Ion Exchange Membranes: Fundamentals and Applications

ION EXCHANGE MEMBRANES: FUNDAMENTALS AND APPLICATIONS Membrane Science and Technology Series Volume 1: Volume 2: Volu...

Author: Yoshinobu Tanaka

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ION EXCHANGE MEMBRANES: FUNDAMENTALS AND APPLICATIONS

Membrane Science and Technology Series Volume 1: Volume 2: Volume 3: Volume 4: Volume 5: Volume 6: Volume 7: Volume 8:

Volume 9: Volume 10: Volume 11: Volume 12:

Pervaporation Membrane Separation Processes Edited by R.Y.M. Huang (1991) Membrane Separations Technology, Principles and Applications Edited by R.D. Noble and S.A. Stern (1995) Inorganic Membranes for Separation and Reaction By H.P. Hsieh (1996) Fundamentals of Inorganic Membrane Science and Technology Edited by A.J. Burggraaf and L. Cot (1996) Membrane Biophysics Edited by H. Ti Tien and A. Ottova-Leitmannova (2000) Recent Advances in Gas Separation by Microporous Ceramic Membranes Edited by N.K. Kanellopoulos (2000) Planar Lipid Bilayers (BLMs) and their Applications Edited by H.T. Tien and A. Ottova-Leitmannova (2003) New Insights into Membrane Science and Technology: Polymeric and Biofunctional Membranes Edited by D. Bhattacharyya and D.A. Butterfield (2003) Ion-Exchange Membrane Separation Processes By H. Strathmann (2004) Nano and Micro Engineered Membrane Technology By C.J.M. vanRijn (2004) Membrane Contactors: Fundamentals, Applications and Potentialities By E. Drioli, A.Criscuoli and E. Curcio (2006) Ion Exchange Membranes: Fundamentals and Applications By Y. Tanaka

Membrane Science and Technology Series, 12

ION EXCHANGE MEMBRANES: FUNDAMENTALS AND APPLICATIONS Edited by

Yoshinobu Tanaka IEM Research Ibaraki, Japan

Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo

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Preface Ion exchange membranes function as concentrating or desalting electrolyte solutions. Paying attention to this phenomenon in 1940, Meyers and Straus electrodialyzed a 0.01 M KCl solution using a cellophane cation exchange membrane and an artiﬁcial intestinal wall anion exchange membrane and realized doubled KCl concentration (Meyer and Straus, 1940). In 1950, Juda and McRae synthesized ion exchange membrane (Juda and McRae, 1950) and this invention started the industrial application of ion exchange membranes. In 1952, Ionics Inc. developed a test electrodialyzer integrated with the synthesized ion exchange membranes for desalting a salt solution, and further in 1954, operated the practical scale desalting plant. Ion exchange membrane technology was applied afterward in the ﬁelds of desalination and concentration of electrolyte solutions. The largest scale application in the desalting ﬁelds is the demineralization of salt solutions. Other applications are desalination and reuse of sewage or industrial waste, treatment of radioactive waste, reﬁning of amino acid solutions and desalination of milk, whey and sugar liquor etc. The applications in the concentrating ﬁelds are recovery of useful components from industrial waste or a metal surface treatment process, seawater concentration, production of inorganic chemicals and organic acid concentration etc. Electrodialysis (ED) is assumed to be the fundamental technology based on the ion exchange membrane, and it is applied thereafter to the succeeding technology such as electrodialysis reversal (EDR), bipolar membrane electrodialysis (BP), electrodeionization (EDI), electrolysis (EL), diffusion dialysis (DID), redox ﬂow battery (RFB), fuel cell (FC) etc. This book interprets the ion exchange membrane technologies dividing them into the volume of Fundamentals and that of Applications. The author tried to discuss the various phenomena exhibited by ion exchange membranes in the Fundamentals and review the applications of ion exchange membranes in ED, EDR, BP, EDI, EL etc., in the Applications. However, such a volume classiﬁcation is extremely audacious, so that the author excuse beforehand that some instances in applications are discussed in the volume of Fundamentals, and other ones in fundamentals are reviewed in the volume of Applications. In the Fundamentals, Chapter 1 introduces general procedures to prepare the ion exchange membranes. Chapter 2 comments on the membrane property measurement processes deﬁnitely. Chapter 3 discusses the ionic transport and permselectivity across the membranes. Both Chapters 4 (Theory of Teorell, Meyer and Sievers) and 5 (Irreversible thermodynamics) are classical basic theories of the transport phenomena across the ion exchange membrane. Chapter 6 (overall mass transport) describes the practical concept on the transport phenomena based on the irreversible thermodynamics and it is applicable to analyze electrodialysis phenomena. Chapter 7 is about concentration polorization arising in a boundary layer formed on the membrane surface and investigated widely. Chapter 8 discusses water dissociation caused by the concentration

polarization. However, the mechanism of this phenomenon has not been cleared. Current density distribution (Chapter 9) is an inevitable phenomenon occurring in a practical apparatus. However, the investigation on this phenomenon is relatively few. Hydrodynamics (Chapter 10) is an extremely important phenomenon, in spite of the fact that the discussion in this ﬁeld is also few. Limiting current density (Chapter 11) has been discussed widely so far. This phenomenon is discussed in this book paying attention to the effect of distribution of circumstances in the operating apparatus. Chapter 12 consists of electric current leakage and solution leakage and they are unavoidable phenomena in the apparatus. The latter is discussed using the overall mass transport in Chapter 6. Chapter 13 is a simpliﬁed explanation of the energy consumption computation (ED program) based on Chapters 6, 9, 10 and 11. The concept in this chapter must be developed further. Chapter 14 consists of membrane characteristic deterioration, surface fouling and organic fouling. Industrial application of ion exchange membranes started at ﬁrst in the ﬁeld of electrodialysis and it induced the development of the fundamental theory. Because of this fact, many phenomena explained in the Fundamentals are described taking the electrodialysis into account. The author gives several opinions in the Fundamentals based on his investigations. It is grateful for reviewing the opinions. In the Application, Chapter 1 consists of various applications of desalination, concentration and separation technologies in electrodialysis. Many descriptions refer to the information presented in the Meeting of the Research Group of Electrodialysis and Membrane Separation Technology. Chapter 2 explains an improved electrodialysis technology (electrodialysis reversal) to prevent scale formation by means of intermittent polarity reverse. The information was offered by Ionic Incorporation. Chapter 3 explains bipolar membrane electrodialysis, which is functioned by a bilayered membrane consisting of a cation exchange layer and an anion exchange layer and available to recovering or producing acids or hydroxides, etc. Chapter 4 describes an electrodeionization system including ion exchange membranes and ion exchange resins, which is also used to produce pure water. The descriptions refer to the information discussed in the Meeting of the EDI Workshop in the said Research Group. Chapter 5 focuses on sodium chloride electrolysis to produce chlorine and caustic soda using perﬂuorinated cation exchange membranes. This process is the basic technology in the chlor-alkali industry. Chapter 6 discusses diffusion dialysis, which is applied to recover acid from an electrolyte solution applying high mobility of H+ ions across an anion exchange membrane. Chapter 7 explains a unique process (Donnan dialysis) caused by ionic diffusion and electro-neutrality. It is applied to recovering, extracting or removing ionic spices in a solution. Chapter 8 consists of dialysis battery, redox ﬂow battery and fuel cell. Technology of fuel cells and redox ﬂow batteries is now developing progressively for generating or storing electric power. The author appreciates the persons concerned offering the above information. vi

The ion exchange membrane phenomena are very often expressed using equations. Equations facilitate the explanation, but some times they make understanding difﬁcult. In order to avoid such a trouble, in this book, the phenomena are explained using the ﬁgures and tables as much as possible. Accordingly, the readers can understand the events explained in this book by skipping the equations and reading only the text with ﬁgures and tables. We pay attention to the experiments and make efforts to explain the phenomena using the experimental results. Further we tried to explain plant operating performance and economical evaluation of the technology. Application of ion exchange membranes is extending widely and spreading even now. Accordingly the fundamental studies are assumed to develop further in many ﬁelds. In spite of broadly expanding ﬁelds in which ion exchange membranes are applied, published textbooks of the ion exchange membrane might be relatively few. The author feels that it is very difﬁcult to explain such an ion exchange membrane technology inclusively. So, the content of this book is insufﬁcient but it must be supplemented in future. The references are cited on author’s personal preference. It must be noticed that there are many excellent investigations not being cited. In writing this book, the author thanks deeply to the colleagues in Japan Tobacco & Salt Public Corporation (formerly Japan Monopoly Corporation) for cooperating in the investigation. The author expresses his appreciation to persons concerned in the Research Group of Electrodialysis and Membrane Separation Technology in the Society of Sea Water Science Japan, Asahi Chemical Company, Tokuyama Incorporation and Asahi Glass Company for offering information and discussing. This book is written on the basis of author’s experience with ion exchange membranes during 40 years. I’m grateful to Elsevier B.V. for proofreading, checking and publishing the book. Finally, I thank my wife Satsuko for supporting my research life. REFERENCES Meyer, K. H., Straus, W., 1940, La permeabilite des membranes VI. Sur le passage du courant electrique a travers des membranes selectives, Helv. Chim. Acta, 23, 795–800. Juda, W., McRae, W. A., 1950, Coherent ion-exchange gels and membranes, J. Am. Chem. Soc., 72, 1044.

Yoshinobu Tanaka

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Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Fundamentals 1 Preparation of Ion Exchange Membranes . . . . . . . . . . . . . . . . . . . 3 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Invention of an Ion Exchange Membrane . Sandwich Method . . . . . . . . . . . . . . . . . . Latex Method . . . . . . . . . . . . . . . . . . . . Block Polymerization . . . . . . . . . . . . . . . Paste Method . . . . . . . . . . . . . . . . . . . . . Irradiation Graft Polymerization . . . . . . . Heterogeneous Membrane . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . .

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2 Membrane Property Measurements . . . . . . . . . . . . . . . . . . . . . . 17 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

Sampling and Pretreatment of Membranes . Electric Resistance . . . . . . . . . . . . . . . . . . Ion Exchange Capacity and Water Content. Transport Number . . . . . . . . . . . . . . . . . . Solute Permeability Coefﬁcient. . . . . . . . . . Electro Osmotic Coefﬁcient . . . . . . . . . . . . Water Permeation Coefﬁcient . . . . . . . . . . Swelling Ratio . . . . . . . . . . . . . . . . . . . . . Mechanical Strength . . . . . . . . . . . . . . . . . Electrodialysis . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

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17 18 19 20 23 25 26 28 28 33 36

3 Membrane Characteristics and Transport Phenomena . . . . . . . . . . 37 3.1 3.2 3.3 3.4 3.5 3.6 3.7

Permselectivity between Ions Having Different Charged Sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Permselectivity between Ions Having the Same Charged Sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electric Conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . Membrane Potential . . . . . . . . . . . . . . . . . . . . . . . . . . Concentration Diffusion . . . . . . . . . . . . . . . . . . . . . . . Mechanism to Decrease Divalent Ion Permeability . . . . Research on Membrane Treatment to Decrease Divalent Ion Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Theory of Teorell, Meyer and Sievers (TMS Theory) . . . . . . . . . . 59 4.1 4.2 4.3 4.4

Membrane Potential . Diffusion Coefﬁcient . Electric Conductivity. Transport Number . . References . . . . . . . .

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5 Irreversible Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.1 5.2 5.3 5.4

Phenomenological Equation and Phenomenological Coefﬁcient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reﬂection Coefﬁcient . . . . . . . . . . . . . . . . . . . . . . Electrodialysis Phenomena. . . . . . . . . . . . . . . . . . . Separation of Salt and Water by Electrodialysis . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Overall Mass Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.1 6.2 6.3 6.4

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Overall Membrane Pair Characteristics and Mass Transport Across a Membrane Pair . . . . . . . . . . . The Overall Mass Transport Equation and The Phenomenological Equation. . . . . . . . . . . . . . . . . Reﬂection Coefﬁcient s, Hydraulic Conductivity LP and Solute Permeability o . . . . . . . . . . . . . . . Pressure Reﬂection Coefﬁcient and Concentration Reﬂection Coefﬁcient: Electric Current Switching Off Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irreversible Thermodynamic Membrane Pair Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Concentration Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

Current–Voltage Relationship . . . . . . . . . . . . . . . . . . Concentration Polarization Potential . . . . . . . . . . . . . Chlonopotentiometry . . . . . . . . . . . . . . . . . . . . . . . . Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . Natural Convection . . . . . . . . . . . . . . . . . . . . . . . . . Fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overlimiting Current . . . . . . . . . . . . . . . . . . . . . . . . . Mass Transport in a Boundary Layer . . . . . . . . . . . . . Concentration Polarization on a Concentrating Surface of an Ion Exchange Membrane . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8 Water Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 8.1 8.2 8.3 8.4 8.5

Current–pH Relationship . . Diffusional Model. . . . . . . . Repulsion Zone . . . . . . . . . Membrane Surface Potential Wien Effect . . . . . . . . . . . .

