the tubular coolers were determined using the following equations: ˙ =m ˙ c p ∆T Q (25.21) ˙ = U A ∆T Q lm lm ˙ is the energy gained by the product. where Q The results of the calculations are summarized in Figure 25.5. It can be seen from this ﬁgure that the overall heat transfer coefﬁcient was always higher (more than double) in the Multicoil heat exchanger than in the tubular coolers. Based on the limited experimental runs, there does not seem to be any effect of set point temperature on the overall heat transfer coefﬁcient. The next study was conducted with the objective of determining the effect of the diameter of the helical coil on the overall heat transfer coefﬁcient. In order to determine this, we conducted experiments with water as the product and pumped it through both the inner and outer coils separately, but at the same ﬂow rate. A similar analysis to the one performed above was carried out to determine the overall heat

© 2003 by CRC Press LLC

10.0 9.0

U (W/m2-K)

8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 3

4

5

7

6

8

9

10

Flow rate (gpm) Outer, 93 °C

Outer, 121 °C

Outer, 149 °C

Straight tube

FIGURE 25.5 Overall heat transfer coefﬁcient in helical and straight heat exchangers. 11,000 10,000 9,000

U (W/m2-K)

8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 2.5

3.5

4.5

5.5

6.5

7.5

8.5

9.5

Flow Rate (gpm) Inner 93

Outer 93

FIGURE 25.6 Overall heat transfer coefﬁcient in the inner and outer coils of the Multicoil heat exchanger.

transfer coefﬁcient. The results of the calculations are summarized in Figure 25.6. It can be seen from this ﬁgure that the overall heat transfer coefﬁcient was always higher in the coil of smaller radius than in the coil of larger radius. Another study was conducted to directly compare the amount of energy transferred in the Multicoil heat exchanger and in tubular coolers. In order to perform this, the product (water) was pumped through the same system as described above at a speciﬁc ﬂow rate (0.26 kg/sec) and a speciﬁc set point temperature (121°C) through one of the coils (outer coil), with hot water ﬂowing through the system at 10.25 kg/sec. The mass ﬂow rates of city water in the ﬁrst and second coolers were

© 2003 by CRC Press LLC

TABLE 25.2 Comparison of Tubular and Multicoil Heat Exchangers (at 0.26 kg/sec) Multicoil Heat Exchanger Energy gained by product = 118,244 W 2 Overall heat transfer coefﬁcient = 3,889 W/m -K Cooler #1 Energy lost by product = 66,989 W 2 Overall heat transfer coefﬁcient = 2,020 W/m -K Cooler #2 Energy lost by product = 24,701 W 2 Overall heat transfer coefﬁcient = 1,603 W/m -K Cooler #3 Energy lost by product = 11,166 W 2 Overall heat transfer coefﬁcient = 901 W/m -K Cooler #4 Energy lost by product = 7950 W 2 Overall heat transfer coefﬁcient = 927 W/m -K a Net gain in energy based on the inlet and exit temperatures of the product = 6441 W a Net gain in energy based on energy gained in heater and energy lost in coolers = 7438 W a

The difference in the above two values is due to experimental errors and the fact that we neglected heat loss in the holding tube.

1.58 and 0.94 kg/sec, respectively, while the mass ﬂow rates of glycol in the third and fourth coolers were 0.74 and 0.47 kg/sec, respectively. The results of the experiments are summarized in Table 25.2. A similar experiment was conducted at a product ﬂow rate of 8.16 g/min. The only other change in the experimental conditions was that the mass ﬂow rate of city water in the ﬁrst cooler was 1.71 instead of 1.58 kg/sec. The results of this experiment are summarized in Table 25.3. From Tables 25.2 and 25.3 it can be seen that the energy transferred in the Multicoil heat exchanger was much higher than that transferred in each of the coolers. This is further seen from the fact that the overall heat transfer coefﬁcient in the Multicoil heat exchanger was much higher than that in any of the coolers. This is due to two factors: 1. The outside heat transfer coefﬁcient was much higher in the Multicoil heat exchanger due to the high ﬂow rate of the heating medium and the presence of the bafﬂes. 2. The high inside heat transfer coefﬁcient in the Multicoil heat exchanger was due to the development of secondary ﬂow.

© 2003 by CRC Press LLC

TABLE 25.3 Comparison of Tubular and Multicoil Heat Exchangers (at 0.52 kg/sec) Multicoil Heat Exchanger Energy gained by product = 235,857 W 2 Overall heat transfer coefﬁcient = 6,107 W/m -K Cooler #1 Energy lost by product = 97,680 W 2 Overall heat transfer coefﬁcient = 2612 W/m -K Cooler #2 Energy lost by product = 49,268 W 2 Overall heat transfer coefﬁcient = 2195 W/m -K Cooler #3 Energy lost by product = 24,916 W 2 Overall heat transfer coefﬁcient = 1287 W/m -K Cooler #4 Energy lost by product = 18,895 W 2 Overall heat transfer coefﬁcient = 1246 W/m -K a Net gain in energy based on the inlet and exit temperatures of the product = 47,006 W a Net gain in energy based on energy gained in heater and energy lost in coolers = 45,098 W a

The difference in the above two values is due to experimental errors and the fact that we neglected heat loss in the holding tube.

25.3 CONCLUDING REMARKS Numerous studies have been conducted on secondary ﬂow in helical tubes in order to either understand the fundamental principles of ﬂow and heat transfer in coils or to determine friction factors, pressure drops, extent of secondary ﬂow, axial dispersion coefﬁcient, critical Reynolds number, or Nusselt number, and how various system and process parameters affect them. However, there is no standard correlation or law that can be applied to all scenarios of helical tube ﬂow (unlike in straight tubes); hence, readers are cautioned to carefully review the conditions under which the equations are applicable. Based on the experiments conducted in the Multicoil heat exchanger and tubular cooling units, it can be seen that the overall heat transfer coefﬁcient in the Multicoil heat exchanger is much higher than that in the tubular coolers. It was also seen that the smaller the radius of the coil of the heat exchanger, the higher the heat transfer coefﬁcient. However, it should be noted that the pressure drop in a coil of smaller radius is higher than that in a coil of larger radius. In conclusion, it is noted that the use of helical heat exchangers can result in rapid and relatively uniform processing of a product, thereby resulting in a high quality product.

© 2003 by CRC Press LLC

NOMENCLATURE 2

A cp C1, C2 d dp D Dvertical Ef f g h k L ˙ m

Area, m Speciﬁc heat, J/kg-K Constants Diameter of tube, m Particle diameter, m Coil diameter, m Vertical dimension, m Energy loss due to friction, J/kg Friction factor 2 Acceleration due to gravity, m/sec 2 Convective heat transfer coefﬁcient, W/m -K Thermal conductivity, W/m-K Length of pipe, m Mass ﬂow rate, kg/sec

NDe

Dean number N De = N Re r / R

NGr

Grashof number N Gr =

NGz

Graetz number N Gz =

NNu

Nusselt number N Nu =

βf g ρf (Tsurface − T∞ ) D3vertical µ 2f

N Re N Pr x/D

NPe

hD kf Peclet number NPe = (NRe)(NPr)

NPr

Prandtl number N Pr =

NRa

Rayleigh number NRa

NRe

Reynolds number N Re =

N Rec

Critical Reynolds number

˙ Q r R T Tsurface T∞ u U ˙ V x z

Energy transferred per unit time, W Radius of tube, m Radius of helical coil, m Temperature, K Surface temperature, K Bulk ﬂuid temperature, K Average velocity, m/sec 2 Overall heat transfer coefﬁcient, W/m -K 3 Volumetric ﬂow rate, m /sec Distance from entrance, m Ratio of thickness of thermal to velocity boundary layer

© 2003 by CRC Press LLC

C Pf µ f kf = (NGr)(NPr) ρf uD µr

SUBSCRIPTS b c f lm p s w

Bulk ﬂuid temperature Coiled (or helical) tube Fluid Logarithmic mean Particle Straight tube Wall temperature

GREEK SYMBOLS β δ ∆Pf ∆T µ ρ

−1

Coefﬁcient of volumetric thermal expansion, K Dimensionless curvature Pressure loss due to friction, Pa Change in temperature, K Viscosity, Pa-sec 3 Density, kg/m

REFERENCES Abul-Hamayel, M.A. and Bell, K.J., Heat Transfer in Helically Coiled Tubes with Laminar Flow, Presented at the annual meeting of the American Society of Mechanical Engineers (Heat Transfer Division), 1979. Bara, B., Nandakumar, K., and Masliyah, J.H., An experimental and numerical study of the Dean problem: ﬂow development towards two-dimensional multiple solutions, J. Fluid Mech., 244, 339–376, 1992. Berger, S.A., Talbot, L., and Yao, L.S., Flow in curved pipes, Annu. Rev. Fluid Mech., 15, 461–512, 1983. Carlson, V.R., Enhancement of Heat Transfer in Heat Exchangers for Aseptic Processing, Presented at the ASAE Annual International Meeting, Paper No. 916608, 1991. Castelain, C., Mokrani, A., Legentilhomme, P., and Peerhossaini, H., Residence time distribution in twisted pipe ﬂows: helically coiled system and chaotic system, Exper. Fluids, 22, 359–368, 1997. Cheng, K.C., Lin, R.C., and Ou, J.W., Fully developed laminar ﬂow in curved rectangular channels, J. Fluids Eng., 98, 41–48, 1976. Choi, U.S., Talbot, L., and Cornet, I., Experimental study of wall shear rates in the entry region of a curved tube, J. Fluid Mech., 93, 465–489, 1979. Colebrook, C.F., Friction factors for pipe ﬂow, Inst. Civil Eng., 11, 133, 1939. Dean, W.R., Note on the motion of ﬂuid in a curved pipe, Philosophical Magazine, Series 7, 4, 208–223, 1927. Dean, W.R., The stream-line motion of ﬂuid in a curved pipe, Philosophical Magazine, Series 7, 5, 673–695, 1928. Dean, W.R. and Hurst, J.M., Note on the motion of ﬂuid in a curved pipe, Mathematika, 6, 77–85, 1959. Dennis, S.C.R. and Ng, M., Dual solutions for steady laminar ﬂow through a curved tube, Q. J. Mech. Appl. Math., 35, 305–324, 1982.

© 2003 by CRC Press LLC

Dravid, A.N., Smith, K.A., Merrill, E.W. and Brian, P.L.T., Effect of secondary ﬂuid motion on laminar ﬂow heat transfer in helically coiled tubes, AIChE J. 17, 1114–1122, 1971. Duh, T.Y. and Shih, Y.D., Fully developed ﬂow in curved channels of square cross sections inclined, ASME J. Fluids Eng., 111, 172–177, 1989. Fiedler, H.E., A note on secondary ﬂow in bends and bend combinations, Exp. Fluids, 23, 262–264, 1997. Futagami, K. and Aoyama, Y., Laminar heat transfer in a helically coiled tube, Int. J. Heat Mass Transfer, 31, 387–396, 1988. Janssen, L.A.M. and Hoogendoorn, C.J., Laminar convective heat transfer in helical coiled tubes, Int. J. Heat Mass Transfer, 21, 1197–1206, 1978. Kao, H.C., Torsion effect on fully developed ﬂow in a helical pipe, J. Fluid Mech., 184, 335–356, 1987. Koutsky, J.A. and Adler, R.J., Minimization of axial dispersion by use of secondary ﬂow in helical tubes, Can. J. Chem. Eng., 42, 239–246, 1964. Kumar, K.R., Rankin, G.W., and Sridhar, K., Fully developed ﬂow of power law ﬂuids in curved ducts with heat transfer, Numerical Heat Transfer Part A, 16, 101–118, 1989. Kutateladze, S.S. and Borishanskii, V.M., A Concise Encyclopaedia of Heat Transfer, Pergamon Press, London, 1966, p. 114. Liu, Y. and Zuritz, C.A., Mathematical modeling of particulate two-phase ﬂow in a helical pipe, J. Food Process Eng., 18, 321–341, 1995. Manlapaz, R.L. and Churchill, S.W., Fully developed laminar ﬂow in a helically coiled tube of ﬁnite pitch, Chem. Eng. Commun., 7, 57–78, 1980. Masliyah, J.H., On laminar ﬂow in curved semicircular ducts, J. Fluid Mech., 99, 469–479, 1980. Moody, L.F., Friction factors for pipe ﬂow, ASME Trans., 66, 671–684, 1944. Mori, Y. and Nakayama, W., Study of forced convective heat transfer in curved pipes, Int. J. Heat Mass Transfer, 8, 67–82, 1965. Muguercia, I., Li, W., and Ebadian, M.A., An experimental investigation of the secondary ﬂow inside a helicoidal pipe, Contrib. Papers Fluids Eng., 170, 19–24, 1993. Nandakumar, K. and Masliyah, J.H., Bifurcation in steady laminar ﬂow through curved tubes, J. Fluid Mech., 119, 475–490, 1982. Oliver, D.R. and Asghar, S.M., Heat transfer to Newtonian and viscoelastic liquids during laminar ﬂow in helical coils, Trans. Inst. Chem. Eng., 54, 218–224, 1976. Ozisik, M.N. and Topakoglu, H.C., Heat transfer for laminar ﬂow in a curved pipe, J. Heat Transfer, 90, 313–318, 1968. Patankar, S.V., Prediction of laminar ﬂow and heat transfer in helically coiled pipes, J. Fluid Mech., 62, 539–551, 1974. Popiel, C.O. and Wojtkowiak, J., Simple formulas for thermophysical properties of liquid water for heat transfer calculations (from 0°C to 150°C), Heat Transfer Eng., 19, 87–101, 1998. Sandeep, K.P., Zuritz, C.A., and Puri, V.M., Velocity and Temperature Proﬁles in Two-Phase Non-Newtonian Flow in Conventional and Helical Holding Tubes, Presented at the ASAE Annual International Meeting, Chicago, June 18–23, 1995, Paper No. 956534. Sandeep, K.P., Zuritz, C.A., and Puri, V.M., Residence time distribution of particles during two-phase non-Newtonian ﬂow in conventional as compared with helical holding tubes, J. Food Sci., 62, 647–652, 1997. Saxena, A.K. and Nigam, K.D.P., Coiled conﬁguration for ﬂow inversion: its effect on residence time distribution, AIChE J., 30, 363–368, 1984. Seban, R.A. and McLaughlin, E.F., Heat transfer in tube coils with laminar turbulent ﬂow, Int. J. Heat Mass Transfer, 6, 387–395, 1963.

© 2003 by CRC Press LLC

Taylor, G., Dispersion of soluble matter ﬂowing slowly through a tube, Proc. R. Soc. London, Series A, 219, 186–203, 1953. Taylor, G.I. and Yarrow, F.R.S., The criterion for turbulence in curved pipes, Proc. R. Soc. London, Series A, 124, 243–249, 1929. Thomson, D.L., Bayazitoglu, Y., and Meade, A.J., Jr., Low Dean number convective heat transfer in helical ducts of rectangular cross-section, Trans. ASME J. Heat Transfer, 120, 84–91, 1998. White, C.M., Streamline ﬂow through curved pipes, Proc. R. Soc. London, Series A, 123, 645–663, 1929. White, C.M., Fluid friction and its relation to heat transfer, Trans. Inst. Chem. Eng., 18, 66–86, 1932. Yang, G. and Ebadian, M.A., Mixed convective ﬂow heat transfer in a vertical helicoidal pipe with ﬁnite pitch, Comput. Mech., 14, 503–512, 1994. Yang, G. and Ebadian, M.A., Effect of pitch on fully developed turbulent ﬂow in the helicoidal pipe, ASME Thermal Eng. Conf., 1, 425–432, 1995. Yang, R. and Chang, S.F., Combined free forced convection for developed ﬂow in curved pipes with ﬁnite curvature ratio, Int. J. Heat Fluid Flow, 15, 470–476, 1994.

© 2003 by CRC Press LLC

26

Relating Food Frying to Daily Oil Abuse. Part I. Determination of Surface Heat Transfer Coefﬁcients with Metal Balls K.S. Pannu and M.S. Chinnan

CONTENTS 26.1 Introduction 26.2 Materials and Methods 26.3 Results and Discussion 26.4 Conclusions Nomenclature Acknowledgments References

26.1 INTRODUCTION During immersion frying, convective heat transfer occurs at the food–oil interface (Singh, 1995; Sahin et al., 1999; Costa et al., 1999). The mode of heat/mass transfer in deep fat frying is rather complex because it is difﬁcult to precisely deﬁne and/or quantify the vigorous movement of water vapor bubbles escaping at the food surface. An added complication is that the thermophysical properties of the food material continually change due to moisture depletion and temperature change (Costa et al., 1999; Hallstrom et al., 1988). Data on the convective surface heat transfer coefﬁcients (h values) obtained during food frying through the use of metal transducers, food, and model foods have been reported in the literature (Sahin et al., 1999; Costa et al., 1999; Pannu and Chinnan, 1999; Dincer, 1996; Miller et al., 1994). Selected results are presented in Table 26.1 to show the large range that exists for these reported results. For the development of predictive models, it is usually assumed that the h value is constant during immersion frying. Comprehensive mathematical models were developed by Farkas et al. (1996a, b) and Farid and Chen (1998) to quantify heat

© 2003 by CRC Press LLC

TABLE 26.1 Some Reported h Value Data Obtained for Food Frying 2 h Value (W/m °C)

~110 90–200 250–300 250–600 300–650 a ~14 a

Temp. (°°C)

Material/Shape

Source

140–160 150–190 170–190 140–180 140–180 180

Potato/ﬁnite cylinder Model food/ﬁnite slab Metal/sphere Potato/French fry Metal/French fry Potato/long cylinder

Pannu and Chinnan (1999) Sahin et al. (1999) Miller et al. (1994) Costa et al. (1999) Costa et al. (1999) Dincer (1996)

Heat and mass transfer have been decoupled; h-value is only for heating.

and mass transfer during food frying. Large variations in h value data obtained during frying, with food vs. without food, have led researchers to use two h values for the development of predictive models (Farkas, 1996a; Costa et al., 1999). One h value is used in the absence of bubbling and another for the bubbling phase. It is also assumed that a nonbubbling phase is followed by an enhanced bubbling phase, and that at the end there is reduced bubbling as less moisture is evaporated. However, this is not true when commercially prepared frozen foods are deep fried. Under such conditions there is an instantaneous condition of high turbulence or, more speciﬁcally, forced convection conditions are created as the surface ice melts, producing a vigorous bubbling action. Costa et al. (1997) also reported that the bubbling action increases to a maximum value prior to decreasing, and this can be related to the water loss rate. Thus, bubbling may be expected to have an inﬂuence on h values. In the absence of bubbling, h value data reported in the literature, and obtained through the use of metal trans2 ducers, range between 220 and 300 W/m °C (Miller, et al., 1994; Tseng et al., 1996; Pannu and Chinnan, 1999). Fellows (1996) provided similar data for the nonbubbling 2 phase, along with h values of 800 to 1000 W/m °C for the surface boiling conditions. Based on product surface temperatures, Hubart and Farkas (1998) predicted that for 2 frying at 180°C, the h value started at 300 W/m °C, increased to a maximum value 2 2 of 1100 W/m °C and then decreased to below 200 W/m °C after 900 sec of frying. Pannu and Chinnan (1999) conducted a heat transfer study by heating ﬁnite potato cylinders (with a diameter and length of 2.54 cm) in hot oil at 70 and 90°C (no moisture loss) and compared these results with those obtained during frying at 160°C. Their results show that the heating rate index values obtained at the food center and the mid-plane (between center and surface) were identical for the ﬁrst two cases. In addition, similar values were obtained under frying conditions for the ﬁrst 120 sec at the mid-plane and for 200 sec at the food center. Based on these and additional data for moisture loss, the h value was computed to range between 100 2 and 130 W/m °C. These values are similar to those reported by Sahin et al. (1999), 2 but lower than the h value of about 250 W/m °C obtained with metal transducers. Additional details on methods that can be employed to obtain a value for the overall

© 2003 by CRC Press LLC

convective surface heat transfer coefﬁcient (U) from moisture loss data are provided in Part 2 of our study (Pannu and Chinnan, Chap. 27, this volume). Sahin et al. (1999) used a model food made from aluminum wool and mashed potatoes to conduct their study. Thin square slabs (0.3 × 5 × 5 cm) were vertically suspended in hot oil to minimize the variability of h values on product geometry. In essence, h values were determined by solving the conduction equation after compiling a database on transducer moisture loss and product temperature as a function of time, and by varying the thermal properties as a function of temperature and moisture. The h values obtained by Sahin et al. (1999) show a stepwise increase 2 from 90 to 200 W/m °C as oil temperature increased from 150 to 190°C. In comparison, Costa et al. (1999) reported that h values are time dependent. Data with metal transducers show that h values peak 10 to 40 sec after frying begins and thereafter start to decline. For potato crisps the peak occurs before that for French fries, and the peak also occurs earlier as the frying oil temperature increases, indicating that h values are tied to the moisture evaporation characteristics. Essentially, the peak is related to the high moisture evaporation regions because higher moisture loss rates induce more bubbling and provide higher h values. Thus, peak h values occur shortly after immersion for the thin potato crisps. This suggests that frozen foods should provide the highest h value immediately after they are immersed into the hot oil. The experimental data of Costa et al. (1999) showed peak h values 2 2 of about 750 W/m °C (after 15 sec of frying) and 650 W/m °C (after 35 sec of frying) for crisps and French fries, respectively, at a frying temperature of 180°C. However, the peak h value measured directly from French fries at a processing 2 temperature of 140°C was about 600 W/m °C and higher than the value of 440 2 W/m °C obtained with the metal transducer. Data in the literature suggest that the oil viscosity, heat capacity, and surface tension are the primary physical properties that may inﬂuence the product heating rate (Blumenthal, 1991; Miller et al., 1994). Blumenthal (1991) outlines the surfactant theory and suggests that the heat transfer rate from oil to food can change as the oil quality degrades through use. It is clearly stated that during food frying heat is transferred from the nonaqueous medium (oil) into the mostly aqueous medium (food). Thus, during food frying there is an oil–water interface that does not exist when metal transducers are used to ascertain the h value. Therefore, metal transducers may not register changes in h values due to the buildup of surfactants. This is supported by results presented by Tseng et al. (1996), who showed that the h value is not affected until the oil discard point is reached. Surfactants should be regarded as wetting agents that increase the contact time between oil and food (Blumenthal, 1991) through the oil–water interface. Therefore, excessive darkening and drying at the food surface as a result of oil breakdown may be related to the above phenomenon and not to h values obtained with metal transducers. Parameters commonly used to deﬁne discard point are foaming due to buildup of surfactants, oil color, smoke point, dielectric properties, free fatty acid (FFA) levels, and total polar compounds. The ﬁrst three are visual parameters and probably the ones most commonly used. Miller et al. (1994) used h value data to study the inﬂuence of temperature and oil type on oil use (abuse) and found that the major effect was due to viscosity. However, the differences in h values were rather small.

© 2003 by CRC Press LLC

Further, although the transient heating equations indicate that h values for heating and cooling should be similar, no comparative data are available. The objectives related to this part of our research were to estimate h values with metal balls in a range of food frying conditions. Speciﬁc objectives were to: determine h value without food; compare h value data for heating vs. cooling in the same temperature range; determine h value during the frying of commercial grade frozen French fries (par-fries) and breaded chicken ﬁllets; observe the inﬂuence of loading condition (less food vs. more food); and study the inﬂuence of oil abuse on h value data.

26.2 MATERIALS AND METHODS A schematic of the equipment and tools required to conduct this research is presented in Figure 26.1. Although the picture shows one metal ball suspended in the pot fryer, four metal balls were simultaneously immersed into the hot (or cold) oil to obtain the time–temperature data. A ﬁne wire (36 gauge, type K) thermocouple was positioned at the geometric center of each ball. To accomplish this task, a 0.8-mm hole was drilled into each ball in the central axis up to a depth equivalent to half the ball diameter. Omegabond 200 (Omega Engineering Inc., Stamford, CT), a high temperature, high thermal conductivity epoxy cement, was used to bond the thermocouples in place. The diameter of the small aluminum and stainless steel balls used in this study was 1.27 cm (0.5 inch), and the large balls had a diameter of 2.54 cm (1.0 inch). The four balls were suspended on a frame to facilitate their simultaneous immersion into the frying medium and were identiﬁed as Al- 1 2 , SS- 1 2 , Al-1 and SS-1 (Figure 26.2), with 1 2 and 1 indicating ball diameters of 1.27 cm and 2.54 cm, respectively. The ﬁfth thermocouple used to measure the oil temperature was also attached to the frame and positioned at the same height as the balls. Kitchen pot fryers (3.5 l capacity) were employed for this study, and commercial grade hydrogenated soybean oil was used as the food frying medium. Commercial grade, frozen (for the food service sector) breaded uncooked chicken ﬁllets (~85 g of breast meat) and par-fries (1-cm thick French fries) were used. A 1:7.5 food-to-oil ratio was used, i.e., ~340 g of food were fried in 2.6 kg

Thermocouple wire: Type K - 36 gauge

Pot Fryer

Metal ball FIGURE 26.1 Schematic of “tools” used to conduct the frying study.

© 2003 by CRC Press LLC

00

200

40

80

120

Oil Al-1/2

150

Al-1

-1

SS-1

SS-1

Ln (T. R.)

Temp. (C)

SS-1/2

Abused Oil FFA > 1.5

50

Al-1

-2

-3 SS-1/2

-4

0 0

20

40 Time (sec) 80

100

120

Al-1/2

Time (sec)

FIGURE 26.2 Typical temperature data registered by the metal balls during heating in oil at 190°C. Data in the right graph were used to obtain h value data. (Al and SS refer to aluminum and stainless steel, respectively; sufﬁx 1 2 or 1 refers to the metal ball diameter in inches.)

of oil. Food batches were fried every 20 min at a temperature of 180°C for 5 min (cook cycle) followed by drain/cool for 5 min (Table 26.2). The 10 min gap between batches provided time for preparation of the next batch and permitted the pot fryers to return to the initial set temperature. Twenty food batches were fried daily over a 7.5 h period, and make-up oil was added after 10 batches had been fried. At the end of each day, the frying oil was ﬁltered to remove debris and charred materials, and make-up oil was added to maintain the 2.6 kg level after a 50 ml oil sample was removed for analysis (Table 26.2). Days 1, 4, and 7 were chosen to conduct the variable food mass study using six batches of French fries and 14 batches of chicken ﬁllets. The frying protocol for the variable food mass study is detailed in Part 2 (Pannu and Chinnan, Chap. 27, this volume). On days 2, 3, 5, 6, and 8, two batches of French fries and 18 batches of chicken ﬁllets were fried, as shown in Table 26.2. The overall mass of food fried each day was approximately 6.7 kg, with the normal loading condition deﬁned as 340 g of French fries or four chicken ﬁllets. For a few experiments, chicken ﬁllet and French fry pieces were instrumented to obtain temperature proﬁles. Fine wire (36 gauge, type K) thermocouples were positioned at the geometric center of a 7-cm French fry and a chicken ﬁllet. Thermocouples were also inserted close to the food surface. Food surface for the chicken ﬁllet represented the top part of the breading layer. The instrumented French fry was placed on top of the four chicken ﬁllet pieces and subsequently processed in 180°C oil. Experiments with metal balls were conducted at varying intervals to cover the 8-day test period. Temperature data from the metal balls were recorded at 0.5 sec intervals. The exterior food temperature data were recorded prior to the commencement of food frying, i.e., in between batches. The experiments with food were conducted by immersing the metal transducers 60 to 90 sec after commencement of food frying. A time delay was employed for safety reasons because of enhanced bubbling and oil splattering at the commencement of frying due to ice melt conditions.

© 2003 by CRC Press LLC

TABLE 26.2 Example of Experimental Protocol Used in Frying Studies File Name: ABC-2 Frying Cycle 2 of 8 days Weight of Empty Fryer: 1.612 kg Batch # 1 2 3 4 5 6 7 8 9 10

Time

Food (g)

9:00 325.6 9:20 332.8 9:40 348.3 10:00 340.7 10:20 310.2 10:40 319.9 11:00 313.2 11:20 350.4 11:40 350.6 12:00 346.5 TOTAL W1 = 3338.2

Product CH-4 CH-4 CH-4 CH-4 CH-4 CH-4 CH-4 CH-4 FF CH-4

Batch #

Date: April 30, 1999 Weight of Oil: 2.615 kg Time

Food (g)

11 13:20 356.8 12 13:40 308.5 13 14:00 310.7 14 14:20 313.3 15 14:40 313.9 16 15:00 340.5 17 15:20 351.4 18 15:40 324.8 19 16:00 344.4 20 16:20 407.3 TOTAL W2 = 3371.6

Product CH-4 CH-4 CH-4 CH-4 CH-4 CH-4 CH-4 CH-4 FF CH-4

Note: FF: French fries; CH, chicken. 1) Weight of fryer + oil + basket: 2) Weight of fryer + oil + basket: a) Oil loss = 1–2 3) Weight of fryer + oil + basket: 4) Weight of fryer + oil + basket: b) Oil loss = 1–2 c) Total oil loss = a + b d) Total food fried = W1+W2

4440 4412 28 g 4440 4415 25 g 53 g 6710

g at start g at noon g after oil addition g at end

g

Note: Frying basket weight = 4440 – (1612 + 2615) = 213 g

In addition, when 340 g of frozen food are rapidly immersed in hot oil, very unstable processing conditions exist in the beginning, resulting in a rapid drop in oil temperature. Such conditions make it difﬁcult to obtain accurate time–temperature data during the ﬁrst 60 sec of frying. Further, the metal balls were immersed in cold oil (room temperature) at all times when not in use. This was done to ensure that the balls had a uniform initial temperature. Thus, for the cooling experiments, the balls were returned to the cold oil reservior (also 2.6 kg of oil) after the balls had attained steady temperature in the heating cycle. Time–temperature data for this study were recorded using the HP34970 (Hewlett Packard, Palo Alto, CA) data acquisition unit. The natural logarithm (ln) of the dimensionless temperature ratio was plotted against time to provide a value for the inverse slope and used to determine h value by the lumped capacity method. Equation (26.1) was used to compute h values from temperatures registered at the geometric center of the metal balls. The terms A, ρ, Cp and V represent the solid surface area, density, speciﬁc heat, and volume, respectively. Subscripts for

© 2003 by CRC Press LLC

temperature (T) listed as a, i, and (t) denote ambient (oil), initial (metal ball), and the variable time-dependent temperature (metal ball), respectively. Ta − T( t ) −(hA/ρCpV)t = T. R. = θBall = e Ta − Ti

(26.1)

Thermal property data for ρ and Cp used to estimate the h values were (Holman, 1976): 3 ρStainless steel = 7897 kg/m CpStainless steel = 452 J/kg°C 3 ρAluminum = 2707 kg/m Cp Aluminum = 896 J/kg°C

26.3 RESULTS AND DISCUSSION Typical time–temperature data obtained during the heating of metal balls in oil are shown in Figure 26.2. The graph on the right shows that there were no lag factors, and straight lines were obtained when the natural logarithm of the dimensionless temperature ratio was plotted vs. time. The data presented also show that the smaller metal balls heated faster and that aluminum balls registered accelerated heating in comparison to stainless steel balls. Table 26.3 summarizes the data for h values obtained under free convection heating conditions. The results show that transducer material and ball diameter do not appear to appreciably inﬂuence the h value data. However, if average values are considered, the 2 large and small balls provide mean h values of 230 and 250 W/m °C, respectively. These results are similar to those reported by Miller et al. (1994). The low Biot numbers (Bi = h R/k) of 0.015 and 0.06 obtained for the large aluminum and stainless steel balls, with thermal conductivity, k, of 204 and 50 W/m°C, respectively, indicate minimal internal resistance to heat transfer and justify the use of the lumped capacity approach. Results presented in Table 26.3 also show that the h values are not inﬂuenced by oil abuse, as FFA values increased from a low of 0.05 (fresh oil) to a high of 1.55 on day 8.

TABLE 26.3 Comparison of h Value Data for Fresh vs. Used Frying Oil (Free Convection) 2 h Value (W/m °C)

Day 1 2 4 6 8

FFA

Temp. (°°C)

Al- 1 2

SS- 1 2

Al-1

SS-1

<0.05 0.22 0.67 1.10 1.55

185 190 180 185 185

220 270 235 260 230

250 255 275 250 250

220 245 245 230 240

215 230 225 220 225

Note: FFA: Free fatty acids

© 2003 by CRC Press LLC

The surfactant theory should not be questioned, since metal balls cannot be compared to food pieces as they do not have an oil–water interface. Indeed, the surfactant theory results correctly predicted food surface color darkening through increased oil use/abuse. Heating/cooling characteristics similar to those outlined above are depicted in Figure 26.3. However, a visual comparison of the log-normal temperature data shows that h values during cooling were lower than for heating (steeper slopes), and this is validated by results detailed in Table 26.4.

TABLE 26.4 Comparison of h Value Data for Heating vs. Cooling (Free Convection) 2 h Value (W/m °C)

Temperature (°°C)

Heating

Cooling

Cold

Heat

Cool

Al-1

SS-1

Al-1

SS-1

22 25 26 30 27

135 150 175 180 192

22 25 26 30 27

185 200 235 220 235

180 195 225 215 230

150 160 170 175 185

160 165 185 185 195

Heating

Cooling Temperature (C)

200 SS-1/2 Al-1/2

Al-1 SS-1

Fresh Oil FFA < 0.1 0

20

40

60

80

100

120

150 Al-1

100 SS-1 Al-1/2 SS-1/2

50 0

0

Time (sec)

20

40

60

80

100

Time (sec) 0

SS-1 Al-1 SS-1/2

Ln(T.R.)

Al-1/2

SS-1

-1 Al-1/2

-2

SS-1/2

Al-1

-3 -4

FIGURE 26.3 Temperature data comparing heating vs. cooling conditions. (Al and SS refer to aluminum and stainless steel, respectively; sufﬁx 1 2 or 1 refers to the metal ball diameter in inches.)

© 2003 by CRC Press LLC

TABLE 26.5 h Value Data without Food and during Frying with Food 2 h Value (W/m °C)

Condition

Temp. (°°C)

Time (sec)

185 185 185 185 185

— 90 60 60 60

No food CH, 4 pieces CH, 4 pieces FF, 340 g FF, 340 g

a

Al- 1 2

SS- 1 2

Al-1

SS-1

220 400 550 1070 960

250 345 510 885 850

220 340 480 780 725

215 405 440 450 620

Note:CH: chicken ﬁllet; FF: French fries. a

Time after commencement of food frying.

HEATING COOLING

FIGURE 26.4 A pictorial representation of the plume effect.