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Protonation and Deprotonation Reactions . . . . . . . . . Hydrolysis of Magnesium Ions. . . . . . . . . . . . . . . . . . Experimental Research on the Water Dissociation . . . . Water Dissociation Arising in Seawater Electrodialysis. Mechanism of Water Dissociation . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9 Current Density Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 187 9.1 9.2

Current Density Distribution in an Electrodialyzer . . . . . . . . . . . . . . . . 187 Current Density Distribution Around an Insulator and Electric Current Shadowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

10 Hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Solution Flow and I–V Curves. . . . . . . . . . . . . . . . . . . . . . . . . Effect of a Spacer on Solution Flow (Theoretical) . . . . . . . . . . . Effect of a Spacer on Solution Flow (Experimental). . . . . . . . . . Local Flow Distribution in a Flow Channel . . . . . . . . . . . . . . . Effect of Solution Flow on Limiting Current Density and Static Head Loss in a Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Air Bubble Cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 Friction Factor of a Spacer and Solution Distribution to Each Desalting Cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.8 Pressure Distribution in a Duct in an Electrodialyzer . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 10.2 10.3 10.4 10.5

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11 Limiting Current Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 11.1 Concentration Polarization, Water Dissociation and Limiting Current Density . . . . . . . . . . . . . . . . . . . . . . 11.2 Diffusion Layer and Boundary Layer . . . . . . . . . . . . . . 11.3 Limiting Current Density Equation Introduced from the Nernst–Planck Equation . . . . . . . . . . . . . . . . . . . . . . . 11.4 Dependence of Limiting Current Density on Electrolyte Concentration and Solution Velocity of a Solution . . . . 11.5 Limiting Current Density Analysis Based on the Mass Transport in a Desalting Cell . . . . . . . . . . . . . . . . . . . . 11.6 Solution Velocity Distribution Between Desalting Cells in a Stack. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7 Limiting Current Density of an Electrodialyzer . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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12 Leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 12.1 Electric Current Leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 12.2 Solution Leakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

13 Energy Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 13.1 Energy Requirements in an Electrodialysis System . . . . . . . . . . . . . . . . . 285 xi

13.2 Energy Consumption in a Stack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

14 Membrane Deterioration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 14.1 Membrane Property Change with Elapsed Time 14.2 Surface Fouling . . . . . . . . . . . . . . . . . . . . . . . 14.3 Organic Fouling . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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293 300 308 316

Applications 1 Elecrodialysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 1.1 1.2 1.3 1.4 1.5 1.6

Overview of Technology . . . . . . . . . . . . . . . . . . . . . Electrodialyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electrodialysis Process. . . . . . . . . . . . . . . . . . . . . . . Energy Consumption and Optimum Current Density . Surrounding Technology . . . . . . . . . . . . . . . . . . . . . Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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321 321 327 340 340 343 379

2 Electrodialysis Reversal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Overview of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . Spacer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prevention of Scale Formation. . . . . . . . . . . . . . . . . . . . . . Anti-organic Fouling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Colloidal Deposit Formation on the Membrane Surface and Its Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nitrate and Nitrite Removal . . . . . . . . . . . . . . . . . . . . . . . Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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383 385 389 391 392

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393 394 395 403

3 Bipolar Membrane Electrodialysis . . . . . . . . . . . . . . . . . . . . . . 405 3.1 3.2 3.3 3.4

Overview of Technology . . . . . . . . . Preparation of Bipolar Membranes. . Performance of a Bipolar Membrane Practice . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . .

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405 409 415 428 434

4 Electro-deionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 4.1 4.2 4.3 4.4 4.5 4.6

Overview of Technology . . . . . . . . . . . . . . . . . . . . . . Mass Transfer in the EDI System. . . . . . . . . . . . . . . . Structure of the EDI Unit and Energy Consumption . . Water Dissociation in an EDI Process . . . . . . . . . . . . Removal of Weakly-Ionized Species in an EDI Process Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

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437 439 445 446 448 452 459

5 Electrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 5.1 5.2 5.3 5.4 5.5

Overview of Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ion Exchange Membrane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material Flow and Electrode Reaction in an Electrolysis System. Electrolyzer and its Performance . . . . . . . . . . . . . . . . . . . . . . . Puriﬁcation of Salt Water in an Electrolysis Process. . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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461 463 469 473 479 484

6 Diffusion Dialysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 6.1 6.2 6.3 6.4

Overview of Technology . . . . . . . . . . . . . . Transport Phenomena in Diffusion Dialysis Diffusion Dialyzer and its Operation . . . . . Practice . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

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487 487 489 491 494

7 Donnan Dialysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 7.1 7.2 7.3

Overview of Technology . . Mass Transport in Donnan Practice . . . . . . . . . . . . . . References . . . . . . . . . . . .

....... Dialysis . ....... .......

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495 496 498 503

8 Energy Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 8.1 8.2 8.3

Dialysis Battery . . . Redox Flow Battery Fuel Cell . . . . . . . . References . . . . . . .

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505 508 514 522

INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

xiii

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Fundamentals

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Chapter 1

Preparation of Ion Exchange Membranes 1.1.

INVENTION OF AN ION EXCHANGE MEMBRANE

In 1953, W. Juda and W. A. MacRae in Ionics Inc. applied for a patent of ‘‘ion-exchange materials and method of making and using the same’’ (Juda and MacRae, 1953). This patent attracted a great deal of attention, and contributed to the succeeding development of membrane synthesis technology. Here, we glance over the following practicing example: ‘‘preparation of membranes of phenol sulfonic acid–formaldehyde’’ in the patent at ﬁrst. The impregnating, low molecular weight polymer was prepared as follows: Aqueous phenol sulfonic acid (65%)–50 parts Aqueous formaldehyde (35.4%)–24.7 parts The acid and the formaldehyde are shaken together and partially polymerized at 501C in a closed container (to retain the moisture and formaldehyde). This pre-curing requires 1.5 to 2 h, after which the viscous mixture was used to impregnate reinforcing webs such as Saran, vinyon, glass cloth and similar materials resistant to strong acid. It was poured into a mold to form the cast disks. The curing (until the polymer turned dark brown or black) was carried out at 1001C, in a closed system and in the presence of moisture. This process requires 2 h to two days depending upon the quantity and geometry of polymerizing mass. It was found that the speciﬁc conductivity (1.4 102 O1 cm1) of the membrane in equilibrium with 1 N hydrochloric acid was greater than that in the 1 N hydrochloric acid (0.36 101 O1 cm1) itself. 1.2.

SANDWICH METHOD

This method is developed by Ionics Inc. and the following practicing instance is found in the patent (MacDonald et al., 1992). Referring to Figs. 1.1 and 1.2, the numerical 10 indicates a continuous substrate, which is played out from substrate roll 10A. Substrate 10 passes over roll 10B and continues downwardly in a vertical direction between horizontal rolls 11B and 110 B. Numerous 11 and 110 represent pliable ﬁlms having compositions which are not soluble or swollen in the polymerizable liquid. In addition they should release easily from the ﬁnished polymer sheet. Liquid is prepared from the mixture of the following components to form polymer, 54.6% divinylbenzene (16.6 l), vinyl toluene (5.5 l) and dixylyl ethane DOI: 10.1016/S0927-5193(07)12001-5

4

Ion Exchange Membranes: Fundamentals and Applications 10B

14B

10 14

11B 11'

11

11'A

19'B

20'A S 11A

12A

12'A 20' 14A

13 10A

Figure 1.1

16A

15A 15B

19A 16B

16C

16D

16E

16F

16G

16H

5

p 17A 16A 16B

16I

16J

16K

16L

16M

16N

16O

21A

16P

22 19B 20A

P

P

21B 20

Membrane synthesizing apparatus (Ionics, Inc.) (MacDonald et al., 1992). 10B

11B 10D

10C

14

11C 12B

11D 14B

12A

13 14A 15A

Figure 1.2

Membrane synthesizing apparatus (Ionics, Inc.) (MacDonald et al., 1992).

(18.9 l), with the following polymerization initiators: bis (4-tertiary-butylcyclohexyl)peroxyl dicarbonate (650 g), dilauroyl peroxide (410 g) and dibenzoyl peroxide (410 g). The mixture is thoroughly deoxygenated and is fed to an apparatus as shown in Fig. 1.1 through conduit means 14. Films 11 and 110 are Mylar (3 mils thick and 24 inches wide). Substrate 10 is an acrylic plain weave fabric (20 inches wide and 19 mils thick). The linear velocity is adjusted to give polymerization time of about 25 min. Element 16A is inert and exerts a pressure of about 4 g cm2 on sandwich S. Element 16B and D are fan, regulated manually to control the temperature of sandwich S. Element 16C and E are inert

Preparation of Ion Exchange Membranes

5

and exert a pressure of about 0.6 g cm2 on sandwich S. Element 16I through N are heated electrically to cause the temperature of sandwich S to increase from about 601C, at element 16I to about 1101C at element N. Elements 16A through E and I through 16 M are separated from sandwich S by Kapton adherent ﬁlm anchored to the apparatus. Means 12A and B (Fig. 1.2) and 120 A and B (Fig. 1.2) are heat welding elements (120 B lies behind 120 A in Fig. 1.1 and behind 12B in Fig. 1.2). Element 13 is a capacitative sensor. Roll 15A and 19A are covered with 30 durometer rubber to a depth at least 1 cm. Roll 15B and 19B are chrome steel. The edges of the sandwich are slit by element 17A and B and ﬁlms 20 and 200 (i.e., 11 and 110 ) taken up by rolls 20A and 200 A, respectively. Polymer sheet P is cut by shear 22 into lengths of about 40 inches each. The resulting sheets are leached in methylene dichloride to remove the dioxyl ethane and sulfonated. The resulting cation exchange membranes have ion exchange capacities of about 2.8 meq g1 dry membrane and water contents of about 50% of wet membrane. The membranes are useful in the electrodialytic production of potable water from brackish water. 1.3.

LATEX METHOD

This method is for producing a styrene–butadiene membrane practiced by Asahi Glass Co. (Hani et al., 1960). Threads (grass ﬁber, reinforcement) are immersed into styrene–butadiene rubber latex for 1 h, then pulled up and dried at 801C for 6 h to obtain a ﬁlm. The ﬁlm is sulfonated and cross-linked in a 96.5% sulfuric acid solution. A cation exchange membrane is obtained by immersing it into 80%, 60% and 30% sulfuric acid solutions for 30 min, respectively, in sequence, and ﬁnally washing with water. In order to produce an anion exchange membrane, the ﬁlm described above is cross-linked and ringlinked by immersing it into 301C titanium tetrachloride (bridging agent) for 1 h, and washed by methanol (solvent). It is dried, chloromethylated in a 301C chloromethyl ether solution containing titanium tetrachloride (catalyst) and tetrachloroethane (expansive agent) for 5 h, and is washed with methanol (solvent). Consecutively, dried, chloromethylated (chloromethyl ether, titanium tetrachloride catalyst, tetrachloroethane expansive agent, 301C, 5 h) and washed by methanol (solvent), and further, aminated (0.5 N trimethylamine–methanol solution) and washed. Finally, an anion exchange membrane is obtained by converting the form of functional groups into Cl type in a NaCl solution. Synthetic reaction of styrene–butadiene membrane is shown in Figs. 1.3 and 1.4. An excellent characteristic of this membrane is owing to the stretching performance of long-chain hydrocarbons existing between benzene rings allowing dimensional change of polymer structure and preventing the cracking of the membrane body. On the other hand, the method has a weak point such that after the completion of the reaction, double bonds are remained and apt to be

6

Ion Exchange Membranes: Fundamentals and Applications

CH2 CH CH CH2 CH CH2 CH2 CH CH CH2

conc. H2SO4

CH2 CH CH CH2 CH CH2 CH2 CH CH CH2 CH2 CH CH CH2 SO3H

Figure 1.3

Styrene–butadiene cation exchange membrane.

CH2 CH CH CH2 CH CH2 CH CH CH2

CH2 CH CH CH2 CH CH2 CH CH CH2 CH2 CH

CH2 CH CH CH2

CH CH CH2 ClCH2 O CH3

CH2 CH CH2

CH2Cl (CH3)3N CH2 CH CH2

CH2N+ (CH3)3 Cl−

Figure 1.4

Styrene–butadiene anion exchange membrane.

7

Preparation of Ion Exchange Membranes

cut off during membrane working. The anion exchange membranes are synthesized through three steps (bridging, chloromethylation and amination), so reacting solutions are contaminated during the steps. Because of these defects, this method is not applied now in the membrane manufacturing process.

1.4.

BLOCK POLYMERIZATION

The method was developed by Asahi Chemical Co. The material composing the membrane is a styrene–divinylbenzene copolymer ﬁlm (Figs. 1.5 and 1.6) which is obtained by slicing up from a block polymer. Following is an example of the practicing instance appeared in the patent (Tsunoda et al., 1957). Styrene monomer (400 parts) is partially polymerized in nitrogen gas (1001C, 12 h). Divinylbenzene (100 parts, containing 60% ethylvinyl benzene), dimethyl phthalate (120 parts, plasticizer), benzoyl peroxide (0.4 parts, catalyst) are added into a linear partially polymerized material solution and mixed. The solution is introduced into a rectangular cubic vessel substituted by nitrogen gas, CH=CH2

CH=CH2

CH=CH2

CH2 CH CH2 CH CH2 CH

CH2 CH CH2 CH CH2 CH

H2SO4 CH2 CH CH2 CH CH2 CH

SO3H SO3H SO3H CH2 CH CH2 CH CH2 CH

SO3H

Figure 1.5

SO3H

Styrene–divinylbenzene cation exchange membrane.

8

Ion Exchange Membranes: Fundamentals and Applications

CH=CH2

CH=CH2

CH=CH2

CH

CH2

CH

CH2

CH

CH

CH2

CH

CH2

CH

CH3OCH2CI CH

CH2

CH2CI CH CH2

CH2CI

CH

CH2

CH

CH2

CH2CI CH CH2

(CH3)3N CH

CH2

CH

CH2CI CH

CH2CI

CH

CH2N+(CH3)3 CH2N+(CH3)3 CH2N+(CH3)3 CI− CI− CI− CH CH2 CH CH2 CH

CH2N+(CH3)3 CI−

Figure 1.6

CH2N+(CH3)3 CI−

Styrene–divinylbenzene anion exchange membrane.

and induces polymerization and cross-linking reaction (1001C, 48 h) to obtain a block polymerized material (e.g. 100 cm 100 cm 0.7 cm). The block material is sliced up using a cutter into ﬁlms (e.g. 0.2 mm thick) and the plasticizer including in the ﬁlms is extracted using ethanol. A cation exchange membrane is

9

Preparation of Ion Exchange Membranes

11

5

4

9 8

3 6

10 1

2 7

2

10 7

1

8

3

Figure 1.7 1974).

Membrane-synthesizing apparatus (Asahi Chemical Co.) (Misumi et al.,

obtained by sulfonation (98% sulfuric acid, 901C, 10 h) of the ﬁlm. An anion exchange membrane is obtained by chloromethylation (chloromethyl ether, aluminum chloride catalyst, 201C, 4 h) and amination. A feature of this method is that cracking is prevented by adding partially polymerized styrene into a raw material. However, reinforcements are not incorporated into the membrane, so that the membrane is easy to break. Now, this method is improved as described below. Polymerization is proceeded in the doughnut shaped space 10 (diagonal lines) formed between drum 1 and drum 2 (Fig. 1.7) (Misumi et al., 1974). At ﬁrst, a polypropylene net (reinforcement) is placed upon a polyester ﬁlm (tearing material) and they are wound round the inner drum (drum 1) on which outer drum (drum 2) is set. A monomer mixture (styrene 80 parts, divinylbenzene 20 parts, dioctyl phthalate plasticizer 80 parts, benzoyl peroxide reaction initiator 0.5 parts) is injected at 101C into the doughnut shaped space 10 in Fig. 1.7. Supplying circulation water for adjusting temperature into inner part of drum 1 from valve 4 to valve 5 and outer part of drum 2 from valve 7 to valve 8, polymerization is started at 301C and proceeded for about 10 days changing temperature and controlling the reaction states. Next, drum 1 and drum 2 are separated, the block polymerized material is taken out and rewound, and it is separated into a tearing material and a polymerized membrane ﬁlm. Dioctyl

10

Ion Exchange Membranes: Fundamentals and Applications

phthalate in the membrane ﬁlm is extracted by washing the ﬁlm with methanol. Finally, a cation exchange membrane is obtained by sulfonation of the ﬁlm. An anion exchange membrane is obtained through chloromethylation and amination. Now, the reinforcement (polypropylene) is pre-irradiated by an electron beam before winding process around drum 1 (Araki et al., 1981). Accordingly, graft polymerization takes place between polypropylene and styrene and the strength of the membrane is increased. Further, it was taken notice of that chloromethyl ether is a carcinogenic substance and is potentially harmful to human health. To avoid this trouble, chloromethylation is canceled by using chloromethyl styrene instead of styrene. 1.5.

PASTE METHOD

This is styrene–divinylbenzene co-polymerization process developed by Tokuyama Corp. (Mizutani et al., 1964). At ﬁrst, a paste solution is prepared by adding polyvinyl chloride powder (100 parts) into monomer mixture consisting of styrene (80 parts), divinylbenzene (10 parts), dioctyl phthalate (25 parts) and benzoyl peroxide (1 part). The solution is introduced into the vessel 5 (Fig. 1.8). A polyvinyl chloride net (reinforcement) being wound up to the roll 4 is passed 2 3

1

9

9 8

4

7

6 5

10

Figure 1.8

Membrane-synthesizing apparatus (Tokuyama, Inc.) (Mizutani et al., 1964).

Preparation of Ion Exchange Membranes

11

through the paste solution 6 in vessel 5, and is wound round roll 3 pressing by roll 2 with vinylon ﬁlm (tearing material) moving from roll 1. After the winding process, roll 3 is dismantled and put into a sealed reaction vessel, in which the monomer mixture is polymerized at 1301C for 30 min and 801C for 10 h. In this situation, polyvinyl chloride powders expand with including monomer mixtures and form thin ﬁlms. Cross-linking reaction between styrene and divinylbenzene is advanced in the ﬁlms. Accordingly, three-dimensional conﬁgurations obtained by the cross-linking reaction are mixed and intertwined uniformly with polyvinyl chloride molecular chains. Further, graft polymerization arises between monomer mixtures and polyvinyl chloride molecular chains owing to the chain reaction in the polymerization process. After the polymerization reaction, the roll is rewound and base ﬁlm is taken out. A cation exchange membrane is obtained by sulfonation of the ﬁlm. An anion exchange membrane is obtained by chloromethylation and amination. The synthetic reaction is the same to that indicated in Figs. 1.5 and 1.6. At present, the anion exchange membrane is synthesized using chloromethyl styrene instead of styrene. The synthetic process adopted now by Asahi Glass Co. (Mineki et al., 1972) is estimated to be considerably the same to that described above. There is another method for synthesizing an anion exchange membrane using vinylpyridine instead of styrene for obtaining vinylpyridine-divinylbenzene copolymer (Fig. 1.9). A practicing instance in the patent for the paste method (Mizutani et al., 1965) is described below. The paste materials containing styrene (50 parts), 2-methyl vinylpyridine (50 parts), benzoyl peroxide (2 parts) and polyvinyl chloride (50 parts) are coated to a polyvinyl chloride net and wound round roll 3 (Fig. 1.8) with a vinylon ﬁlm. The roll 3 is dismantled and the paste materials are polymerized (1101C, 30 min and 701C, 10 h). A rewound ﬁlm is quaternarized by methyl iodide (251C, 24 h), then an anion exchange membrane is produced. 1.6.

IRRADIATION GRAFT POLYMERIZATION

Irradiation graft polymerization is illustrated in Fig. 1.10 indicating that radicals are generated by irradiating an electron beam to a main chain of a trunk polymer A (polyethylene etc.) and monomer B (styrene, chloromethyl styrene etc.) is bonded with the radicals. The nomenclature ‘‘graft polymerization’’ is derived from monomer B being grafted on the trunk polymer A. American Machine & Foundary Co. developed the method forming graft polymer ion exchange membranes as follows (Chen, 1966). A polyethylene ﬁlm 4 mils thick and 3 inches square was immersed in styrene monomer for about 30 min. Absorption or swelling reached an equilibrium maximum within this time and the whole system was next irradiated by exposure for 5 h to a Co-60 source. The total radiation dose was about 1.5 106 R. The ﬁlm was removed from monomer and washed for several hours with benzene to remove

12

Ion Exchange Membranes: Fundamentals and Applications

CH=CH2

CH=CH2 N

CH=CH2

CH2

CH

CH2

CH

CH2

CH

CH2

CH2

CH

CH2

N

CH

N

+

CH +

N

N CH3I−

CH2

CH

CH2

CH

CH2

+

+

N CH3I− CH2

CH +

CH2

N CH3I−

Figure 1.9

CH N CH3I−

CH

CH2

CH +

N CH3I−

Styrene–vinylpyridine anion exchange membrane.

unpolymerized and homopolymerized styrene. The copolymer ﬁlm was sulfonated at room temperature for 40 min by immersion in chlorosulfonic acid. It was then immersed in carbon tetrachloride and washed with water to remove excess acid. Finally, it was heated in about 20% caustic soda for about 15 min at 60–701C. Japan Atomic Energy Research Institute developed irradiation graft polymerization technology. The following experiment is seen in a patent (Machi et al., 1980). A polyethylene ﬁlm of thickness 20 mm was irradiated with 20 Mrad in a nitrogen gas atmosphere at a dose rate of 2 MeV electron beams from a cascade type accelerator. The irradiated ﬁlm was immersed in an aqueous acrylic acid solution deaerated by bubbling nitrogen in a glass ampoule. 0.25 wt% of Mohr’s salt (ferrous ammonium sulfate) was added into the monomer solution to minimize homopolymerization. The graft polymerization was proceeded at 251C for 5 h. After grafting, the ﬁlm was taken out and washed thoroughly with

13

Preparation of Ion Exchange Membranes

Radical A A A Initial film

B B B A A A Grafted film (Base membrane)

Monomer B

CH2 CH2

n

CH=CH2

CH=CH2 B:

A A A

(Electron beam)

Grafting

A:

•

Irradiation

or CH2Cl

Figure 1.10

Irradiation graft polymerization.

distilled water to remove residual monomer and homopolymer contained in the ﬁlm. The membrane obtained was treated in a 25% aqueous KCl solution at 901C for 120 min. Speciﬁc electric resistance of the membrane was 16 O cm in 40% aqueous KCl. This technology is applied to produce the diaphragm of a battery (Ishigaki et al., 1982). Another synthetic research (Tanaka, 1999) of irradiation graft polymerization is as follows. A polyethylene ﬁlm of 100 mm thickness was irradiated with 200 kGy electron beams under nitrogen gas and free radicals were formed in the ﬁlm. The irradiated ﬁlm was put into an evacuated glass ampoule (Fig. 1.11). A mixed solution of styrene or chloromethyl styrene and benzene (swelling solution) which had been deaerated by nitrogen gas was introduced into the ampoule and graft polymerization was carried out at 501C. After the polymerization, the ﬁlm was washed repeatedly with benzene and methanol and was dried under a vacuum. The styrene grafted ﬁlm was put into a 10% chlorosulfonic acid solution of dichloromethane at 0–21C for 1 h. After sulfonation, a cation exchange membrane was obtained by washing with methanol and distilled water. The chloromethyl styrene grafted ﬁlm was put into a 10% trimethylamine aqueous solution at 501C for 1 h. After quaternarization, an anion exchange membrane was obtained by washing repeatedly with distilled water. From studies on graft polymerization, it is evident that the following factors can inﬂuence the efﬁciency of the grafting operation (Chen et al., 1957): (1) temperature, as it deﬁnes the reaction rates and solubility of monomer in polymer ﬁlm; (2) gamma-dose rate; (3) diffusion rate of monomer into polymer

14

Ion Exchange Membranes: Fundamentals and Applications

Vacuum line N2 gas

Glass ampule

Reaction solution

Irradiated film

Deaerator

Figure 1.11

Graft polymerization apparatus (Tanaka, 1999).

as dependent upon ﬁlm thickness; and (4) variation of the solubility of monomer in polymer as a function of the degree of grafting with subsequent variations in radiation sensitivity of the derived structures. 1.7.

HETEROGENEOUS MEMBRANE

Heterogeneous membranes are durable at temperature up to 501C. In a strong alkali, acid and oxidizer, membrane properties are quite stable. These enable us to employ effective hard chemical cleaning for preventing fouling of the membrane (Kishi et al., 1977). Further, the price of the membrane is reasonable and they are apt to dry store and convenience to transportation (Yingqui and Zhongqin., 1990). However, electric resistance of heterogeneous membranes is relatively high comparing to that of homogeneous membranes. Mitsubishi Petrochemical Co. developed the following technology to decrease speciﬁc resistance of heterogeneous membranes (Tamura and Kihara, 1977). Suspension polymerization was proceeded using styrene monomer (92 parts) and divinylbenzene (8 parts) with benzoyl peroxide (catalyst). Granular copolymers obtained were sulfonated adding fuming sulfuric acid and ion exchange resins (ion exchange capacity: 4.5 meq g1) were produced. The granular resins were crushed to powdered resins (>325 mesh) using a vibration mill. The powder (60 parts) was mixed with polypropylene (40 parts), kneaded using a roller and pressed to obtain an ion exchange membrane. Na+ ion transport number ( t ) and speciﬁc resistance (r) of the membrane were measured after it was immersed in a T1C saturated NaCl solution for 30 min, obtaining the following results.

15

Preparation of Ion Exchange Membranes

(A)

(B)

(C)

Figure 1.12 Schematical micro-structure of heterogeneous cation exchange membranes: (A) before treatment; (B) after treatment with hot water; (C) after treatment with hot aqueous solution of NaCl (Tamura, 1976).

T (1C) t r (O cm)

80 0.93 255

90 0.92 230

95 0.93 196

100 0.92 115

105 0.93 130

The events described above are understandable as follows (Tamura, 1976). When the membranes are treated with a hot NaCl solution, cation exchange resin particles swell and expand pushing away the polypropylene matrix of the membrane; the above treatment results the formation of narrow cavities between cation exchange particles and polypropylene matrix (Fig. 1.12), and the formation of ﬁne micro-cracks in the polypropylene matrix, resulting the decrease of speciﬁc electric resistance of the membrane. REFERENCES Araki, K., Daido, H., Sasaki, T., Suzuki, H., Tsushima, S., Misumi, Y., 1981, Production of polymer structure of an ion exchange membrane including polypropylene strings, JP Patent, S56-8857.

16

Ion Exchange Membranes: Fundamentals and Applications

Chen, W. K. W., 1966, Method of forming graft copolymer ion exchange membranes, US Patent, 3,247,133. Chen, W. K. W., Mesrobian, R. B., Ballantine, D. S., Metz, D. J., Glines, A., 1957, Studies on graft copolymers derived by ionizing radiation, J. Polym. Sci., 23, 903–913. Hani, H., Hiraga, T., Nisihara, H., 1960, Production of an ion selective membrane, JP Patent, S35-13009. Ishigaki, I., Sugo, T., Okamoto, J., Machi, S., 1982, J. Appl. Polym. Sci., 27, 1033. Juda, W., MacRae, W. A., 1953, Ion exchange material and method of making and using the same, US Patent, 2,636,851. Kishi, M., Serizawa, S., Nakano, M., 1977, New electrodialyzer system with automatic chemical cleaning, Desalination, 23, 203–212. MacDonald, R. J., Hodgdon, R. B., Alexander, S. S., 1992, Process for manufacturing continuous supported ion selective membranes using non-polymerizable high boiling point solvent, US Patent, 5,145,618. Machi, S., Ishigaki, S., Sugo, T., 1980, Production of new ion exchange membranes, JP Patent, S55-106231. Mineki, Y., Gunzima, T., Arai, S., 1972, Production of an ion exchange membrane, JP Patent, S47-40868. Misumi, T., Kawashima, Y., Takeda, K., Kamaya, M., 1974, Production of an ion exchange membrane structure and an apparatus, JP Patent, S49-34476. Mizutani, Y., Tezima, W., Akiyama, S., Yamane, R., Ihara, H., 1965, Production of ion exchange membrane, JP Patent, S40-28951. Mizutani, Y., Yamane, R., Kimura, K., 1964, Production of ion exchange membrane, JP Patent, S39-27861. Tamura, N., 1976, Effects of post-treatment on the properties of heterogeneous cation exchange membranes synthesized from ground powder of cation exchange resins and polypropylene, Bull. Chem. Soc., Jpn., 1976, 1118–1124. Tamura, N., Kihara, K., 1977, Production of improved cation exchange membranes, JP Patent, S52-3912. Tanaka, Y., 1999, Regularity in ion exchange membrane characteristics and concentration of seawater, J. Membr. Sci., 163, 277–287. Tsunoda, Y., Seko, M., Watanabe, M., Ehara, R., Misumi, Y., 1957, Production of a spherical and granular ion exchange resin doing not crack in a manufacturing process and of polymer structure suitable to produce a large-sized ion exchange resin, JP Patent, S32-6387. Yingqui, Y., Zhongqin, L., 1990, A brief account of the development of ion exchanges in China, Technol. Water Treat., 16, 119–121.