Figure 26.4 is a pictorial representation of what probably occurs during heating and cooling. During heating, density differentials force the oil plume to move downwards, and there is a negligible impact on the heating rate, whereas during cooling hot oil begins to move upward. As cooling occurs due to oil mixing, a shroud is created around the hot ball, and the cooling rate is altered. It is important to understand that we are addressing the issue of what occurs under free convection conditions. In addition to the above, results presented in Table 26.4 also compare what occurs as the temperature differential (δT) is increased. It can be observed that higher h values were obtained as δT was increased. Although it should be possible to link this phenomenon to the system dependent average oil viscosity value, this was not done. Results for h values obtained under a variety of different food frying conditions are presented in Tables 26.5 and 26.6. Table 26.5 compares the h value data for no food with food frying conditions. Results show that the metal balls provided h values about two- to fourfold higher than those obtained without food. Further, values 2 higher than 1000 W/m °C were obtained when metal balls were immersed along with the frozen food. However, it was difﬁcult to analyze such data because the oil temperature in the pot fryer rapidly dropped by 15 to 20°C due to ice melt, providing an unstable variable ambient temperature condition. In addition, because the metal

© 2003 by CRC Press LLC

TABLE 26.6 Inﬂuence of Loading Condition on h Value for French Fries 2 h Value (W/m °C)

Loading a

Mass (g)

%

FF: FF: FF: FF:

70 100 115 130

a

220 340 390 440

Temp. (°°C)

Al- 1 2

SS- 1 2

Al-1

SS-1

180 180 180 180

1000 860 890 650

605 510 745 840

500 425 705 650

580 445 615 560

340 g was the standard mass and considered 100% for the comparison study

200

Chicken 4 pcs 340 g

French Fries 340 g

No food SS-1/2

150

Al-1

Al-1/2

Al-1/2

SS-1/2 Al-1

Al-1

SS-1

SS-1/2 Al-1/2

SS-1

SS-1

50

0

0

20

40

60

0

20

40

60

80

0

20

40

60

80

100

120

Time (sec)

FIGURE 26.5 Temperature data comparing different food frying conditions. (Al and SS refer to aluminum and stainless steel, respectively; sufﬁx 1 2 or 1 refers to the metal ball diameter in inches.)

balls were in contact with the food, there was a large variability in the h value data. All told, the results clearly show that the h values dramatically increased due to bubbling and forced convection conditions. The data presented in Figure 26.5 give a visual perspective of what occurs. Information in this ﬁgure shows that metal balls immersed in the fryer containing French fries (FF) registered the fastest rise in temperature in comparison to chicken ﬁllets (CH) and the no food frying conditions. This occurred despite the facts that the metal balls were immersed approximately 60 sec after commencement of frying, and that oil temperature (Ta) dropped by more than 30 and 10°C for FF and CH, respectively, primarily due to ice melt and water evaporation. Before looking at some interesting summarized results, it is pertinent to further elaborate the ice melt phenomenon. Thermocouple locations in CH and FF were described in an earlier section. However, additional observations about the thermocouple location were obtained by examining the initial temperatures registered and are shown in Figure 26.6. Surface thermocouples showed initial temperatures slightly in excess of 0°C (indicating food–air interface), and the thermocouples located at

© 2003 by CRC Press LLC

0

190

100

200

300

0

CH-BL

140

-0.25

FF-BL French fry

90

Chicken

French fry

Chicken

-0.75

40

-10

0

40

80

120 160 200 240 280 320 360

Time (sec)

Ln (Temp Ratio)

Temperature (C)

Oil

-1.00

Time (sec)

FIGURE 26.6 Temperature data comparing cooking characteristics of French fry to those of chicken ﬁllet. (CH, chicken ﬁllet; FF, French fry; BL, boundary layer.)

the center indicated temperatures below zero. The data also showed that the French fries thawed rapidly. After commencement of frying, the FF were completely thawed after 10 sec, whereas the CH piece took approximately 100 sec to register center temperatures in excess of 0°C. A rapid increase in temperature at the surface (boundary layer: BL) and temperatures in excess of 100°C suggest that these thermocouples were protruding slightly outside the food surface. Overall, the time–temperature data presented in Figure 26.6 provide clariﬁcation on why rapid and larger temperature drops were registered during the processing of frozen FF. Similar, but smaller, temperature drops occur in food service commercial fryers because these units employ more powerful heating elements. Returning to the data presented in Table 26.5, it can be observed that during the frying of chicken ﬁllets, lower h values were obtained at the 90 sec mark in comparison to 60 sec after the start of frying. This shows that as turbulence subsided after the rapid melt of the surface ice layer, the h values were reduced. These results are comparable to those provided by Costa et al. (1999) and Hubart and Farkas (1998), in which it was shown that the variable h value is reduced as frying progresses. Comparing data from chicken to that of French fries shows that higher h values were obtained during the immersion of FF. Costa et al. (1999) compared potato crisps with French fries and reported higher h values for the crisps. Thus, higher evaporative rates provide more turbulent frying conditions and larger associated h values. Prior to discussing the somewhat contradictory results presented in Table 26.6, it is pertinent to deﬁne the three major measurement and evaluation errors. It is believed that the primary error related to h value determination during the cooking of French fries was due to transducer (ball) contact with the food particulates. When bubbling food particulates are in contact with or in close proximity to the transducer, the heating boundary layer is continually altered. Because bubbles can adhere to and/or burst on the ball surface, an error is incorporated into the temperatures registered by the metal balls. Thus, there was a noticeable scatter in the h value data obtained. The second error is due to the fact that the Biot criterion (Bi ≤ 0.1) is not

© 2003 by CRC Press LLC

2

satisﬁed for stainless steel balls when h values increase beyond 400 and 800 W/m °C for the large and small balls, respectively. Error 3 is unique and to the best of our knowledge a subject that has not received much attention. This error can possibly be explained on the basis of the theory of turbulence and forced convection. Bubbling induces turbulent forced convection heating conditions, and as such the ball diameter needs to be taken into account and tied to the dimensionless Nusselt number (Nu). Thus, a question to be addressed in future studies is whether the lumped capacity approach can be used to estimate h values under turbulent bubbling conditions. Although the results obtained and presented here are exciting, a link between h values and Nu was not established. However, in general terms it can be stated that the lower h values provided by larger balls need to be associated with Nu. Thus, information for the associated Reynolds number and the Prandtl number is required, along with temperature-dependent data for the oil thermal conductivity and viscosity. The data presented in Table 26.6 show that due to errors associated with the measurement of h values, we were unable to quantify the inﬂuence of more food vs. less food. Fryer limitation was also a negative factor, because under high loading conditions the large temperature drop suffered was followed by a long period of slow recovery or, more speciﬁcally, almost no recovery (see Figure 26.5). However, the scattered data indicate that metal transducers consistently registered higher h values due to turbulent bubbling conditions. The highest h value obtained for the least food (220 g) situation was due to turbulence and the fact that there was a smaller temperature drop in the fryer because less food was fried. Our experience with this part of the study showed that there is a need to cage (isolate) transducers so that more consistent data can be obtained. Not precluding the above, one ﬁnal hypothesis also needs to be considered with respect to loading conditions and different food materials. In very simple terms it can be deﬁned as the microclimate/environment that exists in the fryer when different food products are fried. When the data for FF provided in Table 26.5 are combined 2 with the data in Table 26.6, average h values of 905, 740, 630, and 545 W/m °C are obtained for Al- 1 2 , SS- 1 2 , Al-1, and SS-1, respectively, and these data appear to be closely grouped together for each transducer. This shows that there is a need to link Nu to fryer oil temperature, transducer size, and transducer material. For this reason, h value data should be related to the product being fried. A case on microclimate is put forth because the data of Costa et al. (1999) showed that crisps and French fries provided noticeably different peak h values. We believe that the results presented and discussed in this chapter will help other researchers to further elaborate the data on h values associated with deep fat frying.

26.4 CONCLUSIONS The experimental data presented show that metal transducers provide relatively high h values when food materials are being cooked in hot fryer oil, and this was associated with the turbulent mixing regime. It is interesting to note that the degree of oil abuse did not appear to inﬂuence the h value (Table 26.2). The comparison of chicken ﬁllet vs. French fries shows that larger pieces lose moisture at a slower

© 2003 by CRC Press LLC

rate (due to larger mass to surface area ratios), and because bubbling was reduced, the apparent h value was smaller (Table 26.5).

NOMENCLATURE A Bi Cp H K R T T T.R. V θ ρ

2

Surface area (m ) Biot number Speciﬁc heat (J/kg°C) 2 Convective surface heat transfer coefﬁcient (W/m °C) Thermal conductivity (W/m°C) Ball radius (m) Time (sec) Temperature (°C) Temperature ratio 3 Volume (m ) Temperature ratio 3 density (kg/m )

ACKNOWLEDGMENTS The authors thank Glenn D. Farrell (Research Coordinator I) and Vijaya Mantripragada (Lab Technician II) for their assistance. Author Pannu thanks the Biological Systems Engineering Department of Washington State University and Dr. Gustavo V. Barbosa-Cánovas for time and facilities provided for the preparation of this manuscript.

REFERENCES Blumenthal, M.M., A look at the chemistry and physics of deep-fat frying, Food Technol., 45, 68–71, 1991. Costa, R.M., Fernanda, A.R.O., Delaney, O., and Gekas, V., Analysis of the heat transfer coefﬁcient during potato frying, J. Food Eng., 39, 293–299, 1999. Costa, R.M., Oliveira, F.A.R., and Gekas, V., Application of image analysis to the study of water losses from potato slices during frying, in Engineering and Food at ICEF 7, Part I, Jowitt, R., Ed., Shefﬁeld Academic Press, Shefﬁeld, 1997. Dincer, I., Modelling for heat and mass transfer parameters in deep-frying of products, Heat Mass Transfer, 32, 109–113, 1996. Farid, M.M. and Chen, X.D., The analysis of heat mass transfer during frying of food using a moving boundary solution procedure, Heat Mass Transfer, 34, 69–77, 1998. Farkas, B.E., Singh, R.P., and Rumsey, T.R., Modeling heat and mass transfer in immersion frying. I. Model development, J. Food Eng., 29, 211–226, 1996a. Farkas, B.E., Singh, R.P., and Rumsey, T.R., Modeling heat and mass transfer in immersion frying. II. Model solution and veriﬁcation, J. Food Eng., 29, 227–248, 1996b. Fellows, P.J., Food Processing Technology — Principles and Practice, Woodhead Publishing Ltd., Cambridge, U.K., 1996.

© 2003 by CRC Press LLC

Hallstrom, B., Skjoldebrand, C., and Tragardh, C., Heat Transfer and Food Products, Elsevier Applied Science, New York, 1988. Holman, J.P., Heat Transfer, 4th ed., McGraw-Hill, New York, 1976. Hubart, J.L. and Farkas, B.E., Determination of the convective heat transfer coefﬁcient during frying, in Drying ’98, Aktridis, C.B., Marinos-Kouris, D., and Saravakos, G.D., Eds., Ziti Editions, Thessaloniki, 1998. Miller, K.S., Singh, R.P., and Farkas, B.E., Viscosity and heat transfer coefﬁcient for canola, corn, palm and soybean oil, J. Food Process. Preserv., 18, 461–472, 1994. Pannu, K.S. and Chinnan, M.S., Heat Transfer Coeffecient Associated with Heating/Frying of Food Pieces in Oil, abstract (#8–11), Annual Meeting of the Institute of Food Technologists, Chicago, July 23–28, 1999. Pannu, K.S. and Chinnan, M.S., chap. 4.1, this volume. Sahin, S., Sastry, S.K., and Bayindirli, L., The determination of convective heat transfer coefﬁcient during frying, J. Food Eng., 39, 307–311, 1999. Singh, R.P., Heat and mass transfer in foods during deep-fat frying, Food Technol., 49, 134–137, 1995. Tseng, Y.C., Moreira, R., and Sun, X., Total frying-use time effects on soybean-oil deterioration and on tortilla chip quality, Int. J. Food Sci. Technol., 31, 287–294, 1996.

© 2003 by CRC Press LLC

Part IV Combined Transfer Phenomena

© 2003 by CRC Press LLC

27

Relating Food Frying to Daily Oil Abuse. Part 2. A Practical Approach for Evaluating Product Moisture Loss, Oil Uptake, and Heat Transfer K.S. Pannu and M.S. Chinnan

CONTENTS 27.1 Introduction 27.2 Materials and Methods 27.3 Results and Discussion 27.3.1 Moisture Loss 27.3.2 Oil Uptake 27.3.3 Heat Transfer 27.4 Conclusion Nomenclature Acknowledgments References

27.1 INTRODUCTION During deep fat frying a series of complex physical and chemical changes commences immediately after the immersion of high-moisture food products into hot oil (Singh, 1995; Saguy and Pinthus, 1995; Saguy et al., 1998). The chemical reactions alter the product characteristics as well as the quality of the cooking medium, i.e., the frying oil. Essentially, frying is a heat–mass transfer operation where the cooking oil/fat imparts several desirable quality attributes such as ﬂavor, texture, appearance, and mouthfeel to the food products. These desirable changes imparted to the cooked food are a combined result of moisture loss, crust formation, protein denaturation, starch gelatinization, oil/fat uptake, and numerous microstructural

© 2003 by CRC Press LLC

changes within the food (Blumenthal, 1991; Saguy and Pinthus, 1995; Saguy et al., 1998). However, undesirable changes are imparted to the cooking medium due to oil–water interaction and oxidation, along with changes caused by heating, cooking, the transfer of foreign materials from food to oil, and the accumulation of food residues/debris (Blumenthal, 1991; Saguy et al., 1998). Experimental data from studies that simulate and resemble normal cooking (food processing) conditions are required for the development and validation of predictive mathematical models. Food processing methods, including deep fat frying, utilize heat for product cooking. Thus, a set of boundary conditions is deﬁned and a value is assigned for the convective heat transfer coefﬁcient (h value) to facilitate the development of models to predict the initial and subsequent transfer of heat from the medium to the food solids (Singh, 1995; Farkas et al., 1996). Pannu and Chinnan (Chap. 26, this volume) provided a brief overview of methods currently employed to obtain data for this critical parameter, i.e., the h value. Through the presentation of literature data and experimental results they showed that the large variability in h values obtained with metal transducers was process related. Thus, a simple method was developed to obtain data for the apparent and/or overall heat transfer coefﬁcient directly from food pieces by using the product moisture loss data (Pannu and Chinnan, 1999) and elaborated here. In comparison to frying, the cooking of solids in steam, water, or sauce is a simple operation because heat transfer predominates, and mass transfer effects are usually ignored for mathematical model development. Such simplifying assumptions are not valid for cooking by deep fat frying, as three (and often four) dominant energy-demanding processes commence simultaneously after the food is immersed into hot oil. These processes can be deﬁned to represent heating, moisture loss, crust formation (Singh, 1995; Saguy et al., 1998), and the less recognized fourth process of thawing (ice to water, as in the case of frying frozen food). Oil uptake need not be included in the above category because it can be reasoned that this process is not energy demanding, and its inﬂuence on thermal property data can be incorporated into the heat transfer equations during process calculations. Thawing during frying of frozen products can signiﬁcantly affect the product temperature rise and in turn the cook value. Data presented by Pannu and Chinnan (Chap. 26, this volume) show that it takes approximately 100 sec for complete ice meltdown to occur at the center of a 340 g chicken ﬁllet during ο frying at 160 C. Results provided by Rao and Delaney (1995) indicate that it takes 400 sec for the core temperature of a prebreaded frozen chicken thigh to reach the melting ο point (0 C). Thus, consideration should be given to this aspect of deep fat frying, especially for the establishment of product cook values related to food safety issues. In addition, instantaneous sputtering and bubbling occur as a result of ice melting during frying of frozen products. This indicates that water evaporation starts immediately after the frozen food is immersed into hot oil. Because of this, the moisture loss curves obtained with frozen foods do not depict the customary lag characteristics found at the beginning of a typical drying curve. Little or no information is available in the literature on lag factors associated with moisture loss during the deep fat frying of food products. Products that are not frozen and/or food materials with less surface moisture depict some form of lag because there is a noticeably subdued time-delayed bubbling action. The bubbling action, whether vigorous (turbulent) or subdued, is a result of moisture ﬂashing to steam and the vapor channeling its way through the oil. Thus, it can

© 2003 by CRC Press LLC

be reasoned that higher bubbling rates indicate that the product is losing larger amounts of moisture. Most of the research related to studying the moisture loss characteristics of food during deep fat frying has been conducted by removing selected food pieces at set intervals from the fryer during the cooking process and then assessing the amount of moisture loss (Baumann and Escher, 1995; Ufheil and Escher, 1996). Such tests are valuable because information is simultaneously obtained for moisture loss, crust development, and oil migration/uptake. However, a major limitation of this method is that the initial mass and the ﬁnal mass of each individual food particle must be known, and several precisely manufactured uniform food pieces of the same size and shape must be available. Further, because the tests are conducted with few food pieces, it is difﬁcult to precisely quantify oil migration and moisture losses that occur during the transfer process from the fryer to the weighing container (Ufheil and Escher, 1996). Limitations related to sample preparation make it difﬁcult to ascertain the moisture loss characteristics of commercially prepared frozen foods during deep fat frying by the above method. Pannu and Chinnan (1999) developed a simple technique called active moisture loss measurement and obtained moisture loss data by placing a pot fryer on a balance and by recording the fryer weight change at 20 sec intervals. Through active moisture loss measurements, it was also possible to map the transition phase that occurs when food materials become buoyant and move from the sink to ﬂoating stage. Moisture loss characteristics change during ﬂoating because the oil transfers less heat to the food. The active moisture loss method provides good bulk data and a clearer picture of the food dehydration process during deep fat frying. The process of quantifying oil/fat migration into food products is challenging. It is difﬁcult to precisely deﬁne the time period and amount of oil/fat absorbed by the food due to the vacuum effect created by product cooling after the product is removed from the hot oil (Ufheil and Escher, 1996; Saguy et al., 1998). Ufheil and Escher (1996) stated that oil content analysis conducted on potato slices removed from hot oil during frying does not provide conclusive evidence on when and how much oil is transferred to the food. Thus, the authors conducted experiments with Sudan Red used as a lipid staining dye to deﬁne the time period at which oil migration occurs during the frying of potato slices. Their results indicate that majority of oil was absorbed by the potato slices after removal from the frying medium. In addition, their experimental results also indicate that oil uptake by potato slices manufactured from potato tubers with higher density was lower than for slices from lower density potato tubers. In general, it can be stated that oil uptake is a function of product type, initial moisture content, product thickness, frying temperature, and frying time (Ufheil and Escher, 1996; Saguy et al., 1998). It has been shown that oil uptake increases as the product moisture content increases, thickness decreases, oil temperature decreases, and frying time increases (Blumenthal, 1991; Ufheil and Escher, 1996; Saguy et al., 1998). However, Saguy and Pinthus (1995) indicated that food additives affect oil uptake and moisture loss characteristics, and this may be one reason why donuts made from dough with higher initial moisture content absorb less oil. Thus, the use of different formulations and food additives can alter the water retention capability of food and in turn inﬂuence its oil uptake capacity (Saguy and Pinthus, 1995). Product heating, dehydration, crust formation, the inﬂuence of surfactant buildup due to oil reuse/abuse, and oil uptake are all tied together. The continuous outﬂow of

© 2003 by CRC Press LLC

steam during the entire cooking period indicates that the pressure inside the food is greater than that of the environment. This phenomenon limits the entry of oil through the surface (crust) to within the food. Thus, oil uptake is localized to the crust region, and the polymers present in the frying oil are mainly adsorbed on the outer layers of the deep fat fried food (Blumenthal, 1991; Ufheil and Escher, 1996; Saguy et al., 1998). As the fryer oil becomes contaminated through repeated use, the surface tension of the oil at the oil–food interface is reduced because surface active agents are produced by lipid oxidation (Blumenthal, 1991; Singh, 1995; Saguy et al., 1998). An increase in the surfactant levels also induces increases in the food–oil contact time, heat transmission to the food surface, and oil adsorption by the crust. Although excessive heat is available at the food surface due to more oil–food contact, the amount of thermal energy utilized and transmitted by conduction to the interior remains unaltered (is constant). Therefore, foods cooked in used/abused oil depict excessive darkening and drying at the food surface (Blumenthal, 1991). The results presented by Pannu and Chinnan (Chap. 26, this volume) support the above-described phenomenon as the convective heat transfer coefﬁcients estimated with metal transducers did not change through oil use (day 1 vs. day 8). Although the surface food color and off-ﬂavor effects are marginally acceptable at the 1.5% free fatty acids (FFA) level but are more pronounced at the 3% FFA level (Jacobson, 1991), we did not attain the higher degree of oil abuse in our eight-day study. Thus, it is probable that the moisture loss characteristics of the food may not be affected at the 1.5% FFA level. Research on the chemistry of oil breakdown and the role of surfactants in deep fat frying is well documented (Perkins, 1967; Blumenthal, 1991; Pinthus and Saguy, 1994; Saguy and Pinthus, 1995; Paul and Mittal, 1996; Saguy et al., 1998) and is not reviewed here. The objectives of this research were divided into two parts. The ﬁrst objective was to estimate the moisture loss and oil uptake characteristics of commercially prepared frozen par-fries and breaded chicken ﬁllets. The active measurement procedure was employed to study the inﬂuence of (1) fryer loading condition (less food vs. more food) and (2) oil abuse on moisture loss and oil uptake by food. The second objective was to determine the overall convective heat transfer coefﬁcient (U) by using food moisture loss data. Moisture loss data from frozen French fries and breaded chicken ﬁllets were evaluated to determine whether comparable U values were obtained for the food under different loading conditions.

27.2 MATERIALS AND METHODS A kitchen pot fryer (3.5 liter capacity) and commercial grade hydrogenated soybean oil were used for the food frying study. Figure 27.1 is a schematic representation of the method employed and the tools required. The fryer was placed on an Ohaus laboratory balance (Model 120W, Florham, NJ), and a preweighed lot of food was then placed into the fryer basket, as depicted in Figure 27.1 (center). Thereafter, the balance was tared to zero and the food basket was immersed into the hot cooking oil. Weight changes (negative numbers) due to moisture evaporation (Figure 27.1, left) were manually ο recorded on a data sheet at 20 sec intervals. Food frying was conducted at 180 C for 5 min. After completion of the cook cycle, the food basket was removed from the hot oil and the product was allowed to drain/cool for an additional 5 min (similar to

© 2003 by CRC Press LLC

BALANCE - 037 g

BALANCE 000 g

Time(sec) Wt. (g) ---------------------------0 0.0 20 5.0 40 8.5 60 12.0 80 18.0

FIGURE 27.1 Pot-fryer with food fried on a balance for moisture loss determination. Study compares fresh oil vs. abused oil (oil used for more than one day.

Figure 27.1, center). Product weight loss during this cooling/drain period was recorded every 60 sec. Thereafter, the contents of the food basket were transferred to a container, and the fried product weight was recorded. The ﬁnal balance weight with the empty basket was also recorded to determine the degree of oil loss by the fryer. Although such losses were small, they provided a means for crosschecking the overall success of each moisture loss experiment and validating the oil uptake data. Oil uptake was calculated as total moisture loss less the product (food) weight change. Total moisture loss was the ﬁnal negative value provided by the tared (active) balance. Product weight change was deﬁned as the difference between the initial product weight before frying and the weight of the fried product recovered from the fryer basket. It should be noted that after oil is absorbed by the product, the value for active moisture loss recorded during frying will be larger than the value obtained for product weight change. Details on methodology and protocol employed are detailed elsewhere (Pannu and Chinnan, Chap. 26, this volume). For the variable food mass study (days 1, 4, and 7), six batches of par-fries and 14 batches of chicken ﬁllets were fried in the order outlined in Table 27.1. Variable food mass for French fries was designated as ±15 and ±30% above or below the normal batch weight of 340 g and for chicken as 3, 4, and 5 ﬁllets. This was done to ensure that the same mass of food was fried each day. The normal weight was deﬁned as 340 g because the average weight of a chicken ﬁllet was approximately 85 g, and four chicken ﬁllets were designated as the standard loading condition. Unfortunately, a transcribing error was made during the protocol preparation and instead of 290 g (85% of normal loading) of French fries 220 g (65% of normal loading) were processed under batch 5 (Table 27.1). Thus, no data are available for the 85% loading level of French fries. In addition, we did not identify whether all the breaded chicken came from the same lot. At the data analysis stage, it was realized that the breaded chicken pieces were from two different lots. Breaded chicken ﬁllets cooked on most days had an average mass of 85 g, whereas those utilized on the morning of day 7 weighed slightly more (95 g) and were most likely from a different

© 2003 by CRC Press LLC

TABLE 27.1 Experimental Protocol for the Variable Food Mass Frying Study, Along with Data Compiled for Product and Oil Usage File Name: ABC-1; Frying Cycle 1 of 8 days; Weight of Empty Fryer: 1.629 kg; Batch #

Time

Food (g)

Product

1 2 3 4 5 6 7 8 9 10

9:00 317.6 CH-4 9:20 235.1 CH-3 9:40 385.4 CH-5 10:00 330.2 CH-4 a 10:20 223.6 FF (−35%) a 10:40 393.3 FF 11:00 328.7 CH-4 11:20 340.2 FF (base-line) 11:40 347.0 CH-4 12:00 345.3 CH-4 TOTAL W1 = 3246.3 Note: FF, French fries; CH, chicken.

Date: April 29, 1999 Weight of Oil: 2.615 kg Batch # 11 12 13 14 15 16 17 18 19 20

1) Weight of fryer + oil + basket: 2) Weight of fryer + oil + basket: a) Oil loss = 1–2 3) Weight of fryer + oil + basket: 4) Weight of fryer + oil + basket: b) Oil loss = 3–4 c) Total oil loss = a + b d) Total food fried = W1 + W2

Time

Food (g)

13:20 13:40 14:00 14:20 14:40 15:00 15:20 15:40 16:00 16:20 TOTAL W2 =

4443 g 4379 g 54 g 4431 g 4374 g 57 g 111 g 6646 g

306.4 240.9 440.2 325.0 310.5 331.3 316.1 341.7 293.8 303.8 3199.8

Product CH-4 FF (–30%) FF (+30%) CH-4 CH-4 CH-4 CH-4 FF (base-line) CH-4 CH-4

at start at noon after oil addition at end

a

Due to a transcribing error, ~220 g of French-fries (–35%) were processed for batch 5 instead of the required ~290 g (−15%). Thus, no data were obtained for the −15% level.

manufactured lot (later veriﬁed). Because the moisture loss and oil uptake data were drastically affected, we suspect that the preparation method and breading were different for the two lots. Fryer limitations also contributed to an error because it was ο not possible to precisely maintain the 180 C initial cooking temperature. Moisture loss results for the extra studies (deﬁned later) were analyzed to obtain data on the rate of moisture loss for each of the three food frying conditions. The following explains how moisture loss data can be used to obtain a value for the overall convective surface heat transfer coefﬁcient (U). The primary assumption required ο to obtain U is that after the food temperature has stabilized to 100 C, most of the thermal energy (qHT) provided by the hot oil is utilized for moisture evaporation (qML). It should be noted that due to constant moisture evaporation the food temperature remains steady ο at approximately 100 C for an extended period of time. Thus, it can be stated that:

© 2003 by CRC Press LLC

qHT ≈ qML

(27.1)

qHT = U A (∆T) ≈ qML = mλ

(27.2)

2

with q as energy (W), U as the overall heat transfer coefﬁcient (W/m °C), λ = 2257 J/g (latent heat for evaporation/g of water), m as the mass of water loss per unit time and ∆T = TOil − 100. As an example, in Equation (2) the surface area (A) of an average 2 French fry (30.84 cm ) was obtained by weighing a batch, counting the number of fries, and determining the weight per unit length and the average fry thickness. The term ∆T is the fryer oil temperature less 100°C. qML is obtained by multiplying λ by the moisture loss (ML in g/sec) data obtained during active frying for a ﬁxed time period.

27.3 RESULTS AND DISCUSSION 27.3.1 MOISTURE LOSS The active moisture loss measurement method was simple, rapid and effective. The method also helped provide a better understanding of the frying process because it allowed differentiation between the sink and ﬂoating conditions that are a norm of the deep fat frying process. Typical moisture loss curves obtained for this three-day comparative study are presented in Figures 27.2 and 27.3. The data show that in comparison to French fries (FF), chicken ﬁllets (CH) lose less moisture; CH also lose moisture at a uniform rate. The FF data for moisture loss appear to follow a curvilinear mode. Thus, questions related to the constant rate drying characteristics of FF and CH during deep fat frying need to be addressed. A careful inspection of the data for French fries showed that the reduced moisture loss phase commenced after 200 sec of cooking. It was observed that the point at which FF started to ﬂoat was close to this time. After ﬂotation occurs, more than a quarter of the food surface is exposed to air. Because heat transfer decreases, the rate of moisture loss also decreases. Thus, moisture loss characteristics are altered at this point, and this is the reason for the downward dip in the moisture curve. Further, ﬂotation or buoyancy are related to the product bulk density and provide visual veriﬁcation of the fact that the cooked

% Moisture Loss

15

Day 1-m

Day 4-m

Day 7-m

245 g (3 pcs) 325 g (4 pcs) 370 g (5 pcs)

260 g (3 pcs) 335 g (4 pcs) 410 g (5 pcs)

280 g (3 pcs) 385 g (4 pcs) 480 g (5 pcs)

10

5

Product Change 0 0

100

200

Time (sec)

300 0

100

200

Time (sec)

300 0

100

200

300

Time (sec)

FIGURE 27.2 Moisture loss curves comparing the inﬂuence of oil use and loading conditions for deep fat fried chicken ﬁllets.

© 2003 by CRC Press LLC

% Moisture Loss

40

Day 1-m

Day 4-m

40

Day 7-m

30

30

20

20

10

10 230 g 340 g 390 g

0 0

100

200

220 g 340 g 390 g

300 0

Time (sec)

100

200

220 g 340 g 390 g

300 0

100

200

0 300

Time (sec)

Time (sec)

FIGURE 27.3 Moisture loss curves comparing the inﬂuence of oil use and loading conditions for French fries deep fat fried in the morning. 50

% Moisture Loss

40

FF: 240 g FF: 340 g FF: 440 g CH: 270 g (3 pcs) CH: 360 g (4 pcs) CH: 455 g (5 pcs)

30

French fries: float 20

Chicken: float 10

0 0

100

200

Time (sec)

400

500

600

FIGURE 27.4 Moisture loss curves comparing the inﬂuence of oil use and loading conditions for French fries and chicken ﬁllets deep fat fried for 10 minutes.

product has attained a density equivalent to that of the hot oil. Since the density of 3 the hot cooking oil is about 800 kg/m at 160°C, this suggests that at the point of ﬂotation the high moisture frozen FF have lost about 20 to 25% of their initial mass through water evaporation. The FF data support this phenomenon because the moisture loss curves show that the point of inﬂection occurs after FF lose 20% moisture. Additional tests with a longer cook period (10 min) were later conducted to verify the constant rate dehydration phenomenon for the deep fat frying of frozen products. These results are presented in Figure 27.4 and clearly show the two distinct constant rate dehydration rates for FF. It is to be noted that a majority of the predictive mathematical models developed do not take into account the inﬂuence of ﬂotation. Therefore, further research in this area is warranted.

© 2003 by CRC Press LLC

At ﬁrst glance, the data for moisture loss by the CH (Figure 27.2) do not provide a clear picture of the process. Product change is probably the only valid explanation for moisture loss (and oil uptake) differences recorded on day 7. A quick calculation for product mass (with the data on product mass provided in Figure 27.2) showed that the day 7 ﬁllets weighed approximately 10% more than those used on the previous days. Data for day 1 and 4 show that CH registered a moisture loss of approximately 11% (w.b.). The small differences in moisture loss data are attributed to the variability in oil temperature and the surface area effects. The kitchen fryer was limited in its ability to maintain a constant temperature and rapidly regain the temperature losses suffered due to food surface ice melt. Thus, the temperature lowering effect was less pronounced when less food was cooked, and this produced a slightly higher moisture loss. The CH moisture loss data (Figure 27.2) provide some interesting observations on the lag phenomenon mentioned earlier. The day 4 and day 7 data elaborate this point, as it can be clearly observed that more moisture was lost in the ﬁrst 20 to 40 sec of frying. The data show that the accelerated moisture loss phase is followed by a curvilinear lag phase and subsequently by constant rate dehydration. Results in Figure 27.4 also clearly deﬁne the three stages and show that the constant rate period for CH commences after 140 sec of cooking. In comparison, FF data (Figure 27.3) show that ice melt (thawing) and the lag phase occur simultaneously and terminate after 40 to 50 sec. Smaller and less deﬁned lag phases are expected with smaller size food particles. Comparative results show that after 300 sec of cooking, FF lose more moisture than CH, 30 vs. 11%, respectively. The four major differences between the two products are surface area, product thickness, food type/structure, and the initial moisture content (69 and 59% for FF and CH, respectively). Besides product differences, a simple calculation shows that mass to surface area ratios for FF and CH were approximately 2 0.21 and 0.48 g/cm , respectively. Thus, higher moisture losses by FF, a product with a smaller mass–area ratio, are in agreement with theory (Saguy et al., 1998). Reduced moisture loss due to temperature lowering effects (fryer limitation) were also noted for FF. On the afternoon of day 7, the cooking of FF at locations 12 and 13 (Table 27.1) was switched, and more food was followed by less food. It was observed that in comparison to other days, less moisture loss was recorded by 240 g of FF. Although loading conditions may inﬂuence the moisture loss rate during frying, no conclusions could be drawn in this study because the processing temperatures were not constant. Further, the data presented in Figure 27.3 for the 340 g tests show that an increase in FFA from 0.05% (day 1) to 1.3% (day 7) did not affect the moisture loss characteristics of the frozen FF. Thus, it can be concluded that oil abuse had negligible inﬂuence on product moisture loss. Because surfactants promote enhanced oil–food contact, one would expect the product heating rate to increase. However, this did not occur. The moisture loss characteristics remained unaltered and did not increase as would be expected. This suggests that the value of the apparent heat transfer coefﬁcient was not affected, as FFA values increased to the 1.55% test levels, and it is supportive of the h value data reported in Pannu and Chinnan, Chap. 26, this volume. Thus the rate at which thermal energy was absorbed and utilized for moisture loss by the FF remained unaltered, and excess heat available due to enhanced oil–food contact induced surface burning (charring) effects.

© 2003 by CRC Press LLC

27.3.2 OIL UPTAKE The consolidated data for oil uptake are presented in Table 27.2. To make a justiﬁable comparison, it is pertinent to look at the data for case 2 (column 5) where 340 g of product were cooked. The data for chicken show no oil uptake by this product. However, because breading picks up oil/fat, the results indicate that some form of oil/fat migration occurs from the chicken to the fryer oil. Overall, it can be stated that the results for chicken tend to indicate that there is no or negligible change in the fryer oil content. Data presented in the study by Pannu and Chinnan (Chap. 26, this volume), where only two batches of FF were processed on day 2, show that only 53 g of oil were lost after 6710 g of product was fried, and oil uptake was less than 1% for the entire day. In this variable mass study, however, where six batches of FF were fried (Table 27.1) 1.7% oil was lost or picked up by the food. Thus, accounting for oil losses due to splattering and other experimental errors, it can be stated that the global results match well with the active data. The results for FF show that oil uptake at the 340 g level is consistent and indicate that on average the product absorbed an additional 3.8% oil. The 3.8% oil uptake was calculated on a wet basis and translates to 5.6% of the ﬁnal product weight, assuming 32% moisture loss (Figure 27.3). We use the word “additional” for

TABLE 27.2 Oil Uptake by Chicken Fillets (CH) and French Fries (FF) % Oil Uptake a

Day

FFA

1 4 7 1 1 4 4 7 7 Avg. FF e Extra Extra

<0.05 0.67 1.30 <0.05 0.10 0.67 0.77 1.30 1.40 — 0.20 0.20

a

Product CH CH CH FF–m FF–a FF–m FF–a FF–m FF–a FF CH FF

b

Case 1 0.6 0.6 2.8 5.9 4.0 7.9 3.7 4.2 5.0 5.1 1.6 6.7

d

(252–3) (273–3) (283–3) (234) (246) (221) (240) (221) (241) (230) (268–3) (243)

c

Case 2

Case 3

−0.1(323–4) −0.9(328–4) 2.8(386–4) 4.1 (341) 4.0 (343) 3.4 (341) 3.1 (341) 4.0 (343) 4.1 (343) 3.8 (342) −0.7(361–4) 7.2 (341)

−0.4(367–5) 0.5(413–5) 2.5(485–5) 4.9 (390) 4.2 (445) 5.5 (391) 3.7 (439) 6.0 (390) 4.9 (441) 4.9 (415) −0.1(453–5) 5.9 (442)

Average 0.0 0.1 2.7 5.0 4.1 5.6 3.5 4.7 4.7 4.6 0.2 6.6

FFA: Free fatty acids. CH: chicken ﬁllet; FF–m: French fries–morning; FF–a: FF–afternoon. Also note that chicken ﬁllets received from supplier for day 7 were from a different batch. c Values in parentheses for FF refer to product mass in grams. For CH, they refer to chicken ﬁllets, mass and number of pieces. d Cases 1, 2, and 3 refer to variable mass of food fried (value in parentheses). Case 2 is the norm (340 g or four pieces of chicken). Cases 1 and 3 are less and more than the norm, respectively. e Tests were conducted after the 8-day study, and product was cooked for 10 min (norm was 5 min). b

© 2003 by CRC Press LLC

FF because the par-fries already contained oil/fat from prior processing. Data provided by Saguy et al. (1998) indicate that cooked FF have an oil content between 7.6 and 14.8 g/100 g. The FF processed in this study fall within the above range after an appropriate number is added to the 5.6% value. However, because oil uptake levels remained constant, it can be stated that surfactant buildup (at the level tested) does not appear to affect the oil uptake characteristics of the frozen FF. Oil uptake data presented for cases 1, 2, and 3 (Table 27.2) refer to less food, daily norm (340 g), and greater food loading conditions, respectively. The data on oil uptake are in agreement with other data in the literature. By comparing the data for the 10min cooking period with the other results for FF (normally cooked for 5 min), it can be observed that oil uptake increases as processing time is lengthened (Table 27.2). Further, the cooking oil temperatures for cases 1 and 3 were higher and lower than for case 2, respectively. This was because the fryer registered higher temperature drops when more food was cooked. This inﬂuenced oil uptake; results show that on average there was more oil uptake by FF for higher and lower cooking temperatures. Finally, to validate our oil uptake data, a global calculation was made with data presented in Table 27.1. The information presented shows that 1980 g of FF were cooked on day 1. Using the overall oil uptake number of 4.6% (Table 27.2; average data for FF), 91 g (1980 g × 0.046) of oil was absorbed by the FF. This number is slightly lower than the tabulated value of 111 g (Table 27.1, item c: total oil loss), indicating that CH pieces did not pick up oil, and suggesting that the loss of fat by the meat is balanced by the oil uptake by the breading. The process of oil movement and/or exchange needs to be studied. In addition, there is also a need to clarify why two similar breading compositions provided such different oil uptake data for CH pieces.

27.3.3 HEAT TRANSFER Figure 27.5 graphically depicts temperatures during the food frying process and shows that the product internal temperature did not increase beyond 100°C during the water evaporation stage. This also holds true for a point located just below the food surface. In their study, Pannu and Chinnan (Chap. 26, this volume) reported that the center temperature of the FF and CH reached 100°C after 70 and ~320 sec, respectively. Since FF and CH begin to ﬂoat after 200 and 440 sec (Figure 27.4), 200

Temperature (°C)

160

Oil 120 80 Surface Center 40

0 Time (sec)

FIGURE 27.5 Temperature proﬁles normally obtained for deep fat frying.

© 2003 by CRC Press LLC

TABLE 27.3 Data Obtained for the Overall Convective Heat Transfer Coefﬁcient (U) Test

Mass (g)

Number of Pieces

ML (g/sec)

FF-1 FF-2 FF-3

243 341 442

37 52 67

0.36 0.46 0.51

CH-1 CH-2 CH-3

268 361 456

3 4 5

0.13 0.19 0.22

a

∆T (°C)

2

U (W/m °C)

70 102 67 96 51 109 Average of above: 102.3 65 80 66 86 59 87 Average of above: 84.3

Note: ML: moisture loss. ∆T as deﬁned in Equation 27.2 (Frying oil temperature – 100°C).

a

respectively, the time period selected for moisture loss data used to calculate U was deﬁned as 80 to 180 sec for FF and 320 to 420 sec for CH. 2 Results tabulated in Table 27.3 indicate that U is approximately 102 W/m °C 2 for FF and 84 W/m °C for CH. For food frying, U and h should be the same because of the assumption that food is homogenous and h is uniform under transient heating conditions. A distinction is made here because of the controversy that surrounds the means to correctly determine and/or deﬁne h. Further, an examination of the moisture loss curves (Figures 27.2–4) shows that a distinct lag phase occurs prior to the commencement of constant rate dehydration. During this lag period, part of the energy is used for product heating and the other part for water evaporation at the food surface. Since only a very small fraction of energy is required for product heating, an overall 2 h (U) or an apparent h value of 100 W/m °C should satisfy this requirement. Data reported by Dincer (1996) deﬁne the decoupled h value component for 2 heating during food frying as 14 W/m °C. This implies that an overall h of 100 2 W/m °C will provide 14% of the energy (on a declining scale) for product heating and the rest for dehydration and food structural changes. The U values obtained and reported here are similar to the h value obtained by Pannu and Chinnan (1999) and those reported by Sahin et al. (1999). Further, the heat transfer data show that loading conditions did not alter the U value. This indicates that moisture loss rates are not inﬂuenced by loading conditions but are related to the fryer oil temperature.