Chapter 2

Membrane Property Measurements Ion exchange membranes were developed at ﬁrst for advancing the electrodialysis technology of seawater and brackish water, which have been a main subject to be discussed at present. Because of this reason, the membrane property measuring method is standardized referring to electrodialysis of seawater and brackish water (Kosaka and Emura, 1963; Yamabe and Seno¯ , 1964; Takemoto, 1966; Seno¯ and Tanaka, 1984). Now, the application of ion exchange membranes is extended to many ﬁelds such as electrodeionization, bipolar membrane electrodialysis, electrolysis, fuel cells etc. The circumstances in which the ion exchange membrane is placed differ in each ﬁeld, so that the measuring conditions deﬁned in this chapter might not be reasonable in the other ﬁelds. However, the method described here is assumed to be applicable to the other ﬁelds by changing appropriately the measuring conditions, because the basic theory of the measuring method is universal. 2.1.

SAMPLING AND PRETREATMEMT OF MEMBRANES

A membrane sheet about 5 cm 5 cm breadth is cut off, conﬁrmed pinholes not to be detected and preserved in a 0.5 M NaCl solution for over one day and night, and then pretreated as follows. (1)

(2)

Cation exchange membrane: A sample membrane is immersed in a 4% HCl solution for 2 h. In the meantime, the solution is stirred every 10 min, renewed every 20 min, and then washed three to four times with water. Next, it is immersed in a 2 M NaCl solution for 2 h; meanwhile, the solution is stirred every 10 min, renewed every 20 min, and then washed with a 0.5 M NaCl solution three to four times and immersed in a 0.5 M NaCl solution. Anion exchange membrane: A sample membrane is immersed in a 4% NaOH solution or 4% NH4OH solution for 1 h. In the meantime, the solution is stirred every 10 min, renewed every 20 min and washed three to four times with water. Next, the membrane is washed with a 0.5 M NaCl solution three to four times and immersed in a 0.5 M NaCl solution.

DOI: 10.1016/S0927-5193(07)12002-7

18

2.2.

Ion Exchange Membranes: Fundamentals and Applications

ELECTRIC RESISTANCE

2.2.1

Alternating Current Electric Resistance Electric resistance is practically important because this parameter relates directly to energy consumption in an electrodialysis process. The relationship between electric resistance R (O), area S (cm2), thickness d (cm) and speciﬁc resistance n (O cm) is expressed as follows: nd (2.1) S where n is a membrane characteristic and equivalent to R at d ¼ 1 cm and S ¼ 1 cm2. Practical electric resistance r ¼ nd (O cm2) is equivalent to r at S ¼ 1 cm2. Electric resistance is measured as follows. A membrane sample is immersed in a 0.5 M NaCl solution for about 2 h and the membrane surface is wiped with a ﬁlter paper, and then it is incorporated with the apparatus shown in Fig. 2.1 (effective membrane area: 1 cm2, electrodes: platinum black). A 0.5 M NaCl solution is supplied into the cells in the apparatus, which is left in a 251C thermostat. After temperature in the cells becomes 251C, electric resistance (R1) is measured with an alternating current bridge (frequency: 1000 Hz). Next, the membrane sample is taken away, the apparatus is re-integrated without a membrane, and electric resistance (R2) is measured. n is calculated substituting R ¼ R1R2, S ¼ 1 cm2 and d measured with a micrometer into Eq. (2.1). R¼

2.2.2

Direct Current Electric Resistance The electric resistance of an ion exchange membrane described in Section 2.2.1 is measured passing an alternating current, and is referred here as the alternating current electric resistance ralter. In the electrodialysis of an electrolyte solution, a direct current is passed across the membrane, so that the electric resistance in this circumstance which is referred as the direct current electric resistance rdire is different from ralter. Accordingly, it is necessary to estimate rdire from ralter, which is explained in this section (Tanaka, 2000). An ion exchange membrane is set in a two-cell apparatus (Fig. 2.1), and a low-concentration NaCl solution (speciﬁc conductivity, klow (mS cm1)) is supplied into the cells. Electric resistance of the membrane (r0dire (O cm2)) is measured at 251C applying a direct current. The relationship between klow and r0dire =ralter is expressed by the following empirical equation: 0 r (2.2) log dire ¼ a1 þ a2 log klow þ a3 ðlog klow Þ2 ralter Next, a low-concentration NaCl solution is supplied to the desalting side and a high-concentration NaCl solution (speciﬁc conductivity, khigh) is supplied to the concentrating side of the apparatus (Fig. 2.1). The electric resistance of the membrane rdire is measured at 251C by applying a direct current and

19

Membrane Property Measurements

4

2

3

5

4

4

2

1

6

6

1. Pt electrode 2. Pt wire 3. Terminal 4. Solution injection hole; Thermometer inserting hole 5. Air extracting hole 6. Rubber gasket

Figure 2.1

Electric resistance measuring apparatus (Takemoto, 1966).

subtracting the effect of membrane potential. The empirical relationship between khigh/klow and rdire =r0dire is obtained as follows: khigh rdire (2.3) ¼ 1:000 þ b log r0dire klow rdire is estimated from ralter measured in Section 2.2.1 using rdire/ralter obtained by multiplying Eq. (2.2) by Eq. (2.3). It should be noticed that rdire includes the electric resistance of a boundary layer formed on the desalting surface of the membrane due to the concentration polarization. 2.3.

ION EXCHANGE CAPACITY AND WATER CONTENT

A membrane consists of cross-linked polyelectrolytes and forms gel structure that absorbs water in an aqueous solution. The water content of an ion

20

Ion Exchange Membranes: Fundamentals and Applications

exchange membrane is deﬁned as the weight of water included in a 1 g swelled membrane in pure water (g H2O (g wet membrane)1). The ion exchange capacity is deﬁned as milli-equivalent of ion exchange groups included in a 1 g dry membrane (meq (g dry membrane)1). The ion exchange group concentration is obtained from the ion exchange capacity divided by the water content in 1 g dry membrane (meq (g H2O)1). In order to measure the ion exchange capacity of a cation exchange membrane, a sample membrane is left at ﬁrst in a 1 M HCl solution for over 6 h, changing the solution and converting perfectly the exchange groups to an H type, and then it is washed with water sufﬁciently until the washed water does not exhibit acidity recognized by the reaction with methyl red. Next, the membrane is immersed in a 2 M NaCl solution (about 30 ml) which is changed two times every 1 h and is further immersed in a 2 M NaCl solution for over 6 h and washed sufﬁciently with water. The immersed solutions and washed water are collected, and ﬁnally, H+ ions dissolved into the collected solution are analyzed with a 0.1 M NaOH and a phenolphthalein indicator (a meq). In order to measure the ion exchange capacity of an anion exchange membrane, a sample membrane is left at ﬁrst in a 2 M NaNO3 solution for 30 min.Then it is immersed in a 2 M NaCl solution for over 6 h, changing the 2 M NaCl solution until the exchange groups convert perfectly to a Cl type. Next, the Cl type membrane is washed with water until the washed water does not exhibit white muddiness owing to the reaction with AgNO3. Next, the membrane is immersed in a 2 M NaNO3 solution (about 30 ml) which is changed two times every 1 h and is further immersed in a 2 M NaNO3 solution for over 6 h and washed sufﬁciently with water. The immersed solutions and washed water are collected, and Cl ions dissolved into the collected solution and the washed water are analyzed with a 0.1 M AgNO3 and a K2CrO4 indicator (a meq). In order to measure the water content, the moisture adhered on the sample membrane is wiped with a ﬁlter paper and the membrane is weighed (d g). The membrane is dried in a 651C thermostat until the weight becomes constant (c g). The ion exchange capacity AR and water content W are calculated as follows: a AR ðmeq ðg dry membraneÞ1 Þ ¼ c W ð%Þ ¼

2.4.

100ðd cÞ c

TRANSPORT NUMBER

When an ion exchange membrane is placed in an electrolyte solution, concentration ratio of counter-ions in the membrane is extremely larger than

21

Membrane Property Measurements

that of co-ions, so that the greater part of an electric current is carried across the membrane by counter-ions. The transport number of an ion exchange membrane ¯ti is deﬁned as a ratio of an electric current Ii carried by speciﬁc ions i against total electric current I: ¯ti ¼

Ii I

(2.4)

An electrolyte solution dissolves cations and anions. A cation and an anion exchange membrane pass mainly cations and anions, respectively. This event is represented by the following equation introduced from Eq. (2.4): zþ J þ zþ J þ þ z J z J ¯t ¼ zþ J þ þ z J ¯tþ ¼

(2.5)

where z is the electric charge of cations (+) and anions (), and J the ionic ﬂux across the membrane. The transport number is classiﬁed into the apparent transport number and the actual transport number. The apparent transport number is applied widely because it is measured easily. However, the actual transport number is important for theoretical discussion of transport phenomena. 2.4.1

Apparent Transport Number When both surfaces of an ion exchange membrane are in contact with a solution of different concentrations dissolving monovalent cations and anions, membrane potential E generated between the solutions contacting with both membrane surfaces is expressed by the following Nernst equation: RT a2 (2.6) ln E ¼ ð¯tþ ¯t Þ a1 F where ¯tþ and ¯t are the apparent transport number of a cation and an anion exchange membrane, ¯tþ þ ¯t ¼ 1; R the gas constant, T the absolute temperature and a1/a2 the electrolyte activity ratio in the solutions in contact with both membrane surfaces. The apparent transport number is measured using a two-cell apparatus (Fig. 2.2), in which a sample membrane immersed in a 1 M NaCl for over 2 h is integrated between the cells. A 251C 0.5 M NaCl solution and a 2.5 M NaCl solution are poured into the cells, and the apparatus is left for about 5 min.Membrane potential (a V) is measured by connecting both cells and calomel electrodes through KCl bridges and letting both solutions ﬂow toward the membrane surface. The apparent transport number is calculated using the

22

Ion Exchange Membranes: Fundamentals and Applications

4

4

2

5

3

1 1. Membrane 2. Solution inlet 3. Solution outlet 4. Salt bridge inserting hole 5. Rubber gasket

Figure 2.2

Apparent transport number measuring apparatus (Takemoto, 1966).

following equations introduced from Eq. (2.6): ¯t ¼

aþb 2ab

c1 f 1 b ðVÞ ¼ 0:5915 log c2 f 2 where c1 and c2 are the NaCl concentrations in both cells (M) and f1 and f2 the NaCl activity coefﬁcients in both cells. 2.4.2

Actual Transport Number A sample membrane is incorporated with a two-cell apparatus as shown in Fig. 2.3 (effective membrane area: 4 cm2). Accurately measured 30 cm3 of a 0.5 M NaCl solution is put in a desalting cell and 30 cm3 of a 0.5 M NaCl is put in a concentrating cell. Next, Ag–AgCl electrodes washed sufﬁciently with water and left for over one night are put in both cells. The apparatus is set in a 251C thermostat, and an electric current of 40 mA (1 A dm2) is passed for 40 min and 10 s (1 mF) through the electrodes, making ions in the desalting cell transfer toward the concentrating cell. Then, the solution in the concentrating cell is discarded and that in the concentrating cell is taken out into a 250 cm3 measuring ﬂask. Further, the inside of the desalting cell is washed sufﬁciently with water and the washed water is collected into a 250 cm3 measuring ﬂask. The electrode (anode) used in the desalting cell is washed sufﬁciently with water and immersed in water in a 30 cm3 beaker. Both washed water and immersed water are collected into the 250 cm3 measuring ﬂask. Finally, the volume of the solution in the

23

Membrane Property Measurements

4

6 5

1

6

2

3

1. Membrane 2. Desalting cell 3. Concentrating cell 4. Stirrer 5. Ag-AgCl electrode 6. Rubber gasket

Figure 2.3

Actual transport number measuring apparatus (Takemoto, 1966).

measuring ﬂask is adjusted to 250 cm3 by adding water, and the quantity of Cl ions in the solution is analyzed using an AgNO3 standard solution. The actual transport number is calculated using the following equations: Transport number of a cation exchange membrane; ¯tþ ¼ a b Transport number of an anion exchange membrane; ¯t ¼ 1 þ a b where a is the analytical value of Cl ions in the desalting cell before passing an electric current (meq) and b the analytical value of Cl ions in the desalting cell after passing an electric current (meq). In case of transport number evaluation of a cation exchange membrane, NaCl concentration in the desalting cell decreases and that in the concentrating cell increases during passage of electric current, resulting in NaCl diffusion across the membrane. In order to decrease the experimental error due to the event described above, the NaCl concentration in the desalting cell is adjusted beforehand at larger than 0.5 M, and that in the concentrating cell is at less than 0.5 M. Further, the NaCl concentrations in both cells are devised to be reversed during passage of electric current and the experimental error to become a minimum. In case of an anion exchange membrane, the device mentioned above is not necessary. 2.5.

SOLUTE PERMEABILITY COEFFICIENT

When an ion exchange membrane is placed in an electrolyte solution and the ionic concentration difference between both surfaces of the membrane is

24

Ion Exchange Membranes: Fundamentals and Applications

maintained at DC, ions in a concentrating side diffuse toward a desalting side. The ionic ﬂux JS in this system is represented by the following Fick’s diffusion equation: DS DC (2.7) d where d is the thickness of the membrane and DS the diffusion constant. DS/d is deﬁned as the solute permeability coefﬁcient, which is measured as follows. A sample membrane immersed into a 0.5 M NaCl solution is washed with water, wiped with a ﬁlter paper and integrated in the two-cell apparatus as shown in Fig. 2.4 (effective membrane area: 4 cm2). Accurately measured 15 cm3 of water is put in the desalting cell and a 4 M NaCl solution is supplied into the concentrating cell so that the solution level in both cells is the same. The apparatus is left in a 251C thermostat for 30 min exactly, during which the solution in the desalting cell and that in the concentrating cell are stirred violently by air blowing and stirrer, respectively. Afterward, the solution in the desalting cell is taken out immediately and NaCl concentration is measured using a ﬂame spectrochemical analyzer (a M). The solute permeability coefﬁcient is calculated JS ¼

6

5

4

1

3 2 1. Membrane 2. Desalting cell 3. Concentrating cell 4. Stirrer 5. Air blowing inlet 6. Rubber gasket

Figure 2.4

Solute permeability coefﬁcient measuring apparatus (Takemoto, 1966).

25

Membrane Property Measurements

using the following equation: DW 15a ðcm s1 Þ ¼ d 4 4 1800 2.6.

ELECTROOSMOTIC COEFFICIENT

When ions are transferred across an ion exchange membrane, a solution is transported under applying current density i. The solution ﬂux JV is expressed by the function of the electroosmotic coefﬁcient b as follows: J V ¼ bi

(2.8)

A sample membrane is immersed for over a whole day and night in a 0.5 M NaCl solution. b is measured using a two-cell apparatus (Fig. 2.5) in 9

7

8

5

8

5 3

6

4 1

2

2

7

1. Membrane 2. Measuring cell 3. Membrane holding plate 4. Pipette holding hole 5. Solution injecting hole 6. Cock 7. Electrode inserting hole 8. Air extracting hole 9. Rubber gasket

Figure 2.5

Electroosmotic coefﬁcient measuring apparatus (Takemoto, 1966).

26

Ion Exchange Membranes: Fundamentals and Applications

which the sample membrane is incorporated with Ag–AgCl electrodes. The apparatus is placed in a 251C thermostat. Electroosmotic coefﬁcient of a cation exchange membrane is measured, putting a 251C 0.5 M NaCl solution in both cells and an electrode (cathode) in the measuring cell, and then applying current density of 1 A dm2. In this case, NaCl concentration in the measuring cell increases and that in the other cell decreases during passage of electric current, resulting in solution permeation across the membrane due to an NaCl concentration difference generated in the cells. In order to decrease the experimental error due to the event described above, the NaCl concentration in the measuring cell is adjusted beforehand at less than 0.5 M, and that in the other cell is at larger than 0.5 M. Further, the NaCl concentrations in both cells are devised to be reversed during passage of electric current, resulting in minimum experimental error (cf. Section 2.5). In case of an anion exchange membrane, the device mentioned above is not necessary. The solution volume increase in the measuring cell is measured accurately for 60 min after 10 min from the beginning of passage of electric current using a measuring pipette (a cm3). b is calculated using the following equation: ð102 =3600Þa S where S is the effective membrane area (cm2). Temperature changes and bubbles generated from a cathode during passage of electric current cause an experimental error, so the temperature must be adjusted accurately and the cathode should be prepared perfectly to be an AgCl type. b ðcm3 A1 s1 Þ ¼

2.7.

WATER PERMEATION COEFFICIENT

When an electrolyte concentration difference DC is established between both membrane surfaces, water permeates across the membrane owing to osmotic pressure. Water ﬂux JW in this situation is expressed by the following equation: DW DC (2.9) d where d is the thickness of the membrane and DW the concentration difference permeation constant. DW/d is deﬁned as the water permeability coefﬁcient, which is measured as follows. A sample membrane immersed into a 0.5 M NaCl solution is washed with water, wiped with a ﬁlter paper and integrated in the two-cell apparatus (Fig. 2.6). Then 251C water is put in the measuring cell, and a 4 M NaCl solution is put in the other cell so that the solution level in both cells is the JW ¼

27

Membrane Property Measurements

7

7 2 6

4

3 1 5

5

8

7

7 3

4

1 1. Measuring cell 2. Membrane holding plate 3. Magnetic stirrer 4. Pipette holding plate 5. Solution injecting hole 6. Cock 7. Air extracting hole 8. Rubber gasket

Figure 2.6

Water permeation coefﬁcient measuring apparatus (Takemoto, 1966).

same. The apparatus is left in a 251C thermostat and the solutions in both cells are stirred violently using magnetic stirrers. After 10 min, a decrease of the volume in the measuring cell is observed for 60 min using a measuring pipette (a cm3). The water permeation coefﬁcient is calculated using the following equation: DW a 103 ðcm4 s1 mol1 Þ ¼ d 4 3600S

28

Ion Exchange Membranes: Fundamentals and Applications

2.8.

SWELLING RATIO The measuring procedure is as follows:

(1) (2)

(3) (4) (5)

A sample membrane is immersed in a 0.5 M NaCl solution for 24 h, during which the solution is substituted more than three times. A vertical (a mm) and a horizontal (b mm) length of the membrane are measured using a ruler, and a thickness (c mm) is measured using a micrometer. The sample membrane is immersed in a 3.5 M NaCl solution for 24 h, during which the solution is substituted more than three times. A vertical (a0 mm) and a horizontal (b0 mm) length and a thickness (c0 mm) is measured as described in (2). The swelling ratio is calculated as follows:

Vertical swelling ratio ð%Þ ¼

ða a0 Þ 100 a

Horizontal swelling ratio ð%Þ ¼ Thickness swelling ratio ð%Þ ¼ 2.9.

ðb b0 Þ 100 b

ðc c0 Þ 100 c

MECHANICAL STRENGTH

A sample membrane is immersed in a 0.5 M NaCl solution for 24 h, during which the solution is substituted more than three times. Then, the bursting strength and tensile strength are measured as follows. 2.9.1

Bursting Strength A sample membrane sheet (about over 6 cm 6 cm width) is ﬁxed into a Mullen tester and inﬂated injecting glycerol. The maximum pressure when the membrane bursts is the bursting strength. 2.9.2

Tensile Strength A sample membrane sheet (about 10 cm length 1 cm width) is ﬁxed to a Schopper’s tension tester. The tensile strength is the maximum strength when the sample is cut off. The tensile strength value is inﬂuenced by the thread (reinforcement) put in the membrane. So it is reasonable to cut off the sample membrane, for example, as an angle of the thread to the sample length to be 451. The characteristics of commercially available ion exchange membranes are listed in Table 2.1.

Company

Ionics

Asahi Chemical

Commercially available ion exchange membranesa Product

Nepton

Aciplex

Name

Electric resistanceb [O cm2]

Cation membrane

0.6–0.7

10

Cation membrane

0.56–0.58

2

Anion membrane Anion membrane

0.5 0.57

3.4 3

Strong acidic cation membrane (Na+)

0.13–0.17

K501

Strong acidic cation membrane (Na+)

K541

A201 A221 A501 Selemion

Thickness [mm]

CR61CMP447 CR67HMR412 AR103-QDP AR204UZRA412 K192

A192

Asahi Glass

Type (counter-ions)

CMT CMV

Transportc number

Bursting strengthd [kg cm2]

Features

17

Desalination

0.89

7.0

Desalination

0.95 0.95

22 7.0

Desalination Desalination

1.5–1.9

1.0–2.5

0.16–0.20

2.0–3.5

3.5–6.0

Strong acidic cation membrane (Na+) Strong basic anion membrane (Cl)

0.25–0.40

5.0–8.0

6.0–8.0

o0.15

1.8–2.1

>2

Strong basic anion membrane (Cl) Strong basic anion membrane (Cl) Strong basic anion membrane (Cl)

0.22–0.24

3.6–4.2

2.6–3.8

0.17–0.19

1.4–1.7

2.5–3.5

0.14–0.18

2.0–3.5

4.5–5.5

Strong acidic cation membrane (Na+) Strong acidic cation membrane (Na+)

0.20–0.25

4.0–6.0

>0.94

6–8

Monovalent cation permeable, concentration High strength, desalination, concentration High strength, low resistance, electrolysis Monovalent anion permeable, concentration High acid diffusion, desalination High acid diffusion, diffusion dialysis High strength, desalination, concentration Desalination

0.13–0.15

2.5–3.5

>0.94

3–5

Concentration

Membrane Property Measurements

Table 2.1

29

30

Table 2.1. (Continued ) Company

Product

Name

Features

0.13–0.15

2.27

Strong basic anion membrane (Cl) Strong basic anion membrane (Cl) Strong basic anion membrane (Cl)

0.20–0.25

3.5–5.5

>0.96

6–8

H+ permselective, acid concentration H+ permselective, corrosion resistant, acid concentration Desalination

0.13–0.15

2.0–3.0

>0.96

3–5

Concentration

0.13–0.15

3.0–3.5

>0.97

3–5

AAV

Anion membrane

0.11–0.14

4.0–6.0

>0.95

1.5–2.0

AMP DSV

Anion membrane Strong basic anion membrane (Cl) Strong basic anion membrane (Cl) Fluoro-sulfonic acid membrane (H+) Fluoro-sulfonic acid membrane (H+)

0.15–0.20 0.13–0.17

8–10 0.9–1.2

2–3 1.5–2.0

Monovalent anion permselective, concentration + H low permeable, acid concentration Alkaline resistant Acid diffusion permeation

0.13–0.18

0.2–0.5

2–3

0.183

2.0

AMV ASV

APS N-117 N-324 NE-424

Fluoro-sulfonic acid membrane (H+)

NE-2010WX

Fluoro-sulfonic/ carboxylic membrane (K+)

4.8

3–5

High acid diffusion permeation Water hydrochloric acid electrolysis, fuel cell Composite membrane, sodium chloride electrolysis Waste acid recovery, metal recovery, KOH production Sodium chloride electrolysis

Ion Exchange Membranes: Fundamentals and Applications

Cation membrane (Na+) Cation membrane (Na+)

AMT

Naﬁon

Bursting strengthd [kg cm2]

Electric resistanceb [O cm2]

HSF

Dupont

Transportc number

Thickness [mm]

HSV

Type (counter-ions)

Tokuyama

Neocepta

CM-1

Fluoro-sulfonic/ carboxylic membrane (K+) Strong acidic cation membrane (Na+)

Sodium chloride electrolysis 0.13–0.16

0.8–2.0

1.5–3.0

CM-2

Strong acidic cation membrane (Na+)

0.12–0.16

2.0–3.5

1.5–3.0

CMX

Strong acidic cation membrane (Na+)

0.16–0.20

2.0–3.5

3.5–6.0

CMS

Strong acidic cation membrane (Na+)

0.14–0.17

1.5–3.5

2.0–3.5

CMB

Strong acidic cation membrane (Na+) Strong basic anion membrane (Cl)

0.22–0.26

3.0–5.0

5.0–8.0

0.12–0.16

1.3–2.0

2.0–4.0

AM-3

Strong basic anion membrane (Cl)

0.11–0.16

2.8–5.0

2.0–4.0

AMX

Strong basic anion membrane (Cl)

0.14–0.18

2.0–3.5

4.5–5.5

AHA

Strong basic anion membrane (Cl) Strong basic anion membrane (Cl) Strong basic anion membrane (Cl)

0.18–0.24

3.5–5.0

6.0–10.0

0.10–0.13

3.5–5.5

1.5–3.5

0.12–0.20

3.0–6.0

2.0–4.0

Strong basic anion membrane (Cl)

0.09–0.12

1.5–2.0

1.3–2.0

AM-1

ACM ACS ACS-3

Low electric resistance, desalination, concentration Low diffusion, desalination, concentration High strength, desalination, concentration Monovalent cations permselective, acid removal High strength, alkaline resistant, electrolysis Low electric resistance, desalination, concentration Low diffusion, desalination, concentration High strength, desalination, concentration High strength, alkaline resistant, electrolysis Low acid permeability, acid concentration Monovalent anions permselective, desalination Monovalent anions permselective, salt production

Membrane Property Measurements

N-981-WX

31

32

Table 2.1. (Continued ) Company

Product

Name

Type (counter-ions)

Thickness [mm]

Electric resistanceb [O cm2]

Transportc number

Bursting strengthd [kg cm2]

AFN

Strong basic anion membrane (Cl)

0.15–0.18

0.2–1.0

2.0–4.0

AFX

Strong basic anion membrane (Cl) Bipolar membrane

0.14–0.17

0.5–0.7

2.5–4.5

BP-1

0.20–0.35

4–7

Features

High acid diffusion, diffusion dialysis, desalination High acid diffusion, diffusion dialysis Organic/inorganic acid production Ion Exchange Membranes: Fundamentals and Applications

Source: Fukuda, K. (2004), Representative commercially available ion exchange membranes, In: Seno, M., Tanioka, A., Itoi, S., Yamauchi, A., Yoshida, S. (Eds.), Functions and Applications of Ion Exchange Membrane, Industrial Publishing & Consulting Inc., Tokyo, pp. 279–280. a Quoted from maker’s catalogs and technical data. b Nepton: measured in 0.1 M NaCl (CR61CMP-447; 0.01 M NaCl); Aciplex, Neocepta: measured in 251C 0.5 M NaCl using an alternate current bridge; Selemion: measured in 0.5 M NaCl under 1000 Hz (AAV; 0.5 M HCl); Naﬁon: measured in 0.6 M KCl. c Nepton: measured from current efﬁciency in 1.0 M NaCl; Selemion: measured from membrane potential in 0.5 M NaCl 1.0 M NaCl. d Mullen bursting strength; however, Aciplex A201 and A221 possess tensile strength (kg cm2).

33

Membrane Property Measurements

2.10.