27.4 CONCLUSION A simple method has been presented to study moisture loss and oil uptake and to quantify the rate of heat transfer during deep fat frying. The results from our pot fryer study show that moisture loss is product dependent and that the rate of moisture loss increases at higher temperatures. Oil uptake is also product dependent. Oil uptake by frozen French fries (par-fries) was approximately 4.6% (wet basis),

© 2003 by CRC Press LLC

but chicken ﬁllets did not appear to have any net oil uptake. Because breading absorbs some frying oil, this suggests that the ﬁllets released a small amount of chicken fat. Our experimental data and procedure show that it is possible to obtain an estimate for the overall heat transfer coefﬁcient with the moisture loss data. U 2 was estimated as 84 and 102 W/m °C for chicken ﬁllets and French fries, respectively. However, moisture loss data show that this value decreases after the product becomes buoyant.

NOMENCLATURE A h m q U ∆T λ

2

Surface area (m ) 2 Convective surface heat transfer coefﬁcient (W/m °C) Mass (g) Energy (W) 2 Overall surface heat transfer coefﬁcient (W/m °C) Temperature differential (°C) Latent heat for evaporation (J/g)

ACKNOWLEDGMENTS The authors thank Glenn D. Farrell (Research Coordinator I) and Vijaya Mantripragada (Lab Technician II) for their assistance. Author Pannu thanks the Biological Systems Engineering Department of Washington State University and Dr. Gustavo V. BarbosaCánovas for time and facilities provided for the preparation of this manuscript.

REFERENCES Baumann, B. and Escher, F., Mass and heat transfer during deep-fat frying of potato slices. I. Rate of drying and oil uptake, Lebensm.-Wiss. Technol., 28, 395–403, 1995. Blumenthal, M.M., A look at the chemistry and physics of deep-fat frying, Food Technol., 45(2), 68–71, 1991. Dincer, I., Modelling for heat and mass transfer parameters in deep-frying of products, Heat Mass Transfer, 32, 109–113, 1996. Farkas, B.E., Singh, R.P., and Rumsey, T.R., Modeling heat and mass transfer in immersion frying. I. Model development, J. Food Eng., 29, 211–226, 1996. Jacobson, G.A., Quality control in deep-fat frying operations, Food Technol., 45(2), 72–74, 1991. Pannu, K.S. and Chinnan, M.S., Heat Transfer Coefﬁcient Associated with Heating/Frying of Food Pieces in Oil, Abstr. (#8–11), Annual Meeting of the Institute of Food Technologists, Chicago, July 23–28, 1999. Pannu, K.S. and Chinnan, M.S., chap. 3.7, this volume. Paul, S. and Mittal, G.S., Dynamics of fat/oil degradation during frying based on physical properties, J. Food Process Eng., 19, 201–221, 1996. Perkins, E.G., Formation of non-volatile decomposition products in heated fats and oils, Food Technol., 21, 125, 1967. Pinthus, E.J. and Saguy, I.S., Initial interfacial tension and oil uptake by deep fat fried foods, J. Food Sci., 59, 804–807, 1994.

© 2003 by CRC Press LLC

Rao, V.N.M. and Delaney, R.A.M., An engineering perspective on deep-fat frying of breaded chicken pieces, Food Technol., 49(4), 138–141, 1995. Saguy, I.S. and Pinthus, E.J., Oil uptake during deep-fat frying: factors and mechanism, Food Technol., 49(4), 142–145, 1995. Saguy, S., Ufheil, G., and Livings, S. Oil uptake in deep-fat frying: review, OCL, 5(1), 30–35, 1998. Sahin, S., Sastry, S.K., and Bayindirli, L., The determination of convective heat transfer coefﬁcient during frying, J. Food Eng., 39, 307–311, 1999. Singh, R.P., Heat and mass transfer in foods during deep-fat frying, Food Technol., 49(4), 134–137, 1995. Ufheil, G. and Escher, F., Dynamics of oil uptake during deep-fat frying of potato slices, Lebensm.-Wiss. Technol., 29, 640–644, 1996.

© 2003 by CRC Press LLC

28

Heat and Mass Transfer during the Frying Process of Donuts J.F. Vélez-Ruiz and M.E. Sosa-Morales

CONTENTS 28.1 Introduction. 28.2 Heat and Mass Transfer Modeling 28.3 Materials and Methods 28.3.1 Donut Preparation 28.3.2 Frying Equipment 28.3.3 Temperature Proﬁles 28.3.4 Frying Experiments 28.3.5 Determination of Moisture and Oil Contents 28.3.6 Evaluation of Transport and Physical Properties 28.3.7 Experimental Design and Data Analysis 28.4 Results and Discussion 28.4.1 Moisture and Oil Contents 28.4.2 Heat Transfer 28.4.3 Mass Transfer 28.4.4 Experimental Correlations 28.5 Conclusions Nomenclature References

28.1 INTRODUCTION Frying is a traditional means of food preparation, and many fried food items have physical and sensory attributes that consumers consider desirable. The frying process produces physicochemical changes and presents engineering challenges due to the applied high temperatures and combined heat and mass transfer mechanisms during this type of cooking. In addition, ﬂour transformation during cooking involves complex phenomena, in which water as an essential ingredient has an important role, since it determines the conformational state of proteins and carbohydrates, affects

© 2003 by CRC Press LLC

© 2003 by CRC Press LLC

the interactions between the formulation constituents, and contributes to dough structuring (Maache-Rezzoug et al., 1998). Some advances have been reached in relation to deep fat frying of foods, covering different aspects such as chemical deterioration of frying oil, inﬂuence of physical properties of vegetable oil on food products, effects of physical and chemical characteristics of foodstuffs on the ﬁnal product, mass and heat transfer during frying, and mathematical modeling of transfer phenomena of foods with deﬁned geometries (Vélez and Xique, 1999). Although some studies on donuts have been reported, data on physical changes and transport phenomena during frying of donuts are scarce. Therefore, the objectives of this chapter are to introduce proposed analytical solutions for heat and mass transfer phenomena and to analyze the effect of three oil temperatures (180, 190, and 200°C) and different residence times on the physical characteristics of donuts and oil through the frying process.

28.2 HEAT AND MASS TRANSFER MODELING During frying, heat and mass transfer take place simultaneously. Heat is transferred to the surface by convection and to the product inside by conduction. Even though most frying processes are conducted at high oil temperatures (150–200ºC), the temperature of the food product is only about 100ºC, at which water changes from liquid to vapor. With the increase of product temperature, other biochemical transformations occur, such as starch gelatinization and protein denaturation, among others. At the same time, the mass transfer phenomenon has been focused on two ﬂuids—oil and water; water in a frying food migrates from the central portion to the outside, replacing the evaporated mass, while fat is initially absorbed and later desorbed (Ateba and Mittal, 1994). Since the pioneering work of Rice and Gamble (1989) on the modeling of moisture loss, several approaches have been proposed. Rice and Gamble (1989) developed a mass transfer model for potato slices during frying, taking Newman’s solution to the differential equation of mass transfer and considering the slice as an inﬁnite slab. They applied Equation (28.1) to calculate apparent diffusion coefﬁcients (Da) of potato slices during the frying process, where C1 was assumed as negligible, and second and subsequent series terms become so small as to be negligible: w − c1 8 = 2 c 0 − c1 π

∞

∑ n=0

 1  2  (2 n + 1)

 (2 n + 1) 2 π 2 D a t   exp −   d 2   4 

(28.1)

Ateba and Mittal (1994) solved the heat and mass transfer equations for deep fat frying of beef meatballs that were used to simulate the frying process. The fat diffusivity, conductivity, and equilibrium fat content were determined from simulation and compared with experimental data from the frying of this meat product. Singh (1995) and Farkas et al. (1996) established four partial differential equations (Equations (28.2–5)) for heat and mass transfer phenomena of the core and crust regions in an inﬁnite slab, based on four distinct stages of the frying process:

© 2003 by CRC Press LLC

1. Heat transfer in core region: k II

∂2 T ∂T ∂T + NβxCpβ = (εβρβCpβ + ε σρσ Cpσ ) 2 ∂x ∂x ∂t

(28.2)

2. Mass transfer in core region: ∂Cβ ∂t

= Dβα

∂ 2 Cβ ∂x 2

(28.3)

3. Heat transfer in crust region: (ε γ ργ Cp γ + ε σρσ Cpσ )

∂T ∂2 T ∂T = k I 2 + Nγ xCp γ ∂t ∂x ∂x

(28.4)

4. Mass transfer in crust region: ∂  ∂Pγ  ρ =0 ∂x  γ ∂x 

(28.5)

To solve Equations (28.2–28.5) using three initial and eight boundary conditions, an implicit ﬁnite difference method was used to convert those partial differential equations into nonlinear algebraic ones. A mainframe computer using the Gauss–Seidel iteration was used to solve the nonlinear equations; initial moisture content, oil temperature, and physical properties were needed to run the simulation. Both computed and measured results were obtained and compared, and very good agreement was obtained. Dincer and Yildiz (1996) utilized a model in which a new parameter (frying proﬁle) was deﬁned by analogy to a cooling proﬁle. They developed the analytical solution for cylindrical shape and applied the solution to the frying process of sausages at 180ºC. The thermal and mass diffusivities for sausage samples were predicted; the comparison between determined and experimental data showed high accuracy. Most of the analytically developed models have practical limitations due to the need for complex calculations; therefore, most of them have been completed with numerical equations and solutions by applying the ﬁnite element method. Rao and Delaney (1995) used a ﬁrst-order approximation for time and a second-order approximation for space derivatives, in which the ﬁnite difference method was conducted using a Fortran program. Equation (28.6) became the computational model, which evaluates the future value (n + 1) of the central node from the present values (n) in all six surrounding nodes: T (i, j, k, n + 1) = {1 − 2m (xd + yd + zd)} · T (i, j, k, n) + m · xd [T (i + 1, j, k, n) + T (i − 1, j, k, n)] + m · yd. [T (i, j + 1, k, n) + T (i, j − 1, k, n)] + m · zd. [T (i, j, k + 1, n) + T (i, j, k − 1, n)]

© 2003 by CRC Press LLC

(28.6)

Alternatively, empirical models, though lacking a theoretical basis, may provide suitable and simpler relationships. For instance, Gamble et al. (1987), Costa and Oliveira (1999), and Vélez-Ruiz et al. (2001) proposed empirical models for water loss and/or oil uptake contents through the frying process of foods such as potato slices, potato tubers, and chicken strips, respectively. The three approaches have advantages and limitations, but they represent useful tools in the interpretation of the frying process. In this work, the phenomena of heat and mass transfer during the frying of donuts was studied.

28.3 MATERIALS AND METHODS 28.3.1 DONUT PREPARATION The dough was prepared using a laboratory mixing apparatus, Kitchen Aid KSM 90 model (St. Joseph, MI). To get the same characteristics in all batches, a precise order for adding the ingredients (wheat ﬂour, water, egg, butter, sugar, salt, and others) was followed. Each batch required a mixing time of 12 to 18 min. After mixing, the dough was removed and extended with a roller to reach a sheet thickness of 1.5 to 2.0 cm with the help of an aluminum platform. The dough was then cut, and donut specimens were formed with a special device. For fermented dough, a rest time of 30 min was allowed at 35ºC. After that, the same methodology for donut preparation was followed.

28.3.2 FRYING EQUIPMENT Immersion frying was carried out on a batch operation basis. A commercial batch fryer (F2 model, Mexican Taurus, Tlaxcala, México) with a stainless steel tank of 5 L capacity was used, in which the oil was heated by electrical resistors at the bottom of the tank.

28.3.3 TEMPERATURE PROFILES A thin thermocouple was speciﬁcally inserted in the ring half of the donut samples, ensuring the position by measurement of the sample dimensions. The temperatures at the geometric center of the sample and bulk oil were measured by means of thermocouples attached to a Digi-Sense data logger (Scanning Thermocouple Thermometer, 92800–00 model, Cole–Parmer Instruments Co., Barrington, IL), with a sampling frequency of 15 sec.

28.3.4 FRYING EXPERIMENTS Sunﬂower oil was used as the cooking medium, utilizing the commercial fryer for processing three to six samples, depending on the experimental conditions. The experiment was initiated once the desired oil temperature was reached, and the oil bath temperature was thermostatically controlled. Samples were taken by periodically removing a sample from the fryer and placing it on absorbent paper until it reached room temperature. Then, the speciﬁc measurements were taken.

© 2003 by CRC Press LLC

28.3.5 DETERMINATION

OF

MOISTURE

AND

OIL CONTENTS

Moisture content was determined following the ofﬁcial method 39.1.02 (AOAC, 1995) by drying in a hot-air oven (HDP 334 model, MAPSA, Monterrey, México); at least four donut samples were used for moisture determination. Oil content was determined (at least in duplicate) using the Goldﬁsch method (3500100 model, Labconco, Co. Kansas City, MO), using 30–40 ml of petroleum ether and an extraction time of six hours.

28.3.6 EVALUATION

OF

TRANSPORT

AND

PHYSICAL PROPERTIES

An overall heat transfer coefﬁcient was obtained from the heat transfer gained by the donut (Equation (28.7)) for some speciﬁc frying periods. The heat transfer was evaluated as the net energy gained by the donut through heating, water heating, and evaporation corresponding to the sensible (mDCpdT + mwCpdT) and latent heat (mW λ), respectively. Therefore, by using a heat transfer surface of the immersed donut, the heat transfer was computed with Equation (28.7): Q = [mD(CpD dT/dt) + mW(CpwdT + λ)] = UAs∆T

(28.7)

A convective heat transfer coefﬁcient was evaluated from the donut temperature proﬁle through the frying process and oil heating by using Equation (28.8): Q = m O Cp O

dT = hA s (Toil − Tdonut ) dt

(28.8)

This differential equation can be solved with initial condition T = T0 for t = 0, as:  T − Toil  hA s = ln t   T0 − Toil  moCpo

(28.9)

Thus, according to Rahman (1995), the values of h may be calculated from the slope of the line by plotting ln [(T − Toil)/(T0 − Toil)] vs. t. Thermal conductivity, volumetric speciﬁc heat, and thermal diffusivity were measured with a Thermolink instrument (Decagon Devices Inc., Pullman, WA) at room temperature. Mass transfer diffusivity was evaluated by solving proposed differential equations (Crank, 1975) for two geometries: a hollow cylinder and a twisted inﬁnite cylinder. The internal radius (a) and external radius (b) were measured for this purpose with a Vernier scale (Mod. Scala, MetroMex, México).

28.3.7 EXPERIMENTAL DESIGN

AND

DATA ANALYSIS

A factorial design with three temperatures (180, 190, and 200ºC) and nine to 13 sampling times was employed. ANOVA was conducted using specialized software. Fitting models were obtained from Microcal Origin 3.0, CA-Cricket Graph III 1.5.2 and/or JMP SAS 3.02 versions.

© 2003 by CRC Press LLC

28.4 RESULTS AND DISCUSSION 28.4.1 MOISTURE

AND

OIL CONTENTS

The values for average moisture content of the donuts and its standard deviation as a function of time at each oil temperature are presented in Figure 28.1 (a = 180°C; b = 190°C; c = 200°C). The oil content of donuts, including total and gained oil, during the frying process is shown in Figure 28.2. The oil content was expressed in two ways: total oil and gained oil (Figure 28.2, above and below, respectively). The latter was obtained as the difference between the total oil content and the dough oil content. The evaporation rate was higher during the ﬁrst 30 sec of frying, becoming fairly constant as the process continued. Moisture transfer during the frying process appears to be similar to a drying proﬁle, with an initial rapid fall period followed by a constant drying stage, with a shorter initial period at higher temperatures. This double mass transfer rate has been commonly observed in deep fat frying products such as potato slices (Gamble et al., 1987), tortilla chips (Moreira et al., 1995), and tapioca chips (Vasanti et al., 1996), and also for bakery products such as biscuits (Turhan and Ozilgen, 1991). Similarly, the oil uptake increased with the frying time and in reverse order to temperature (Figure 28.2, below), exhibiting a rapid increase during the ﬁrst 30–45 sec, which can be attributed to replacement of the evaporated water. In the last part of the curve at all three temperatures, an apparent oil desorption was observed. This increasing trend of oil content and gained oil as a function of frying time agrees with ﬁndings by other authors (Gamble et al., 1987; Ateba and Mittal, 1994; Moreira et al., 1995), but disagrees with ﬁndings on temperature effect on snacks such as amaranth, black gram, and green gram prepared from some cereals and legumes (Annapure et al., 1998). In the ﬁnal stages of the process an apparent desorption was observed at the three studied temperatures; the structure of the food was compacted and did not admit more fat sorption in the puffed space. This effect was also observed by Balasubramanian et al. (1995) for chicken nuggets and by Ateba and Mittal (1994), who reported that the oil desorption was due to capillarity action.

28.4.2 HEAT TRANSFER The heat transfer phenomenon was driven by two physical aspects; the ﬁrst was the sensible energy required to heat the donut from an initial temperature to the boiling point; the second thermal change was the energy needed to evaporate water at the boiling point. The requirements of sensible heat decreased as the frying process developed, and vaporization heat was dependent upon the amount of evaporated water. The temperature history of the solid ring center of the donut and the frying oil are given in Figure 28.3, at the three experimental temperatures (a = 180°C; b = 190°C; c = 200°C). The central ring temperature increased rapidly at the beginning and plateaued at around 90–105°C from 60 to 180 sec, depending on the oil temperature. This proﬁle is basically due to unstable heating of the sample and the water evaporation phenomenon from the surface. Within the experimental conditions studied, a difference between the asymptotic sample temperature and the oil temperature was recorded, in which the central temperature of the samples never reached 93 for

© 2003 by CRC Press LLC

Moisture content (%wb)

38 36 experimental average @180°C

34 32

Fitting (log)

30 28 26 24 22 20 0

15

30

45

60

75

90

105

120

135

150

165

180

Frying time (sec)

(a)

Moisture content (%wb)

38 36

experimental average @190°C Fitting (log)

34 32 30 28 26 24 22 20 0

15

30

45

60

75

90

105

120

135

150

165

180

Frying time (sec)

(b)

Moisture content (%wb)

40 38 36

experimental average @200°C

34

Fitting (log)

32 30 28 26 24 22 20 0

15

30

45

60

75

90

105

120

135

150

165

180

Frying time (sec)

(c)

FIGURE 28.1 Moisture transfer proﬁles of donuts during deep fat frying at three oil temperatures: a) 180°C; b) 190°C; and c) 200°C.

© 2003 by CRC Press LLC

Total content and gained oil (%)

18 16 14 180…C 190…C 200…C 180…C 190…C 200…C

12 10 8 6 4 2 0 0

20

40

60

80

100

120

140

Frying time (sec)

FIGURE 28.2 Oil content proﬁle (total: above; gained: below) of deep fat fried donuts as inﬂuenced by frying temperature and time.

180°C, 96 for 190°C, or 108 for 200°C, respectively. So, the observed asymptotic sample temperature followed a trend with respect to the oil temperature, in contrast to the temperature difference of 87, 94, and 92°C between sample and oil, respectively. Thermal properties of donuts for each oil temperature, measured at different frying times, are summarized in Table 28.1. Basically, the thermal conductivity was constant for donuts (0.0968–0.0978 W/mºC), at the three temperatures and during the entire frying process. The speciﬁc heat varied somewhat with oil temperature and showed a small increase with process time. Thus, from the speciﬁc heat, temperature difference, and evaporated water, the involved energy was evaluated, and the overall heat transfer coefﬁcient was computed (Equations (28.7) and (28.8)); the obtained values are included in Table 28.1. Even though the Biot number is large (>30), the lumped parameter approach (Equation (28.9)) allows evaluation of the convective heat transfer coefﬁcient. The surface heat transfer coefﬁcient changed for each experimental temperature (Table 28.1). As expected, the heat transfer coefﬁcient increased with oil temperature, in agreement with Miller et al. (1994), who reported the corresponding coefﬁcients for canola, 2 corn, palm, and soybean oils from 250 to 276 W/m °C, and with Vijayan and Singh 2 (1997), who employed surface heat transfer coefﬁcients of 300 and 500 W/m °C for simulation of the frying process for frozen foods. Temperature predictions using Equations (28.7–28.9) exhibited error percentages less than 12.5% for 180 and 200°C (Figure 28.3a and 28.3c). On the other hand, for frying of donuts at 190°C, the error for temperature prediction was only 4.3% (Figure 28.3b).

28.4.3 MASS TRANSFER In order to determine the moisture diffusivities for water loss, the moisture content proﬁle was utilized, assuming a diffusional mechanism for mass transfer. Two equations were obtained for diffusion in a cylinder; the corresponding differential

© 2003 by CRC Press LLC

Donut temperature (°C)

200 180 160 140

average temperature fitting oil temperature

120 100 80 60 40 20 0 0

15

30

45

60

75

90

105

120

105

120

Frying time (sec)

(a) 200

Donut temperature (°C)

180 160

average temperature fitting oil temperature

140 120 100 80 60 40 20 0 0

15

30

45

60

75

90

Frying time (sec)

(b)

Donut temperature (°C)

220 200 180 160 140

average temperature fitting oil temperature

120 100 80 60 40 20 0 0

15

30

45

60

75

90

105

120

Frying time (sec)

(c)

FIGURE 28.3 Temperature proﬁles of donuts during deep fat frying at three oil temperatures: a) 180°C; b) 190°C; and c) 200°C.

© 2003 by CRC Press LLC

© 2003 by CRC Press LLC

TABLE 28.1 a,b Transport Properties and Computed Heat Transfer for Donuts during the Frying Process Time (sec)

k (W/mºC)

Cp (kJ/kgºC)

Average Water Loss (kg)

Average ∆T (ºC)

c

2

Q (W)

U (W/m ºC) d

180ºC 15–30 45–75 90–180

0.0978 (0.0005) 0.0975 (0.0001) 0.0974 (0.0001)

2.436 (0.011) 2.714 (0.015) 2.714 (0.015)

0.00121 0.00022 0.00030

151.08 126.67 96.83

255.89 89.19 50.61

h = 158.63 216.31 93.47 75.63

190ºC 15–30 45–75 90–180

2.165 (0.005) 2.539 (0.004) 2.728 (0.006)

0.00135 0.00020 0.00023

146.08 101.03 88.95

310.14 85.15 25.16

h = 269.54 253.62 105.37 35.54

d

0.0972 (0.0002) 0.0968 (0.0001) 0.0972 (0.0001)

d

293.20 122.96 28.46

h = 296.84 222.76 132.99 37.15

200ºC 15–30 45–75 90–180 a

0.0974 (0.0001) 0.0974 (0.0001) 0.0970 (0.0001)

2.331 (0.003) 2.647 (0.003) 2.963 (0.003)

Average of nine samples. Values in parentheses are standard deviations. c Equation (28.7). d Equation (28.9). b

0.00135 0.00027 0.00027

169.64 122.48 95.60

6

2

D (× 10 m /sec)

1.361 (0.398) 0.551 (0.121) 0.295 (0.057) 1.434 (0.410) 0.603 (0.135) 0.326 (0.078) 1.060 (0.237) 0.508 (0.106) 0.282 (0.047)

equations (Equations (28.10) and (28.12)) proposed by Crank (1975) were solved for the ﬁrst series term, and solutions (Equations (28.11) and (28.13)) presented: 1. For a hollow cylinder (where r is a ring point [a ≤ r ≤ b]): J 0 (aα n )U 0 ( rα n ) C − C0 exp − Dα 2n t = 1− π α α C1 − C0 J a + J b ( n ) 0( n ) n =1 0 ∞

∑

(

)

(28.10)

with a = 0.0122 m, b = 0.0385 m, r = 0.02535 m, C0 = initial moisture content, and C1 = C2 = 0. C = C0 (1.204314e −14205.8Dt )

(28.11)

2. For a twisted inﬁnite cylinder: C − C1 2 = 1− C 0 − C1 a

∞

∑ n =1

exp( − Dα 2n t )J 0 ( rα n ) α n J1 (aα n )

(28.12)

with c = 0.0115 m, r = 0.00575 m, and C1 = 0. C = C0 (1 − 1.07511e −42553.9 Dt )

(28.13)

Thus, the diffusion coefﬁcients were evaluated for each sampling time, ranging −7 −6 2 from 1.41 × 10 to 3.86 × 10 m /sec; the corresponding average mass diffusion coefﬁcients, obtained from the hollow cylinder solution, which had a better ﬁt than the twisted inﬁnite cylinder, are included in Table 28.1. Mass diffusion coefﬁcients are not temperature dependent from the statistical viewpoint (α = 0.01); therefore, −6 a D average of 1.285 × 10 was obtained, based on the ﬁrst 30 sec of frying for the three temperatures. D values were higher than those reported for other fried products, such as potato (Rice and Gamble, 1989), tortilla chips (Moreira et al., 1995), sausage (Dincer and Yildiz, 1996), and chicken strips (Vélez-Ruiz et al., 2001), as a consequence of differences in moisture content, product porosity and structure, and product shape, among other variables. Mass diffusion coefﬁcients exhibited a decreasing trend for the three periods at each temperature. As expected, this decreasing trend as a function of frying time indicates a moisture content less available for evaporation and a higher internal resistance due to structural changes of the donut. Moisture content predictions using the solution for the hollow cylinder are better than for the twisted inﬁnite cylinder, with errors less than 10.5% in comparison with the predicted values obtained for the other geometry.

© 2003 by CRC Press LLC

28.4.4 EXPERIMENTAL CORRELATIONS Based on the central temperature, average moisture content, average gained oil, and measured thermal properties of donuts, some empirical models were generated for each frying temperature. Of the applied mathematical relationships, one ﬁtted the experimental data very well. The best ﬁtted equations are included in Table 28.2, corresponding to each frying temperature. The aforementioned parameters were ﬁtted by different mathematical relationships. Central temperature was well ﬁtted (r = 0.99) by a linear equation (Equations (28.14–17)), though the frying time was only 120 sec; furthermore, the central temperature proﬁle was described by two linear trends for 190 and 200ºC. For the whole frying process (180 sec), the moisture content was adequately ﬁtted (r ≥ 0.92) by logarithmic relationships (Equations (28.18–20)), whereas the gained oil was ﬁtted (r ≥ 0.92) by quadratic equations (Equations (28.21–23)) at the three oil temperatures. Additionally, the average moisture content and average oil content of donuts (Table 28.2) were correlated to the square of the frying time as proposed by Gamble et al. (1987); as expected, the ﬁtting was better than the log model used. In comparison with the obtained logarithmic equations, for moisture content at 180 and 200ºC and for oil content, the regression values were very good, r = 0.93, 0.96, and 0.95 for 180, 190, and 200ºC, respectively. The relationship between moisture loss and oil absorption of donut samples and the square root of frying time suggests a convective mass transfer controlled exchange. In such an exchange the outer water is rapidly lost, generating a stream of vapor bubbles and producing a dry surface. This external dryness provides a diffusion gradient favoring the moisture transfer from internal cells, and then oil may adhere to the donut and enter free spaces formed as the water escapes. Also, for practical purposes, both moisture and oil contents for donuts were correlated and the corresponding equations are also included in Table 28.2 for each frying temperature; thus, if the moisture content is measured, the oil content may be quickly quantiﬁed by means of these generated equations (Equations (28.30–32)).

28.5 CONCLUSIONS The process of immersion frying of donuts was studied experimentally at three oil temperatures. After investigation of the effects of temperature, moisture, oil, and transport properties, it was concluded that all parameters were inﬂuenced by two variables: oil temperature and frying time. The present study underlines the importance of the interactive effects of the two frying variables on the heat and mass transfer phenomena and the physical properties of donuts through the deep fat frying process. The analytical and empirical approaches were satisfactorily employed to generate the corresponding mathematical relationships of the donut parameters and properties given in this work. Some of the presented data, such as thermal conductivity, diffusion coefﬁcients, and empirical correlations, can be employed in analogue food products in order to predict or design deep fat frying processes and equipment.

© 2003 by CRC Press LLC

© 2003 by CRC Press LLC

TABLE 28.2 Empirical Relationships for Temperature, Moisture, and Gained Oil of Donuts during the Frying Process Parameter

Frying Temperature (°C)

Best Equation 0.505t 1.035t 1.415t 0.155t

0.994 0.988 0.994 0.999

0–120 0–180 0–45 60–120

(28.14) (28.15) (28.16) (28.17)

0.933 0.959 0.918

0–180 0–180 0–180

(28.18) (28.19) (28.20)

0.924 0.949 0.951

0–180 0–180 0–180

(28.21) (28.22) (28.23)

T T T T

Moisture content

180 190 200

W = 36.99 – 5.57 log t W = 37.03 – 5.95 log t W = 39.61 – 7.48 log t

Gained oil

180 190 200

OG = 1.313 + 0.160t – 0.0010t 2 OG = 0.602 + 0.113t – 0.0005t 2 OG = 0.595 + 0.162t – 0.0012t

180 190 200

W = 34.09 – 0.790 t 1/2 W = 34.14 – 0.869 t 1/2 W = 33.27 – 0.833 t

1/2

0.960 0.946 0.962

0–180 0–180 0–180

(28.24) (28.25) (28.26)

180 190 200

O = 9.122 + 0.689 t 1/2 O = 7.519 + 0.650 t 1/2 O = 9.596 + 0.601 t

1/2

0.934 0.958 0.949

0–180 0–180 0–180

(28.27) (28.28) (28.29)

180 190 200

O = 34.26 – 0.726 W O = 28.50 – 0.593 W O = 32.41 – 0.683 W

0.970 0.955 0.948

0–180 0–180 0–180

(28.30) (28.31) (28.32)

W/O relationship

+ + + +

Equation

180 190 200

1/2

22.72 17.77 21.69 80.67

Time Range (sec)

Central temperature

As a function of t

= = = =

r

2

The obtained empirical models for donuts can be applied to make valid and valuable predictions about central temperature, moisture, and oil contents, as well as product dimensions in the different stages of deep fat frying. Good agreement was observed between the proposed model and measured parameters at the three experimental temperatures. According to the results obtained in this investigation, donuts processed in our laboratory could have been fried in 75–120 sec, in reverse relation to the oil temperature. Therefore, we can conclude that it should be possible to produce fried food products of any kind with desired quality attributes by using mainly controlled frying process conditions. However, more research is needed to further elucidate the characteristics of the heat transfer phenomena and the physical property changes incurred during the frying process.

NOMENCLATURE a As b c c0 c1 C C0 C1 C2 Cp CpD CpO CpW d D Da dT/dt e i, j, k I, II h J0 J1 k

Internal radius (m) (Equations (28.10) and (28.11), also in As) 2 2 Heat transfer surface of the immersed donut, As = π(b – a ) + (1/2)(2πeb + 2πea) External radius (m) (Equations (28.10) and (28.11), also in As) Inﬁnite cylinder radius (Equation (28.13)) Initial concentration (%), Surface concentration (%) Water content (kg of water/kg of sample) at any time t (Equations (28.10–28.13)) Initial moisture content (Equations (28.10) and (28.11)) Moisture content at the internal part of the donut (kg of water/kg of sample) (Equations (28.10) and (28.11)) Moisture content at the external part of the donut (kg of water/kg of sample) Speciﬁc heat (J/kgºC) Donut-speciﬁc heat (J/kgºC) Oil speciﬁc heat (J/kgºC) Speciﬁc heat of water (J/kgºC) Slice thickness (m) (Equation (28.1)) 2 Diffusivity or mass diffusion coefﬁcient (m /sec) (Equation (28.1)) 2 Apparent diffusion coefﬁcient (m /sec) Proﬁle temperature Donut thickness in As (m) Direction vectors in the x, y, and z direction, and n is the present time (Equation (28.6)) Crust region and core region (Equations (28.2–28.5)) 2 Convective heat transfer coefﬁcient (W/(m °C)) Bessel function of ﬁrst kind of order zero Bessel function of the ﬁrst kind of ﬁrst order Effective thermal conductivity (W/mºC)

© 2003 by CRC Press LLC

m mD mW mO n N O OG P Q r t T T(i, j, k, n) ∆T U U0 w x xd yd zd σ ε γ φ σ ρ λ

2/3

Modulus proportional to δt/(δxδyδz) (Equation (28.6)) Mass of donut (kg) Mass of evaporated water (kg) Oil mass (kg) Number of series terms 2 Flux of the liquid water (kg/m sec) Oil content (%) Gained oil (%), OG = oil content of donut – initial oil of dough Pressure (Pa) Energy gained by the donut (W) Point in the donut ring (a ≤ r ≤ b), (m) Time (sec), incremental time (Equation (28.6)) Temperature (ºC) Temperature at i, j, and k at time n (Equation (28.6)) temperature difference, ∆T = Toil − Tdonut 2 Overall heat transfer coefﬁcient (W/m °C) (rαn) equal to J0(rαn) Y0(bαn) − J0(bαn) Y0(rαn), and αns are the positive roots of U0(rαn) = 0, Y0 is the Bessel function of second kind of order zero Moisture content (% w.b.) (Equation (28.1)) Transfer direction (m) 2 2/3 Equal to (δy × δz/δx ) 2 2/3 Equal to (δx × δz/δy ) 2 2/3 Equal to (δx × δy/δz ) Liquid water fraction 3 3 Volume fraction (m /m ) Water vapor fraction Oil fraction Solid fraction 3 Density (kg/m ) Vaporization heat of water (2256 J/kg)

REFERENCES Annapure, R.S., Singhal, R.S., and Kulkarni, P.R., Studies on deep-fat fried snacks from some cereals and legumes, J. Sci. Food Agric., 76, 377–382, 1998. A.O.A.C. Ofﬁcial Methods of Analysis, Association of Ofﬁcial Analytical Chemists, Washington, D.C., 1995. Ateba, P. and Mittal, G.S., Modeling the deep-fat frying of beef meatballs, Intl. J. Food Sci. Technol., 29, 429–440, 1994. Balasubramaniam, V.M., Mallikarjunan, P., and Chinnan, M.S., Heat and mass transfer during deep-fat frying of chicken nuggets coated with edible ﬁlm: inﬂuence of initial fat content, Proceedings 4th Conference on Food Engineering Narsimhan, G., Okos, M.R., and Lombardo, S., Eds., AIChE, New York, 103–106, 1995. Costa, R.M. and Oliveira, F.A.R., Modeling the kinetics of water loss during potato frying with a compartmental dynamic model, J. Food Eng., 41, 177–185, 1999. Crank, J., The Mathematics of Diffusion, Oxford University Press, Bristol, 1975, pp. 69–88.

© 2003 by CRC Press LLC

Dincer, I. and Yildiz, M., Modeling of thermal and moisture diffusions in cylindrically shaped sausages during frying, J. Food Eng., 28, 35–43, 1996. Farkas, B.E., Singh, R.P., and Ramsey, T.R., Modeling heat and mass transfer in immersion frying. II. Model solution and veriﬁcation, J. Food Eng., 29, 227–248, 1996. Gamble, M.H., Rice, P., and Selman, J.D., Relationship between oil uptake and moisture loss during frying of potato slices from c.v. record U.K. tubers, Intl. J. Food Sci. Technol., 22, 233–241, 1987. Maache-Rezzoug, Z., Bouvier, J.M., Allaf, K., and Patras, C., Effect of principal ingredients on rheological behaviour of biscuit dough and on quality of biscuits, J. Food Eng., 35, 23–42, 1998. Miller, K.S, Singh, R.P., and Farkas, B.E., Viscosity and heat transfer coefﬁcients for canola, corn, palm, and soybean oil, J. Food Process. Preserv., 18, 461–472, 1994. Moreira, R., Palau, J., and Sun, X., Simultaneous heat and mass transfer during the deep fat frying of tortilla chips, J. Food Process Eng., 18, 307–320, 1995. Rahman, S., Food Properties Handbook, CRC Press Inc., Boca Raton, FL, 1995. Rao, V.N.M. and Delaney, A.M., An engineering perspective on deep-fat frying of breaded chicken pieces, Food Technol., 49(4), 138–141, 1995. Rice, P. and Gamble, M.H., Technical note: modelling moisture loss during potato slice frying, Int. J. Food Sci. Technol., 24, 183–187, 1989. Singh, R.P., Heat and mass transfer in foods during deep-fat frying, Food Technol., 49(4), 134–137, 1995. Turhan, M. and Ozilgen, M., Effect of oven temperature variations upon the drying behaviour of thin biscuits, Acta Aliment., 20(3–4), 197–203, 1991. Vasanti, C.K., Seow, C.C., and Sulebele, G.A., Effects of frying parameters on physical changes of tapioca chips during deep-fat frying, Int. J. Food Sci. Technol., 31, 249–256, 1996. Vélez, J.F. and Xique, J., Review: frying process of foods, Int. J. Technol. Inf. (Chile), 10(2): 127–134, 1999. Vélez-Ruiz, J.F., Vergara-Balderas, F.T., Sosa-Morales, M.E., and Xique-Hernández, J., Effect of temperature on the physical properties of chicken strips during deep-fat frying, Int. J. Food Prop., 5(1), 127–144, 2001. Vijayan, J. and Singh, R.P., Sensitivity to Processing Conditions during frying of frozen foods, in Proceedings 7th International Congress of Engineering Food, part 2, Jowitt, R., Ed., Academic Press, Shefﬁeld, 1997, H49–52.