ELECTRODIALYSIS

Main components of an electrodialyzer are desalting cells (Fig. 2.7 (1)), concentrating cells (Fig. 2.7 (2)), solution feeding frames (Fig. 2.7 (3)), electrode cells (Fig. 2.7 (4)) and spacers (Fig. 2.7 (5)). An electrodialyzer is assembled integrating these components with cation and anion exchange membranes (Fig. 2.8). An electrodialysis system is formed using a circulating tank, a reserve tank, a pump, a ﬂow meter and the electrodialyzer described above (Fig. 2.9). The circulating tank is immersed in a thermostat adjusted at a constant temperature. An electrolyte solution is put into concentrating cells through a deﬂating tube and the head of a concentrated solution extracting tube is adjusted at a reasonable level h. A 0.5 M NaCl solution is put into electrode cells. The electrolyte solution is put into the reserve tank. The electrolyte solution in the reserve tank is supplied into the circulating tank through the ﬂow meter F1 and further supplied to the electrodialyzer through the ﬂow meter F2 adjusting the solution velocity in desalting cells at 4– 5 cm s1. This situation is left as such for several hours, during which it is conﬁrmed that an outﬂow from the concentrated solution extracting tube due to solution leakage is negligible. When the outﬂow is recognized, the assembling work is estimated to be imperfect, so that the electrodialyzer is disassembled and assembled again. A slight level change in the concentrated extracting tube is prevented by regulating the height h indicated in Fig. 2.9. Next, an electric circuit is formed putting an Ag electrode into the anode cell and an AgCl electrode into the cathode cell. A 0.5 M NaCl solution is dropped into the electrode cells and the electrolyte solution is supplied into the circulating tank at the amount Q (Eq. (2.10)) through the ﬂow meter F1. Q¼

NSZi F aC

(2.10)

where Q is the amount of ﬂow indicated by F1 (cm3 min1), N the number of membrane cell pairs, S the effective membrane area (cm2 per pair), a the desalting ratio, Z the current efﬁciency, i the current density (A cm2), F the Faraday constant (1608 A min eq1 and C the ionic concentration in the feeding electrolyte solution (eq cm3). An electric current is passed, an overﬂow from the concentrated solution extracting tube is collected and its concentration is observed by a refraction meter. Conﬁrming that the electrolyte concentration of the concentrated solution has become constant, the volume q (cm3 s1), ionic concentration C00 (eq cm3) and pH are measured. At the same time, the solution at the inlets of desalting cells and that at the outlet are collected, and their ionic concentration and pH are measured. Further, voltage difference V between the concentrating cells integrated at both ends of the electrodialyzer is measured using

34

1

2

3

4 1. Desalting cell: Rubber 0.75 mm thick 2. Concentrating cell: Rubber 0.75 mm thick 3. Feeding frame: Transparent PVC 4. Electrode cell: Transparent PVC 5. Spacer: Polyethylene diagonal net 0.7-0.8mm thick

Figure 2.7

Components of an electrodialyzer (Seno¯ and Tanaka, 1984).

Ion Exchange Membranes: Fundamentals and Applications

5

Membrane Property Measurements

35

K: Action exchange membrane A: Anion exchange membrane D: Desalting cell C: Concentrating cell F: Solution feeding frame

Figure 2.8

Electrodialyzer (Seno¯ and Tanaka, 1984).

R: Reserve tank of an electrolyte solution, Cir: Circulating tank, E: Electrodialyzer, P: Pump, F: Flow meter, Con: Concentrated solution, De: Desalted solution

Figure 2.9

Electrodialysis system (Seno¯ and Tanaka, 1984).

Pt electrodes put in these cells. During the passage of current, Ag and AgCl are converted to AgCl and Ag, respectively, so that both electrodes must be replaced appropriately. A time limit of replacement is decided from abrupt increase of the voltage difference.

36

Ion Exchange Membranes: Fundamentals and Applications

REFERENCES Kosaka, Y., Emura, T., 1963, General characteristics and performance measuring methods, In: Kosaka, Y., Shimizu, H. (Eds.), Ion Exchange Membrane, Kyoritu-Shuppan Co. Ltd., Tokyo, Japan, pp. 117–177. Seno¯ , M., Tanaka, Y., 1984, Ion exchange membrane experimental method, In: Nakagaki, M. (Ed.), Membrane Science Experimental Method, Kitami Shyobo Co., Tokyo, Japan, pp. 191–207. Takemoto, N., 1966, Measuring methods of ion exchange membrane characteristics, In: Scientiﬁc Paper of the Central Research Institute, Japan Monopoly Corporation, Japan, pp. 295–303. Tanaka, Y., 2000, Current density distribution and limiting current density in ion exchange membrane electrodialysis, J. Membr. Sci., 173, 179–190. Yamabe, T., Seno¯ , M., 1964, Ion Exchange Resin Membrane, Gihodo Co, Tokyo, Japan pp. 213–240.

Chapter 3

Membrane Characteristics and Transport Phenomena 3.1. PERMSELECTIVITY BETWEEN IONS HAVING DIFFERENT CHARGED SIGN A cation and an anion exchange membrane permeate, respectively, cations and anions selectively. This phenomenon is based on the following Donnan equilibrium theory (Donnan, 1934). The electro-chemical potential of component i in a system is deﬁned as mi ¼ m0i þ RT ln ai þ ðP P0 Þvi þ zi F c

(3.1)

where m0i is standard chemical potential, R gas constant, T absolute temperature, ai activity, P pressure, P0 standard pressure (1 atm.), vi partial molar volume of component i, zi charge number, F Faraday constant, and c electric potential. Assuming cation X and anion Y to be dissolved into a solvent W, Eq. (3.1) becomes mX ¼ m0X þ RT ln aX þ ðP P0 ÞvX þ zX F c mY ¼ m0Y þ RT ln aY þ ðP P0 Þ þ zY F c mW ¼ m0W þ RT ln aW þ ðP P0 Þ

(3.2)

The Donnan equilibrium state is represented by Eq. (3.3) showing that the electro-chemical potential of component i in a solution phase mi is equivalent to that in a membrane phase m¯ i : mi ¼ m¯ i From Eqs. (3.2) and (3.3) aX ¯ cÞ ¼ 0 ¯ PÞvX zX F ðc RT ln ðP a¯ X

(3.3)

(3.4)

RT ln

aY ¯ cÞ ¼ 0 ¯ PÞvY zY F ðc ðP a¯ Y

(3.5)

RT ln

aW ¯ PÞvW ¼ 0 ðP a¯ W

(3.6)

From Eqs. (3.4) and (3.5), the Donnan potential difference between both phases EDon is introduced as 1 ai ¯ ðRT ln pvi Þ E Don ¼ c c ¼ (3.7) a¯ i zi F DOI: 10.1016/S0927-5193(07)12003-9

38

Ion Exchange Membranes: Fundamentals and Applications

The pressure difference between both phases p is obtained as RT aW ¯ ln p¼PP¼ a¯ W vW

(3.8)

One mole of electrolytes is dissociated into vX moles of cations X and vY moles of anions Y, so we have vX zX þ vY zY ¼ 0

(3.9)

Canceling EDon from Eq. (3.7) for cation X and anion Y, and taking account of Eq. (3.9) vX vY aX aY (3.10) ¼ pvXY RT ln a¯ X a¯ Y vXY is the partial molar volume of electrolyte XY deﬁned by vXY ¼ vX vX þ vY vY

(3.11)

Substituting Eq. (3.8) into Eq. (3.10), the following Donnan equilibrium equation is introduced: vX vY aX aY vAX aW ¼ ln (3.12) ln a¯ X a¯ Y vW a¯ W Putting r ¼ vXY/vW in Eq. (3.12) avXX avYY a¯ vXX a¯ vYY ¼ r a¯ W arW

(3.13)

When aW A¯aW holds avXX avYY ¼ a¯ vXX a¯ vYY

(3.14)

Putting the activity coefﬁcient of cations X and anions Y to be 1 in Eq. (3.14) v

v

¯ YY ¯ XX C C vXX C vYY ¼ C

(3.15)

Equation (3.15) is an approximated expression of the Donnan equilibrium phenomenon. When a Na-type cation exchange membrane is immersed in a NaCl solution, Eq. (3.15) becomes ¯ Na C¯ Cl C Na C Cl ¼ C

(3.16)

¯ Cl CNa, CCl are concentration of Na ions and Cl ions in a solution and C¯ Na ; C are concentration of Na+ ions and Cl ions in a membrane. The electro-neutrality in the membrane is expressed as +

¯ Cl þ C ¯R C¯ Na ¼ C where C¯ R is concentration of ion exchange groups R in a membrane.

(3.17)

39

Membrane Characteristics and Transport Phenomena

Combining Eq. (3.16) with Eq. (3.17) qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¯ Na ¼ 1 ¯ 2 þ 4C Na C Cl þ C ¯R C C 2 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 ¯ Cl ¼ 1 ¯R C¯ þ 4C Na C Cl C C

(3.18)

2

Putting NaCl concentration in a NaCl solution as C ( ¼ CNa ¼ CCl) in Eq. (3.18) qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¯ 2 þ 4C 2 C¯ R ¯ Cl C C R ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ (3.19) ¯ C Na ¯ 2R þ 4C 2 þ C¯ R C ¯ R ¼ 4 and 8 mol dm–3 in Eq. (3.19), and ¯ Cl =C¯ Na is computed by putting C C ¯ Na increases toward 1 with the plotted against C (Fig. 3.1) showing that C¯ Cl =C increase of C and decreases toward 0 with the decrease of C. In the same way, ¯ Na is computed by putting C as a pa¯ R and C¯ Cl =C the relationship between C ¯ Cl =C¯ Na to approach 1 at inﬁnitely small C¯ R : rameter (Fig. 3.2), showing C Putting a cation exchange membrane in a NaCl solution and passing an electric current across the membrane through electrodes placed in both sides of the membrane, Na+ ions transfer from the anode toward the cathode and Cl 1

10-1 10-2

m -3 qd m -3 qd

10-5

8e

R=

4e

10-4 C

CCl /CNa

10-3

10-6 10-7 10-8 10-3

10-2

10-1 1 C (eq dm-3)

101

102

Figure 3.1 Relationship between NaCl concentration in a solution and Cl–/Na+ ratio in a cation exchange membrane.

40

Ion Exchange Membranes: Fundamentals and Applications

1

10 -1 0.5 dm eq

C=

10 -2

-3

eq dm

-3

CCl / CNa

0.1

10 -3

10 -4

10 -5

10 -6 10 -3

10 -2

10 -1

1

10 1

10 2

CR (eq dm-3)

Figure 3.2 Relationship between ion exchange group concentration and Cl–/Na+ ratio in a cation exchange membrane.

ions transfer from the cathode toward the anode. In this situation, the transport number of Na+ ions ¯tNa and that of Cl ions ¯tCl passing through the membrane are approximately represented by the following equation. u¯ Na C¯ Na ¯ ¯ Cl u¯ Na C Na þ u¯ Cl C u¯ Cl C¯ Cl ¼ ¯ Na þ u¯ Cl C ¯ Cl u¯ Na C

¯tNa ¼ ¯tCl

(3.20)

Diameter of ﬁne pores in an ion exchange membrane distributes within the range of 0.005–0.1 mm and shape of the pores is winding (Mizutani and Nishimura, 1970). Hydrated radius of Na+ ions and Cl ions are 4.5 and 3 A˚, respectively (Conway, 1952). Mobility of monovalent counter-ions (excepting H+ and OH ions) and that of divalent counter-ions passing through an ion exchange membrane are, respectively, about 1/10 and 1/20–1/50 of the values in an aqueous solution (Yamamoto, 1968). Based on these experimental results, the ionic mobility in the membrane is estimated to be decreased due to mainly steric hindrance in the pore. However, we have to pay attention to that sulfonic acid groups ﬁxed to the polymer structure of a cation exchange membrane exert electrical attraction on Na+ ions and electrical repulsion on Cl ions.

41

Membrane Characteristics and Transport Phenomena

The molar conductivity of Na+ ions and Cl ions in water are measured as follows (Convington and Dickinson, 1973): FuNa ¼ 50:11 S cm2 mol1 FuCl ¼ 76:35 S cm2 mol1 u¯ Cl =¯uNa in the cation exchange membrane is possible to be deﬁned by the following equation including the mobility ratio in water uCl/uNa and the mobility ratio parameter n. u¯ Cl uCl n ¼ 1:524n (3.21) ¼ u¯ Na uNa where n is less than 1 due to the attraction between sulfonic acid groups and Na+ ions, and the repulsion between sulfonic acid groups and Cl ions. Substituting Eq. (3.21) into Eq. (3.20) ¯tNa ¼

1 ¯ Na Þ ¯ Cl =C 1 þ 1:524nðC

(3.22)

¯R ¯tNa is calculated using Eqs. (3.19) and (3.22), and plotted against C and C putting n as a parameter (Figs. 3.3 and 3.4). In these ﬁgures, n is estimated to decrease with decreasing C and increasing C¯ R because of Donnan exclusion 1.0 0.1

0.9 0.8 0.7

0.5

tNa

0.6 0.5

n =1

0.4 0.3 0.2

CR= 4 eq/dm3

0.1 0.0 10 -2

10 -1

1 C (eq dm-3)

10 1

10 2

Figure 3.3 Relationship between NaCl concentration in a solution and Na+ ion transport number in a cation exchange membrane.

42

Ion Exchange Membranes: Fundamentals and Applications

1.0 0.9

0.1

0.8 0.7

tNa

0.6

0.5

0.5 0.4

n =1

0.3

C = 0.1 eq/dm3NaCl

0.2 0.1 0.0 10 -3

10 -2

10 -1 CR (eq dm-3)

1

101

Figure 3.4 Relationship between ion exchange group concentration and Na+ ion transport number in a cation exchange membrane.

development and resulting increase of repulsion (attraction) between sulfonic acid groups and Cl (Na+) ions. In this circumstance, however, ¯tNa is increased ¯ Na to be decreased toward 0 (Figs. 3.1 and 3.2). On ¯ Cl =C toward 1 because of C the other hand, n is estimated to increase toward 1 with increasing C and decreasing C¯ R because of Donnan exclusion decline and resulting decrease of repulsion (attraction) between sulfonic acid groups and Cl (Na+) ions. 3.2. PERMSELECTIVITY BETWEEN IONS HAVING THE SAME CHARGED SIGN When Na+ ions and Ca2+ ions are dissolved in a solution, the permeation of these ions through a cation exchange membrane is not equivalent each other. This phenomenon is termed ‘‘the permselectivity between ions having the same charged sign’’, and discussed in this section. An ion exchange membrane consists of a three-dimensional cross-linked polymer net structure combined with many ion exchange groups. The membrane exhibits gelling states in an electrolyte solution due to water absorption. The ion exchange groups are charged and absorb the ions having different charged sign (counter-ions) selectively. An electrical current applied in this system generates the ﬂuxes Ji of counter-ion i across the membrane which is indicated generally by the following extended Nernst–Planck equation added the convection term

43

Membrane Characteristics and Transport Phenomena

(third term) to the Nernst–Planck equation (Planck, 1890). RT d C¯ i ¯ i dc þ C ¯ iv zi u¯ i C u¯ i (3.23) dx F dx ¯ i is the concentration, ui the mobility, zi the charge number, d C¯ i =dx the C concentration gradient and these are the values of counter-ions i in the membrane. dc/dx is the potential gradient and v the convection velocity in the membrane. The ﬁrst, the second and the third term in Eq. (3.23) mean the ionic ﬂuxes of ions i caused by diffusion, electro-migration and convection, respectively. The structure of an ion exchange membrane is generally rather dense so that the effect of diffusion and convection on the ﬂux is possible to neglect, resulting the simpliﬁcation of Eq. (3.23) as Ji ¼

¯ i dc (3.24) J i ¼ zi u¯ i C dx Transport number of ions i, ¯ti ; in the membrane is introduced from Eq. (3.24) as (cf. Eq. (3.20)) zJ z2 u¯ C¯ ¯ti ¼ Pi i ¼ Pi 2i i zi J i zi u¯ i C¯ i

(3.25)

If ions A and B transport across the membrane, then the ﬂux ratio of these ions is introduced from Eq. (3.24) as ¯B zB J B ¯tB z2 u¯ B C ¼ ¼ 2B ¯A zA J A t¯A zA u¯ A C

(3.26)

Permselectivity coefﬁcient of ion B against ion A, T BA is deﬁned using Eq. (3.26) as follows: zB J B ¯ AÞ zB u¯ B ðC¯ B =C z J (3.27) T BA ¼ A A ¼ zB C B zA u¯ A ðC B =C A Þ zA C A

3.3.

ELECTRIC CONDUCTIVITY The convection velocity v in Eq. (3.23) is expressed as (Helfferich, 1962) o¯u0 dc dx ðF C¯ R Þ u¯ 0 ¼ ðro Þ v¼

(3.28)

44

Ion Exchange Membranes: Fundamentals and Applications

o is the charge number of ion exchange groups, being 1 for a cation exchange membrane and +1 for an anion exchange membrane. u¯ 0 and e are the mobility and the volume ratio of a solution in the membrane, respectively. The ﬁrst term (diffusion term) in Eq. (3.23) is generally negligible in an ion exchange membrane, so we have the following equation taking account of Eq. (3.28). dc (3.29) J i ¼ C¯ i ðzi u¯ i o¯u0 Þ dx Equation (3.29) indicates that the velocity of counter-ions is increased and that of co-ions is reduced by u¯ 0 in the membrane. Here, the electric current density i is deﬁned by the following equation. X i ¼ zi J i (3.30) F The electro-neutrality is given by the following equation. X ¯R ¼0 ¯ i þ oC zi C (3.31) The electric current density is expressed using Eqs. (3.29), (3.30) and (3.31) as follows: X dc (3.32) i ¼ F z2i u¯ i C¯ i þ u¯ 0 C¯ 0 dx Accordingly, the speciﬁc electric conductivity of the membrane k is X ¯ i þ u¯ 0 C ¯0 k¼F z2i u¯ i C (3.33) In an ion exchange membrane, the speciﬁc ﬂow resistance is generally large enough because of extremely dense structure of the membrane. Accordingly the second term (convection) in Eqs. (3.32) and (3.33) is also negligible and the conductivity of a cation exchange membrane immersed in a NaCl solution is presented by the following equation: u¯ Cl ¯ ¯ ¯ (3.34) C Cl k ¼ F ð¯uNa C Na þ u¯ Cl u¯ Cl Þ ¼ F u¯ Na C Na þ u¯ Na k is calculated using Eqs. (3.18), (3.20), (3.21) and (3.34) assuming Na+ ion mobility in the membrane is one-tenth of the value in the solution; F u¯ Na ¼ ¯R 50:11=10 ¼ 5:011 S cm2 mol1 (cf. Section 3.1). k is plotted against C and C putting n as a parameter (Figs. 3.5 and 3.6). In these ﬁgures, n increases toward 1 ¯ R: with the increase of C and the decrease of C 3.4.

MEMBRANE POTENTIAL

When both surfaces of a cation exchange membrane are in contact with NaCl solutions of different concentrations, Na+ ions diffuse from a

45

Membrane Characteristics and Transport Phenomena

10 4

CR= 4 eq/dm3

(Scm)

n= 0.5 1 0.1

10 3

10 2

10 1 10 -2

1

10 -1

C (eq

10 1

10 2

dm-3)

Figure 3.5 Relationship between NaCl concentration in a solution and speciﬁc conductivity of a cation exchange membrane. 10 3

C = 0.1 eq/dm3 NaCl

(Scm)

10 2

10 1

n=1 1

0.5 0.1

10 -1 10 -3

10 -2

1 10 -1 CR (eq dm-3)

10 1

10 2

Figure 3.6 Relationship between ion exchange group concentration and speciﬁc conductivity of a cation exchange membrane.

46

Ion Exchange Membranes: Fundamentals and Applications

high-concentration side to a low-concentration side, however, the diffusion of Cl ions in this system is rather restricted. These phenomena make the spheres in the low-concentration side charge positively and the spheres in the high-concentration side negatively and generate the potential difference (membrane potential) which hinders still more diffusion of Na+ ions. When an anion exchange membrane is placed in the above mentioned circumstances, the low- and high-concentration sides charge, respectively, negatively and positively. Now, an electric potential difference dE is assumed to be applied to a ﬁne section in a membrane with passing 1 Faraday of an electric current, and then the energy consumed in this system is FdE. If the changes are reversible, FdE is equivalent to the free energy change dG. dG ¼ FdE

(3.35)

The ionic movement generates an electric current, and chemical potential change owing to the ionic movement is equivalent to the free energy change. The events described here are represented by the following equation for ions i. dG i ¼

ti ti dm ¼ RTd ln ai zi i zi

(3.36)

ti, zi, mi and ai are the transport number, charge number, chemical potential and activity of ions i, respectively. From Eqs. (3.35) and (3.36), the following Nernst equation (Nernst, 1888, 1889) is introduced. E¼

RT F

Z X ti d ln ai zi

(3.37)

If a solution 1 and solution 2 dissolving the same kind of electrolytes are partitioned by an ion exchange membrane, Eq. (3.37) becomes E¼

¯tþ RT ðaþ Þ2 ¯t RT ða Þ2 ln ln þ zþ F ðaþ Þ1 z F ða Þ1

(3.38)

t+ and t are the transport number of cations and anions in the membrane, respectively. (a+)2/(a+)1 and (a)2/(a)1 are the activity ratio of cations and anions between both solutions, respectively. If the solution dissolves electrolytes consisting of monovalent cations and monovalent anions and (a+)2/ (a+)1 ¼ (a)2/(a)1 holds, the following equation is introduced. E ¼ ð¯tþ ¯t Þ

RT a2 ln a1 F

(3.39)

47

Membrane Characteristics and Transport Phenomena

Equation (3.39) is expressed for a cation and an anion exchange membrane, respectively, as follows: RT a2 ln E ¼ ð2¯tþ 1Þ a1 F (3.40) RT a2 ln E ¼ ð2¯t 1Þ a1 F 3.5.

CONCENTRATION DIFFUSION

Electrolyte solutions of different concentrations dissolving one kind of cations and anions are assumed to be placed on both sides of an ion exchange membrane and the electrolytes are assumed to diffuse from a high-concentration side to a low-concentration side. In this system, the mechanism of the concentration diffusion is considered as follows: Canceling the third term in Eq. (3.23) and applying the Nernst–Einstein equation; (Eq. 3.41) (Crank, 1957; Ilschner, 1958) indicating the relationship between the ionic mobility ui and the ionic diffusion constant Di, we obtain Eq. (3.42) (Nernst–Planck equation) expressing the ﬂux of cations J+ and of anions J across the membrane. ui ¼

Di F RT

¯ ¯ þ dc ¯ þC ¯ þ d C þ zþ D J þ ¼ D dx dx ¯ d C dc ¯ ¯ C ¯ z D J ¼ D dx dx From the electrical neutrality in the membrane ¯R ¼0 Z þ C¯ þ þ z C¯ þ oC Differentiating Eq. (3.43) ¯ d C¯ þ dC þ z ¼0 dx dx From no electric current zþ

(3.41)

(3.42)

(3.43)

(3.44)

Z þ J þ þ z J ¼ 0 In a steady state,

(3.45)

J þ ; J ¼ constant Canceling dC/dx in Eq. (3.42) and applying Eqs. (3.44) and (3.45)

(3.46)

Jþ ¼

¯ Þ d C ¯ þD ¯ ðz2þ C¯ þ þ z2 C ¯þ D 2 2 ¯ ¯ ¯ ¯ dx zþ D þ C þ þ z D C

(3.47)

48

Ion Exchange Membranes: Fundamentals and Applications

J ¼

¯ Þ d C ¯ þD ¯ ðz2þ C¯ þ þ z2 C ¯ D ¯ þ þ z2 D ¯ dx ¯ þC ¯ C z2þ D

(3.48)

The form of Eqs. (3.47) and (3.48) is the same to the Fick’s diffusion equation. Electro-neutrality held in the membrane accelerates the movement of ions showing lower diffusion coefﬁcient, and it decelerates that of ions showing larger diffusion coefﬁcient. This event makes the movement of co-ions accelerate and that of counter-ions decelerate in an ion exchange membrane (cf. Section 3.1). The phenomenon described above is due to the Donnan potential generated at a membrane/solution interface, which result the Donnan exclusion against coions. When the concentration of co-ions is decreased extremely in the membrane, the diffusion ﬂux of the counter-ions is decreased remarkably owing to the dominant Donnan exclusion as expressed by the following equation introduced from Eqs. (3.47) and (3.48). In a cation exchange membrane, ¯ lim J þ ¼ D

C¯ !0

¯þ dC dx

(3.49)

In an anion exchange membrane, ¯þ lim J ¼ D

C¯ þ !0

d C¯ dx

(3.50)

Equations (3.49) and (3.50) suggest that the diffusion velocity of counter-ions is inﬂuenced by a small amount of co-ions remained in the membrane. 3.6.

MECHANISM TO DECREASE DIVALENT ION PERMEABILITY

In the electrodialysis process for concentrating seawater, formation of a polycation layer on a desalting surface of a cation exchange membrane results in a reduction of Ca2+ ions permeability and avoids the precipitation of CaSO4 in concentrating cells. An example of the ploycation is di-cyandiamide formaldehyde condensate (the reagent Nonisold) (Daiichi Industrial Pharmaceutical, 1970) including many quaternary ammonium groups as indicated in Fig. 3.7 (Wolf and Spiethoff, 1967). In seawater, the reagent dissociates into polycations and Cl counter-ions. The polycations thus formed move to the cation exchange membranes under the inﬂuence of an electric ﬁeld, and reach the membrane surface, where they combine with the sulfonic acid exchange groups. The reagent molecule is too large to permeate the membrane, so it accumulates on the membrane surface to form a reagent layer. The reagent layer ﬁxed on a membrane surface is illustrated schematically in Fig. 3.8. In the reagent layer, positively charged quaternary ammonium groups pack closely together, and Coulomb and Born repulsive forces exert on surrounding cations. The potential produced by

Membrane Characteristics and Transport Phenomena

Figure 3.7 1981).

49

Suggested molecular formulae of the reagent Nonisold (Tanaka and Seno¯ ,

two adjacent quaternary ammonium groups is illustrated in Fig. 3.9; under the inﬂuence of an electric ﬁeld, a mobile cation Q moves across the lowest potential barrier between two quaternary ammonium groups E1 and E2. Any mobile cation must pass over the potential barrier of the reagent layer in order to permeate the membrane. Under these circumstances, the transport of divalent ions across the membrane becomes more difﬁcult than for monovalent ions, because greater energy is required for doubly charged cations to pass over the barrier. A representative potential proﬁle for mobile cations under the inﬂuence of an electric ﬁeld is illustrated in Fig. 3.10. The mechanism of decreased permeability of divalent ions will now be discussed based on this proﬁle (Tanaka and Seno¯, 1981). First, we consider the case in which no reagent layer is formed on the membrane surface. The feed solution contains monovalent cation A and divalent cation B with common anions. The potential proﬁle is depicted schematically by the continuous line in Fig. 3.10. Under the applied current density, the relationship between the ionic concentration in the desalted solution and in the membrane is approximately expressed as follows, applying the Boltzmann distribution

50

Figure 3.8

Ion Exchange Membranes: Fundamentals and Applications

Reagent ﬁxed on the membrane (Tanaka and Seno¯ , 1981).

law (Debye and Huckel, 1923) and taking the potential height in the desalted solution phase as standard. ¯ cA 0 ¯ C A ¼ C A exp RT ¯ (3.51) cB ¯ B ¼ C 0B exp C RT ¯ 0i the concentration ¯ i is the concentration of ion i in the membrane (mol cm–3), C C ¯ i potential height in the memof ion i in the desalted solution (mol cm–3) and c brane measured from the desalted solution phase for ion i (J mol–1). From Eqs. (3.24) and (3.51) the ionic ﬂuxes are expressed as ¯ ¯ ¯ c dc 0 dc 0 ¯ ¼ zA u¯ A C A exp A J A ¼ zA u¯ A C A RT dx dx ¯ ¯ c d c¯ 0 dc 0 ¯ ¼ zB u¯ B C B exp B J B ¼ zB u¯ B C B RT dx dx

(3.52)

Membrane Characteristics and Transport Phenomena

Figure 3.9

51

Potential distribution in the reagent layer (Tanaka and Seno¯ , 1981).