© 2003 by CRC Press LLC

29

Inﬂuence of Liquid Water Transport on Heat and Mass Transfer during Deep-Fat Frying O. Vitrac, A.-L. Raoult-Wack, and G. Trystram

CONTENTS 29.1 Introduction 29.2 Materials and Methods 29.2.1 Calcium Alginate Gels 29.2.2 Frying Equipment 29.2.3 Temperature Measurements inside the Frying Material 29.2.4 Geometry of the Frying Material 29.2.5 Kinetics of Water Losses 29.2.6 Procedure to Assess Water Losses in Liquid State during Frying 29.3 Results and Discussion 29.3.1 Mass Transfer 29.3.1.1 Kinetic of Water Losses 29.3.1.2 Mass Flow Rate of Water at the Exchange Surface 29.3.2 Temperature Distribution 29.3.2.1 T∞ = 120°C 29.3.2.2 T∞ = 180°C 29.3.3 Assessment of Liquid Water Mobility in Gel Slices 29.4 Conclusion Nomenclature References

29.1 INTRODUCTION Deep-fat frying is one of the most common unit operations used in the preparation of cooked, dried, textured, and formulated foods such as ﬁsh, chicken, and vegetables, especially potatoes. This unit operation may be also used for unconventional applications such as a texturization step for oily materials prior to oil extraction

© 2003 by CRC Press LLC

(Hounhouigan et al., 1997), dehydration of fruits by vacuum frying (Aw et al., 1998), and drying and formulation of wood (Vitrac et al., 1999). This unit operation is carried out by immersing materials with a high water content in hot oil, with the temperature generally ranging between 30 to 80°C above the boiling point of water. As a result, both high temperature and high oil density lead to a high heat transfer rate between the oil and the wet material. Furthermore, steam bubbles escaping from the material surface are gassed, drastically improving heat transfer (Farkas and Hubbard, 2000). Materials subjected to severe surface temperature and heat ﬂuxes undergo various physicochemical and biochemical changes related to internal vaporization of water. Short frying times lead to ﬁnal products with a dried crispy exterior, which contrasts with a soft and rich crumb, such as French fries or doughnuts. Long frying times lead to products made of a continuous dried crust, such as chips or crisps. In both cases, the ﬁnal structure, achieved by water removal, inﬂuences ﬁnal texture (Pinthus et al., 1995, 1998) and oil absorption during the cooling stage (Ufheil and Escher, 1996; Saguy et al., 1997; Moreira et al., 1997). However, the effect of such a structure on heat and mass transfer during frying has not been assessed very much. Until now, it was assumed that the steam ﬂowed through the dried porous crust following a pressure gradient and that the liquid water migrated in the saturated region according to a diffusional (Farkas et al., 1996) or a capillary mechanism (Ni and Datta, 1999). The regions would have been separated by a dehydration front moving toward the center of the material. Such a hypothesis was attractive since it offered a simple distribution of vaporization location inside the frying material and opened the way to a macroscopic modeling of heat and mass transfer during frying (Mittelman et al., 1984). Recent results suggest that the position of the theoretical moving vaporization front, such as in chip making, might not be proportional to the vaporization rate, since no increase in the inner thermal resistance, as well as no decrease in the convective heat ﬂux, were observed in cassava slices with thickness ranging between 1 and 2 mm (Vitrac, 2000; Vitrac et al., 2001). The objective of this work is to test an alternative assumption, according to which liquid water may be transported inside the material (sometimes with high relative velocity) during frying following total pressure and deformation gradients, and not by a diffusion-like mechanism as previously described in the literature. Indeed, during other operations of intense drying, this transport of water is known to occur signiﬁcantly in the following situations: High permeability of the solid matrix to vapor and liquid water High friction losses in the porous material leading to ﬁltration of liquid water towards the outer surface driven by the inner steam overpressure Failures in the solid matrix In order not to induce any pressure release by intrusive measurements, experiments were carried out on formulated thermostable gels (calcium alginate gels) enabling embedding instruments inside the material. Moreover, to widen the investigation scope, two model gel materials with the availability of water for transport were tested.

© 2003 by CRC Press LLC

29.2 MATERIALS AND METHODS 29.2.1 CALCIUM ALGINATE GELS Calcium alginate (type SG 300, SKW System, France) gels without starch, denoted S0, or with potato native starch (23% wet basis), denoted S1, were made in the presence of tetra-sodium-diphosphate as calcium chelatant. Their ﬁnal water contents were, respectively, 73 and 93% w/w (wet basis). Gels were prepared at 55°C, cast in Teﬂon cylindrical molds (80 mm diameter × 5 mm long) including prepositioned thermocouples. After geliﬁcation, the location of the sensors was observed through gels under intense lighting. The gel cylinders were then secured together with their Teﬂon mold to a rigid anchoring apparatus that was used to immerse and hold gels vertically under the oil surface.

29.2.2 FRYING EQUIPMENT A large household deep fat fryer, ﬁlled with 5 kg of palm oil, and supplied with a 1600 W submerged electrical resistance, was used in all tests. The frying temperature was controlled by a numerical proportional-integrated-derived (PID) controller using the average of ﬁve type T thermocouples located at different depths in the oil bath. All the acquisitions (acquisition rate of 5 Hz) and controls were programmed on LabView 5.0 (National Instruments, Austin, TX) and achieved respectively with a high precision temperature data logger (model PC4350 for ISA bus, National Instruments) and a multifunction analog I/O data acquisition card (model ATMIO16E for ISA bus, National Instruments) connected to a thyristor power controller (model TE10A, Eurotherm, France).

29.2.3 TEMPERATURE MEASUREMENTS INSIDE THE FRYING MATERIAL An approximation of the temperature proﬁle inside the frying material was obtained by the temperatures of three K micro-thermocouples (∅ = 0.25 mm) located at various depths in 5 mm gel slices.

29.2.4 GEOMETRY

OF THE

FRYING MATERIAL

An approximation of the geometry of the slice immediately after frying (2 to 4 sec) was obtained by three-dimensional reconstruction (i.e., by creating a three-dimensional photorealistic computer model of the real fried slice). Our technique combines distance measurements and 16-bit digital pictures (resolution 640 × 480) carried out with a 5 × 5 laser grid generator and a digital camera (model QuickCam Pro, Logitech, Fremont, CA), as described in Figure 29.1. The heights of the 25 vertices projected on each slice surface were measured by triangulation according to Equation (29.1) and notations presented in Figure 29.1

© 2003 by CRC Press LLC

FIGURE 29.1 Methodology for three-dimensional reconstruction of slices immediately after frying: (a) experimental device: (b) principle of three-dimensional reconstruction with a reference plane (step 1: reference image, step 2: slice image, step 3: three-dimensional deformation of image 2); (c) orthogonal basis for triangulation; (d) principle of displacement ﬁeld analysis between two images (local and global).

by comparing pictures with and without samples.  d(1115 , ) tan(β + δ ) − tan δ =  β such as : 2 δ 5 25) d( ,  tan cos β 2    α i = arcsin[cos(β + y i δ ) cos(x i δ)]   h i = tan(α i )d( Pi , Q i )( O,x,y ) 

(29.1)

where δ is the angle of the laser cone (here 9.6°) and d is the Euclidian distance operator.

© 2003 by CRC Press LLC

Calibration was carried out on rough and smooth samples with known geometries with 0.1 mm accuracy. The three-dimensional computed models of the initial and fried slice were used to assess the global shrinkage of the slice in volume and in cross section. In particular, it was veriﬁed that additional shrinkage was not observed during the few seconds required to remove the slice from oil and to position it under the laser and camera device.

29.2.5 KINETICS

OF

WATER LOSSES

Water content of gels was obtained after frying and draining on paper towel by drying a 5 g sample for 24 h at 103°C in an air oven. The water content of each slice was expressed in kg of water per kg of nonfat dry solids, noted WS, according to Equation (29.2). WS( t ) = η( t ) ⋅ (t)

W(t) 1 − W0

(29.2)

0

where W and W are the water content on a wet basis, respectively, at time t and (t) t = 0 and η is the apparent frying yield (i.e., the ratio between ﬁnal and initial slice masses) at time t. Kinetics of water losses were smoothed using an inﬁnite sum of exponential decays as follows: n

WS( t ) ≈ WS∞ +

∑

λi ⋅ e

−

t τi

(29.3)

i =1

where WS∞ = water content at thermal equilibrium with oil. Nonlinear parameters (τi ) were adjusted by a direct research method (Nelder and Mead’s simplex), whereas linear parameters (λi) were computed from a Newton least square method. The development order n was deﬁned by the rank of the covariance matrix computed after QR decomposition (generally order 2 or 3 was required). Equation (29.3) was used to compute the ﬂow rate of water at the −2 −1 exchange surface in kg⋅m ⋅s (qm) in both liquid and steam states from Equation (29.4). q (mt) = ρS( t ) ⋅ E ( t ) ⋅

(t) dWS( t ) 1 dWS = ρS0 ⋅ E 0 ⋅ ( t ) ⋅ dt dt αΣ −3

(29.4) (t)

where ρS( t ) = apparent solid density (kg of nonfat solids ⋅m of slice), E = half thickness of the slice, and α (Σt ) = cross-section shrinkage of the slice.

29.2.6 PROCEDURE TO ASSESS WATER LOSSES DURING FRYING

IN

LIQUID STATE

Gel slice cylinders were deep fat fried in a 2 kg sedimentation ﬂask ﬁlled with 1 kg of palm oil previously heated to 180°C, as shown in Figure 29.2. The sample was maintained immersed at the top of the ﬂask while digital pictures (resolution 640 × 480)

© 2003 by CRC Press LLC

FIGURE 29.2 Procedure to visualize liquid release from gel slices (a) during frying, (b) after cooling. (c) Detail of liquid water volume recovered at the bottom of the ﬂask.

of the ﬂask bottom were recorded at 10 Hz using a digital camera (model QuickCam Pro, Logitech, Fremont, CA) with contrasted lighting. After 60 sec of frying, 1 kg of palm oil at room temperature (20°C) was added to reduce the oil temperature below the boiling point. Then, the heavy liquid recovered from the bottom of the ﬂask was removed and centrifuged. The supernatant was eliminated with a pipette, and the remaining volume of water was measured. It was also veriﬁed that liquid did not come from possible steam condensation at the top of the ﬂask.

29.3 RESULTS AND DISCUSSION 29.3.1 MASS TRANSFER 29.3.1.1 Kinetic of Water Losses Figure 29.3 presents the residual content of 5 mm thick cylinders vs. frying time at 120, 150, and 180°C for both formulations, S0 and S1. Each point was achieved from mass balance over an individual slice of gel. As previously described by Baumann and Escher (1995), immersion in hot oil led to an intense drying that was variable

© 2003 by CRC Press LLC

FIGURE 29.3 Kinetics of water losses during deep-fat frying of 5 mm thick gel slices formulated without (S0) and with (S1) starch.

between samples. Dispersion was higher when the water content decreased sharply; this was interpreted as a high sensibility of transfers to initial frying conditions or material behavior. Respective to formulations S0 and S1, this initial high drying rate was followed by shrinkage of about 30 and 20% in the radial direction and of about 25 and 10% in the transverse direction after the vaporization of 50% of initial water content. Further drying did not induce signiﬁcant additional shrinkage regardless of the frying temperature. Hence, the porous solid structure was not apparently deformable. The assessed drying kinetics conﬁrmed trends that have been previously observed on real materials of similar geometry, in particular exponential decay of water content and higher drying rates when the oil temperature is higher. Thus, half of the initial water content was removed during the ﬁrst 3 min of frying at 120°C (oil temperature 20°C above the boiling point of water) for both S0 and S1 gels. For the S1 gel, this time duration was divided by two and three when the difference of temperature between the oil and the boiling point of water increased respectively up to 2.5 (at 150°C) and 4 times (at 180°C).

© 2003 by CRC Press LLC

FIGURE 29.4 Flow rate of water (liquid and steam) at the exchange surface vs. residual water content during frying of 5-mm thick gel slices formulated without (S0) and with (S1) starch.

For the S0 gel, this typical time duration at 120°C was drastically reduced by 6 down to 30 sec for temperatures greater than or equal to 150°C. However, the kinetics of the S0 gel presented other unusual features, such as: 1. Higher drying rates for S0 gel than for S1, whereas the initial water content in S0 gel was 24% higher (m/m wet basis) than in S1 gel 2. Similar drying kinetics of S0 gel when the residual water was above 40% of the initial water content and oil temperature ranged between 150 and 180°C These results suggest that the mechanisms of heat and mass transport responsible for gel dehydration might be different at temperatures above 150°C than at 120°C. Moreover, the intensity of mass transfer would be much higher for the S0 gel than for the S1 gel since the drying time of the S0 gel was shorter, and the initial amount of water reported to solid mass was four times higher. 29.3.1.2 Mass Flow Rate of Water at the Exchange Surface Figure 29.3 shows the mass ﬂow rate of water per unit of area (qm) vs. residual water content computed from discrete water losses (see Figure 29.3) and by taking into account the modiﬁcation of surface exchange area due to the slice shrinkage. The curves conﬁrmed that at the initial state of frying a signiﬁcant amount of water was

© 2003 by CRC Press LLC

vaporized at an almost constant rate for both formulations. However, for similar external conditions and surface area, qm values were more than twice as high for the S0 gel than for the S1 one. For the S1 gel and different external conditions, maximum values were almost in the expected proportion of temperature difference between oil and saturation (T∞ − Tsat). In the S0 gel, the effect of external conditions was less signiﬁcant when the oil temperature was higher. The low curvature of qm vs. WS implies that transfers were controlled by a combination of internal and external conditions and not only by the thickening of the dried region (Derdour et al., 2000). If we assume that only the external conditions prevail when a constant rate is achieved with a surface temperature of about Tsat, the convective heat transfer coefﬁcient is given by: h max = ∆H v

q max m T∞ − Tsat

(29.5) 6

−1

where ∆Hv = latent heat of water vaporization (2.44⋅10 J⋅kg ). Equation (29.5) implies that water losses can be achieved only by internal or 3 −2 −1 superﬁcial vaporization. This has led to maximum values of h over 8.5⋅10 W⋅m ⋅K , 3 −2 −1 increasing with T∞ up to 2.5⋅10 W⋅m ⋅K . For both formulations, such results were quite unexpected, since: • The magnitudes were twice to ten times higher than those generally cited in the literature, with maximum values between 0.4 and 0.8 (Costa et al., 3 −2 −1 1999) and 1.1⋅10 W⋅m ⋅K (Farkas and Hubbard, 2000; Hubbard and Farkas, 1999) when the vaporization rate is maximum. • Both external and internal resistances were signiﬁcantly lower at higher temperature. Thus, the drying behavior of the material during frying might depend not only on external conditions (heat ﬂux, temperature) and the amount of residual water, but also on the ability of liquid water to migrate towards the exchange surface. In particular, it was demonstrated that, in the case of materials with high initial water content, migration of liquid water according a total pressure gradient could be signiﬁcant (Vitrac et al., 2000; Vitrac, 2000; Ni and Datta, 1999). Microscopic observations also showed that the difference in frying material behavior according to oil temperature could also be related to different physicochemical modiﬁcations of the exchange surface, such as transition from rubbery to glassy state resulting from a competition between heating and intense drying.

29.3.2 TEMPERATURE DISTRIBUTION In order to assess heat transfer within slices, the temperature distribution at three different vertical positions was measured during frying for both compositions and for two extreme frying temperatures, 120 and 180°C. The results are given in Figure 29.5 for an initial slice temperature of 25°C.

© 2003 by CRC Press LLC

FIGURE 29.5 Temperature distribution in 5-mm thick gel in function of gel formulation and frying temperature: (a) S0 gel, 120°C; (b) S1 gel, 120°C; (c) S0 gel, 180°C; (d) S1 gel, 180°C.

© 2003 by CRC Press LLC

29.3.2.1 T∞ = 120°C At low temperature (120°C), similar distributions were measured for both compositions. After a rapid increase above the boiling point, the temperature remained approximately constant somewhat above 100°C. The duration of the temperature plateau was longer when the thermocouple probe was deeper in the material. It was assumed to correspond to a temperature of a gel core (or crumb) ﬁlled with free water, the volume of which was decreasing progressively as the vaporization front moved deeper inside the material. When the thermocouple was located behind the drying front, its temperature increased rapidly up to the oil temperature. Note that after the surface temperature reached the boiling point of water at atmospheric pressure inside the material, it increased and seemed to remain between 110 and 115°C for a short time before returning more or less rapidly to the boiling point of water at atmospheric pressure. Such a situation was observed in all conditions and was sometimes followed by an inﬂexion in temperature proﬁle characterized by the center temperature overtaking the intermediate temperature (Figure 29.5a). This outstanding but signiﬁcant phenomenon should be interpreted as reﬂecting transient shifts in liquid–vapor water equilibrium induced by a local increase in total pressure inside the material leading to radial heterogeneity in longitudinal temperature proﬁle. In fact, an overpressure front would start close to the surface and move with the vaporization front towards the center of the material (Perré et al., 1993; Vitrac et al., 2000). The overpressure value would be strongly dependent on values of steam permeability in the crust, the drying rate, and the distance between the evaporation location and the surface. At the beginning of frying, it would not exceed 70 or 80 kPa (corresponding to an increase in boiling temperature of about 15–20°C) and would be maximal at the center of the slices during the rest of frying, with values between 30 and 40 kPa (corresponding to an increase in boiling temperature of about 5–10°C). Inﬂexion in temperature proﬁle or disruptions in variation of temperature with time would be the result of a pressure release caused by the opening of cracks (experimentally observed after frying) at the material surface. Such a mechanism would dramatically affect the spatial distribution of vaporization locations by enhancing moisture migration on the way to the outer surface, in particular close to the cracks. Thus, this transport would prevent the outer surface from a temperature increase (i.e., a signiﬁcant overheating above the boiling point) and induce an apparent cooling effect. 29.3.2.2 T∞ = 180°C At higher temperature (180°C), similar phenomena were reproduced with similar overpressure effects. However, different temperature proﬁles were signiﬁcantly obtained for both formulations. The temperature gradient in S1 gel slices did not exceed 20°C on half thickness (2.5 mm), while it was three times higher in S0 gel slices. Thus, strong differences in S0 gel matrix structure and water content were observed between the outer surface and the center. Two minutes after frying, the outer surface was dry and highly porous,

© 2003 by CRC Press LLC

whereas the crumb was apparently not very different from the initial gel. Such high differences between the temperature proﬁles in S0 and S1 gel slices were unexpected, since the drying rate value at the “almost constant drying rate period” was at least twice as high as in S0 gel than in S1 (Figures 29.3 and 29.4). Indeed, in S1 gel the temperature difference between the outer surface and oil, to which the overall heat transfer rate was proportional, was about 60–70°C, while it was only about 20–25°C in S0 gel slices. Many hypotheses could be put forward: 1. Higher convective heat transfer coefﬁcient in gel with higher water content caused by higher bubbling intensity 2. Steam ﬁlm (of low thermal conductivity) surrounding gel slices that would reduce heat transfer in S1 gel slices and prevent them from superﬁcial overheating 3. A penetration front of oil into the material during frying 4. A strong mechanism of liquid water transport toward/up to the outer surface occurring during frying that would partially uncouple heat and mass transfer The ﬁrst hypothesis assumes that only external heat transfer would control the drying rate and that the inner thermal resistance would be nonsigniﬁcant, and that was not compatible with a high temperature gradient within slices. The second hypothesis does not agree with the experiment, since no slug or ﬁlm steam ﬂow was observed during frying of S1 gel slices; moreover, such ﬂows would be more probable at very high drying rates, such as those determined during frying of S0 gel slices. In the same manner, oil migration into a wet material vs. steam ﬂow and a total pressure gradient was not realistic during frying and in contradiction with the literature. Thus, the last hypothesis was retained by default. However, it brought forth two questions: 1. Why were more noisy data obtained for the outer temperature surface of S0 gel slices (whatever the replication)? 2. Why were possible water losses in the liquid state not followed by temperatures around the boiling point (maximal theoretical temperature of the liquid phase)?

29.3.3 ASSESSMENT

OF

LIQUID WATER MOBILITY

IN

GEL SLICES

Finally, so as to determine if the previously assessed transport of a signiﬁcant amount of liquid water decreased drastically close to the outer surface or was able to cross the porous dried crust, the amount of liquid water ejected directly in hot oil was appraised with a modiﬁed frying device previously described. Figure 29.6 shows the phenomenon observed at the bottom of the ﬂask, twenty-ﬁve centimeters below the location where the S0 gel slice was fried. During the ﬁrst 30 seconds, vapor bubbles ejecting from the gel slice were observed at the top of the ﬂask without noticeable changes at the bottom. At around 30 seconds after immersion in hot oil, falling droplets were observed, initially with large diameter around 2–3 mm but quickly becoming smaller in size and higher in

© 2003 by CRC Press LLC

FIGURE 29.6 Visualization of liquid water ejection during frying at 180°C of a 5-mm thick gel slice formulated without starch (S0).

concentration. No further vaporization of the liquid recovering at the bottom of the ﬂask and denser than oil was noticed (no bubbles were seen rising at the bottom of the ﬂask). After the oil cooled below the boiling point, it was veriﬁed that the liquid was water. After 1 minute of frying, 25 to 30% of the initial water of the slice was recovered at the bottom of the ﬂask. This experiment showed that at least 25% of initial water was removed from the slice without vaporization and energy consumption. Similar phenomena were observed in S1 gel, but during the same time period the mass of liquid ejected without vaporization did not exceed 3 to 8% of the initial mass of water at 180°C. These results showed clearly that liquid water could be transported inside frying material from the core on the way to the outer surface. Such a mechanism enhanced heat and mass transfer during frying (1) by improving the convective heat ﬂux by protecting the temperature at the surface from heating signiﬁcantly over the boiling point, and (2) by allowing dehydration without requiring heat consumption. Two conditions might inﬂuence this transport and therefore the behavior of the frying material: 1. Materials with high permeability to steam (large pores, low tortuosity) would also have a high permeability to liquid water (as S0 gel did) and would then allow high liquid velocity ﬂow within the dried zone 2. Materials that present, during frying, a well-deﬁned and thick porous crust (as the S1 gel did) would develop high-pressure gradients. They would induce a gradual ﬁltration of liquid water in the crust, the porosity and the steam permeability of which would be reduced sharply by normal stresses in the direction of water ﬂow and by the presence of liquid water. respectively. In the ﬁrst case described, the high velocity of liquid water ﬂow relative to the solid matrix would lead to unexpected phenomena such as nonthermal equilibrium among all phases (solid, steam, liquid water) close to the outer surface. Thus, this interpretation would explain why noisy surface temperatures signiﬁcantly above the boiling point were measured at the surface of S0 gel slices fried at 180°C, despite the fact that a large amount of liquid water ﬂowed through the surface. This phenomenon, which was observed during frying of fruits (e.g., apple), as well as water

© 2003 by CRC Press LLC

losses in the liquid state, would be responsible for a rapid heating and darkening of the material surface. Starchy materials such as potato, cassava, or plantain (with chip or French fry geometry) would belong to the second category (i.e., as S1 gels) according to their behavior during frying. According to these results, the limit condition of heat transfer at the exchange surface in the form of Equation (29.5) should be modiﬁed in order to take into account (1) high mass transfer rate at the exchange surface in both vapor and liquid states and (2) possible partial uncoupling between heat and mass transfer at material scale. The general limit condition could be written for equal temperatures among all phases (condition of local thermal equilibrium) and a shrinking material as follows. r r r r [( k eff ∇T) + Γ( q m ) ⋅ ∆H v ⋅ ρl (v l − v S )] ⋅ n = h ( q m ) ⋅ (TΣ − T∞ )

(29.6)

where keff = effective thermal conductivity of the exchange surface, ρ1 = intrinsic r r density of water, v l and v S = averaged velocity of liquid water and solid matrix, r n = normal vector to the exchange surface, and TΣ = averaged surface temperature. In Equation (29.6), Γ( q m ) is a phenomenological adimensioned coefﬁcient that takes a value between 0 and 1 depending on vaporization rate and the structure of the frying material. For dense materials such as starchy products or wood (nonfood application), Γ( q m ) would be close to 1. It would be lower than 1 for water-rich materials such as fruits, vegetables, gels, and sludges (nonfood application). Meat products could be intermediate.

29.4 CONCLUSION Model gels formulated with (S1) and without (S0) starch were used to assess the transport of liquid water within the material during deep fat frying. This transport, not previously described in the literature, was proposed as a possible explanation of some unexpected results concerning the overall drying kinetics or temperature of the studied materials, such as apparent uncoupling between drying rate and heat transfer rate. The mechanism of liquid water transport appeared in zones where water was highly available (i.e., free water saturated zones) and was the consequence of a total pressure gradient created by friction losses in steam ﬂow escaping from the frying material. Thus, the large unsaturated volumes created in alginate gels made possible a migration of liquid water in the crumb and towards the dried crust. In S1 gel slices, this transport led at high temperature to a cooling effect of the outer surface, improving convective heat transfer and minimizing the thermal gradient inside the material. In materials with high porous crust and high liquid water mobility in the crumb, such as S0 gel slices, a signiﬁcant amount of liquid water appears to be pushed outside the material without vaporization. In this last case, no cooling effect was observed, and surface temperature remained at a temperature signiﬁcantly higher than the boiling point. These outstanding phenomena of nonthermal equilibrium would be promoted by intense shrinkage (i.e., strong deformation gradient) and ruptures in crust solid matrix, and underlined the complexity of the physics of frying.

© 2003 by CRC Press LLC

According to these results, previous predictive models of frying unit operation must be modiﬁed in order to be generalized to new materials (e.g., fruits, vegetables, and gels) or new applications (e.g., frying of wood or sludge). A minimal modiﬁcation is proposed by introducing a new and more general heat transfer limit condition for deep frying. From the technological point of view, the results of partial uncoupling between heat and mass transfer require complementary studies in order to: 1. Classify frying behaviors (i.e., levels of uncoupling between materials with different composition and structure) 2. Assess the implication of such uncoupling on frying functionalities (i.e., drying, cooking, creation of structure/texture, formulation, microbial inactivation) for food and nonfood materials and on the ﬁnal product quality (texture, coloration, aroma and vitamin losses, oil uptake, etc.) 3. Possibly improve such a mechanism of uncoupling and thus reduce heat consumption for water removal during frying

NOMENCLATURE E O P Q T W d h k n q t x y z

Half thickness [m] Origin Laser grid vertex on reference plane (Oxy) Laser grid vertex at slice surface Temperature [°C] −1 Water content [kg⋅kg ] Euclidian distance operator −2 −1 Height relative to (Oxy) or convective heat transfer coefﬁcient [Wm ·K ] −1 −1 Heat conductivity [Wm ⋅K ] Normal vector −2 −1 Mass ﬂow rate per unit of area [kg⋅m ⋅sec ] Time (sec) Coordinate along (Ox) Coordinate along (Oy) Coordinate along (Oz)

GREEK SYMBOLS ∆Hv α β δ η λ ρ, ρ τ

−1

Latent heat of vaporization of water [J⋅kg ] 2 −2 OPS or OQS angle [rad] or cross-section shrinkage [m ⋅m ] Laser angle with (Oz) [rad] Angle of laser cone [rad] −1 Frying yield [kg⋅kg ] Amplitude coefﬁcient of continuous in time water content approximation −1 [kg⋅kg ] −3 −3 Intrinsic density [kg⋅m ], apparent density [kg⋅m ] −1 Time constant of continuous in time water content approximation [sec ]

© 2003 by CRC Press LLC

SUBSCRIPTS eff i l m v s Σ ∞

Effective Index of vertices [1–25] or of coefﬁcient Relative to mass ﬂow of liquid water Relative to mass ﬂow of water (liquid and vapor) Relative to mass ﬂow of steam Relative to solid matrix Relative to slice cross-section Relative to oil (far from the slice)

EXPONENTS 0 Initial ∞ Inﬁnite in time

REFERENCES Aw, B., Dornier, M., Dubois, C., Guillaumont, A., Aymard, C., and Reynes, M., Optimisation des conditions de conﬁsage friture de tranches d’ananas par la methodologie des plans d’experiences, Sci. Aliment., 18, 313–322, 1998. Baumann, B. and Escher, F., Mass and heat transfer during deep-fat frying of potato slices. I. Rate of drying and oil uptake, Lebensm.-Wiss. Technol., 28(4), 395–403, 1995. Costa, R.M., Oliveira, F.A.R., Delaney, O., and Gekas, V., Analysis of the heat transfer coefﬁcient during potato frying, J. Food Eng., 39, 293–299, 1999. Derdour, L., Desmorieux, H., and Andrieu, J., A contribution to the characteristic drying curve concept: application to the drying of plaster, Drying Technol., 18(1,2), 237–260, 2000. Farkas, B.E. and Hubbard, L.J., Analysis of convective heat transfer during immersion frying, Drying Technol., 18(6), 1269–1285, 2000. Farkas, B.E., Singh, R.P., and Rumsey, T.R., Modeling heat and mass transfer in immersion frying. I. Model development, J. Food Eng., 29, 211–226, 1996. Hounhouigan, J., Rouzière, A., Noël, J.M., Bricas, N., Marouzé, C., and Raoult-Wack, A.L., Relance de la production d’huile de coco par la technique de séchage friture, Récents Progrès Génie Procédés, 59, 121–130, 1997. Hubbard, L.J. and Farkas, B.E., A method for determining the convective heat transfer coefﬁcient during immersion frying, J. Food Process Eng., 22(3), 201–214, 1999. Mittelman, N., Mizrahi, S., and Berk, Z., Heat and mass transfer in frying, in Engineering and Food, McKenna, B.M., Ed., Elsevier Applied Science, Amsterdam, 1984, pp. 109–116. Moreira, R.G., Sun, X., and Chen, Y., Factors affecting oil uptake in tortilla chips in deepfat frying, J. Food Eng., 31, 485–498, 1997. Ni, H. and Datta, A.K., Moisture, oil and energy transport during deep-fat frying of food materials, Food Bioprod. Process., 77(C3), 194–204, 1999. Perré, P., Moser M., and Martin M., Advances in transport phenomena during convective drying with superheated steam and moist air, Int. J. Heat Mass Transfer, 36(11), 2725–2746, 1993. Pinthus, E.J., Singh, R.P., Saguy, I.S., and Fan, J., Formation of resistant starch during deepfat frying and its role in modifying mechanical properties of fried patties containing corn, rice, wheat, or potato starch and water, J. Food Process. Preserv., 22, 283–301, 1998.

© 2003 by CRC Press LLC

Pinthus, E.J., Weinberg, P., and Saguy, I.S., Oil uptake in deep fat frying as affected by porosity, J. Food Sci., 60(4), 767–769, 1995. Saguy, I.S., Gremaud, E., Gloria, H., and Turesky R.J., Distribution and quantiﬁcation of oil 14 uptake in french fries utilizing radiolabeled C palmitic acid, J. Agric. Food Chem., 45, 4286–4289, 1997. Ufheil, G. and Escher F., Dynamics of oil uptake during deep-fat frying of potato slices, Lebensm.-Wiss. Technol., 29, 640–644, 1996. Vitrac, O., Caractérisation Expérimentale et Modélisation de l’Opération de Friture, thesis, ENSIA, Massy, France, 2000. Vitrac O., Bailleres H., Meot, J.M., and Raoult-Wack, A.L., Procédé et Dispositif pour le Traitement du Bois ou des Matériaux Similaires, French Patent FR99/14672, PCT#FR00/03245, 1999. Vitrac, O., Dufour, D., Trystram, G., and, Raoult-Wack, A.L., Characterization of heat and mass transfer during deep-fat-frying and its consequence on cassava chips quality, 53(2), 161–176, 2002. Vitrac, O., Trystram, G., and Raoult-Wack, A.-L., Deep-fat frying of food: transfer, transformations and reactions inside the frying material, Eur. J. Lipid Sci. Technol., 102, 529–538, 2000.

© 2003 by CRC Press LLC

30

Numerical Simulation of Transient Two-Dimensional Proﬁles of Temperature, Concentration, and Flow of Liquid Food in a Can during Sterilization A.G. Abdul-Ghani, M.M. Farid, and X.D. Chen

CONTENTS 30.1 Introduction 30.2 Computational Fluid Dynamics (CFD) and the Food Industry 30.3 Basic Model Equations and Solution Procedure 30.3.1 Computational Grid 30.3.2 Convection and Temporal Discretization 30.3.3 Computational Model and Governing Equations 30.3.3.1 Energy Balance 30.3.3.2 Momentum Balance in the z Direction 30.3.3.3 Momentum Balance in the r Direction 30.3.3.4 Continuity Equation 30.3.3.5 Mass Balance for Bacteria 30.3.3.6 Mass Balance for Vitamins 30.3.4 Kinetics of Deactivation of Bacteria and Destruction of Vitamin C 30.3.5 Assumptions Made in the Current Numerical Simulation 30.4 Temperature Measurements in the Can during Sterilization 30.5 Results and Discussion 30.5.1 Flow Pattern 30.5.2 Slowest Heating Zone (SHZ) and Temperature Proﬁle 30.5.3 Concentration Proﬁles of Bacteria and Vitamins 30.6 Conclusions

© 2003 by CRC Press LLC

Nomenclature Acknowledgments References

30.1 INTRODUCTION Canning is one of the most effective means of food preservation, and it is used to preserve a large part of our food supply. Despite signiﬁcant advances in food processing operations involving the use of thermal energy, conventional thermal sterilization is still common. Thermal sterilization is the process of heating at a speciﬁed temperature/time to eliminate pathogenic spores from the food product. In the canning industry, this process usually involves the application of steam to heat the food in the can to a given temperature; the can is then held at that temperature for a period sufﬁcient to kill the microorganisms. The sterilization process not only extends the shelf life of the food, but also affects its nutritional and sensory quality. One of the challenges to the food canning industry is to minimize these quality losses, meanwhile providing an adequate process to achieve the desired degree of sterility. The optimization of such a process is possible because of the strong temperature dependence of bacterial spore inactivation as compared to the rate of quality destruction, sensory as well as nutritional (Lund, 1977). For this reason, an estimate of the heat transfer rate is required in order to obtain optimum processing conditions and to improve product quality. Also, a better understanding of the mechanism of the heating process will lead to improved performance in the process, and perhaps to energy savings. Basic principles for determining the performance of different but related processes have been presented by May (1997) and Wilbur (1996). Foods such as canned tuna, thick syrups, purees, and concentrates are usually assumed to be heated by pure conduction. For these foods, the required processing time is generally determined by analytical or numerical solution to the heat conduction equation (Datta et al., 1986). For example, Dincer et al. (1993) studied transient heat transfer during sterilization of canned foods using a conduction equation with constant wall temperature as a boundary condition. Lanoiselle et al. (1986) developed a linear recursive model to represent the heat transfer inside a can during sterilization in a retort and predicted the internal temperature distribution in canned foods during thermal processing. Akterian (1994) developed a numerical model for the determination of the unsteady state temperature ﬁeld in conduction heated canned foods of various shapes and boundary conditions. A number of numerical heat transfer studies have been conducted to model sterilization, taking into account the effect of natural convection. Datta and Teixeira (1987, 1988) predicted transient temperature and velocity proﬁles during natural convection heating of canned liquid foods. They also predicted distinct internal circulation at the bottom of the can and showed that the slowest heating zone is a doughnut-shaped region located near the bottom of the can at about one tenth of the can height. Kumar and Bhattacharya (1991) carried out a simulation of the sterilization of viscous liquid food in a metal can in an upright position and heated

© 2003 by CRC Press LLC

from the side wall (T = 121°C) in a still retort. They also presented a simulation of the same can when its bottom and top surfaces were insulated (Kumar et al., 1990). The results indicated that natural convection tends to push the slowest heating region to the bottom of the can. The simulation of Ghani et al. (1998) showed that the presence of an air gap at the top of a can ﬁlled with a viscous liquid carboxymethyl cellulose (CMC) had no signiﬁcant effect on the rate of heating. This was due to the strong effect of the natural convection current, even though the liquid was highly viscous. Ghani et al. (1998) also studied the effect of the convective boundary caused by steam heating. The results were similar to the constant wall temperature case, due to the high value of the heat transfer coefﬁcient of the condensing steam. This suggests that the assumption of constant wall temperature is appropriate for any general-purpose simulation. In the above simulations the temperature distribution at the end of the heating process in the can was assumed to be an important measure of sterility of food products. However, it is necessary to keep the food under that condition for a speciﬁed period of time to ensure an efﬁcient kill of microorganisms. In reality, the death of microorganisms is expected to begin at an early stage of heating, especially at locations near the wall, where the temperature approaches 121°C very quickly. Hence, it is necessary to solve the partial differential equation governing bacterial concentration, coupled with the equations of continuity, momentum, and energy. Datta (1991) followed this approach to study sterilization of liquid food in a nonagitated cylindrical enclosure heated from all sides and described the computational procedure for obtaining the full range of biochemical changes during processing without explicitly following the liquid elements. This author showed that the lowest sterilization achieved by any portion of the ﬂuid in the system was considerably more than the sterilization level normally calculated by using the temperature of the slowest heating zone (SHZ). In the analysis presented by Datta (1991), the bacteria were assumed to undergo convective motion only (i.e., diffusion was neglected). Ghani et al. (1999b) developed a computational procedure for describing the changes in concentrations of live bacteria and their transient spatial distributions during the sterilization process. In addition to convective transfer, the effect of diffusion of bacteria in liquid food was also studied, and the bacteria were assumed to diffuse in the liquid food following the modiﬁed Brownian diffusion equation. It was found that the motion of bacteria was controlled by convective motion, and that the diffusion effect was negligible. In this work, liquid food was tagged and followed, which is computationally difﬁcult for most ﬂow situations of interest (Datta, 1991). Chemical and biochemical reactions in liquid food during heating are temperature dependent. Such reactions not only destroy microorganisms, but also some valuable nutrients. Because such destruction processes are temperature dependent, the distribution of temperature results in unavoidable spatial distributions of the reaction products. These distributions can be easily quantiﬁed in the case of conductive heating of solid materials. However, the situation becomes complex when the ﬂuid is in motion. In this case, temperature and concentration proﬁles are inﬂuenced strongly by the natural convection in the liquid food (Ghani et al., 1999b). The destruction of vitamins follows a ﬁrst order reaction similar to microbial destruction.

© 2003 by CRC Press LLC

In general, the value of the decimal reduction time (D), the time needed to destroy 90% of the microorganisms or a particle or food component is higher for vitamins than for microorganisms and enzymes. As a result, nutritional proprieties may be better retained by the use of higher temperatures and shorter times during heat processing(Fellows, 1996). This was studied by Ghani et al. (1999c, 2000), in studies in which more detailed mechanisms of heating in ﬂuid motion were considered, and the effects of increasing sterilization temperature on deactivation of bacteria and vitamin C destruction were analyzed.

30.2 COMPUTATIONAL FLUID DYNAMICS (CFD) AND THE FOOD INDUSTRY CFD offers a powerful design and investigative tool to process engineers. Its application would assist in a better understanding of the complex physical mechanisms that govern the thermal, physical, and rheological properties of food materials. CFD has only recently been applied to food processing applications. CFD has seen applications in many different processing industries, including airﬂow in clean rooms, ovens, and chillers; ﬂow of foods in continuous-ﬂow systems; and convection patterns during thermal processing (Scott and Richardson, 1997). The observation of the slowest heating zone is a difﬁcult task and requires knowledge of detailed transient ﬂow patterns and temperature proﬁles, due to the complex nature of heat transfer in natural convection heating. The partial differential equations governing such a system need to be solved in their entirety using numerical techniques. In this work, sterilization of canned liquid food (carrot–orange soup) in a still retort was studied and analyzed using CFD. The results were presented in the form of transient temperature, concentration, and velocity proﬁles. The PHOENICS code used in this work is based on the ﬁnite volume method, as developed by Patankar and Spalding (1972). The key characteristic of this method is the immediate discretization of the integral equation of ﬂow into the physical three-dimensional space, i.e., the computational domain covers the entire can, which is divided into a number of divisions in the three dimensions. The details of this code can be found in the PHOENICS manuals, especially the PHOENICS Input Language (PIL) manual.

30.3 BASIC MODEL EQUATIONS AND SOLUTION PROCEDURE 30.3.1 COMPUTATIONAL GRID The boundary layer at the heated walls and its thickness are important parameters of the numerical convergence of the solution. Temperature and velocities have their largest variations in this region. To adequately resolve this boundary layer ﬂow, i.e., to keep discretization error small, the mesh should be optimized, and a large concentration of grid points is needed in this region. If the boundary layer is not resolved adequately, the underlying physics of the ﬂow will be lost, and the simulation will

© 2003 by CRC Press LLC

be erroneous. On the other hand, in the rest of the domain, where the variations in temperature and velocity are small, the use of a ﬁne mesh will lead to increases in computation time without any signiﬁcant increase in accuracy. Thus, a nonuniform grid system is needed to resolve the physics of the ﬂow properly (Ghani et al., 2000). A nonuniform grid system was used in the simulation with 3500 nodal points: 70 in the axial direction and 50 in the radial direction, graded in both directions with a ﬁner grid near the wall. The computations were performed for a can with a radius of 0.037 m and height of 0.11 m. The can’s outer surface (top, bottom, and side) was heated at a constant temperature (121°C) throughout the heating period. The natural convection heating of carrot–orange soup was simulated for 3000 sec. Ten steps were taken to achieve the ﬁrst 200 sec of heating, another 10 steps to reach 1000 sec, and 30 steps for the total of 3000 sec of heating. This required 4 h of CPU time on the UNIX IBM RS6000 workstations at the University of Auckland. Solutions were obtained using a variety of grid sizes and time steps, and the results show that the solutions are time-step independent and weakly dependent on grid variation.

30.3.2 CONVECTION

AND

TEMPORAL DISCRETIZATION

An important consideration in CFD is the discretization of the convection terms in the ﬁnite volume equations. The accuracy, numerical stability, and boundedness of the solution depend on the numerical scheme used for these terms. The central issue is the speciﬁcation of an appropriate relationship between the convected variables stored at the cell center, and its value at each of the cell faces (Malin and Waterson, 1999). The convection discretization scheme used for all variables in our simulations was the hybrid-differencing scheme (HDS). The HDS of Spalding (1972), used in PHOENICS, switches the discretization of the convective terms between central differencing scheme (CDS) and upwind differencing scheme (UDS), according to the local cell Peclet number. The cell Peclet number Pe (ratio of mass convection to diffusion) for both bacteria and vitamin C within the ﬂow domain in the z direction is: Pe =

u∆z α

(30.1)

where u and ∆z are the typical velocity and cell depth in the z direction. The mass diffusivity α of the bacteria and the vitamins in the ﬂuid is given by the Stockes– Einstein equation: α=

KT 6 πµa

(30.2)

where K is the Boltzman constant, T is the temperature, µ is the apparent viscosity and a is the radius of the particle. The calculated cell Peclet numbers within the 3 4 ﬂow domain in this study were of the order of 10 –10 ; hence the diffusion of bacteria and vitamin C was ignored.

© 2003 by CRC Press LLC

30.3.3 COMPUTATIONAL MODEL

AND

GOVERNING EQUATIONS

Because of the axisymmetry of the cylindrical can used in our simulation, heat transfer was simpliﬁed into a two-dimensional problem. The partial differential equations governing natural convection of the ﬂuid being heated are given below: 30.3.3.1 Energy Balance k  1 ∂  ∂T  ∂2 T  ∂T ∂T ∂T +v +u = r  + ∂t ∂r ∂z ρC p  r ∂r  ∂r  ∂z 2 

(30.3)

In order to simplify the analysis, the buoyancy force caused by density variation with temperature is deﬁned by the Boussinesq approximation shown in Equation (30.4): ρ = ρref [1 − β(T − Tref )]

(30.4)

which is used in the body force term of the momentum equation in the vertical direction: 30.3.3.2 Momentum Balance in the z Direction  1 ∂  ∂u  ∂2 u  ∂u ∂u  ∂p  ∂u ρ + v +u  =− + µ  r  + 2  + ρref g[1 − β(T − Tref )]  ∂t ∂r ∂z  ∂z  r ∂r  ∂r  ∂z 

(30.5)

where β is the thermal expansion coefﬁcient of the liquid and Tref and ρref are the reference temperature and density respectively. The momentum equation in the radial direction is: 30.3.3.3 Momentum Balance in the r Direction 2  ∂ 1 ∂ ∂v ∂v  ∂p  ∂v  ∂ v ρ +v +u  =− + µ  ( rv) + 2   ∂t  ∂z  ∂r ∂z  ∂r  ∂r  r ∂r

(30.6)

The above equations were coupled with the equation of continuity: 30.3.3.4 Continuity Equation 1 ∂ ∂ ( rρv) + (ρu) = 0 r ∂r ∂z

(30.7)

In addition to these equations, the following equations for concentrations of bacteria and vitamins are introduced: 30.3.3.5 Mass Balance for Bacteria ∂C r b ∂t

© 2003 by CRC Press LLC

+v

∂C r b ∂r

+u

∂C r b ∂z

= −k bC r b

(30.8)

30.3.3.6 Mass Balance for Vitamins ∂C r v ∂t

+v

∂C r v ∂r

+u

∂C r v ∂z

= −k vC r v

(30.9)

The relative concentrations of bacteria and vitamin (Crb and Crv) in Equations (30.8) and (30.9) were taken as dimensionless species concentrations, deﬁned as the ratio of real time concentrations (Cb and Cv) to the initial concentrations (Cbo and Cvo) multiplied by 100. The boundary conditions used were: 1. 2. 3. 4.

At At At At

wall r = R, 0 ≤ z ≤ H, T = Tw , u = 0, and v = 0 top surface z = H, 0 ≤ r ≤ R, T = Tw , u = 0, and v = 0 bottom surface z = 0, 0 ≤ r ≤ R, T = Tw , u = 0, and v = 0 center line r = 0, 0 ≤ z ≤ H, ∂T/∂r = 0, ∂u/∂r = 0, and v = 0.

The initial conditions used were: T = Tref = 121°C, Crb = 100, Crv = 100, u = 0, and v = 0. The properties of carrot–orange soup used in the simulation were: ρ = −3 −1 −1 −1 −1 −1 1026 kg m , CP = 3880 Jkg K , k = 0.596 Wm K and β = 0.0002 K , as reported by Rahman (1995) and Hayes (1987). The properties were calculated from the values reported for all food materials used in the soup, using their mass fractions. Most previous numerical studies have been applied to Newtonian foods; in reality, foods are generally non-Newtonian. Due to the extremely high viscosity of the liquid food used in our simulation, the shear rate would be small. Hence, viscosity can be assumed independent of shear rate, and the ﬂuid will behave as a Newtonian ﬂuid. This Newtonian approximation is valid for most liquid food materials such as tomato puree, carrot puree, green bean puree, apple sauce, apricot puree, and banana puree, which are regularly canned and usually preserved by heating (Steffe et al., 1986). In the simulation presented in this study, the viscosity was assumed to be a function of temperature, following a second order polynomial. Nonlinear curve ﬁtting was used to the available measurements to obtain the constants of the polynomial. The magnitude of the Grashof number for the viscous liquid used in our simu−2 lation was in the range of 10 (using maximum temperature difference and maximum viscosity), giving a good indication that natural convection ﬂow is laminar. In our previous publications (Ghani et al., 1999a, 2000), the retort temperature was assumed to rise to 121°C instantly. However, in this work the rise in the retort temperature was measured and used in the simulations.

30.3.4 KINETICS OF DEACTIVATION OF BACTERIA AND DESTRUCTION OF VITAMIN C The rates of deactivation of bacteria and destruction of vitamin C are usually assumed to follow ﬁrst order kinetics (Rueter, 1993). It is known that the reaction rate constants are functions of temperature and are usually described by the Arrhenius equation:

© 2003 by CRC Press LLC

For bacteria:  −E b  k b = A b exp   RT 

(30.10)

 −E v  k v = A v exp   RT 

(30.11)

For vitamins:

In food process engineering, decimal reduction time (D) is commonly used to deﬁne the reaction rates of quality changes. The relationship between the reaction rate constant and the decimal reduction time is (Heldman and Hartel, 1997): kT =

2.303 D

(30.12)

The decimal reduction time and activation energy of the deactivation of bacteria (Clostridium botulinum in this study) and the destruction of vitamin C (ascorbic −1 −1 acid) are 0.2 min, 245 min, 300 kJ· (kg mol) , and 100 kJ· (kg mol) , respectively (Fryer et al., 1997). The reaction rate constants kb and kv for bacteria and vitamin C were calculated using Equation (30.12) with the reported values of decimal reduction times. Equations (30.10) and (30.11) were used to calculate the frequency factors 11 −1 of the Arrhenius equation, Ab and Av, giving values of 2.5 × 10 sec for bacteria 9 −1 and 2.85 × 10 sec for vitamin C (ascorbic acid in this study). The Arrhenius equation, used to describe the kinetics of the biochemical changes, is introduced to the existing software package PHOENICS.

30.3.5 ASSUMPTIONS MADE IN THE CURRENT NUMERICAL SIMULATION To simplify the problem, the following assumptions were made: 1. Heat generation due to viscous dissipation is negligible, due to the use of highly viscous liquid with very low velocities (Mills, 1995). 2. Speciﬁc heat (Cp), thermal conductivity (k), and volume expansion coefﬁcient (β) are constants. 3. The assumption of no-slip condition at the inside wall of the can is valid. 4. The thermal boundary conditions were applied to liquid boundaries rather than the outer boundaries of the can, which is reasonable due to the high thermal conductivity of the metal can. 5. The effects of molecular diffusion of bacteria and vitamin C were neglected due to the strong inﬂuence of the convection current. This last assumption has been veriﬁed in our previous publication (Ghani et al., 1999b).

© 2003 by CRC Press LLC

30.4 TEMPERATURE MEASUREMENTS IN THE CAN DURING STERILIZATION The temperature at the geometric center of a can heated in a retort by condensing steam was measured. A single can ﬁlled with carrot–orange soup was placed in an Easteel Pilot Plant Retort, which operates using steam at 121°C. The measurements were performed for a single can having a radius and height of 0.036 m and 0.106 m, respectively. The can was placed in an upright position and heated for 50 min for complete sterilization. The equipment used for these measurements is as follows: 1. 2. 3. 4. 5.

TSC9601 track sense temperature probe Track sense interface station and RS cable Track sense wireless data logging system by ELLAB E-Val software kit, run on a silicon 486 PC Easteel pilot plant retort

A thermocouple probe with the speciﬁcations mentioned above was placed at the bottom of the can, such that the tip of the thermocouple measured the temperature at the geometric center of the can.

30.5 RESULTS AND DISCUSSION 30.5.1 FLOW PATTERN Figure 30.1 shows the velocity and the ﬂow proﬁles of the carrot–orange soup in a can heated by steam condensing along its outside surface. Both proﬁles show that the liquid adjacent to the wall or the top or bottom surfaces will receive heat from the condensing steam, causing it to expand and thus get lighter. The liquid away from the sidewall stays at a much lower temperature. The buoyancy force created by the change in liquid density due to temperature variation (from the wall to the core) produces an upward ﬂow near the sidewall. The hot liquid rising is deﬂected by the top wall and then travels radially towards the core. Being heavier, the liquid in the core moves downward and then towards the wall. Thus, a recirculating ﬂow is created. Figure 30.1 also shows that the liquid adjacent to the wall is at rest because of the no-slip boundary conditions. The magnitude of the maximum axial velocity at –1 the mid-height near the wall is 0.35 mm sec at t = 20 min. These results are in reasonable agreement with the results of Kumar and Bhattacharya (1991), who used high viscosity liquid and the same heating conditions. The magnitude of the velocity vectors obtained can be explained in terms of the Grashof number, which represents the ratio of the buoyancy force to viscous force. As heating progresses, a more uniform temperature is obtained, reducing the buoyancy force in the liquid and leading to signiﬁcant reduction in the velocity. Hiddink (1975) reported that for viscous ﬂuids the thickness of the ascending liquid region near the wall was greater than that of water, which can be attributed

© 2003 by CRC Press LLC

m/sec

Stagnant zones

FIGURE 30.1 Theoretical predictions of streamline and velocity vector proﬁles of carrot– orange soup in a can heated by condensing steam after 20 min. The right-hand side of each ﬁgure is the center line.

to the large difference in the values of viscosity of the two ﬂuids. The reported thickness is about 12–14 mm for the viscous liquid, as compared to 6–7 mm for water. Kumar and Bhattacharya (1991) illustrated that the thickness of ascending liquid for a more viscous liquid is in the range of 15–16 mm. Figure 30.1 shows that the thickness of ascending viscous liquid (carrot–orange soup) was about 18 mm, the distance between the location of the stagnant region and the wall (measured based upon the actual can dimension). Datta and Teixeira (1987) reported the formation of secondary ﬂow (or eddies formation) at the bottom of the can near the centerline. However, a simulation conducted by Kumar and Bhattacharya (1991) for highly viscous liquid (CMC) did not show any formation of secondary ﬂow or eddies. In our simulation, the secondary ﬂow is evident in all the cases studied, which is expected whenever there is heating from the bottom (see Figure 30.1).

© 2003 by CRC Press LLC

30.5.2 SLOWEST HEATING ZONE (SHZ) AND TEMPERATURE PROFILE The temperature proﬁles for different periods of heating are presented in the form of isotherms in Figure 30.2. The isotherms at t = 1 min are almost identical to those that would be produced by pure conduction heating, but over time the isotherms are seen to be strongly inﬂuenced by convection. Within a short period of heating, the ﬂuid near the bottom is still heated by conduction. However, instability results from the large difference in the temperature between the heated bottom surface and the colder liquid coming in contact with it. This instability in the bottom layer gives rise to bursts of convective cells (i.e., the Benard convection cells). For a light viscous liquid food, such as milk, orange juice, or water, the irregular shape of the isotherms appears at the early stage of heating near the bottom. This is caused by the random nature of Benard convective cell formation (Ghani et al., 1999a). The SHZ in the can (i.e., the location of the lowest temperature at a given time) is not a stationary region in the liquid undergoing convection heating. Its location is not at the geometric center of the can, as it is in the case of conduction heating. Initially, the contents of the can are at uniform temperature. As heating progresses, the mode of heat transfer changes from conduction to convection, and the SHZ moves from the geometric center to the heel of the can as shown in Figure 30.2. The SHZ is pushed toward the bottom of the can, and it appears that the SHZ keeps moving during heating and eventually stays in a region at about 10–15% of the can height from the bottom. Traditionally, the movement of the coldest point has been considered a critical parameter in identifying the SHZ for food products in thermal

(a)

(b)

(c)

FIGURE 30.2 Theoretical predictions of temperature proﬁles (°C) in a can ﬁlled with carrot– orange soup and heated by condensing steam after periods of (a) 1 min; (b) 3 min; (c) 50 min. The right-hand side of each ﬁgure is the center line. Convection is the dominating mechanism of heat transfer inside the can.

© 2003 by CRC Press LLC

process designs. Zechman and Pﬂug (1989) reported a location of the SHZ at about 10% height from the bottom, whereas Datta and Teixeira (1987) found that it migrated to slightly higher locations (15% from the bottom). These observations are in agreement with those found in this work and also with those reported by Kumar and Bhattacharya (1991). Figure 30.2 shows that the SHZ develops a peculiar shape after a short period of heating and does not cover the entire bottom section of the can. The simulation also shows that the secondary ﬂow tends to push the SHZ towards the wall, as may be clearly seen in Figure 30.2. According to this ﬁnding, careful consideration must be made in representing the coldest point by the measured temperature at the axis of the can, particularly at extreme locations close to the top and bottom, as may be seen in Figure 30.2. The temperature of the SHZ in the carrot–orange soup reached about 100°C in 33 min, in comparison to 2–3 min for water, which was predicted in our previous simulation (Ghani et al., 1999a). In that simulation, the change of the temperature of the SHZ with heating time based on constant viscosity (measured at the ﬁlm temperature) and the viscosity as function of temperature were presented. When the viscosity is assumed as a function of temperature, a much faster heating rate is observed. This shows the importance of taking into account the variation of viscosity with temperature, which has not been considered in the simulation of water as a liquid food in most previous research. Figure 30.3 shows the result of the simulation for the same can described earlier but based on pure conduction heating. Here it can be seen that the slowest heating zone stays at the geometric center of the can during the entire heating period.

FIGURE 30.3 Theoretical analysis of temperature proﬁles (°C) in a can ﬁlled with carrot– orange soup and heated by conduction only after periods of (a) 1 min; (b) 3 min; (c) 50 min. The right-hand side of each ﬁgure is the center line. Conduction is the only mechanism of heat transfer within the can.

© 2003 by CRC Press LLC

30.5.3 CONCENTRATION PROFILES

OF

BACTERIA

AND

VITAMINS

Figure 30.4 shows the calculated relative bacterial concentration proﬁles in a metal can ﬁlled with carrot–orange soup, heated by steam from all sides, after different periods of heating in a still retort. A higher rate of bacterial deactivation occurs at

FIGURE 30.4 Theoretical predictions of relative bacterial concentration (dimensionless) proﬁles in a can ﬁlled with carrot–orange soup and heated by condensing steam after periods of (a) 3 min; (b) 20 min; (c) 40 min; (d) 50 min. The right-hand side of each ﬁgure is the center line.

© 2003 by CRC Press LLC

the top of the can, where the temperature is higher. However, the bulk of the can remains little affected in regard to bacterial death. It can also be seen that during the early stage of heating, the bacteria are killed only at locations close to the wall of the can, and this is not inﬂuenced by the ﬂow pattern shown in Figure 30.1. After 3 min of heating, the bacterial concentration proﬁle shown in Figure 30.4a seems to be inﬂuenced mainly by the temperature proﬁle (Figure 30.2b). However, the bulk of the can remains little affected with regard to bacterial death. As the heating progressed, the concentration of bacteria dropped to the low practical level, which illustrates what is likely to occur in practice. Figures 30.4b, 30.4c, and 30.4d show the results of the simulation after much longer time periods of 20, 40, and 50 min, respectively. The bacterial concentration proﬁles are very different from those observed at the beginning of heating. Figures 30.4b, 30.4c, and 30.4d show clearly that deactivation of bacteria is inﬂuenced signiﬁcantly by both temperature and ﬂow pattern, unlike that observed in Figure 30.4a. Figure 30.4 also shows that the SHZ and highest bacteria zone (HBZ), which is the location of the highest concentration of bacteria, occur at almost the same region in the can. The position of the HBZ is clearly inﬂuenced by the ﬂow pattern, showing the existence of two stagnant regions. Only after 50 min of heating are most of the bacteria deactivated. It should be noted that this is only true for the highly viscous liquid used in the simulation; a much shorter time would be required for sterilization of liquids of low viscosity such as milk, light orange juice, etc. Figure 30.5 shows the inﬂuence of thermal sterilization on vitamin C in the same can ﬁlled with carrot–orange soup. This ﬁgure concludes the results of the simulation at different heating periods and for a retort temperature of 121°C, showing clearly the effect of ﬂow pattern (Figure 30.1) on vitamin C destruction. The ﬁgure also shows that maximum vitamin C destruction occurs at locations near the wall and especially at the top of the can, which are the locations of highest temperatures. Figures 30.4 and 30.5 show that the concentrations of both bacteria and vitamin C depend not only on the temperature, but also on the ﬂow pattern. These locations of minimum destruction belong to minimum liquid velocity (stagnant zones shown in Figure 30.1) and low temperature zones. The inﬂuence of ﬂow pattern on vitamin C concentrations is even stronger as the location of the high vitamin concentration occurs almost within the stagnant zone. The theoretical predictions of relative bacterial concentrations at the HBZ are shown in Figure 30.6. At the early stage of heating, the HBZ remains at the same initial temperature; hence, Figure 30.6 shows no signiﬁcant reduction in bacteria count. As the heating progresses, the effect of temperature becomes very strong due to its exponential effect on the rate of bacterial deactivation. A minimum process has been established to ensure that the probability of pathogen survival in a food is negligible; this is the 12-D process for low-acid canned foods, which is based on the regulation for low-acid canned food (LACF) established by the Food and Drug Administration in the United States, typical examples of product safety. In this process, the D value for the most thermal resistant pathogenic spores in the product, such as those used in our simulation (Clostridium botulinum), is utilized. The 12-D process suggests that the microbial population will be reduced from some initial population by 12 log cycles, even if the initial population was as high as 1000 spores

© 2003 by CRC Press LLC

FIGURE 30.5 Theoretical predictions of relative concentration proﬁles (dimensionless) of residual vitamin C in a can ﬁlled with carrot–orange soup and heated by condensing steam after periods of: (a) 3 min; (b) 20 min; (c) 40 min; (d) 50 min. The right-hand side of each ﬁgure is the center line.

per unit mass product (Heldman and Hartel, 1997). Figure 30.6 shows that the –10 relative concentration of bacteria dropped from 100% to 1 × 10 % at the HBZ in 50 min, which represents the time required for complete sterilization at 121°C. This 12 means that there is a probability of 1 to 10 of live bacteria remaining, acceptable in the regulation of LACF.

© 2003 by CRC Press LLC

Percentage of bacteria count

100 1 0.01

0.0001 1E-06 1E-08 1E-10

0

10

20

30

40

50

Time (min)

Average relative vitamin C concentration

FIGURE 30.6 Theoretical predictions of relative bacterial concentration at the HBZ vs. time of sterilization. 100

80

60 0

10

20

30

40

50

Time (min)

FIGURE 30.7 Theoretical predictions of average relative concentration of vitamin C vs. time of sterilization.

The relative concentration of bacteria in the SHZ, as shown in Figure 30.4, is a good measure of food sterility. However, in the case of vitamin destruction, it is necessary to calculate the average of relative vitamin concentration in the whole can, which is calculated as the weighted average of the local concentrations as follows: Cave =

2 R2L

L

R

∑ ∑ rC∆zr z=0 r =0

The average percentage destruction of the relative concentration of vitamin C was found to be about 25% at the end of heating period. The inﬂuence of sterilization on the destruction of vitamins B1 (thiamin) and B2 (riboﬂavin) has been well studied by Ghani et al. (1999d). The results showed the strong inﬂuence of sterilization on vitamin B1, which is in good agreement with ﬁndings reported by Fellows (1996) for percentage loss of vitamins in canned and bottled foods. The calculated average vitamin C concentrations are plotted in Figure 30.7. Figures 30.6 and 30.7 show that the rate of deactivation of bacteria is higher than the rate of destruction of vitamin C for the same time of heating, due to the higher decimal reduction times (D) of vitamins than those of microorganisms. This suggests that applying higher sterilization temperatures will reduce sterilization time. However, the use of higher temperatures will also cause more destruction of vitamins. Hence, it is likely that the best sterilization temperature may not always be 121°C, depending on the types of food to be sterilized.

© 2003 by CRC Press LLC

120

Temperature (°C)

100 80 60 40 Experimental Theoretical-Convection Theoretical-Conduction

20 0

0

10

20

30

40

50

Time (min)

FIGURE 30.8 Experimental measurements and theoretical predictions of temperature at the geometric center of a can heated in a retort by condensing steam.

Figure 30.8 shows a comparison between the measured temperature at the geometric center of the can and that obtained from computer simulations. Here, it can be seen that the calculated center temperature of the can is higher than that measured experimentally. This is to be expected due to the strong effect of the temperature probe, which tends to reduce the convection current in the can because of its signiﬁcant size. However, Figure 30.6 shows that the measured temperature lies between the predicted temperatures based on convection and conduction, suggesting that the presence of the thermocouple probe reduced the convection in the can. Based on this ﬁnding, we believe that measurements usually carried out in industry with such a probe lead to longer sterilization time than necessary.

30.6 CONCLUSIONS Transient temperature, velocity distribution, bacterial deactivation, and vitamin C destruction evolving during natural convection heating of a viscous liquid (carrot– orange soup) in a cylindrical metal can have been theoretically simulated. A computational ﬂuid dynamics software package (PHOENICS) was used for this purpose. The governing equations for continuity, momentum, and energy conservation were solved, together with those for bacteria and vitamin C concentrations. The Arrhenius equation was used to describe the temperature dependency of the rates of deactivation of bacteria and destruction of vitamin C. The results of the simulation show a recirculating ﬂow inside the can consisting of liquid rising near the wall, radial ﬂow, and uniform core ﬂow downwards near the axis. The liquid inside the container showed an increase in temperature towards the top. The SHZ (i.e., the location of the slowest heating zone) covered the cross sectional area of the can at the early stages of heating while it migrated towards the bottom of the can. The secondary ﬂow at the bottom of the can pushed the SHZ closer to the wall. The slowest heating zone developed a peculiar shape after a short period of heating. Also, the SHZ kept moving during heating and eventually stayed in a region of about 10–15% of the can height from the bottom.

© 2003 by CRC Press LLC

The simulations illustrate the effect of heating on deactivation of bacteria and vitamin C destruction during thermal sterilization. Live bacteria and residual vitamin C concentrations were found to depend on both temperature and ﬂow pattern. It was also found that the time needed for complete sterilization at 121°C for the carrot–orange soup used in the simulation was about 50 min.

NOMENCLATURE Ab Av a Cb Cv Cbo Cvo Crb Crv CP D Db Dv Eb Ev Gr g K k kb kv L Pe p r ro R t T Tw Tref u v z α β µ

−1

Reaction frequency factor of bacteria, sec −1 Reaction frequency factor of vitamin, sec Radius of the particle, m −3 Concentration of bacteria in food liquid, number of bacteria, m −3 Concentration of the vitamins in food liquid, kg m −3 Initial concentration of bacteria, number of bacteria m −3 Initial concentration of vitamins, kg m Relative bacteria concentration (Cb/Cbo) Relative vitamin concentration (Cv/Cvo) −1 −1 Speciﬁc heat of liquid food, J kg K Decimal reduction time, min 2 −1 Diffusion coefﬁcient of bacteria, m sec 2 −1 Diffusion coefﬁcient of vitamins, m sec −1 Activation energy of bacteria deactivation, kJ (kg mol) −1 Activation energy of vitamins destruction, kJ (kg mol) gβ∆TL3ρ2 Grashof number, G r = µ2 −2 Acceleration due to gravity, m sec Boltzman constant −1 −1 Thermal conductivity, W m K −1 Reaction rate constant of bacterial deactivation, sec −1 Reaction rate constant of vitamin destruction, sec Height of the can, m u∆z Peclet number, Pe = α Pressure, Pa Radial position from center line, m Radius of the can, m −1 −1 Gas constant, kJ (kg mol) K Heating time, sec Temperature, °C Wall temperature, °C Reference temperature, °C −1 Velocity in vertical direction, m sec −1 Velocity in radial direction, m sec Distance in vertical direction from the bottom, m 2 −1 Mass diffusivity of bacteria or vitamin C, m sec −1 Thermal expansion coefﬁcient, K Apparent viscosity, Pa.sec

© 2003 by CRC Press LLC

−3

ρ Density, kg m −3 ρref Reference density, kg m

ACKNOWLEDGMENTS The authors thank Collin Watson, process and development manager at Heinz Watties Australasia, for allowing the experimental work to be done at the company site located in Hastings, New Zealand. The authors also acknowledge Associate Professor Peter J. Richards of the mechanical engineering department for his valuable discussions.

REFERENCES Akterian, S.G., Numerical simulation of unsteady heat conduction in arbitrary shaped canned foods during sterilization processes, J. Food Eng., 21, 343–354, 1994. Datta, A.K., Mathematical modeling of biochemical changes during processing of liquid foods and solutions, Biotechnol. Prog., 7, 397–402, 1991. Datta, A.K. and Teixeira, A.A., Numerical modeling of natural convection heating in canned liquid foods, Transactions of the American Society of Agricultural Engineers, No. 86–6516, St. Joseph, MI, 1987. Datta, A.K. and Teixeira, A.A., Numerically predicted transient temperature and velocity proﬁles during natural convection heating of canned liquid foods, J. Food Sci., 53(1), 191–195, 1988. Datta, A.K., Teixeira, A.A., and Manson, J.E., Computer based retort control logic for online correction process derivative, J. Food Sci., 51(2), 480–483, 1986. Dincer, I., Varlik, C., and Gun, H., Heat transfer rate variation in a canned food during sterilization, Int. Comm. Heat Mass Transfer, 20, 301–309, 1993. Fellows, P.J., Food Processing Technology: Principles and Practice, Woodhead Publishing, Cambridge, U.K., 1996. Fryer, P.J., Pyle, D.L., and Rielly, C.D., Chemical Engineering for the Food Industry, Blackie, Glasgow, 1997. Ghani, A.G., Mohammed, M.F., and Chen, X.D., A CFD Simulation of the Coldest Point During Sterilization of Canned Food, The 26th Australian Chemical Engineering Conference, Port Douglas, Queensland, No. 358, September 28–30, 1998. Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P., Numerical simulation of natural convection heating of canned food by computational ﬂuid dynamics, J. Food Eng., 41(1), 55–64, 1999a. Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P., An investigation of deactivation of bacteria in canned liquid food during sterilization using computational ﬂuid dynamics (CFD), J. Food Eng., 42(2), 207–214, 1999b. Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P., Heat Transfer and Biochemical Changes in Liquid Food during Sterilization Using Computational Fluid Dynamics (CFD), The Australian Chemical Engineering Conference, September 26–29, 1999, New Castle, 1999c. Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P., Numerical Simulation of Biochemical Changes of Canned Food during Sterilization of Viscous Liquid Using Computational Fluid Dynamics, Tenth World Congress of Science & Technology, October 3–8, 1999, Sydney, Australia, 1999d.

© 2003 by CRC Press LLC

Ghani, A.G., Farid, M.M., Chen, X.D., and Richards, P., A CFD study on the effect of sterilization temperature on bacteria deactivation and vitamin destruction, J. Process Eng., 215 Part E, 9–17, 2000. Hayes, G.D., Food Engineering Data Handbook, John Wiley and Sons Inc., New York, 1987. Heldman, D.R. and Hartel, R.W., Principles of Food Processing, Chapman and Hall, New York, 1997. Hiddink, J., Natural Convection Heating of Liquids, with Reference to Sterilization of Canned Food, Agricultural Research Report No. 839, Center for Agricultural Publishing and Documentation, Wageningen, The Netherlands, 1975. Kumar, A. and Bhattacharya, M., Transient temperature and velocity proﬁles in a canned nonNewtonian liquid food during sterilization in a still-cook retort, Int. J. Heat Mass Transfer, 34(4/5), 1083–1096, 1991. Kumar, A., Bhattacharya, M., and Blaylock, J., Numerical simulation of natural convection heating of canned thick viscous liquid food products, J. Food Sci., 55(5), 1403–1411, 1990. Lanoiselle, J.L., Candau, Y., and Debray, E., Predicting internal temperature of canned food during thermal processing using a linear recursive model, J. Food Sci., 60(3), 715–719, 1986. Lund, D.B., Maximising nutrient retention, J. Food Technol., 31(2), 71–80, 1977. Malin, M.R. and Waterson, N.P., Schemes for convection discretization on PHOENICS, PHOENICS J., 12(2), 173–201, 1999. May, N., Guidelines No. 13, 16, and 17. The Campden & Chorleywood Food Research Association, Campden, U.K., 1997. Mills, A.F., Basic Heat and Mass Transfer, Irwin, Ontario, Canada, 1995. Patankar, S.V. and Spalding, D.B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic ﬂows, Int. J. Heat Mass Transfer, 15(10), 1787–1806, 1972. PHOENICS Reference Manual, Part A: PIL, Concentration Heat and Momentum Limited, TR200A, Bakery House, London, 1991. Rahman, R., Food Properties Handbook, CRC Press, Inc., Boca Raton, FL, 1995. Reuter, H., Aseptic Processing of Foods, Technomic, Lancaster, PA, 1993. Scott, G. and Richardson, P., The application of computational ﬂuid dynamics in the food industry, J. Trends Food Sci. Technol., 8, 119–124, 1997. Spalding, D.B., A novel ﬁnite-difference formulation for differential expressions involving both ﬁrst and second derivatives, Int. J. Numerical Meth. Eng., 4, 551, 1972. Steffe, J.F, Mohamed, I.O., and Ford, E.W., Rheological properties of ﬂuid foods: data compilation, in Physical and Chemical Properties of Foods, Okos, M.R., Ed., Transaction of American Society of Agricultural Engineers, St. Joseph, MI, 1986. Wilbur, A., Unit operation for the food industries, in Food Processing and Technology, Ohio State University, Columbus, 1996, pp. 125–136. Zechman, L.G. and Pﬂug, I.J., Location of the slowest heating zone for natural convection heating ﬂuids in metal containers, J. Food Sci., 54(1), 205–209, 1989.

© 2003 by CRC Press LLC

31

Heating Behavior of Canned Liquid/Particle Mixtures during End-over-End Agitation Processing S.S. Sablani, H.S. Ramaswamy, and H. Krishnamurthy

CONTENTS 31.1 Introduction 31.2 Theoretical Development 31.2.1 Transient Conduction Heat Transfer 31.2.2 Transient Convection Heat Transfer 31.2.3 Convective Heat Transfer Coefﬁcients 31.3 Materials and Methods 31.4 Data Analysis 31.5 Results and Discussion 31.5.1 Temperature Proﬁles 31.5.2 Heating Behavior of Newtonian Liquid/Particle Mixtures 31.5.3 Heating Behavior of Non-Newtonian Liquid/Particle Mixtures 31.6 Conclusions Nomenclature References

31.1 INTRODUCTION Mechanical agitation of cans in rotary retorts enhances heat transfer rates to liquid particle mixtures that might otherwise heat at much slower rates (conduction to mild convection). Agitation processing not only has the potential to improve quality retention, but also to reduce energy consumption during processing. Semisolid and viscous foods such as sauces and soups containing meat or vegetables are mostly

© 2003 by CRC Press LLC

processed in rotational retorts. Thermal sterilization of such products requires that the center of the target particle receive a predetermined minimum heat process. Heat transfer in such systems has been analyzed using heat penetration parameters (heating rate index, fh, and heating lag factor, jch) and convective heat transfer coefﬁcients (overall heat transfer coefﬁcient, U, and ﬂuid-to-particle heat transfer coefﬁcient, hfp). Early studies focused only on convective heat transfer rates to canned liquids (Berry et al., 1979; Berry and Bradshaw, 1980, 1982; Berry and Dickerson, 1981). These were product-speciﬁc studies on the inﬂuence of agitation on heat transfer rates. Some later studies evaluated heat transfer coefﬁcients for liquid–particle mixtures in cans subjected to axial and end-over-end agitation (Lenz and Lund, 1978; Anantheswaran and Rao, 1985; Deniston et al., 1987; Fernandez et al., 1988; Rao and Anantheswaran, 1988; Stoforos and Merson, 1991, 1992). These studies mostly used a rigid thermocouple to measure the liquid and particle temperatures, and the motion of test particles was restricted. Naveh and Kopelman (1980) studied the effect of orientation of agitation on the overall heat transfer coefﬁcient and found that U was improved by a factor of two to three in end-over-end rotation compared with an axial mode of rotation. Parchomchuk (1977) proposed a new method of circular oscillation for agitation processing of canned food and reported that the agitating forces produced were similar to those caused by end-over-end rotation. The heat transfer rates to canned liquids when using a smaller radius of rotation during circular oscillation were reported to be comparable to those obtained during end-over-end agitation. More recently, several studies were conducted on heat transfer to liquid–particle mixtures in cans undergoing end-over-end processing at the McGill University (Sablani and Ramaswamy, 1995, 1996, 1997, 1998, 1999; Ramaswamy and Sablani, 1997a, b; Pandey et al., 1997; Krishnamurthy et al., 2000) using Newtonian as well as non-Newtonian liquids. In these studies, a technique was developed using a ﬁne ﬂexible thermocouple to measure the convective heat transfer coefﬁcients associated with end-over-end rotational processing of canned particulate liquids. The technique allowed sufﬁcient particle motion during processing and provided more realistic transient temperatures for estimation of heat transfer rates. The ﬂexible thermocouple approach was used to quantify the inﬂuence of various system- and product-related parameters on convective heat transfer coefﬁcients and heat penetration parameters. For designing a sterilization process, heat penetration parameters such as heating rate index, fh, and the lag factors, jch and jcc, are frequently used. Few studies have been carried out on the effect of system and product parameters on the heat transfer rates to liquid–particle mixtures in cans. Several factors inﬂuence the heat penetration rate into the food particles in a container during rotational sterilization. The most relevant factors include retort temperature, rotational speed, mode of rotation, radius of rotation, can head space, and product viscosity, as well as the Newtonian/nonNewtonian nature, liquid to particle ratio, particle size, particle shape, etc. (Sablani, 1996). The objective of this chapter is to provide an overview of the inﬂuence of systemand product-related parameters on the heating behavior of canned particulate Newtonian/non-Newtonian liquids during end-over-end agitation rotation processing.

© 2003 by CRC Press LLC

31.2 THEORETICAL DEVELOPMENT In thermal processing of a canned particulate food system, heat is ﬁrst transferred from the heating medium in the retort to liquid inside the can (involving an overall heat transfer coefﬁcient, U) and then from the can liquid to the particles (involving the ﬂuid-to-particle heat transfer coefﬁcient, hfp). Hence, the particle center is the slowest heating/cooling point in the system. In order to establish thermal process schedules for canned liquid/particle mixtures, information on the temperature history at the particle center is needed, in addition to thermal resistance characteristics of the test microorganisms (z and Fo).

31.2.1 TRANSIENT CONDUCTION HEAT TRANSFER The transient heat ﬂow in a spherical particle immersed in ﬂuid of constant temperature can be described by the following partial differential equations: ∂ 2 T 2 ∂T 1 ∂T + = ∂r 2 r ∂r α ∂t

(31.1)

where r represents the radius of the sphere. The solution for the spacial temperature in the form of an inﬁnite summation series is given by: U=

T − Tr 2 Bi = Ti − Tr r / a

∞

∑ n =1

(δ 2n + (Bi − 1) 2 sin(δ n ) sin(δ n r / a ). exp( −δ 2n Fo) δ 2n (δ 2n + Bi(Bi − 1))

(31.2)

where δn is the nth positive root of δ cot δ = 1 − Bi

(31.3)

For sufﬁciently long heating time (Fo > 0.2), the terms in the inﬁnite summation series in Equation (31.2) converge rapidly, and in most cases may be accurately approximated by the ﬁrst term of the series. Furthermore, at the center of a sphere, r = 0, imposing these conditions, Equation (31.2) can be simpliﬁed for center temperatures in a sphere as: U o = R exp( −SFo)

(31.4)

where R and S are the characteristic functions of the Biot number, as given below: R=

2 Bi[δ12 + (Bi − 1) 2 ]sin δ1 [δ12 + Bi(Bi − 1)]δ1 S = δ12

© 2003 by CRC Press LLC

(31.5)

(31.6)

The concept of heating/cooling rate index (fh/fc) and lag factor (jch/jcc) parameters to characterize the temperature history in a food has been well recognized. The heat penetration parameters are obtained from a plot of the logarithm of the temperature difference between the retort (Tr) and the product (T) [i.e., log (Tr − T)] vs. heating time (on linear abscissa)]. The heating rate index, fh, is obtained as the time taken for the straight-line portion of the curve to pass through one log cycle, and jch is obtained as the ratio of (Tr − Tpih) and (Tr − Ti). The experimental time–temperature data obtained at the particle center can be used to make process calculation using the General and Improved General methods. On the other hand, formula methods such as the Ball and Stumbo methods make use of heat penetration data (fh, jch, jcc) in order to establish process calculation. The dimensionless center temperature can be correlated with heat penetration parameters as: T − Tr = j 10 − t / fh Ti − Tr

(31.7)

For a spherical food particle being heated by a medium under conditions of ﬁnite surface and internal resistance, the following can be obtained from Equations (31.3–31.7): fh =

2.303 Sα

jch = R

(31.8) (31.9)

For a given surface heat transfer coefﬁcient/Biot number, the δ can be obtained from Equation (31.3). The constants R and S can be calculated from Equations (31.5) and (31.6). Once R and S are known, the heat penetration parameters can be estimated through Equations (31.8) and (31.9). Details of the equations related to the other geometries can be found in Ball and Olson (1957) and Ramaswamy et al. (1982).

31.2.2 TRANSIENT CONVECTION HEAT TRANSFER In transient convection heat transfer in canned ﬂuid, the temperature at all locations changes with time. The rate of heat transfer from the heating medium to the can ﬂuid will depend on the thickness of the boundary layer between the can ﬂuid and the wall. This heat transfer rate is quantiﬁed in terms of overall heat transfer coefﬁcient. The equation that describes the rate of heat ﬂow from heating medium to the can ﬂuid is: dQ = UA(Tl − T) dt

© 2003 by CRC Press LLC

(31.10)

where U is the overall heat transfer coefﬁcient. In the heating of ﬂuid in the can, the change in the quantity of heat in the ﬂuid per unit of time is a function of the mass of the ﬂuid, m, and the speciﬁc heat, Cpf, and mean temperature: dQ dT = mC pf dt dt

(31.11)

By solving Equations (31.10) and (31.11), and separating the variable and integrating over temperature and time, the Equation (31.12) is obtained: T − Tr = exp( − UAt / 2.303mC pf ) Ti − Tr

(31.12)

By comparing Equation (31.12) with Equation (31.7), the following can be obtained: fh =

2.303mC pf UA jch = 1.0

(31.13) (31.14)

The particle center temperature can also be obtained by knowing the overall convective heat transfer coefﬁcients. In the case of ﬂuid particle mixtures in the can, the heat transfer can be analyzed by the overall heat transfer coefﬁcient, U, and the ﬂuid-to-particle heat transfer coefﬁcient, hfp.

31.2.3 CONVECTIVE HEAT TRANSFER COEFFICIENTS In this approach, the overall energy balance on the canned liquid/particle system can be used: UA c (Tr − Tl ) = m l C pl

d < Tp > dTl + m p C pp dt dt

(31.15)

The following are assumed for deriving Equation (31.15): uniform initial and transient temperatures for liquid, constant heat transfer coefﬁcient, constant thermal and physical properties for both liquid and particles, and no energy accumulation in the can wall. The second term on the right side of Equation (31.15) can be described as the heat transferred to particles from the liquid through the particle surface, and Equation (31.15) can be rewritten as: UA c (Tr − Tl ) = m l C pl

dTl + h fp A p ( Tl − Tps ) dt

(31.16)

It is also assumed that the particle receives heat only from the liquid and not from the can wall when it impacts, i.e., heat is transferred ﬁrst from the can wall to the liquid and then to the particles. The transient heat ﬂow in a particle immersed

© 2003 by CRC Press LLC

in ﬂuid can be described by the following partial differential equations (Jaluria and Torrance, 1996): ∂T ∂t

(31.17)

t=0

(31.18)

t > 0 at the surface

(31.19)

∇.k∇T = ρC p The initial and boundary conditions are: T = Ti −k

∂T = h fp (T − Tl ) ∂n

where n is the normal at the surface taken positive outward. Using the ﬁnite difference method, the ﬂuid-to-particle heat transfer coefﬁcient, hfp, can be estimated by solving the governing partial differential equations (Equations (31.17–19)) of conduction heat transfer. The inverse heat transfer approach, where surface heat ﬂux is estimated using one or more measured temperature histories inside a heat-conducting body, is used to estimate hfp values. The overall heat transfer coefﬁcient, U, can be determined by integrating Equation (31.16) over the set process time (Ramaswamy and Sablani, 1997a,b). In order to calulate U, it is necessary to have the transient temperatures of the liquid and particle surface. In Equation (31.16), the experimentally measured value of the liquid is used, and the transient temperature of the particle surface is computed from Equations (31.17–19). Once the convective heat transfer coefﬁcients (U and hfp) are known for a range of processing conditions, the equations mentioned above (31.15–31.19) can be used to predict the liquid and particle center temperatures. The predicted time–temperature data can then be used to establish the thermal process schedule. In situations where the associated viscosities of the liquid are high (as in the case of highly viscous Newtonian or non-Newtonian carrier ﬂuids), the liquid portion tends to have only limited convection except at high rotation speeds. The system then moves predominantly towards conduction heating behavior, with characteristically nonuniform temperature distribution throughout the container. Under such a scenario, the concept of U and hfp is difﬁcult to recognize; however, the concept of fh and jch would still be valuable for comparative purposes and for the purpose of establishing thermal processing schedules. Hence, in this chapter, we have compared all conditions of rotational processing involving both Newtonian and non-Newtonian liquids using the fh and jch concept.

31.3 MATERIALS AND METHODS Water and high temperature bath oil (model 100 CST at 38°C, Fisher Scientiﬁc Ltd., Montreal), giving different viscosity levels, were used as Newtonian model liquids. Guar gum, a cross-linked waxy starch with commercial applications in several food preparations (soups, gravies, and pudding) was used to prepare non-Newtonian

© 2003 by CRC Press LLC

test samples containing 0–1% (w/v) gum. The gum solutions were made 12 h before the experiment to allow the gum to hydrolyze. The rheological properties of the prepared solutions were determined with a Haake RV2 concentric cylinder rotation viscometer. 3 Nylon spheres (density = 1128 kg/m , heat capacity = 2073 J/kgK, thermal conductivity = 0.369 W/mK) of different diameters (0.01905, 0.02225, and 0.025 m) were used as particles. Can liquid temperature was measured at the geometric center of the cans using CNS needle type thermocouples. For the purpose of measuring particle transient temperatures, a ﬁne hole was drilled to the center of the spherical particle, which was ﬁlled with a 1:1 mixture of epoxy resin and hardener. A ﬁne wire (0.0762 mm diameter) copper-constantan thermocouple was inserted into the center. The thermocouple-equipped particle was mounted inside the can using brass connectors (stufﬁng box for plastic pouches C-5.2, Ecklund Harrison Technologies, Inc., Cape Coral, FL) at half the height of the can. The thermocouple wire attached to the particle was long enough (half the can height) to allow particle movement inside the can, and short enough to avoid entangling with the needle-type thermocouple used for measuring the liquid temperature. In this type of arrangement, the particle was fairly free to move during processing. The thermocouple-equipped particle was positioned near the geometric center of the can. The other ends of both thermocouples were connected to a 32-circuit slip ring assembly through 24 AWG copper-constantan thermocouple wire (Omega Engineering Corp., Stamford, CT). The thermocouple inputs were recorded at 15-sec time intervals using a data acquisition system and LABTECH NOTEBOOK (Laboratory Technologies Corporation, Wilmington, MA) software or an HP datalogger (HP3497/HP34901, Hewlett Packard, Loveland, CO). Cans of size 307 × 409 (0.0873 m diameter × 0.116 m height) containing the test liquid and multiple particles were subjected to end-over-end rotational processing in a pilot scale rotary, single cage, full water immersion retort (Stock RotomatPR900; Hermann Stock Maschinenfabrick, Germany). A common air over pressure of 70 kPa was used for all test runs with the Rotomat. The cans were arranged in vertical orientation (can axis perpendicular to axis of rotation) to give end-over-end rotation to the cans. In some test runs, as opposed to the end-over-end rotation in a continuous fashion, the cage was rotated for a few rounds in one direction, stopped and rotated in the opposite direction giving an oscillatory mode of operation for the end-over-end agitation. With Newtonian liquids (Sablani, 1996), three experimental designs were selected to study the inﬂuence of different system and product parameters. The experimental variables used were: three particle concentrations (20, 30, and 40% v/v); three rotational speeds (10, 15, and 20 r/min); and two kinematic viscosities −6 −4 2 (1.0 × 10 and 1.0 × 10 m /sec). Three rotational speeds (10, 15, and 20 r/min), −6 −4 2 two kinematic viscosities (1.0 × 10 and 1.0 × 10 m /sec), and three particle diameters (0.01905, 0.02225, 0.025 m) were selected to study the inﬂuence of particle size. A can head space of 0.01 m, a radius of rotation of 0.19 m, and a retort temperature of 120°C were used as ﬁxed parameters. In order to study the inﬂuence of mode of end-over-end agitation, the experimental variables were: three radii of rotation (0, 0.13, and 0.26 m); three speeds of rotation (8, 16, and 24 r/min); and

© 2003 by CRC Press LLC

two modes of rotation (continuous and oscillatory). In this case, the particle diameter of 0.025 m, a high temperature bath oil, a can head space of 0.01 m, and a retort temperature of 120°C were used as ﬁxed parameters. A full factorial experimental design was employed in each of the three studies. Four replicate cans were kept at a given radius of rotation, and each processing condition was repeated twice. With non-Newtonian liquids (Krishnamurthy et al., 2000), nine cans at three radii of rotation (0, 0.1, and 0.19 m, three replicates) were loaded into the cage, and the rest of the space was ﬁlled with dummy cans containing water. Five retort temperatures (110, 115, 120, 125, and 130°C), ﬁve rotational speeds (0, 5, 10, 15, and 20 r/min), ﬁve particle concentrations (10, 15, 20, 25, and 30% v/v), and ﬁve guar gum concentrations (0.00, 0.25, 0.50, 0.75, and 1.00% w/v guar gum) were employed as system (operating) variables. A central composite rotatable design (CCRD) was used for the experiments.

31.4 DATA ANALYSIS Since small variations in initial temperature and heating medium temperature were unavoidable, liquid and particle transient temperatures were normalized to an initial temperature of 20°C and the respective retort temperature (110, 115, 120, 125, or 130°C). Heat penetration parameters (fh and jch) were evaluated from the plots of logarithms of differences in the retort temperature and the temperature of liquid/ particle vs. time. The heating rate index and heating lag parameters for liquid and particle were analyzed using statistical analysis software available on the McGill University (Montreal) computer network. An analysis of variance (ANOVA) procedure was used to evaluate the level of signiﬁcance of system and product parameters and their interactions. Process lethality (Fo) and cook value (Co) were calculated for each processing condition by numerical integration of time–temperature data (z = 10°C and reference temperature 121.1°C for Fo, and z = 33°C and reference temperature 100°C for Co):

∫

Fo = 10 ( T −121.1)/ z dt

∫

C o = 10 ( T −100 )/ 33 dt

(31.20)

When the process lethalities of test runs are not constant, as in the present study, the ratio Co/Fo gives a relative parameter for comparing the degree of cooking at various retort temperatures, with higher ratios indicating more severe cooking conditions (Ramaswamy et al., 1993).

31.5 RESULTS AND DISCUSSION 31.5.1 TEMPERATURE PROFILES Typical linear and semilogarithmic time–temperature proﬁles of the can liquid and particle center are shown in Figure 31.1. The retort come-up times varied from 2 to 4 min and showed logarithmic come-up proﬁles. Initially, heat is transferred from the heating medium to the can liquid through the can wall and then to the particle.

© 2003 by CRC Press LLC

140

2.5

120

2.0

100

1.5

Log (Tr – Tpih) Log (Tr – Tih)

Log(Tr – T)

Temperature (°C)

Liquid

80 60 40

1.0 fh 0.5 0.0

Retort

0

Liquid

20

Particle center jch = (Tr – Tpih)/(Tr – Tih)

5

10

15

-0.5

Particle center -1.0

0 0

10

5

15

20

Time (min)

Time (min)

FIGURE 31.1 Typical time temperature proﬁles of liquid and particle.

In the early part of heating, particle center temperature was lower than the liquid temperature; this is due to convective heat transfer resistance at the particle surface and conductive resistance inside the particle. The liquid temperature was lower than the retort heating medium temperature due to conductive resistance of the can wall and to external and internal convective resistance at the can wall surface. In the latter part of heating, the difference between liquid and particle temperatures generally decreased as these temperatures approached the heating medium temperature.

31.5.2 HEATING BEHAVIOR OF NEWTONIAN LIQUID/PARTICLE MIXTURES Analysis of variance of results with Newtonian liquids showed that all factors under study affected fh for both liquid and particle, except the rotation effect on particle fh (Table 31.1). All factors were found to inﬂuence (p < 0.05) liquid and particle jch except the effects of radius of rotation and mode of rotation on particle j and radius of rotation effect on liquid jch. Of the six factors considered, only viscosity inﬂuenced the liquid Co/Fo (p < 0.005). All factors inﬂuenced particle Co/Fo (p < 0.05), except radius of rotation. Although two-way interaction effects were signiﬁcant in some instances, their overall contribution to the main effects was very small. The effects of different factors considered on the heating rate index of the particle and liquid are shown in Figure 31.2. The fh value of liquid decreases with an increasing rotational speed (17% decrease between 10 and 20 r/min), presumably due to the enhanced mixing resulting in faster heat transfer rates. Increasing rotational speed from 10 to 20 r/min decreased the particle f value by 11%. Moving cans away from the center of the cage to 0.13 or 0.26 m radius of rotation did not inﬂuence (p > 0.05) either liquid or particle fh. From a thermal

© 2003 by CRC Press LLC

TABLE 31.1 Analysis of Variance Results (% Sum of Squares and Signiﬁcance Level) Showing the Inﬂuence of System and Product Parameters on Three Variables Considered (fh, jch, and Co/Fo) while Employing Newtonian Liquids A: Parameters for Liquid Portion Rotational speed (RS) Mode of rotation (MR) Radius of rotation (RR) Viscosity (V) Particle concentration (PC) Particle size (PS) B: Parameters For Particles Rotational speed (RS) Mode of rotation (MR) Radius of rotation (RR) Viscosity (V) Particle concentration (PC) Particle size (PS)

Effect of RS, V, PC fh

Effect of RS, V, PS

Co/Fo

fh

a

1.7 — —

3.2 — —

a

a

87.9 —

a

4.8

a

9.4

a

2.7 — — a 18.7 —

a

13.7

jch a

11.0 — —

87.0 a 2.1

a

5.3 a 29.4

8.7 1.9

—

—

—

1.7 — — a 78.6 a 11.7

1.31 — — a 4.7 a 39.4

2.9 — — a 74.0 b 12.4

3.6 — — a 8.0 —

—

—

—

9.1

2.5 — —

a

a

a

Effect of RS, MR, RR

jch

Co/Fo

fh

1.7 — —

1.0 — —

71.9 a 13.8 a 2.0

13.9 a 37 2.0

— —

— —

— —

—

—

—

a

17 —

13.1 —

a

a

a

3.9

b

5.5 — — a 73.4 —

a

9.5

Co/Fo

jch

a

68.4 a 19.0 0.6 — —

a

30.0 2.0 2.8 — —

a

—

—

a

a

2.4 0 2.6

a

66.0 a 21.0 0.5 — — —

Note: RS, rotational speed; MR, mode of rotation; RR, radius of rotation; V, viscosity of ﬂuid; PC, particle concentration; PS, particle size. a b

p < 0.005. p < 0.05.

processing design point of view, this is a desirable situation. The smaller the inﬂuence of radius of rotation, the higher the uniformity in terms of lethality achieved in cans placed at different locations in the retort for processing. Shifting from the continuous mode of end-over-end rotation to the oscillatory mode increased both liquid and particle fh values by 10%. The fh values of liquid and particle were higher at all the processing conditions when high viscosity ﬂuid oil was used; this could be due to the thicker boundary layer (Sablani and Ramaswamy, 1997a). The temperature of the water reached the heating medium temperature more rapidly, indicating a faster rate of heat transfer. Increasing the level of particle concentration from 20 to 40% increased the average fh value of the particle by 28%, but increased that of the liquid only by 5%. Increasing particle concentration resulted in a packed bed situation, reducing the free movement of particles, thus increasing the fh value for the particle. Particle motion and mixing have an important effect on the associated heat transfer rates

© 2003 by CRC Press LLC

min 14

Rotation Speed

12 10

10 rpm

8

15 rpm

6

20 rpm

4

min 14 12 10

Continuous

8

Oscillatory

6

2

4 2

0

0

Liquid

min 14

Liquid

Particle

Radius of Rotation

12 10

0.0 m 0.13 m

8

0.26 m

6

Liquid

Particle

min Particle Concentration

Particle

min 14

Particle Size

12

20%

0.0190 m

10

30%

0.0225 m

8

0.0250 m

40%

6

Oil

6

0

8

Water

8

0

12 10

Viscosity

12 10

4 2

14

Particle

min 14

4 2 Liquid

Mode of Rotation

6 4

4 2

2

0

0 Liquid

Particle

Liquid

Particle

FIGURE 31.2 Effect of processing conditions on heating rate index (fh, min) with Newtonian liquid and particle mixture in cans.

(Ramaswamy and Sablani, 1997a). The presence of multiple particles is expected to cause secondary agitation, which will inﬂuence the mixing of materials in the cans (Sablani and Ramaswamy, 1998). The small increase in liquid fh indicated that increased particle concentration increased the drag forces exerted by the particle on the liquid.

© 2003 by CRC Press LLC

The fh values of liquid increased by 24% when the particle diameter was increased from 0.01905 to 0.025 m. On the other hand, the particle fh increased 27% as particle size increased from 0.01905 to 0.02225 m, while a further increase in diameter up to 0.025 m decreased the fh by 8%. Lenz and Lund (1978) also observed a decrease in heat transfer rates to liquid and particles (U and hfp) as particle diameter increased from 0.021 to 0.03 m in a 60% aqueous sucrose solution. Deniston et al. (1987), however, did not ﬁnd a straightforward relationship for heat transfer rates (U) associated with canned liquids. In general, factors affecting fh also affected the jch values, except that the mode of rotation did not inﬂuence the particle jch, and neither mode of rotation nor speed of rotation inﬂuenced the particle jch. Particle concentration had the greatest inﬂuence on the liquid and particle jch (Figure 31.3). Increasing particle concentration reduced the free movement and liquid/particle mixing, which delayed the constant heating rate of the product. The Fo value (process lethality) of a process indicates process severity with respect to microbial destruction and is the key in process time establishments. Co (cook value), on the other hand, indicates the cumulative equivalent of cooking minutes at 100°C. The ratio Co/Fo gives a relative measure of the degree of cooking and could be a suitable multiplier in cases where process time is not constant (Ramaswamy et al., 1993). Liquid viscosity had the greatest inﬂuence on liquid Co/Fo (p < 0.005). The liquid ratio Co/Fo was 10% higher for oil than for water. Rotational speed and liquid viscosity effects were more pronounced on particle Co/Fo ratio (Figure 31.4). At any condition, the particle Co/Fo was always higher than the ratio Co/Fo of liquid. This is because in the sterilization of canned liquid–particle mixtures, heat is ﬁrst transferred from the heating medium to the canned liquid through the wall, then to the particles. In such a situation, some overprocessing of the liquid portion is normal. Any attempt to minimize the overprocessing of the canned liquid portion will be desirable. Temperature is supposed to be the most inﬂuential factor on Co/Fo (as will be demonstrated with the non-Newtonian ﬂuids), which is part of the reason for the well-accepted phenomenon that high temperature short time (HTST) techniques provide a quality advantage. The bulk of the above studies, however, were carried out at a constant temperature (120°C), and hence the temperature effect is not illustrated.

31.5.3 HEATING BEHAVIOR OF NON-NEWTONIAN LIQUID/PARTICLE MIXTURES Statistical analysis of results with non-Newtonian liquids (Krishnamurthy et al., 2000) on fh, jch, and Co/Fo during the thermal process are presented in Table 31.2. The results revealed that both guar gum concentration and rotational speed inﬂuenced fh signiﬁcantly (p < 0.05). Further, both gum and particle concentrations inﬂuenced the jch (p < 0.05) of liquid, but only particle concentration was important with respect to particle jch. Of the four factors considered, only retort temperature inﬂuenced Co/Fo (p < 0.005). An interaction between the factors retort temperature and gum

© 2003 by CRC Press LLC

min 2

min Rotation Speed 10 rpm

1.5

2

Mode of Rotation

1.5

Continuous

1

Oscillatory

15 rpm 1

20 rpm

0.5

0.5

0

0 Liquid

Liquid

Particle

Particle

min

min 2

Radius of Rotation 0.0 m

1.5

2

Viscosity 1.5

Water

0.13 m 1

0.26 m

0.5

Oil

1 0.5

0

0

Liquid

min 2

Particle

Liquid

Particle Concentration 20%

1.5

30% 40%

1 0.5

Particle

min 2

Particle Size 0.0190 m

1.5

0.0225 m 1

0.0250 m

0.5

0

0 Liquid

Particle

Liquid

Particle

FIGURE 31.3 Effect of processing conditions on heating lag factor with Newtonian liquid and particle mixture in cans.

concentration in their effect on Co/Fo was also observed (0.005 < p < 0.05), but was of less signiﬁcance compared to the main effects. Radius of rotation did not have any signiﬁcant effect on any of the heat transfer parameters considered. All factors that inﬂuenced the heat penetration parameters (fh and jch) with Newtonian liquids also inﬂuenced liquid and particle fh and jch with different magnitudes.

© 2003 by CRC Press LLC

min

min 10

10

Mode of Rotation

Rotation Speed

8

10 rpm

8 Continuous

6

15 rpm

6

4

20 rpm

4

2

2

0

0

Liquid

Oscillatory

Liquid

Particle

Particle

min 10

min 10 Radius of Rotation 0.0 m

8

0.13 m

6

0.26 m

4

Water

6

Oil

4

2

2

0

0

Liquid

min 10

Liquid

Particle

Particle Concentration 20%

8

6

30%

6

40% 4

4

2

2

0

0 Particle

Particle

min 10

8

Liquid

Viscosity

8

Particle Size 0.0190 m 0.0225 m 0.0250 m

Liquid

Particle

FIGURE 31.4 Effect of processing conditions on Co /Fo with Newtonian liquid and particle mixture in cans.

In general, fh and jch values with non-Newtonian liquids were higher than those obtained with Newtonian liquids, indicating that rate of heat transfer to both liquid and particles was slower in the former case. This can be attributed to poor mixing of non-Newtonian liquid and particles. Guar gum concentration was the major factor

© 2003 by CRC Press LLC

© 2003 by CRC Press LLC

TABLE 31.2 Analysis of Variance Results (% Sum of Squares and Signiﬁcance Level) Showing the Inﬂuence of Operating Variables on the Three Variables Considered (fh, jch, and Co /Fo) at Three Radii of Rotation (center, 100, and 190 mm) with Non-Newtonian Liquids fh A: Parameters for Liquid Portion Solution concentration Particle concentration Retort temperature Rotational speed B: Parameters for Particles Gum concentration Particle concentration Retort temperature Rotational speed a b

p < 0.005. p < 0.05.

Center a

100 mm

jch 190 mm

Center

Co/Fo

100 mm

190 mm

Center

100 mm

190 mm

46.0 9.00 8.00 b 12.10

51.14 14.20 10.71 b 20.12

a

42.24 18.52 9.96 b 23.08

a

85.50 b 7.64 1.00 1.00

a

74.00 b 15.55 3.00 4.75

a

71.38 b 14.81 3.03 4.71

a

0.58 7.60 a 70.16 6.40

3.00 5.90 a 83.96 1.44

1.32 7.00 a 84.41 4.90

a

51.38 7.89 7.32 b 31.19

a

51.38 7.89 7.32 b 20.87

a

11.19 b 38.19 4.95 10.27

23.87 b 38.75 6.4 9.51

b

10.27 b 25.61 4.95 10.27

2.34 1.40 a 86.03 1.36

2.08 1.23 a 87.08 1.21

1.00 1.4 a 85.12 0.00

58.38 5.86 9.57 b 24.46

min

min

12

Rotation Speed

10

12

Retort Temperature 130°C

20 rpm

10

8

15 rpm

8

125°C

6

10 rpm

6

120°C

5 rpm

4

0 rpm

2 0

115°C

4

110°C

2 0

Liquid

min 12

Particle

Liquid

Gum Concentration

min 12

Particle

Particle Concentration

10

1.0%

10

8

0.75%

8

0.25%

6

0.5%

6

0.2%

4

0.15%

0.25%

4

0.0%

2

0.3%

0.1%

2

0

0

Liquid

Particle

Liquid

Particle

FIGURE 31.5 Effect of processing conditions on heating rate index (fh, min) with nonNewtonian liquid/particle mixture in cans. (From Krishnamurthy, H., Sanchez, G., Ramaswamy, H.S., Sablani, S.S., and Pandey, P.K., poster presentation at ICEF8, Puebla, Mexico, April 10–13, 2000. With permission.)

accounting for nearly 40 to 50% of the total variation in heating rate index, followed by rotational speed accounting for 12 to 24%. Figure 31.5 demonstrates typical variations in fh under different conditions. In general, fh was found to increase with increasing gum concentration and decreasing rotational speed. This was expected and can be explained based on apparent viscosity, which is highest for 1% guar gum and lowest for water. The decreasing effect of rotational speed on fh results from the forced mixing of can contents due to relative motion (turbulence) of liquid and particles in the can. Guar gum concentration was again the major factor accounting for 74% of the total variation in heating lag (jch) of the liquid (Figure 31.6). Particle concentration came next with 15%. The samples with the highest solution and particle concentrations

© 2003 by CRC Press LLC

min 3.5

Rotation Speed

3

20 rpm

2.5

15 rpm

2 1.5

3

5 rpm 0 rpm

1

0.5

0.5

0

0 Liquid Particle

Gum Concentration 1.0%

2 1.5

min 3.5

125°C 120°C 115°C 110°C

2.5

0.5%

2 1.5

0.0%

Particle Concentration

3

0.75%

0.25%

1 0.5

130°C

Liquid Particle

min 3.5

3 2.5

Retort Temperature

2.5 2 1.5

10 rpm

1

min 3.5

0.3% 0.25% 0.2% 0.15%

1

0.1%

0.5

0

0

Liquid Particle

Liquid Particle

FIGURE 31.6 Effect of processing conditions on heating lag factor with non-Newtonian liquid/particle mixture in cans. (From Krishnamurthy, H., Sanchez, G., Ramaswamy, H.S., Sablani, S.S., and Pandey, P.K., poster presentation at ICEF8, Puebla, Mexico, April 10–13, 2000. With permission.)

exhibited a greater lag factor compared to the other four levels, possibly due to the high initial viscosity (strongly non-Newtonian). Contrary to expectation, retort temperature and rotational speed did not signiﬁcantly affect lag factor. Particle concentration was the only major factor, accounting for 38% of the total variation in particle heating lag. As shown in Figure 31.7, the ratio Co/Fo for non-Newtonian liquids dramatically decreased from about 40 to 1.5 as temperature increased from 110 to 130°C. Overall, the magnitude of Co/Fo for liquid and particle was larger than that observed with Newtonian liquids, suggesting slower heat transfer rates with non-Newtonian solutions. The effect of gum concentration on this ratio was small, but the increasing trend was clear. The cook quality of the product could thus be improved by high temperature short time processing.

© 2003 by CRC Press LLC

Surface Response Graph for Co/Fo (Liquids) 40 35 30

Co/Fo

25 20 15 10 5 0

0.25

0.50

0.75

Gum Concentratio

110 115 (C) 120 ure 1.00 130125 perat

n (%w/v)

ort

Ret

Tem

Surface Response Graph for Co/Fo (Particle) 40 35

Co/Fo

30 25 20 15 10 5 0

110 Gum 0.3 0.5 115 Con 120 cen 0.8 trat ) 1.00 130 125 ion ure (C (%w perat m e T /v) Retort

FIGURE 31.7 Response surface plots of Co /Fo as a function of retort temperature and guar gum concentration. (From Krishnamurthy, H., Sanchez, G., Ramaswamy, H.S., Sablani, S.S., and Pandey, P.K., poster presentation at ICEF8, Puebla, Mexico, April 10–13, 2000. With permission.)

31.6 CONCLUSIONS With Newtonian liquids, liquid viscosity and rotational speed had major effects on fh and Co/Fo, while the effects of particle concentration and rotational speed were more pronounced with jch. The inﬂuence of mode of rotation and particle size on the different thermal process parameters was minimal. The effect of radius of rotation was not signiﬁcant. With non-Newtonian liquids, the gum concentration and rotational speeds had a major effect on the heating rate index (fh) for both liquid and particles, and the effect of particle concentration was especially noticed on lag factor (jch) for

© 2003 by CRC Press LLC

both liquid and particles. Co/Fo was highly inﬂuenced by the retort temperature, and a trend was observed when it came to the effect of gum concentration. Both heating rate index and heating lag factor values were higher with non-Newtonian liquid/particle mixtures than those observed with Newtonian liquid/particle mixtures.

NOMENCLATURE a A Bi Co Cp Fo Fo fh hfp jch k m R S T t U U <>

Radius of sphere, m 2 Total external surface area, m Biot number = hfp a/k Cook value, min Heat capacity, J/kgK 2 Fourier number = αt/a Process lethality, min Heating rate index, sec 2 Fluid-to-particle heat transfer coefﬁcient, W/m K Heating lag factor Thermal conductivity, W/mK Mass, kg A function of Biot number A function of Biot number Temperature, °C Time, sec 2 Overall heat transfer coefﬁcient, W/m K (T – Tr)/(Ti − Tr) Volumetric average

SUBSCRIPTS c i l p r s

Can Initial condition Liquid Particle Retort Surface

GREEK SYMBOLS 2

α Thermal diffusivity, m /sec δ Characteristic root (Equation (31.3))

REFERENCES Anantheswaran, R.C. and Rao, M.A., Heat transfer to model non-Newtonian liquid foods in cans during end-over-end rotation, J. Food Eng., 4, 21–35, 1985. Ball, C.O. and Olson, F.C.W., Sterilization in Food Technology, McGraw-Hill, New York, 1957.

© 2003 by CRC Press LLC

Berry, M.R., Jr. and Bradshaw, J.G., Heating characteristics of condensed cream of celery soup in a steritort: heating penetration and spore count reduction, J. Food Sci., 45, 869–874, 879, 1980. Berry, M.R., Jr. and Bradshaw, J.G., Heat penetration for sliced mushrooms in brine processed in still and agitating retorts with comparisons to spore count reduction, J. Food Sci., 47, 1698–1704, 1982. Berry, M.R., Jr. and Dickerson R.W., Heating characteristics of whole kernel corn processed in a steritort, J. Food Sci., 46, 889–895, 1981. Berry, M.R., Jr., Savage, R.A., and Pﬂug, I.J., Heating characteristics of cream-style corn processed in a steritort: effect of headspace, reel speed and consistency, J. Food Sci., 44, 831–835, 1979. Deniston, M.F., Hassan, B.H., and Merson, R.L., Heat transfer coefﬁcients to liquids with food particles in axially rotating cans, J.Food Sci., 52, 962–966, 979, 1987. Fernandez, C.L., Rao, M.A., Rajavsireddi, S.P., and Sastry, S.K., Particulate heat transfer to canned snap beans in steritort, J. Food Process Eng., 10, 183–198, 1988. Jaluria, Y. and Torrance, K.E., Computational Heat Transfer, Hemisphere Publishing Corporation, New York, 1996, pp. 403–424. Krishnamurthy, H., Sanchez, G., Ramaswamy, H.S., Sablani, S.S., and Pandey, P.K., Heating Rates of Canned Particulate Non-Newtonian Liquids as Inﬂuenced by Product and System Parameters During End-Over-End Agitation Processing in a Rotary Autoclave, Poster #P-203 presented at ICEF8 (International Congress on Engineering and Food), Puebla, Mexico, April 10–13, 2000. Lenz, M.K. and Lund, D.B., The lethality–Fourier number method. Heating rate variations and lethality conﬁdence intervals for forced-convection heated foods in containers, J. Food Process Eng., 2, 227–271, 1978. Naveh, D. and Kopelman, I.J., Effect of some processing parameters on the heat transfer coefﬁcients in a rotating autoclave, J. Food Process. Preserv., 4, 67–77, 1980. Pandey, P.K., Sablani, S.S., and Ramaswamy, H.S., Heat transfer to model non-Newtonian liquid and particle mixtures in cans subjected to end-over-end rotation, Proceedings of the 1997 Annual Conference of the Canadian Society of Agricultural Engineering (CSAE), Norum, D.I. and Savoie, P., Eds., CSCE, Montreal, Volume A, 1997, pp. 235–244. Parchomchuk, P., A simpliﬁed method for agitation processing of canned foods, J. Food Sci., 42, 265–268, 1977. Ramaswamy, H.S., Abbatemarco, C., and Sablani, S.S., Heat transfer rates in a canned food model as inﬂuenced by processing in an end-over-end rotary steam/air retort, J. Food Process. Preserv., 17, 269–286, 1993. Ramaswamy, H.S., Lo, K.V., and Tung, M.A., Simpliﬁed equations for transient temperatures in conductive foods with convective heat transfer at the surface, J. Food Sci., 47(6), 2042–2047, 2065, 1982. Ramaswamy, H.S. and Sablani, S.S., Particle motion and heat transfer in cans during endover-end processing: inﬂuence of physical properties and rotational speed, J. Food Process. Preserv., 21, 105–121, 1997a. Ramaswamy, H.S. and Sablani, S.S., Particle shape inﬂuence on heat transfer in cans containing liquid particle mixtures subjected to end-over-end rotation, Lebensm.-Wiss. Technol., 30, 525–535, 1997b. Rao, M.A. and Anantheswaran, R.C., Convective heat transfer to ﬂuids in cans, Adv. Food Res., 32, 39–84, 1988. Sablani, S.S., Heat Transfer Studies of Liquid Particle Mixtures in Cans Subjected to EndOver-End Processing, Ph.D. thesis, McGill University, Montreal, 1996.

© 2003 by CRC Press LLC

Sablani, S.S. and Ramaswamy, H.S., Fluid to particle heat transfer coefﬁcient in cans during end-over-end processing, Lebensm.-Wiss. Technol., 28(1), 56–61, 1995. Sablani, S.S. and Ramaswamy, H.S., Particle heat transfer coefﬁcients under various retort operating conditions with end-over-end rotation, J. Food Process Eng., 19, 403–424, 1996. Sablani, S.S. and Ramaswamy, H.S., Heat transfer to particles in cans with end-over-end rotation: inﬂuence of particle size and particle concentration (% v/v), J. Food Process Eng., 20, 265–283, 1997. Sablani, S.S. and Ramaswamy, H.S., Multi-particle mixing behavior and its role in heat transfer during end-over-end agitation of cans, J. Food Eng., 37, 141–152, 1998. Sablani, S.S. and Ramaswamy, H.S., End-over-end agitation processing of cans containing liquid particle mixtures. Inﬂuence of continuous vs. oscillatory rotation, Food Sci. Technol. Int., 5(5), 385–389, 1999. Stoforos, N.G. and Merson, R.L., Measurement of heat transfer coefﬁcients in rotating liquid particle systems, Biotechnol. Prog., 7, 267–271, 1991. Stoforos, N.G. and Merson, R.L., Physical property and rotational speed effect on heat transfer in axially rotating liquid/particulate canned foods, J. Food Sci., 57, 749–754, 1992.

© 2003 by CRC Press LLC

32

Dimensionless Correlations for Forced Convection Heat Transfer to Spherical Particles under Tube-Flow Heating Conditions H.S. Ramaswamy and M.R. Zareifard

CONTENTS 32.1 Introduction 32.2 Theoretical Background 32.3 Materials and Methods 32.3.1 Calorimetric Method 32.3.2 Particle Oscillatory Motion Method 32.3.3 Data Analysis 32.4 Results and Discussion 32.5 Conclusions Nomenclature References

32.1 INTRODUCTION One of the potential advantages of aseptic processing of particulate foods is the minimum loss of nutrients and overall quality improvement due to the use of a high temperature, short time processing technique. To design a process that ensures the commercial sterility of processed foods, thermal process calculations require accurate time–temperature data. Due to difﬁculties in measuring the temperature of a particle as it moves through the heat exchanger and holding tube sections of an aseptic processing system, the particle center temperatures are usually predicted by mathematical modeling. Data on residence time distribution (RTD) and associated

© 2003 by CRC Press LLC

ﬂuid-to-particle heat transfer coefﬁcient (hfp) in a continuous ﬂow system are necessary in such models (Dignan et al., 1989). Numerous studies have been carried out to evaluate hfp under a wide range of experimental conditions simulating some aspects of aseptic processing. Several of these studies have made use of particles ﬁxed in a tube for gathering time–temperature data, while others have used novel approaches to monitor transient temperatures of moving particles. Dimensional analysis is a useful technique for generalization of data, as it reduces the number of variables that must be studied and permits the grouping of physical variables that affect the process of heat transfer. In the dimensional analysis of convection heat transfer, the Nusselt number (Nu), a dimensionless measure of convective heat transfer coefﬁcient, is correlated with other dimensionless numbers such as the Reynolds (Re), Prandtl (Pr), and Grashof (Gr) numbers. Kramers (1946), Ranz and Marshal (1952), and Whitaker (1972) were early researchers who presented empirical equations for heat transfer correlations. During the last decade, several researchers have developed different forms of correlations to predict ﬂuid-to-particle heat transfer coefﬁcients for processing of particulate food under a range of tubeﬂow conditions (Sastry and Zuritz, 1987; Chandarana et al., 1988, 1990; Zuritz et al., 1990; Mwangi et al., 1992; Balasubramaniam, 1993; Zitoun and Sastry, 1994a,b; Astrom and Bark, 1994; Bhamidipati and Singh, 1995; Awuah and Ramaswamy, 1996; Chakrabandhu and Singh, 1998). The objectives of this study were to develop dimensionless correlations for experimental data obtained from two techniques allowing particle motion during the heating process: a calorimetric method in which the particle was free to move and rotate along the length of holding tube (Ramaswamy and Zareifard, 2000), and a particle oscillatory motion method in which the particle was allowed controlled movement in an oscillatory fashion (Zareifard and Ramaswamy, 2001).

32.2 THEORETICAL BACKGROUND Heat transfer from liquid to particles in continuous processing of multi-phase systems is affected by both liquid and particle thermophysical properties as well as system parameters. In the dimensional analysis of forced convection heat transfer, the ﬂuid-to-particle heat transfer coefﬁcient (hfp) is expressed in terms of the Nusselt number (Nu), which is generally described as a function of other dimensionless numbers [Nu = f (Re, Pr, Gr)]. Different forms of dimensionless correlations have been published concerning the ﬂow ﬁeld and heat transfer to particles in tube-ﬂow conditions. Kramers (1946), Ranz and Marshal (1952), and Whitaker (1972) presented the following equations for forced convection conditions, respectively: 0.15

Kramers (1946): Nu = 2 + 1.3 Pr

0.31

+ 0.66 Pr 0.5

0.5

© 2003 by CRC Press LLC

0.66

+ 0.06 Re

(32.1)

0.33

Ranz and Marshal (1952): Nu = 2 + 0.6 Re Whitaker (1972): Nu = 2 + (0.4 Re

0.5

Re

+ Pr 0.4

) Pr

(32.2) 0.25

(µ∞/µs)

(32.3)

These correlations involve the Reynolds number as a dominant factor inﬂuencing hfp. However, some researchers have deﬁned the Reynolds number based on either ﬂuid or particle velocity, while others have used the relative velocity between particle and ﬂuid, also called slip velocity, which is the difference between ﬂuid and particle velocities. The slip velocity appears to be more suitable under the conditions of this study. The Whitaker (1972) model suggests that ﬂuid velocity far removed from the particle should be used to calculate Re number. The particle velocity is easy to measure. However, the ﬂuid velocity in tube-ﬂow conditions of a two-phase system is a source of differences among the researchers. In the case of tube-ﬂow conditions with moving particles, several additional factors can inﬂuence particle motion and thus the ﬂuid-to-particle heat transfer coefﬁcient. Particle shape and size, thermophysical properties of both particle and carrier ﬂuid, and system parameters such as tube diameter and ﬂuid ﬂow rate are some inﬂuencing factors. These parameters can be grouped into dimensionless forms and included in the correlations. Further, to improve the prediction of the developed model, other groups of dimensionless numbers, such as the Peclet, Froude, and Rayleigh numbers, or dimensionless ratios 2 such as Gr/Re , d/D, αf/αp, and µ∞/µs have also been included in the empirical equations. Some published empirical equations are presented in Table 32.1. In the present study, the Nusselt number and generalized forms of the Reynolds, Prandtl, and Grashof numbers were used and calculated as follows: Nu = hfp dp/kf

(32.4)

GRe = ρ Vs dp/µ

(32.5)

GPr = Cp µ/kf

(32.6)

2

3

GGr = g β ρ ∆T dp /µ

(32.7)

Vs = Vf − Vp

(32.8)

∆T = (Tf − Tip)/2

(32.9)

where:

2

2

Vf = Q/π (Rt − Rp )

(32.10)

Cp = 1.675 + 0.025 (%W)

(32.11)

n−3

µ=2

n

1−n

m (3n + 1/n) (dp/Vs)

(32.12)

2

(32.13)

kf = [326.575 + 1.0412 T − 0.000337 T ] [(0.796 + 0.009346 (%W)]

© 2003 by CRC Press LLC

© 2003 by CRC Press LLC

TABLE 32.1 Some Published Dimensionless Correlations for Estimating Nusselt Number under Forced Convection Heat Transfer Conditions Reference Kramers (1946) Ranz and Marshal (1952) Whitaker (1972) Zuritz and Sastry (1987) Chandarana et al. (1988) Chandarana et al. (1988) Chandarana et al. (1990) Chandarana et al. (1990) Sastry et al. (1990) Sastry et al. (1990) Zuritz et al. (1990) Awuah et al. (1993) Awuah et al. (1993) Astrom and Bark (1994) Astrom and Bark (1994) Bhamidipati and Singh (1995) Kelly et al. (1995) Baptista et al. (1997a) Baptista et al. (1997a)

Fluid Air, oil, water Air Air, oil, water a CMC Starch Water Starch Water Water Water CMC CMC CMC Silicon oil Silicon oil CMC CMC CMC CMC

Sphere (steel) Sphere Sphere Mushroom (aluminum) Cubes (silicone) Cubes (silicone) Cubes (silicone) Cubes (silicone) b Sphere (hollow al ) moving therm. b Sphere (hollow al ) moving therm. b Mushroom (al ) Cylinders (carrot) Cylinders (potato) Spheres (lead) Cubes (lead) Cylinder (temp. sensor) Sphere, cube, cylinder (aluminum) Sphere (hollow aluminum) stationary Sphere (hollow aluminum) rotating

Chakrabandhu and Singh (1998) Chakrabandhu and Singh (1998)

CMC CMC

Cubes (sodium alginate) stationary Cubes (sodium alginate) rotating

a b

CMC = carboxymethyl cellulose. al = aluminum.

Particle

Equation [Nu = f (Re, Pr…..)] 0.15 0.5 0.31 2 + 1.3Pr + 0.66Re Pr 0.5 0.33 2 + 0.6Re Pr 0.5 0.66 0.4 0.25 2 + (0.4Re + 0.06Re ) Pr (µs/µ∞) 0.21 0.14 2 + 2.95Re Pr 0.44 0.35 0.55Re Pr 0.43 0.85Re 1.6 0.89 2 + 0.028Re Pr 1.08 2 + 0.0333Re 0.00455 6.46E–26[Re (d/D)] 0.0125 85.67 –342.5 2.7E–27Re (d/D) Pr 0.23 0.14 1.79 2 + 28.37Re Pr (d/D) 0.108 2.45(Pr Gr) 0.113 2.02(Pr Gr) 0.54 8 + 2.53Re 0.61 8 + 2.25Re 0.2 0.33 0.27Re Pr 0.132 –0.08 2 + 19.36Re Pr 0.59 0.28 Nus + 0.64Re Pr 0.71 0.42 0.28 Nus + 0.17Re Pr (rp/Rt) 0.33 0.5 Nus = 2 + 0.025 Pr Gr 0.29 1.52 4.35 18197Re Pr (d/D) 0.86 0.22 1.67 338Re Pr (d/D)

2

R — — — 0.99 0.92 0.95 0.79 0.89 0.82 0.92 0.96 0.80 0.88 — — 0.85 0.83 — — 0.91 0.89

32.3 MATERIALS AND METHODS Data from two previous reports (Ramaswamy and Zareifard, 2000; Zareifard and Ramaswamy, 2001) were used for developing correlations under tube-ﬂow conditions. The techniques for evaluating hfp have been detailed by Zareifard and Ramaswamy (1997, 1999). A brief description of the two methods is given below for reference:

32.3.1 CALORIMETRIC METHOD The calorimetric method (Zareifard and Ramaswamy, 1999) involves an indirect measurement of particle temperature. Instead of recording the particle center point temperature, the mass average (bulk) temperature of a freely moving particle, which is not attached to any thermocouple, is estimated using a calorimeter. Therefore, the particle is allowed to ﬂow with the carrier ﬂuid along the tube without any restriction. The technique consists of introducing a particle at an upstream location into a holding tube, in which a carrier ﬂuid under prestabilized temperature and ﬂow conditions is circulated, and retrieving it from a downstream location after a known time interval. The particle is transferred immediately into a specially constructed calorimeter, and its bulk temperature is determined upon equilibration. Knowing the medium temperature, particle initial temperature, exposure time (residence time), and thermophysical properties, the associated hfp is computed from the evaluated bulk temperature of the particle using an iterative numerical technique. The procedure involves numerical computation, by trial and error, of bulk temperature (also known as mass average temperature) for a given heating time (residence time), using the available property data and an assumed hfp value, and comparing it with the experimental value. Aluminium spherical particles of three sizes (19.05, 22.22, and 25.4 mm in diameter) were used as test particles in a Pyrex glass holding tube (45 mm inside diameter).

32.3.2 PARTICLE OSCILLATORY MOTION METHOD The particle oscillatory motion method (Zareifard and Ramaswamy, 1997) involves direct measurement of center point temperature of thermocouple-equipped particles ﬁxed at the center of a set of circular holding tubes of different radii cut out in quarter lengths. An assembly of four such tubes is supported by an aluminum shaft and connected to a programmable servo motor equipped with an electronic board for imparting preset oscillatory motions. Spherical nylon particles of three different sizes (12.7, 16, and 17.5 mm in diameter) as well as spherical particles (17.5 mm in diameter) made of aluminum epoxy (Soudotec Inc., Lachine, Quebec) were used as the test particles. The aluminum epoxy particle was formed by mixing aluminum powder and epoxy resin in a soft form. All test particles were drilled to insert thermocouples to their geometric centers. The assembly of holding tubes containing the particles was kept in a cooling tank at 5°C for equilibration of the temperature in test particles, and an appropriate oscillatory motion was programmed to result in particle linear velocity in the range 0.06 to 0.21 m/sec. The assembly was then transferred to the test tank containing a heating medium at a preset temperature. Time–temperature data were gathered at

© 2003 by CRC Press LLC

3-sec time intervals using a data logger connected to a personal computer. Water as well as two concentrations (0.5 and 1% w/w) of commercial carboxymethyl cellulose, CMC (Sigma, St. Louis, MO) were used as the heating media. Thermophysical properties of the different test particles such as density (ρ), thermal diffusivity (α) and heat capacity (Cp) were experimentally evaluated using procedures described elsewhere (Sablani and Ramaswamy, 1996). The thermal conductivity (k) was calculated as k = ρCpα. Rheological data for test ﬂuids at different concentration and temperature were obtained in the form of power law model parameters [consistency coefﬁcient (m) and ﬂow behavior index (n)] using a rotational viscometer Model RV20 (Haake Mess-Technik, Karlsruhe, Germany) as described by Abdelrahim and Ramaswamy (1995). These data are summarized in Tables 32.2 and 32.3. Data obtained on hfp from the two techniques are given in Tables 32.4 and 32.5 and were used for developing the dimensionless correlations.

TABLE 32.2 Thermophysical Properties of Spherical Test Particles Material

Aluminum 3

Density (kg/m ) Heat capacity (J/kg K) Thermal conductivity (W/m K) 2 Thermal diffusivity (m /sec) a b

a

Aluminum Epoxy

2707 896 204 8.42E–5

b

1750 1370 1.13 4.7E–7

Nylon

1128 2073 0.37 1.58E–7

From Holman, G.P., Heat Transfer, McGraw-Hill, New York, 1990. Measured experimentally.

TABLE 32.3 The Power Law Model Parameters of CMC Solutions for Different Concentrations and Temperatures Determined Using a Rotational Viscometer CMC %

Temp. °C

0.25 0.25 0.25 0.50 0.50 0.50 1 1 1

50 60 70 50 60 70 50 60 70

M n Pa.sec 0.150 0.052 0.011 0.510 0.252 0.115 1.715 1.191 0.778

± ± ± ± ± ± ± ± ±

0.031 0.018 0.028 0.020 0.033 0.045 0.151 0.101 0.082

n 0.785 0.821 0.976 0.590 0.681 0.754 0.560 0.510 0.583

± ± ± ± ± ± ± ± ±

0.030 0.015 0.021 0.011 0.026 0.017 0.019 0.029 0.031

Note: Results are means ± standard deviations of three replicates (m: consistency coefﬁcient; n: ﬂow behavior index).

© 2003 by CRC Press LLC

b

TABLE 32.4 2 Values of hfp (W/m ·K) Associated with Aluminum Spherical Particles of Different Sizes and Fluid Flow Rates with Various Fluid Concentrations and Temperatures Using the Calorimetric Approach % CMC Concentration F (l/min)

9

11

13

16

19

P s m l s m l s m l s m l s m l s m l s m l s m l s m l s m l s m l s m l s m l

T (°C)

0.0

0.25

0.5

50

60

70

50

60

70

50

60

70

1430 (3.5) 1730 (3.5) 2200 (2.7)

50

60

70

70

1730 2150 2550 2030 2300 2660

(5.2) (3.7) (2.3) (3.4) (2.6) (3.4)

920 (2.2) 690 (0.1) 980 (0.1) 890 (2.2) 990 (0.2) 1020 (1.0) 880 (2.3) 930 (2.1) 980 (0.1) 1090 (1.8) 1100 (1.8) 1190 (1.8) 1070 (0.9) 1120 (3.6) 1180 (2.5) 1000 (1.0) 1070 (3.7) 1140 (3.5) 1310 (1.5) 1420 (3.5) 1490 (4.0) 1260 (1.6) 1310 (1.5) 1390 (2.2) 1240 (3.2) 1320 (1.5) 1350 (2.2)

790 880 950 770 830 930 750 810 900

(2.5) (1.1) (1.0) (1.3) (1.2) (1.1) (1.3) (2.5) (1.1)

1 740 (2.7) 800 (2.5) 870 (2.3) 680 (1.5) 730 (1.4) 800 (1.2) 650 (1.5) 700 (1.4) 750 (1.3) 750 (4.0) 860 (1.2) 900 (1.1) 710 (1.4) 780 (1.3) 870 (1.1) 680 (1.5) 720 (1.4) 840 (1.2) 890 (2.2) 910 (2.2) 1020 (2.9) 820 (1.2) 870 (1.1) 970 (1.0) 740 (2.7) 810 (1.2) 890 (2.2)

Note: Values of hfp are the means of four replicates, and the coefﬁcient of variation is given in parentheses. F: ﬂuid ﬂow rate; T: ﬂuid temperature; P: particle size: s, small; m, medium; l, large.

© 2003 by CRC Press LLC

TABLE 32.5 2 Values of hfp (W/m ·K) Associated with Different Fluid Concentrations and Temperatures for Spherical Particles of Different Sizes and Materials at Various Particle Velocities Using the Particle Oscillatory Motion Technique 2

C (% CMC)

T (°C)

0

60

60

0.5

70

80

60

1.0

70

80

2

hfp (W/m ·K)

Vp (m/sec)

AL

0.10 0.16 0.21 0.10 0.16 0.21 0.10 0.16 0.21 0.10 0.16 0.21 0.10 0.16 0.21 0.10 0.16 0.21 0.10 0.16 0.21

1460 (11) 1830 (11) 2020 (9) 590 (15) 950 (6) 1220 (9) 750 (5) — 1360 (9) 1140 (6) 1290 (3) 1380 (12) 530 (10) 570 (10) 630 (11) 650 (7) 730 (10) 880 (7) 720 (10) 1010 (8) 1110 (4)

hfp (W/m ·K)

NL

Vp (m/sec)

NS

NM

1120 (7) 1310 (6) 1410 (6) 460 (15) 620 (7) 690 (9) 500 (18) — 730 (7) 640 (16) 740 (14) 800 (4) 430 (17) 520 (12) 620 (19) 490 (8) 530 (18) 660 (10) 500 (18) 560 (17) 740 (8)

0.06 0.09 0.12 0.06 0.09 0.12 0.06 0.09 0.12 0.06 0.09 0.12 0.06 0.09 0.12 0.06 0.09 0.12 0.06 0.09 0.12

1100 (11) 1250 (12) 1410 (8) 520 (15) 720 (15) 750 (18) 530 (3) — 790 (12) 600 (18) 790 (9) 840 (8) 360 (16) 420 (11) 570 (4) 490 (13) 530 (17) 610 (12) 520 (7) 520 (10) 660 (5)

1070 (11) 1120 (10) 1320 (8) 430 (10) 580 (9) 610 (12) 460(9) — 640 (15) 520 (11) 680 (13) 730 (9) 350 (14) 440 (9) 530 (16) 430 (13) 510 (4) 580 (9) 470 (12) 500 (4) 640 (10)

Note: Values of hfp are the means of four replicates, and the coefﬁcient of variation is given in parentheses. Vp: particle velocity; T: medium temperature; C: medium concentration; AL; aluminum epoxy; NL: nylon large; NS: nylon small; NM: nylon medium.

32.3.3 DATA ANALYSIS In the literature, the heat transfer coefﬁcients associated with pure forced convection with unbounded ﬂow are generally modeled in dimensionless forms, as shown in Equation (32.14). c

d

Nu = A + B Re Pr

(32.14)

For tube-ﬂow conditions involving biphasic systems, other dimensionless terms are added to make the correlations better explain the experimental variability. In the present study, regression analyses were performed starting with the simplest form of correlation: Nu = f (GRe). This was progressively expanded to include other dimensionless numbers such as GPr and GGr as well as other dimensionless groups: 2 αf/αp, GGr/GRe , d/D, Vp/Vf, and Vp/Vs. After successful improvement of the model

© 2003 by CRC Press LLC

prediction by including other variables was observed, a multiple regression technique with a backward elimination procedure using the SAS statistical package (SAS Institute, 1994) to obtain the best model was adopted. The models were individually developed with data from the calorimetric method and particle oscillatory motion method and subsequently with the pooled data (600+ experimental values).

32.4 RESULTS AND DISCUSSION Regression analysis between the Nusselt number and other dimensionless groups 2 resulted in a number of correlations with different coefﬁcients of determination (R ) and coefﬁcients of variation (CV). Overall, these coefﬁcients varied over the fol2 lowing ranges: 0.4 < R < 0.99; 1 < CV < 15%. As more dimensionless groups were 2 added to the correlation, the associated R and CV values demonstrated a progressive improvement of the model. The following is the sequence of the regression analysis with data obtained from the calorimetric method: 0.147

Nu = 2 + 1.84 E–1 GRe

0.601

GPr

0.440

GPr

Nu = 2 + 2.49 E–1 GRe Nu = 2 + 3.51 E–2 GRe

0.448 0.681

0.25

(32.15)

2

(32.16)

2

(32.17)

2

(32.18)

2

(32.19)

(R = 0.71; CV = 6.1) 0.191

GGr

(R = 0.73; CV = 5.8)

–2.18

Nu = 2 + 1.15 E11 GRe GPr −1.125 4.508 × GGr (d/D) 0.479

2

(R = 0.60; CV = 7.1)

−0.655

Nu = 2 + 3.80 E4 GRe GPr 2.293 0.514 × (d/D) (Vp/Vs)

(R = 0.91; CV = 3.2) −0.526

GGr

(R = 0.97; CV = 1.8)

The simplistic form of the correlation relating Nu to just GRe (Equation (32.15)) yielded a fairly poor ﬁt and largely scattered data points (not shown). This was expected because GRe alone cannot be expected to explain all the variability associated with Nu. The second correlation in the form of Nu as a function of Re and Pr (Equation (32.16)) is commonly employed in many published reports including the well known Ranz and Marshal correlation. Logarithmic plots of experimental vs. predicted Nu based on Equations (32.16–19) are presented in Figure 32.1. The 2 R improved somewhat (from 0.6 to 0.7) with the inclusion of Pr in the model (Equation (32.16), Figure 32.1a). Adding Gr to the model (Equation (32.17), 2 2 Figure 32.1b) did not improve R much since the range of Gr/Re employed was less than 1.0, indicating that experimental conditions involved forced convection rather than natural convection. Adding the ratio of particle-to-tube diameter d/D (Equation (32.18), Figure 32.1c) resulted in a good improvement of the model, and 2 R increased from 0.7 to 0.9. Including the ratio of particle-to-slip velocity, Vp/Vs (Equation (32.19), Figure 32.1d), also contributed to improving model prediction. 2 This combination model had an R greater than 0.97. Because additional different forms of dimensionless numbers could have the potential to improve the model performance, a multiple regression technique with backward elimination of statistically insigniﬁcant (p > 0.05) terms was employed to achieve the optimal model conﬁguration. The regression analysis with the backward elimination procedure resulted in the following model equation with the best

© 2003 by CRC Press LLC

2

R2 = 0.71 Predicted Log Nu

Predicted Log Nu

2

1.8

1.6

1.4

1.8

1.6

1.4

1.2

1 1

R2 = 0.73

1.2

1.2

1.4

1.6

1.8

2

1 1

2.2

1.2

1.4

Experimental Log Nu

1.6

1.8

2

2.2

Experimental Log Nu

(a)

(b) 2.2

2

R2 = 0.91 Predicted Log Nu

Predicted Log Nu

2

1.8

1.6

1.4

1.2

1 1

R2 = 0.97

1.8

1.6

1.4

1.2

1.2

1.4

1.6

1.8

2

1 1

2.2

1.2

1.4

Experimental Log Nu

1.6

1.8

2

2.2

Experimental Log Nu

(c)

(d)

FIGURE 32.1 Logarithmic plot of experimental vs. predicted Nusselt numbers using different models: (a) Equation (32.16); (b) Equation (32.17); (c) Equation (32.18); (d) Equation (32.19). 2

ﬁt (R = 0.98), employing about 300 experimental data points obtained from the calorimetric method under different conditions: 0.589

Nu = 2 + 5.89 E24 GRe

0.977

GPr

0.231

GGr

−0.607

(Vp/Vf)

−8.402

0.731

(Vp/Vs)

(αf/αp) (32.20)

Figure 32.2 shows the plot of Nusselt numbers calculated from Equation (32.20) vs. experimental values of Nusselt numbers obtained with the calorimetric method. The same procedure, backward elimination, was also used for data obtained 2 from the particle oscillatory motion method, and the best model (R = 0.88) was found to be: 2.032

Nu = 2 + 2.27 E–8 GPr

© 2003 by CRC Press LLC

1.120

GGr

−1.843

(d/D)

2 −0.316

(GGr/GRe )

0.305

(αf/αp)

(32.21)

2.2

R2 = 0.98

Predicted Log Nu

2

1.8

1.6

1.4

1.2

1 1

1.2

1.4

1.6

1.8

2

2.2

Experimental Log Nu

FIGURE 32.2 Logarithmic plot of experimental vs. predicted Nusselt number for the best model for data from the calorimetric method (Equation (32.20)).

Contributions from natural convection were accounted for by introducing both 2 2 GGr and the GGr/GRe ratio in Equation (32.21). The magnitude of Gr/Re describes the ratio of buoyant to inertia forces indicating free, forced, and mixed convection regimes (Chapman, 1989). Yuge (1960) indicated that forced convection dominates 2 for ﬂow over a sphere when condition Gr/Re < 0.01 is satisﬁed. According to Johnson et al. (1988), mixed convection occurs when the ratio falls between 0.08 and 5.1. Figure 32.3 shows the logarithmic plot of Nusselt numbers calculated from Equation (32.21) vs. experimental values of Nusselt numbers obtained from the particle oscillatory motion method. Model prediction of Nu using Equation (32.20) 2 (developed from the calorimetric approach) resulted in a better ﬁt with an R of 0.98 than model Equation (32.21) (developed from oscillatory motion technique) with an 2 2 2 R of 0.88. The model R represents a combination of partial R associated with individual parameters included in the model. Obviously, it is important to include meaningful dimensionless numbers in the model. In this regard, the variables in Equation (32.20) appear to do a better job (with calorimetric approach data). The same variables did not give similar results with the data obtained from the oscillatory technique. The lack of rotational motion of the particles (because of the attachment of the thermocouple to the particle) could be a reason for the discrepancy. The overall 2 lower R associated with Equation (32.21) also indicates that perhaps some additional parameters may be necessary to describe the rather unusual oscillatory motion for the particles.

© 2003 by CRC Press LLC

2

Predicted Log Nu

R2 = 0.88

1.5

1

0.5 0.5

1

1.5

2

Experimental Log Nu

FIGURE 32.3 Logarithmic plot of experimental vs. predicted Nusselt number for the best model for data from the oscillatory motion technique (Equation (32.21)).

Multiple regression and backward elimination for all of the 600 experimental 2 data values obtained from both methods resulted in the following model (R = 0.91) after including all the possible inﬂuencing factors associated with hfp: 0.555

Nu = 2 + 4.45 E2 GRe 0.227

× (αf/αp)

−0.294

GPr

−0.352

GGr

1.628

(d/D)

1.748

(Vp/Vf)

−0.533

(Vp/Vs)

(32.22)

The validity of the above equation is limited to the following ranges of the dimensionless group numbers: 2.9 < GRe < 7660; 2.5 < GPr < 3077; 4.15 < GGr < 1.5 E7; 0.2 < d/D < 0.6; 0.30 < Vp/Vf < 1; 0.43 < Vp/Vs < 3.37; and 0.33 < αf/αp < 1892. Figure 32.4 shows the logarithmic plot of the Nusselt number calculated from Equation (32.22) vs. experimental values of Nusselt numbers obtained from the pooled data including both calorimetric and particle oscillatory motion methods. It is worth mentioning that in the heat transfer literature the convective heat transfer coefﬁcient in the form of the Nusselt number is correlated to the Reynolds and Prandtl numbers due to the inﬂuence of properties associated with the carrier ﬂuid, which can affect the boundary conditions. The constant value of two has been reported in the developed correlations to be considered as a limiting Nusselt number value for the steady state heat conduction between ﬂuid and sphere. This number may vary for different particle geometry (Whitaker, 1976). In the present study, particle-to-tube diameter ratio (d/D) and thermal diffusivity ratio (αf/αp), as well as velocity ratios (Vp/Vf or Vp/Vs) were found to be appropriate for hfp correlations under tube-ﬂow situations investigated.

© 2003 by CRC Press LLC

2.2

R2 = 0.91

2

Predicted Log Nu

1.8 1.6 1.4 1.2 1 0.8 0.6 0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Experimental Log Nu

FIGURE 32.4 Logarithmic plot of experimental vs. predicted Nusselt number for the overall model from the combined data (Equation (32.22)).

Dimensionless numbers as well as the associated coefﬁcients in the above models are different from those reported in the literature. Attempts to compare the above model with others in the literature resulted in either overestimation or underestimation of the Nusselt number. Comparison with well-known correlations such as those of Ranz and Marshal (1952) or Whitaker (1972) is not possible because these equations were derived for an unbounded ﬂow situation. In general, it is difﬁcult to compare the empirical equations in the literature because of differences in experimental procedures, and most importantly, differences in the range of Re number and other dimensionless numbers which might differ from the experimental condition for the present study.

32.5 CONCLUSIONS Dimensionless correlations between Nusselt number and other dimensionless numbers were developed for data obtained from a particle oscillatory motion method and a calorimetric approach separately as well as for the combination of data from both. A multiple regression analysis with backward elimination procedure was used to obtain the best model with statistically signiﬁcant parameters associated with hfp. Heat transfer to the particle from the carrier medium was modelled using Reynolds, Prandtl, and Grashof numbers. Their relationships were attributed to the carrier ﬂuid and various parameters affecting the boundary condition. In addition, particle-totube diameter ratio (d/D) and thermal diffusivity ratio (αf/αp) as well as velocity ratio (Vp/Vf) were found to be appropriate for hfp correlations under tube-ﬂow and

© 2003 by CRC Press LLC

force convection situations investigated in the present study. Nusselt numbers estimated from the developed models showed good agreement with experimental data 2 (R = 0.88–0.98).

NOMENCLATURE a Cp d D g hfp k m n Rt Rp Tf Ti Tp Vf Vp Vs W

Radius of sphere (m) Heat capacity (J/Kg °C) Particle diameter (m) Inside tube diameter (m) 2 Local acceleration due to gravity (m/sec ) 2 Fluid-to-particle heat transfer coefﬁcient (W/m K) Thermal conductivity (W/m K) n Consistency coefﬁcient (Pa.sec ) Flow behavior index Radius of the tube Radius of the particle Fluid or medium temperature Initial temperature Particle temperature Fluid velocity (m/sec) Particle velocity (m/sec) Slip velocity (m/sec) Moisture content (%)

GREEK LETTERS α β ρ µ µ∞

2

Thermal diffusivity (m /sec) Root of characteristic equation or thermal expansion coefﬁcient (1/K) 3 Density (kg/m ) 2 Dynamic or apparent viscosity (µ = ρυ) (N.sec/m ) 2 Fluid apparent viscosity at bulk ﬂuid temperature (N.sec/m )

DIMENSIONLESS NUMBERS Bi Gr Pr Re Nu

Biot number (hfp a/kp) 2 3 2 Grashof number (g β ρ ∆T d /µ ) Prandtl number (µ Cp/kf or υ/α) Reynolds number (ρ V d/µ) Nusselt number (hfp a/kf)

SUBSCRIPTS f fp i

Fluid Fluid-to-particle Initial

© 2003 by CRC Press LLC

p s ∞

Particle Surface or slip Ambient

REFERENCES Abdelrahim, K.A. and Ramaswamy, H.S., High temperature/pressure rheology of carboxymethyl cellulose (CMC), Food Res. Int., 28(3), 285–290, 1995. Astrom, A. and Bark, G., Heat transfer between ﬂuid and particles in aseptic processing, J. Food Eng., 21, 97–125, 1994. Awuah, G.B. and Ramaswamy, H.S., Dimensionless correlations for mixed and forced convection heat transfer to spherical and ﬁnite cylindrical particles in an aseptic processing holding tube simulator, J. Food Process Eng., 19, 241–267, 1996. Awuah, G.B., Ramaswamy, H.S., and Simpson, B.K., Surface heat transfer coefﬁcients associated with heating of food particles in CMC solutions, J. Food Process Eng., 16, 39–57, 1993. Balasubramaniam, V.M., Liquid-to-Particle Convective Heat Transfer in Aseptic Processing Systems, Ph.D. dissertation, The Ohio State University, Columbus, 1993. Baptista, P.N., Oliveira, F.A.R., Oliveira, J.C., and Sastry, S.K., Dimensionless analysis of ﬂuid-to-particle heat transfer coefﬁcients, J. Food Eng., 31, 199–218, 1997a. Baptista, P.N., Oliveira, F.A.R., Oliveira, J.C., and Sastry, S.K., The effect of transitional and rotational relative velocity components on ﬂuid-to-particle heat transfer coefﬁcients in continuous tube ﬂow, Food Res. Int., 30(1), 21–27, 1997b. Bhamidipati, S. and Singh, R.K., Determination of ﬂuid–particle convective heat transfer coefﬁcient, Trans. ASAE, 38(3), 857–862, 1995. Chakrabandhu, K. and Singh, R.K., Determination of ﬂuid-to-particle heat transfer coefﬁcients for rotating particles, J. Food Process Eng., 21, 327–350, 1998. Chandarana, D.I., Gavin, A., and Wheaton, F.W., Particle/Fluid Interface Heat Transfer During Aseptic Processing of Food, ASAE Paper No. 88–6599, American Society of Agricultural Engineers, St Joseph, MI., 1988. Chandarana, D.I., Gavin, A., and Wheaton, F.W., Particle/ﬂuid interface heat transfer under UHT conditions at low particle/ﬂuid relative velocity, J. Food Process Eng., 13, 191– 206, 1990. Chapman, A.J., Heat Transfer, 4th ed., Macmillan Publishing Co., New York, 1989. Dignan, D.M., Berry, M.R., Pﬂug, I.J., and Gardine, T.D., Safety considerations in establishing aseptic processing for low-acid foods containing particulates, Food Technol., 43, 118–121, 1989. Holman, G.P., Heat Transfer, McGraw-Hill, Inc., New York, 1990. Johnson, A.G., Kirk, G., and Shin, T., Numerical and experimental analysis of mixed forced and natural convection about a sphere, Trans. ASAE, 31(1), 293–299, 1988. Kelly, B.P., Megee, T.R.A., and Ahmed, M.N., Convective heat transfer in open channel ﬂow: effect of geometric shape and ﬂow characteristics, Trans. Inst. Chem. Eng., U.K., 73 (part C), 171–182, 1995. Kramers, H., Heat transfer from spheres to ﬂowing media, Physica, 12, 61, 1946; as cited in Zenz, F.A. and Othmer, D.F., Fluidization and Fluid Particle Systems, Reinhold Pub. Corp., New York, 1960. Mwangi, J.M, Datta, A.K, and Rizvi, S.S., Heat transfer in aseptic processing of particulate foods, 1992, as cited in Singh, R.K. and Nelson, P.E., Advances in Aseptic Processing Technologies, Elsevier, London, 1995, pp. 73–102.

© 2003 by CRC Press LLC

Ramaswamy, H.S., and Zareifard, M.R., Evaluation of factors inﬂuencing tube-ﬂow ﬂuid-toparticle heat transfer coefﬁcient using a calorimetric technique, J. Food Eng., 45, 127–138, 2000. Ranz, W.E. and Marshal, W.R., Evaporation from drop, Chem. Eng. Prog., 48, 141–147, 173–180, 1952. Sablani, S.S. and Ramaswamy, H.S., Particle heat transfer coefﬁcient under various retort operating conditions with end-over-end rotation, J. Food Process Eng., 19, 403–424, 1996. SAS Institute Inc., SAS User’s Guide, version 6, SAS Institute, Cary, NC, 1994. Sastry, S.K., Lima, M., Brim, J., Brunn, T., and Heskitt, B.F., Liquid-to-particle heat transfer during continuous tube ﬂow: inﬂuence of ﬂow rate and particle to tube diameter ratio, J. Food Process Eng., 13, 239–253, 1990. Sastry, S.K. and Zuritz, C.A., A review of particle behavior in tube ﬂow: applications to aseptic processing, J. Food Process Eng., 10, 27–52, 1987. Whitaker, S., Force convection heat transfer calculations for ﬂow in pipes, past ﬂat plates, single cylinder, single sphere and for ﬂow in packed beds and tube bundles, J. AIChE., 18, 361–371, 1972. Whitaker, S., Elementary Heat Transfer Analysis, Pergamon Press, New York, 1976. Yuge, T., Experiments on heat transfer from spheres including combined and forced convection, J. Heat Transfer, 82, 214–220, 1960. Zareifard, M.R. and Ramaswamy, H.S., A new technique for evaluating ﬂuid-to-particle heat transfer coefﬁcients under tube-ﬂow conditions involving particle oscillatory motion, J. Food Process Eng., 20(6), 453–475, 1997. Zareifard, M.R. and Ramaswamy, H.S., A calorimetric approach for evaluation of ﬂuid to particle heat transfer coefﬁcient under tube-ﬂow condition, Lebensm.-Wiss. Technol., 32, 495–502, 1999. Zareifard, M.R. and Ramaswamy, H.S., Evaluation of tube-ﬂow ﬂuid-to-particle heat transfer coefﬁcient under controlled particle oscillatory motion, Food Res. Int., 34(4), 289– 249, 2001. Zitoun, K.B. and Sastry, S.K., Convection heat transfer coefﬁcient for cubic particles in continuous tube ﬂow using the moving thermocouple method, J. Food Process Eng., 17, 229–241, 1994a. Zitoun, K.B. and Sastry, S.K., Determination of convective heat transfer coefﬁcient between ﬂuid and cubic particles in continuous tube ﬂow using noninvasive experimental techniques, J. Food Process Eng., 17, 209–228, 1994b. Zuritz, C.A., McCoy, S., and Sastry, S.K., Convection heat transfer coefﬁcients for irregular particles immersed in non-Newtonian ﬂuids during tube ﬂow, J. Food Eng., 11, 159–174, 1990. Zuritz, C.A. and Sastry, S.K., Convective Heat Transfer Coefﬁcients for Non-Newtonian Flow Past Food-shaped Particulates, ASAE Paper No. 87–6538, 1987.

© 2003 by CRC Press LLC

33

Heat and Mass Transfer Modeling in Microwave and Spouted Bed Combined Drying of Particulate Food Products H. Feng and J. Tang

CONTENTS 33.1 33.2

Introduction Model Development 33.2.1 Transport Relations 33.2.2 Mass Balance 33.2.3 Energy Balance 33.2.4 Governing Equations 33.2.5 Initial and Boundary Conditions 33.3 Model Reduction 33.4 Effective Moisture Diffusivity 33.5 Permeability of Apple Tissues 33.6 Dielectric Properties and Microwave Power Absorption 33.7 Numerical Analysis 33.8 Experimental 33.9 Model Validation 33.10 Conclusions Nomenclature Acknowledgments References Appendix

© 2003 by CRC Press LLC

33.1 INTRODUCTION Microwave drying involves simultaneous heat, mass, and momentum transfer, as well as volumetric heat generation. The internal heat generation results in the development of a gas/vapor pressure gradient from interior to product surface that distinguishes microwave drying from other drying methods (Turner and Jolly, 1991). Internal heat generation also produces a positive temperature gradient (from the interior to the surface), in contrast to the negative temperature gradient produced during drying by conventional hot air heating. A comprehensive heat and mass transfer analysis that takes into account the contribution of the pressure gradient to moisture migration is desirable in order to understand the underlying physics involved in microwave drying and to predict temperature and moisture changes during drying. Moisture exists in porous food material in the forms of free water, bound water, and vapor. The migration of moisture through the food can be caused by the individual or combined contributions of moisture, temperature, and pressure gradients. In microwave drying, free water transport has been attributed to diffusion (Torringa et al., 1996; Adu and Otten, 1996) or capillary ﬂow (Wei et al., 1985; Constant et al., 1996; Lian et al., 1997; Turner et al., 1998; Ni et al., 1999). For vapor migration, diffusion (Lian et al., 1997), capillary ﬂow (Turner et al., 1998; Ni et al., 1999) and a combination of capillary ﬂow and diffusion (Chen and Schmidt, 1990; Constant et al., 1996) have been considered as transport mechanisms. Few studies have considered the migration of bound water. In studies regarding the mechanism of bound water transfer, Turner et al. (1998) assumed that bound water transfer was caused by diffusion, while Chen and Pei (1989) employed a capillary mechanism to characterize bound water ﬂow. Knowledge of thermophysical and dielectric properties is essential to a heat and mass transfer analysis in microwave drying. There is a lack of understanding of the thermophysical and dielectric properties needed in such an analysis, especially for food materials. Moisture diffusivity, permeability, and dielectric properties were used in this study to account for moisture gradient driven ﬂow, pressure gradient driven ﬂow, and microwave heat generation. It is important to understand the effect of moisture content and product temperature on these properties. In order to understand more about microwaves and their application to drying, it is necessary to develop a comprehensive heat and mass transfer model for microwave and spouted bed combined drying of hygroscopic porous food products; to determine moisture diffusivity, permeability, and dielectric properties for a model food, apple tissue; and to experimentally validate the model developed in this study.

33.2 MODEL DEVELOPMENT In this study, drying of a particulate product was conducted in a spouted bed placed in a microwave cavity. Microwave energy was applied to the cavity at a constant and adjustable rate. The hot air velocity was set such that the aerodynamic conditions needed to sustain stable ﬂuidization in the spouted bed could be realized. The pneumatic agitation in the spouted bed helped to improve the heating uniformity among particles during microwave drying. The hot air ﬂow was at constant temperature.

© 2003 by CRC Press LLC

The following assumptions were used in model development: the material is homogeneous and isotropic on the macro scale; transport of free water is governed by the generalized Darcy’s law; bound water transport is driven by chemical potential difference (Stanish et al., 1986; Gong, 1992); and transport in the gas phase is determined by the contribution of convection and diffusion. Other assumptions included: 1. Local thermodynamic equilibrium exists, that is, the solid, liquid, and gas phases are at the same average temperature at any moment in a control volume. 2. Solid, liquid, and gas phases are continuous. 3. The binary gas mixture of air and vapor obeys the ideal gas law. 4. Vapor pressure as a function of moisture content and temperature can be estimated using sorption isotherms. 5. The model material used in this study, diced apples, can be treated as equivalent spheres. 6. The diced apples are exposed to a uniform microwave ﬁeld. 7. Electromagnetic ﬁeld intensity is uniform throughout diced apples. The governing equations for microwave drying were derived at a macroscopic level. Variables examined in this study are averaged values over a control volume. This approach was ﬁrst proposed by Whitaker (1977) and has been widely used in multiphase heat and mass transfer studies related to drying of porous materials (Bories, 1991).

33.2.1 TRANSPORT RELATIONS Fluid velocities in a multiphase porous food system are given by the generalized Darcy’s law: r r Kk rf uf = − (∇Pg − ∇Pc − ρf g) µf

(33.1)

Kk rg r r ug = − (∇Pg − ρg g) µg

(33.2)

where the capillary pressure Pc = Pg – Pf. Diffusion of vapor and air is governed by Fick’s law: r r ρ  jv = − ja = − ρg D av ∇ v   ρg 

(33.3)

In many food materials, bound water migration is important. It has been found that migration of the bound water cannot be simply treated as a diffusion process (Chen and Pei, 1989). In the present study, a universal driving force, the chemical

© 2003 by CRC Press LLC

potential gradient, was employed as the driving force for the bound water ﬂow (Gong, 1992). The bound water ﬂux is then given by: n b = D b (1 − ε ′)

∂ µb ∂z

(33.4)

From the local thermodynamic equilibrium assumption, the chemical potential of bound water, µ′b, equals the chemical potential of vapor, µ′v. Hence thermodynamic relations for vapor can be used to express the bound water ﬂux. A detailed derivation can be found elsewhere (Stanish et al., 1986), and the resulting equation is given in Equation (33.7). Thermal diffusion through a food material is controlled by Fourier’s law: r q = − λ eff ∇T

(33.5)

33.2.2 MASS BALANCE The mass balance equations for free water, bound water, vapor, and air can be written as:

Free water:

(1 − ε )ρs

∂Xf r ˙ + ∇ ⋅n f = − m ∂t

(33.6)

Bound water:

(1 − ε )ρs

∂X b r ˙b + ∇⋅ n b = − m ∂t

(33.7)

∂X v r ˙ +m ˙b + ∇⋅ n v = m ∂t

(33.8)

∂Xa r + ∇⋅ n a = 0 ∂t

(33.9)

(1 − ε )ρs

Vapor:

(1 − ε )ρs

Air:

In Equations (33.6–9), the mass ﬂuxes are speciﬁed by: Free water:

Bound water:

Vapor:

Kk rf Kk rf r r n f = ρf u f = − ρf ∇Pl = − ρf ∇( Pg − Pc ) µf µf

(33.10)

  ε ∇Pv Sv r r n b = ρb u b = −ρb D b (1 − ε ′) − ∇T Mv   ρv

(33.11)

r ρ  Kk rg r r n v = ρv u v + jv = − ρv ∇Pg − ρg Dav ∇ v  µg  ρg 

(33.12)

© 2003 by CRC Press LLC

Air:

r ρ  Kk rg r r n a = ρa u a + ja = −ρa ∇Pg + ρg Dav ∇ v  µg  ρg 

(33.13)

Gas:

Kk rg r r v n g = n a + n v = − ρg ∇Pg µg

(33.14)

In Equation (33.10), the free water transfer caused by gravity is ignored, and in Equation (33.14), ρg = ρa + ρv.

33.2.3 ENERGY BALANCE The total energy balance for a representative elementary volume is written as (Bird et al., 1960): r r ∂ DP +Φ (ρ h ) + ∇ ⋅(ρ uh ) = − (∇ q ) − ( τ: ∇ u) + ∂t Dt

(33.15)

r The viscous dissipation term ( τ:∇µ ) and pressure work term (DP/Dt) are usually negligible. Hence, Equation (33.15) reduces to an enthalpy balance equation: r ∂ (ρ h ) + ∇ ⋅(ρ uh ) = − (∇ q ) + Φ ∂t

(33.16)

ρ h = ρs h s + ρv h v + ρa h a + (ρf + ρb ) h l

(33.17)

r r r r r ρ uh = ρv u v h v + ρa u a h a + (ρf u f + ρb u b ) h l

(33.18)

where

33.2.4 GOVERNING EQUATIONS Due to the geometric symmetry, moisture transfer was assumed to take place only in the radial direction. Hence, a one-dimensional heat and mass transfer problem in spherical coordinates was considered. The total moisture transport equation can be obtained by adding Equations (33.6) to (33.8); the temperature equation was obtained by substituting Equations (33.5), (33.17), and (33.18) into the enthalpy balance equation (Equation (33.16)), and the total pressure equation was obtained from the air balance equation (Equation (33.9)). The resulting drying equations are as follows: ∂ Pg  ∂Xl 1 ∂  ∂T 2 ∂Xl = 2 + DT r 2 + DP r 2 D X r  ∂t ∂r ∂r ∂r  r ∂r 

© 2003 by CRC Press LLC

(33.19)

C TX

∂ Pg  ∂Xl ∂T ∂T 1 ∂  2 ∂Xl + C TT = 2 + D TT r 2 + D TP r 2 D r +Φ r ∂ r  TX ∂t ∂t ∂r ∂r ∂r 

C PX

(33.20)

∂ Pg ∂ Pg  ∂Xl ∂T ∂T 1 ∂  a 2 ∂Xl + C PT + C PP = 2 + D aT r 2 + D aP r 2 D X r  ∂t ∂t r ∂r  ∂t ∂r ∂r ∂r  (33.21) k

In Equations (33.19) to (33.21), Dij and Cij are kinetic and capacity coefﬁcients, respectively. The subscripts i and j can be temperature, moisture, or pressure, while the superscript k denotes air, free water, bound water, or vapor. The expressions for these coefﬁcients are detailed in this chapter’s Appendix

33.2.5 INITIAL

AND

BOUNDARY CONDITIONS

Initial conditions can be written as: Xl

t =0

= X0

T t =0 = T0

Pg

t =0

= Patm

(33.22)

Because of the pneumatic agitation in a spouted bed, it is reasonable to assume that moisture arriving at a sample surface from the interior evaporates immediately and is carried away by the hot air stream. The moisture transfer boundary condition in spherical coordinates is then given by: ∂ Pg   ∂Xl ∂T + DT + DP −(1 − ε )ρs  D X ∂r ∂r ∂ r  

= ε h m (ρ vs − ρ v∞ )

(33.23)

r =R0

An energy balance over the interface can be set up to obtain the temperature boundary condition: − λ eff

∂T ∂r

r =R0

∂ Pg   ∂Xl ∂T = h ( T∞ − Ts ) − ∆h v (1 − ε )ρs  D fX + D Xb + D fT + D Tb + D fP  ∂r ∂r ∂r   (33.24)

(

)

(

)

Pressure at the surface of a spherical particle can be written as: P

r =R0

= Patm

(33.25)

The symmetry condition at the center of the sphere must be satisﬁed: ∂ Xl ∂r

© 2003 by CRC Press LLC

= r=0

∂T ∂r

= r=0

∂ Pg ∂r

=0 r=0

(33.26)

33.3 MODEL REDUCTION To simplify the microwave drying equations given in Equations (33.19–33.21) and (33.22–33.26) for numerical analysis and further elucidation of the mechanisms, a scaling method was used to analyze the magnitude of each term in the equations. The following scaling groups were used (Plumb et al., 1986): r∗ =

r ; R0

X∗l = tc =

t∗ =

Xl ; X0

t ; tc

X∗b =

T∗ =

Xb − Xe ; X0 − Xe

µ a∞ R 20 R0 ; = u c K 0 ( Pmax − Patm )

T − T0 ; Tmax − T0 ρ∗vs = uc =

Pg∗ =

Pg − Patm Pmax − Patm

ρvs P T = vs ∞ ; ρ v∞ Pv∞ Ts

K 0 Pmax − Patm ; µ a∞ R0

(33.27) Φ∗ =

Φ Φ0

In the scaling analysis, a comparison of the magnitude of each dimensionless group helped to determine which terms were insigniﬁcant and hence negligible. In the analysis, a term with a coefﬁcient at least one magnitude smaller than the other terms was considered negligible and was eliminated from the drying equations. The magnitude for each term was assessed by using literature values of the physical, thermal, and transport parameters in the capacity and kinetic coefﬁcients. For moisturedependent parameters, two extreme moistures, X0 = 7.0 (db) and Xl = 0.1 (db), were used to estimate the range of the coefﬁcients. For temperature-dependent parameters, an average drying temperature of 343°K was used. Detailed analyses can be found elsewhere (Feng, 2000). Simpliﬁed drying equations can be written as: ∗ Tc ∂ X∗l ( Pmax − Patm ) ρf Kk rf ∂ Pg   ∂ X1∗ ∂  ∗2  = r D X +  (33.28)  ∂ t∗ R 20 X 0 r ∗2 ∂ r ∗   eff 0 ∂ r ∗ 1− ε ρs µ f ∂ r ∗  

(ρC p )eff

∗ Tmax − T0 ∂ T∗ Tmax − T0 ∂  ∗2 ∂ T  ˙ + Φ Φ∗ = λ r   + ∆h v M 0 ∂ t∗ ∂ r∗  tc R 20 r ∗2 ∂ r ∗  eff

(1 − ε ) =

(33.29)

 ε M a Pmax − Patm ∂ Pg∗ ρaρs X 0 ∂ X∗l  1 − ε ρs + 1 − Xl  ∗ ρf t c ∂ t ε ρf + ρ b  R ′ T tc ∂ t∗  1 R r

2 ∗2 0

∂ ∂ r∗

 ∗2 Kk rg ∂ Pg∗   r ( Pmax − Patm )ρa µ g ∂ r ∗  

(33.30)

The simpliﬁed boundary conditions are given by: ∗ ∂ X∗ P − Patm ρf Kk rf ∂ Pg  1  Deff X 0 ∗l + max ∗   1 − ε ρs µ f ∂ r  R0  ∂r

© 2003 by CRC Press LLC

=− r ∗ =1

ερv∞ h m ∗ (ρ − 1) (1 − ε )ρs vs

(33.31)

−

λ eff (Tmax − T0 ) ∂ T∗ ∂ r∗ R0 −

∆h v (1 − ε )ρs R0

= h (T∞ − T0 ) − hTs∗ (Tmax − T0 )

∗

r =1

∗  ∂ X∗ ( P − P ) ρ Kk rf ∂ Pg  Deff X 0 ∗l + max atm f  1− ε ρs µ f ∂ r ∗  ∂r 

P*| ∂ X ∗l ∂r∗

= r∗ = 0

r*=1

=0

∂T∗

=

∂r∗

∗

r =0

(33.32) (33.33)

∂ Pg∗ ∂r∗

=0

(33.34)

∗

r =0

It can be seen from Equations (33.28–33.34) that terms with capillary pressure were eliminated through the scaling analysis. The remaining unknown parameters in Equations (33.28–33.34) include effective moisture diffusivity, intrinsic and relative permeabilities, and dielectric properties. Experiments were designed and conducted in this study to measure these properties as function of moisture and temperature. All other thermal and transport relations for apples are from the literature and are listed in Table 33.1. TABLE 33.1 Correlations for Physical, Thermal, Thermodynamic, Dielectric, and Mass Transfer Parameters Parameter

Correlation

Reference

1.282 + 1.65(1.899 + X l )X l (1 + 1.65X l )(1.899 + X l )

Porosity, ε'

ε′ =

Viscosity of free water, µf

µ f (T) = µ f 0 exp(a − bT + cT 2 + dT 3 − eT 4 )

Feng, 2000 Turner, 1991

−4

µf0 = 1 × 10 ; a = 29.619; −4 b = 0.152; c = 0.648 × 10 ; −6 −8 d = 0.815 × 10 ; e = 0.120 × 10 Viscosity of gas, µg

µ g (T) = µ g 0 {T 1/ 2 / (a + b / T − c / T 2 + d / T 3 )}

Turner, 1991

a = 0.672; b = 85.229; c = 2111.475; d = 106417.0; µg0 = 1 × 10 Latent heat of water, ∆hv Effective thermal conductivity of apple, λeff Thermal conductivity of air, λa Effective speciﬁc heat of apple, Cpeff Air–vapor binary diffusivity, Dav

© 2003 by CRC Press LLC

−6

6

∆hv = 2.792 × 10 − 160 T − 3.43 T λeff = 0.12631 + 0.0595 Xl

2

λ a = 0.0035 + 7.67 × 10 −5 ∗ T C peff = 1415 +

Turner, 1991 Niesterus, 1996

27.21 X l 1 + Xl

D av = 2.20 × 10 −5

101325  T  Pg  273.15 

Stanish et al., 1986 Donsì et al., 1996

1.75

Stanish et al., 1986

33.4 EFFECTIVE MOISTURE DIFFUSIVITY The effective moisture diffusivity Deff combines the contributions of both bound water and free water. From Equation (33.28), it can be seen that Deff can be determined with a hot air–only drying test at moderate temperatures, in which the internal vapor generation is negligible. Drying tests with apple tissues were conducted, and Deff was obtained using the slope method (Feng et al., 2000a). Deff as function of moisture content and temperature is given in the following equation:  a + a2 ∗ Xl  D eff = a 0 ∗ exp − 1    T −4

3

(33.35) 2

where a0 = 6.273 × 10 ; a1 = 5.843 × 10 ; and a2 = –2.038 × 10 .

33.5 PERMEABILITY OF APPLE TISSUES Intrinsic and relative permeabilities of apple tissues were measured with a set-up designed based on the following relation:

Q g = ug A = − A

K (ε ) k rg ∆Pg µg

H

(33.36)

From Equation (33.36), when the gas phase ﬂow rate Qg and pressure drop over a specimen ∆Pg are determined, the product of intrinsic permeability K and gas relative permeability krg can be obtained. The separation of K with krg was achieved by conducting a dry sample test in which krg = 1 and thus K as function of porosity could be attained. Details of the set-up and experimental procedures can be found in Feng et al. (2002b). The intrinsic permeability K(ε) of apple tissue as a function of porosity was determined by the above method and can be ﬁtted to a Kozeny–Carman equation: K(ε ) = 5.578 × 10 −12

ε3 (1 − ε ) 2

(33.37)

The gas and liquid relative permeabilities for apple tissue were also determined (Feng et al., 2002b) and can be correlated to saturation level S using the following empirical equations: k rg = 1.01 e −10.86 S k rl = S3

© 2003 by CRC Press LLC

(33.38) (33.39)

33.6 DIELECTRIC PROPERTIES AND MICROWAVE POWER ABSORPTION Dielectric constant ε* and loss factor ε″ are important parameters in the determination of microwave penetration depth and volumetric heat generation. The open-ended coaxial probe technique was used to measure ε* and ε″ for apple tissues over a moisture content range of 4 to 87.5% (wb) and at 22 and 60°C. From measured results with apple tissues, a correlation of loss factor ε″ with moisture and temperature changes was obtained (Feng et al., 2000): ε ′′ = a 1 + a 2 T + a 3 T 2 + a 4 X + a 5 X T + a 6 X T 2 + a 7 X 2 + a 8 X 2 T + a 9 X 3 (33.40) where a1 = −23.5999; a2 = 0.158233; a3 = −0.000256978; a4 = −1.87998; a5 = −6 −5 0.00768435; a6 = −5.6363 × 10 ; a7 = 0.0289568; a8 = −7.66337 × 10 ; a9 = −5 −4.09947 × 10 . Microwave power absorption by the sample during drying can be obtained using: Φ = Φ0

ε ′′ ε ′′0

(33.41)

where Φ0 is the absorbed microwave power at the beginning of a microwave and spouted bed drying (MWSB) drying test. It is given by Φ0 = Φinput − Φreﬂect, the difference between measured input and reﬂected power. ε ′′0 is the loss factor corresponding to the value at the beginning of a drying test.

33.7 NUMERICAL ANALYSIS The simpliﬁed drying equations (Equations (33.28) to (33.34)) are coupled and highly nonlinear. The ﬁnite difference method was used to ﬁnd numerical solutions. The analytical domain was a sphere with a diameter of 5 mm divided into 15 layers, each with a thickness δ = 1/3 mm. A time step of 1 sec was selected in the simulation. The Crank–Nicolson scheme was used to discretize the partial differential equations for the internal nodes. The boundary conditions at nodes 0 and 16 were discretized with a three-point formula to obtain the same accuracy as with internal nodes. The moisture, temperature, and gas pressure equations were solved simultaneously. A program was written using Matlab to implement the simulation. Details of the ﬁnite difference formulation can be found elsewhere (Feng, 2000).

33.8 EXPERIMENTAL A microwave and spouted bed combined drying system was developed to conduct drying tests to validate the model simulation. This system consisted of a 2.45 GHz microwave supply system and a hot air system (Figure 33.1). In the microwave supply system, a magnetron generated the microwaves, a wave guide transmitted

© 2003 by CRC Press LLC

1

2

3

4

5

10

11

6

12

7 Air

9

8

FIGURE 33.1 Schematic of 2.45 GHz microwave and spouted bed drying system. 1. Direction coupler; 2. circulator; 3. magnetron; 4. power controller; 5. power meter; 6. temperature controller; 7. HP network analyzer; 8. air pump; 9. heater; 10. three-stub tuner; 11. microwave cavity; 12. spouted bed.

the waves to the cavity, and a directional coupler with power meters measured power components. In the system, a circulator with a water load was installed to absorb the reﬂected power and a three-stub tuner was used to adjust the matching impedance of the drying cavity. The power generated from the magnetron could be continuously adjusted using the power controller. Both the incident and the reﬂected power were measured using HP power meters so that the power absorbed by the drying sample could be accurately determined. Diced Red Delicious apples (Malus domestica Borkh) with average initial moisture content of 20.2% (wb) were used as the model food in the validation. The spouted bed superﬁcial air velocity was 2.1 m/sec in all experiments, the velocity at which a stable particle circulation can be achieved during drying to ensure uniform heating. Forty grams of diced apples were used in each drying test. Moisture loss was monitored by periodically weighing the sample on an electric balance. The average moisture content of samples was determined using the vacuum oven method (AOAC, 1990). The drying temperature of the dice was measured at the core of ten randomly chosen apple pieces with a type T thermocouple (response time 0.8 sec) at predesignated time intervals. The pressure increase during microwave heating was measured using fresh apples with a ﬁber optical pressure probe, which has a resolution of 1 kPa. The pressure probe was led through a hole opened on the wall of the spouted bed and inserted into the center of a fresh-cut apple sample sealed with

© 2003 by CRC Press LLC

vacuum grease to prevent vapor leakage. A data acquisition system was used to record the pressure data.

33.9 MODEL VALIDATION Figure 33.2 compares the predicted and experimentally determined moisture contents for MWSB and spouted bed (SB) drying. In MWSB drying, the data reported were the averages of four replicates, and drying tests were conducted at microwave power density of 4 W/g (wb) and hot air temperature of 70°C. For SB alone drying, the same air conditions as for MWSB drying were used, and experiments were performed in triplicate. Relatively small error bars in Figure 33.2 indicate good repeatability in drying tests. The simulated moisture content followed an exponential decay curve that characterizes drying in the falling rate period for hygroscopic materials. At the beginning of drying, the simulation slightly underestimated moisture loss. The assumption of spherical geometry for apple dice might be a major reason for this discrepancy due to an underestimation of the surface-to-volume ratio. Generally, model predictions were in good agreement with experiments for both drying methods. The temperatures measured from diced apples and predicted with the model are compared in Figure 33.3 for MWSB (MW power 4 W/g and air temperature 70°C) and SB (air temperature 70°C) drying. Temperature prediction in MWSB drying agreed well with the measured values. At the beginning of drying, the hot air heated the apple dice from outside, and the microwaves heated volumetrically. This led to a rapid increase in product temperature. When the apple dice surface temperature surpassed the air temperature, the air started to cool the apple dice. The center temperature, however, continued to increase as a result of microwave heating until it reached about 83°C, when a balance between the energy supplied by microwaves and the heat losses due to surface convective cooling and evaporation was established.

Moisture Content (wb), %

25 Model prediction SB drying test MWSB drying test

20 15 10 5 0 0

10

20

30

40

50

60

70

80

90

Drying Time, min

FIGURE 33.2 Moisture content comparison between model predictions and experimental results for microwave and spouted bed (MWSB) drying and spouted bed (SB) drying. (From Feng, H. et al., AICHE J., 47(7), 1499–1509, 2001. With permission.)

© 2003 by CRC Press LLC

90 80

Bed temperature

Temperature, °C

70 60 50 40 30

Model prediction SB drying test MWSB drying test

20 10 0 0

10

20

30

40

50

60

70

80

90

Drying Time, min

FIGURE 33.3 Temperature comparison between model predictions and experimental results for MWSB and SB drying. (From Feng, H. et al., AICHE J., 47(7), 1499–1509, 2001. With permission.) 10

Over-pressure, kPa

8 6 4 Experiment #1 Experiment #2 Experiment #3 Model

2 0 0

1

2

3

4

5

Drying Time, min

FIGURE 33.4 Comparison of predicted and measured pressures for MWSB drying with microwave power 10 W/g, hot-air temperature 70°C and initial moisture content 84% (wb). (From Feng, H. et al., AICHE J., 47(7), 1499–1509, 2001. With permission.)

The product temperature remained nearly constant throughout the rest of drying. This is a unique feature associated with MWSB drying. The high surface heat transfer in the spouted bed helped to maintain a nearly constant drying temperature. This temperature leveling effect prevents the product from overheating and charring. Therefore, MWSB drying has potential application in drying of heat-sensitive food products. In SB drying, the sample temperature approached air temperature at a slightly lower rate compared to that of MWSB drying, and the predicted temperature agreed well with the bed temperature. The over-pressure readings measured with the ﬁber optical probe are compared to model prediction in Figure 33.4. Experiments to validate model prediction of pressure were conducted at conditions different from those for moisture and

© 2003 by CRC Press LLC

temperature veriﬁcation. This is because at the moisture content of commercial evaporated diced apple (20.2%), and the power level used in moisture and temperature validation tests, the over-pressure generated is lower than the threshold of the pressure probe (1 kPa). To generate a vapor pressure above the threshold of the pressure probe (1 kPa), fresh apple samples in a cylindrical shape (8 mm in diameter and 15 mm in length), and microwave power of 10 W/g and sample moisture of 84% (wb) were used in the tests. The measured pressure increased during the ﬁrst two minutes of drying to reach a peak and started to decrease thereafter. At this stage, the moisture content of the sample remained high, and hence volumetric heating was still intensive enough to maintain the pressure. Therefore, the measured pressure decrease might have been caused by a gradual failure of the seal to the pressure probe.

33.10 CONCLUSIONS The comprehensive heat and mass transfer drying model developed in this study was demonstrated to be an effective tool to predict moisture, temperature, and pressure history and distribution for MWSB of particulate foods. The model prediction of moisture, temperature, and pressure agreed with experimental results. A temperature leveling effect was predicted and in agreement with experiment results. This unique temperature leveling effect in MWSB drying makes it possible to use this method for drying heat-sensitive food products.

NOMENCLATURE C Cp D Dav Db g h ∆hv j kr K m ˙ M n P Pc q R R′ S t

Capacity coefﬁcient −1 −1 Speciﬁc heat, J·kg K Kinetic coefﬁcient; material derivative 2 −1 Binary air–vapor diffusivity, m ·sec 2 −1 Bound water diffusivity, m ·sec −2 Gravitational acceleration, m·sec −1 −2 −1 Enthalpy, J·kg ; surface heat transfer coefﬁcient, W·m K −1 Latent heat of free water, J·kg −2 −1 Diffusive mass ﬂux, kg·m ·sec Relative permeability 2 Intrinsic permeability, m −3 −1 Moisture evaporation rate, kg·m ·sec −1 Molar mass, kg·mol −2 −1 Mass ﬂux, kg·m sec Pressure, Pa Capillary pressure, Pa −2 −1 Heat ﬂux, J·m ·sec −1 Sample radius, m −1 −1 Universal gas constant, J·mol K Saturation Time, sec

© 2003 by CRC Press LLC

T u X

Average absolute temperature, K −1 Spouted bed air superﬁcial velocity, m·sec −1 Moisture content (dry basis), kg H2O·(kg solid)

GREEK SYMBOLS ε ε′ ε* ε″ Φ λ µ µ′ ρ ρs τ

Porosity [(gas + liquid)/total volume], tolerance limit on iteration scheme Porosity deﬁned in Table I (gas volume/total volume); dielectric constant Dielectric constant Dielectric loss factor −3 Heat source, W·m −1 −1 Thermal conductivity, W·m ·K ; wave length, m −1 −1 Dynamic viscosity, kg·m ·sec Chemical potential −3 Density, kg·m −3 Solid density (solid mass/solid volume), kg·m −2 Shear stress tensor, kg·m

SUBSCRIPTS 0 a atm b eff f g l max P s T v w X ∞

AND

SUPERSCRIPTS

At saturated condition or free space; initial condition (refers to fresh sample) Air Atmospheric pressure Bound water, bulk density Effective Free water Gas = air + vapor Liquid = free water + bound water Maximum values Pressure Solid, or relating to surface Temperature Vapor Total moisture = free water + bound water + vapor Moisture Surrounding

ACKNOWLEDGMENTS Support for this research has been provided by Washington State University IMPACT Center and the Northwest Center for Small Fruits Research. Special thanks go to Dr. Ovid Plumb and Dr. Ralph Cavalieri for their valuable input to this work. The authors would like to thank Timothy Wig and Wayne DeWitt for assistance in developing the 2.45 GHz MWSB drying system, and TreeTop, Inc., Selah, WA, for donating evaporated apples.

© 2003 by CRC Press LLC

REFERENCES Adu, B. and Otten, L., Modeling microwave heating characteristics of granular hygroscopic solids, J. Microwave Power Electromag. Energy, 31, 35–42, 1996. AOAC, Ofﬁcial Methods of Analysis, 15th ed, Association of Ofﬁcial Analytical Chemists, Washington, DC, 1990. Bird, R.B., Stewart, W.E., and Lightfoot, N.E., Transport Phenomena, John Wiley and Sons, New York, 1960. Bories, S.A., Fundamentals of drying of capillary-porous bodies, in Convective Heat and Mass Transfer in Porous Media, Kakac, S. et al. (Eds.), Kluwer Academic Publishers, Dordrecht, 1991. Chen, P. and Pei, D.C.T., A mathematical model of drying processes, Int. J. Heat Mass Transfer, 32, 297–310, 1989. Chen, P. and Schmidt, P.S., An integral model for drying of hygroscopic and nonhygroscopic materials with dielectric heating, Drying Technol., 8, 907–930, 1990. Constant, T., Moyne, C., and Perré, P., Drying with internal heat generation: theoretical aspects and application to microwave heating, AIChE J., 42, 359–368, 1996. Donsì, G., Ferrari, G., and Nigro, R., Experimental determination of thermal conductivity of apple and potato at different moisture contents, J. Food Eng., 30, 263–268, 1996. Feng, H., Microwave Drying of Particulate Foods in a Spouted Bed. Ph.D. dissertation, Washington State University, 2000. Feng, H., Tang, J., and Cavalieri, R., Dielectric properties of dehydrated apples as affected by moisture and temperature, Trans. ASAE, 45(1), 129–135, 2002a. Feng, H., Tang, J., Cavalieri, R.P., and Plumb, D.A., Heat and mass transport in microwave drying of porous materials in a spouted bed, AICHE J., 47(7), 1499–1509, 2001. Feng, H., Tang, J., and Dixon-Warren, St.J., Determination of moisture diffusivity of Red Delicious apple tissues by thermogravimetric analysis, Drying Technol., 18(6), 1183–1199, 2000. Feng, H., Tang, J., and Plumb, G., Intrinsic and relative permeability for ﬂow of humid air in unsaturated apple tissues, J. Food Eng., accepted, 2002b. Gong, L., A Theoretical, Numerical and Experimental Study of Heat and Mass Transfer in Wood during Drying, Ph.D. dissertation, Washington State University, 1992. Lian, G., Harris, R.E., and Warboys, M., Coupled heat and moisture transfer during microwave vacuum drying, J. Microwave Power Electromag. Energy, 32, 34–44, 1997. Ni, H., Datta, A.K., and Torrance, K.W., Moisture transport in intensive microwave heating of biomaterials: a multiphase porous media model, Int. J. Heat Mass Transfer, 42, 1501–1512, 1999. Niesterus, R., Changes of thermal properties of fruits and vegetables during drying, Drying Technol., 14, 415–422, 1996. Plumb, O.A., Couey, L.M., and Shearer, D., Contact drying of wood veneer, Drying Technol., 4, 387–413, 1986. Stanish, M.A., Schajer, G.S., and Kayihan, F., A mathematical model of drying for hygroscopic porous media, AIChE J., 32, 1301–1311, 1986. Torringa, E.M., van Dijk, E.J., and Bartels, P.S., Microwave pufﬁng of vegetables: Modeling and measurements, in Proceedings of 31st Microwave Power Symposium, Int. Microwave Power Inst., Manassas, VA, 1996. Turner, I.W., The Modeling of Combined Microwave and Convective Drying of a Wet Porous Material, Ph.D. thesis, University of Queensland, Australia, 1991. Turner, I.W. and Jolly, P.G., Combined microwave and conventional drying of a porous material, Drying Technol., 9, 1209–1269, 1991.

© 2003 by CRC Press LLC

Turner, I.W., Puiggali, J.R., and Jomaa, W., A numerical investigation of combined microwave and convective drying of a hygroscopic porous material: a study based on pine wood, Trans. IChemE, 76, Part A, 193–209, 1998. Wei, C.K., Davis, H.T., Davis, E.A., and Gorden, J., Heat and mass transfer in water-laden sandstone: microwave heating, AIChE J., 31, 842–848, 1985. Whitaker, S., Simultaneous heat, mass, momentum transfer in porous media: a theory of drying, Adv. Heat Transfer, 13, 119–203, 1977.

APPENDIX D fX = −

1 ρf Kk rf  ∂ Pc  ; 1 − ε ρs µ f  ∂ X w  T

D fP =

1 ρf Kk rf 1 − ε ρs µ f

D Xb =

1 − ε ′ D b ε R ′ T  ∂ Pv  1 − ε ρs Pv M v  ∂ X w  T

D Tb = −

D fT = −

1 ρf Kk rf  ∂ Pc    1 − ε ρs µ f  ∂ T  X

ε R ′ T  ∂ Pv   1 − ε ′ D b  Sv b  −   ; D P = 0 1 − ε ρs  M v Pv M v  ∂ T  X  w 

D Xv =

 ∂ Pv  Ma M v (1 − ε )ρs R ′ T( Pg M a + (M v − M a )Pv )  ∂ X w  T

D Tv =

 ∂ Pv  Ma M v   (1 − ε )ρs R ′ T( Pg M a + (M v − M a )Pv )  ∂ T  X

D Pv =

Dav Pg

Dav Pg

1 (1 − ε )ρs

C TX = ∆h v

Mv R′

 P M Kk rg  D av M a M v Pv −  v v  R ′ T( Pg M a + (M v − M a )Pv )   R ′ T µ g  (1 − ε )ρs Pv  (1 − ε )ρs  1 ∂Pv  + ε − X −  ρf + ρ b l  T ∂ X l   ρf + ρ b T 

C TT = (ρC p ) eff + ∆h v

© 2003 by CRC Press LLC

w

(1 − ε )ρs  ∂( Pv / T) Mv  X ε − ρf + ρb l  ∂ T R′ 

w

D TX = ∆h v (1 − ε )ρsD Xv ;

D TT = λ eff + ∆h v (1 − ε )ρsD Tv

D TP = ∆h v (1 − ε )ρsD Pv

C PX =

 1 ∂Pv  ε M a  Pg − Pv  1 − ε ρs   1 − ε ρs − 1 − Xl  −    ε ρf + ρ b  T ∂ X l  R ′  T  ε ρf + ρb  

C PT =

εMa R′

 1 − ε ρs   Pg ∂( Pv / T)  1 − ε ρ + ρ X l   T 2 − ∂ T    f b

C PP =

εMa R′

 1 − ε ρs  1 1 − ε ρ + ρ X l  T   f b  ∂ Pv   ∂X   wT

D aX = − (1 − ε )ρs D Xv = − D av

Pg M a Mv R ′ T Pg M a + (M v − M a )Pv

D aT = − (1 − ε )ρs D Tv = − D av

Pg M a Mv  ∂ Pv    R ′ T Pg M a + (M v − M a )Pv  ∂ T  X

D aP =

( Pg − Pv )M a Kk rg R′T

© 2003 by CRC Press LLC

µg

+ D av

Mv Pv M a R ′ T Pg M a + (M v − M a )Pv

w