J 0i is the ﬂux of ion i when no reagent layer is formed on the membrane surface. ¯ d c=dx is the potential gradient in the membrane. In this situation, the permselectivity coefﬁcient of ion B against ion A, ðT BA Þ0 is expressed using Eqs. (3.27) and (3.52) as follows: zB J 0B ¯ B 0 cB c¯ A zB u¯ B zA J 0A ¼ (3.53) exp TA ¼ zB C 0B zA u¯ A RT zA C 0B Next, when the reagent layer is formed on the membrane surface, the relationship between the ionic concentration in the desalted solution C 0i and in the reagent layer C i is expressed as follows taking the potential height in the desalted solution phase standard: as c A C A ¼ C 0A exp RT (3.54) cB 0 C B ¼ C B exp RT

52

Ion Exchange Membranes: Fundamentals and Applications

C

, i

C *i Reagent layer

Ci

*

Desalted solution

i

Cation exchange membrane Concentrated solution

Figure 3.10 1981).

Potential proﬁle across a cation exchange membrane (Tanaka and Seno¯ ,

ci is the potential height in the reagent layer measured from the desalted solution phase for ion i. From Eqs. (3.24) and (3.54)

dc dc c ¼ zA uA C 0A exp A dx dx RT dc dc c ¼ zB uB C 0B exp B J B ¼ zB uB C B dx dx RT

J A ¼ zA uA C A

(3.55)

The permselectivity coefﬁcient in this situation T BA is exhibited using Eqs (3.27) and (3.55) as follows: zB J B zB uB cB cA zA J A B ¼ (3.56) TA ¼ exp zB C 0B zA uA RT zA C 0B Further, the relationship between the ionic concentration in the reagent ¯ i is indicated as follows taking the layer phase C i and in the membrane phase C

53

Membrane Characteristics and Transport Phenomena

potential in the reagent layer phase as standard: ¯ A Þ ðcA þ c ¯ C A ¼ C A exp RT ðcB þ c¯ B Þ ¯ C B ¼ C B exp RT

(3.57)

From Eqs. (3.24), (3.27) and (3.57) zB u¯ B ðcB cA Þ þ ðc¯ B c¯ A Þ B TA ¼ exp zA u¯ A RT

(3.58)

From Eqs (3.53) and (3.58) cB cA ¼ RT log

T BA ðT BA Þ0

(3.59)

cB cA is plotted against T BA =ðT BA Þ0 and shown in Fig. 3.11 Mg K T Ca Na ; T Na and T Na obtained in the seawater electrodialysis experiment injected the reagent Nonisold into the feeding solution (Tanaka, 1974) are substituted into Eq. (3.59). ci cNa vs. operating time t is shown in Fig. 3.12. 4

*B- *A (KJ/mol)

3

2

1

0

-1 0.0

0.5

1.0

1.5 B/

TA

Figure 3.11

2.0

2.5

B)0

(TA

Relationship between permselectivity and potential in the reagent layer.

54

Ion Exchange Membranes: Fundamentals and Applications

3.0 Mg 2.5 Ca *i - *Na (KJ/mol)

2.0 Mg

1.5

Ca 1.0

0.5 K 0.0 K -0.5

0

5

10

15

20

25

30

35

t(h)

Figure 3.12 Potential change in the reagent layer. Reagent concentration in the feeding seawater Open: 0.1ppm Filled: 0.5ppm Current density 4Adm2

3.7. RESEARCH ON MEMBRANES TREATMENT TO DECREASE DIVALENT ION PERMEABILITY In Japan, salt is produced by concentration of seawater using ion exchange membrane electrodialysis with crystallization of the brine using vacuum evaporators. In the electrodialysis process, it is strongly expected to decrease the transport of divalent ions for preventing scale (CaSO4) formation in concentrating cells. In order to accomplish this purpose, many attempts on the membrane treatment had been made over some period of time as exempliﬁed as follows. (1) Permselectivity coefﬁcient of Ca2+ ions against Na+ ions T Ca Na and electric resistance r of a cation exchange membrane was measured by the electrodialysis of a 0.2 eq dm–3 NaCl+0.2 eq dm–3 CaCl2 solution and obtained T Ca Na ¼ 2:5; r ¼ 7 O. The cation exchange membrane was treated in a 2% aqueous poly-ethylenimine (MW ¼ 30,000) solution and electrodialyzed supplying a 0.2 eq dm–3 NaCl+0.2 eq dm–3 CaCl2 solution. The results were T Ca Na ¼ 0:5; r ¼ 11 O (Mizutani et al., 1971a). The cation exchange membrane was treated in a 20 ppm poly-2-vinyl pyridinium hydrochloric acid salt (MW ¼ 30,000) solution. The results

Membrane Characteristics and Transport Phenomena

55

obtained in the electrodialysis of a 0.2 eq dm–3 NaCl+0.2 eq dm–3 CaCl2 solution were T Ca Na ¼ 0:4 and r ¼ 10 O (Mizutani et al., 1971b). The events in these experiments demonstrate that polycations consisting of imino or pyridinium groups suppress the transport of divalent ions across the cation exchange membrane, and are supported by the theory described in Section 3.6. (2) Materials produced by condensing polymerization between meta-phenylenediamine hydrochloric acid salt, di-cyandiamide and para-formaldehyde were dissolved in water. A cation exchange membrane was immersed in the solution described above. The condensates and the membrane were bonded on the membrane surface by cross-linking with furfural. Permselectivity of the above treated membrane were measured by the electroMg dialysis of seawater as T Ca Na ¼ 0:65; T Na ¼ 0:48: The electric resistance of 2 the membrane was r ¼ 4.22 O cm . Permselectivity and electric resistance Mg of the original cation exchange membrane were T Ca Na ¼ 1:91; T Na ¼ 1:46; 2 r ¼ 4.21 O cm (Mihara et al., 1972). In this experiment, polycations consisting of di-cyandiamide and meta-phenylenediamine are ﬁxed to the membrane surface by a chemical reaction. (3) An anion exchange membrane was treated in a 0.3% aqueous potassium poly-stylene sulfonic acid solution. The treated membrane and the nontreated membrane were integrated into an electrodialyzer and electrodialyzed supplying artiﬁcially prepared seawater. Permselectivity coefﬁcient SO4 of SO2 4 ions against Cl ions T Cl and electric resistance r of nontreated 4 and treated membrane were as follows. Nontreated: T SO Cl ¼ 0:20; 4 ¼ 0:05; r ¼ 6.10 (Mihara et al., 1970). The above r ¼ 6.10. Treated: T SO Cl ion transport across an anion is the experiment for suppressing SO2 4 exchange membrane. The phenomena demonstrate that the divalent ion transport is suppressed due to polyanions created by sulfonic acid groups in the reagent layer. The theory described in Section 3.6 is also applicable to the phenomena mentioned above. In this experiment, a cation exchange layer is formed on the anion exchange membrane. The structure of this membrane is the same to that of an anti-organic fouling membrane (cf. Section 14.3.2). (4) An anion exchange membrane (Membrane X) was synthesized using styrene–butadiene rubber, polyethylene, AlCl3, ether and dichloroethane. Membrane X was immersed in an aqueous meta-phenylenediamine hydrochloric acid solution. The membrane was subsequently immersed in a formaldehyde–hydrochloric acid mixed solution. As a result of these steps, meta-phenylenediamine was combined with formaldehyde by a condensing cross-linking reaction on the surface of Membrane X (Mem4 brane X0 was obtained). T SO Cl measured by the electrodialysis of a 0.5 eq –3 –3 dm NaCl+0.05 eq dm Na2SO4 solution and r of both membranes 2 4 were as follows. Membrane X: T SO Cl ¼ 0:020; r ¼ 4.7 O cm . Membrane

56

Ion Exchange Membranes: Fundamentals and Applications 2 4 X0 : T SO Cl ¼ 0:008; r ¼ 7.4 O cm (Hani et al., 1961 ). In this experiment, SO4 4 T Cl of Membrane X is considerably low, however, T SO Cl of Membrane 0 X is decreased further. Low divalent ion permeability in this investigation was given by the sieving effect of the cross-linked layer, which separates smaller Cl ions from larger SO2 4 ions. The mechanism of this phenomenon is different from that of another ones described in (1)–(3). In order to prevent the increase of electric resistance r, it is necessary to control the thickness of the cross-linked layer.

REFERENCES Convington, A.K., Dickinson, T. (Eds.), 1973, Physical Chemistry of Organic Solvent System, Plenum Press, p. 525, New York. Conway, B. E., 1952, Electrochemical Data, Elsevier Publishing Co, London. Crank, J., 1957, Diffusion coefﬁcients in solids. Their measurement and signiﬁcance, Discuss, Faraday Soc., 23, 99–104. Daiichi Industrial Pharmaceutical, 1970, Product Bulletin, Kyoto, Japan. Debye, P., Huckel, E., 1923, Theory of electrolyte, Physik Z., 24, 185–206. Donnan, F. G., 1934, Die genaue thermodynamik der membrangleichgewichte, Z. Phys. Chem. A, 168(5/6), 369–380. Helfferich, F., 1962, Ion-exchange, McGraw-Hill, New York, p. 393. Hani, H., Nishihara, H., Oda, Y., 1961, Anion-exchange membrane having permselectivity between anions, JP Patent, S36-15258. Ilschner, B., 1958, The adaptability and the relationship of Nernst-Einstein and of Onsager, Z. Electrochem., 62, 989–992. Mihara, K., Misumi, T., Miyauchi, H., Ishida, Y., 1970, Anion-exchange membrane having excellent speciﬁc permselectivity between anions, JP Patent, S45-19980, S45-30693. Mihara, K., Misumi, T., Miyauchi, H., Ishida, Y., 1972, Production of a cation-exchange membrane having excellent speciﬁc permselectivity between cations, JP Patent, S47-3081. Mizutani, Y., Nishimura, M., 1970, Studies on ion-exchange membranes. XXXII. Heterogeneity in ion-exchange membranes, J. Appl. Polym. Sci., 14, 1847–1856. Mizutani, Y., Yamane, R., Sata, T., 1971a, Electrodialysis for transporting selectively smaller charged cations, JP Patent, S46-23607. Mizutani, Y., Yamane, R., Sata, T., Izuo, T., 1971b, Permselectivity treatment of a cation-exchange membrane, JP Patent, S46-42083. Nernst, W., 1888, Zur kintik der in losung beﬁndlichen korper, Z. Phys. Chem., 2(9), 613–637. Nernst, W., 1889, Die elektromotorische wirksamkeit der ionen, Z. Phys. Chem., 4(2), 129–181. Planck, M., 1890, Ueber die potentialdifferenz zwischen zwei verdunnten losungen binarer elektrolyte, Ann. Der. Phys. Chem., 40, 561–576. Tanaka, Y., 1974, Effect of treatment conditions by a reagent on low permeability of cation-exchange membranes for bivalent ions, J. Electrochem. Jpn., 42, 192–198.

Membrane Characteristics and Transport Phenomena

57

Tanaka, Y., Seno¯ , M., 1981, Treatment of ion-exchange membranes to decrease divalent ion permeability, J. Membr. Sci., 8, 115–127. Wolf, F., Spiethoff, D., 1967, Structure of cation-active ﬁxing agent based on dicyandiamide and formaldehyde, Meilliand Textilber, 48(12), 1456–1460. Yamamoto, H., 1968, Mobility of counter ions in an ion exchange membrane, Bull. Soc. Sea Water Sci., Jpn., 22, 323–326.

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Chapter 4

Theory of Teorell, Meyer and Sievers (TMS Theory) Teorell (1935a,b) and Meyer and Sievers (1936a,b) discussed the membrane phenomena in an aqueous electrolyte solution, and revealed the mechanism of fundamental characteristics such as the membrane potential, diffusion coefﬁcient, electric conductivity, transport number, etc. In this theory (TMS theory), the ionic mobility and activity coefﬁcient are assumed to be constant. Strictly speaking, these assumptions do not hold in an ion exchange membrane, because these parameters are inﬂuenced by the electric charge density. Further, the theory does not concern with the ohmic potential gradient as driving force operating in electrodialysis. This situation corresponds to zero current density circumstances in which an electric current is interrupted in the electrodialysis system. In spite of these restrictions, the theory is generally applicable for understanding the mechanism of transport phenomena (Hanai, 1981). The TMS theory is based on the Donnan equilibrium theory (Donnan, 1934) and the Nernst–Planck equation (Planck, 1890). Accordingly, the results introduced from the TMS theory are fundamentally equivalent to the results introduced in Sections 3.1, 3.3–3.5. However, the concrete expression of both results is not always the same. 4.1.

MEMBRANE POTENTIAL

A cation exchange membrane is assumed to be immersed in a solution dissolving monovalent cations and monovalent anions as shown in Fig. 4.1. Ions are transported by the diffusion from the high concentration side to the low concentration side across the membrane. The mobility of ions in the membrane is so small that the Donnan equilibrium theory is approximately applicable at the interface between the membrane and the solution. The ﬂux of ions in the membrane is expressed by the Nernst–Planck equation and the electric neutrality is assumed to be realized in the membrane. In this system, the membrane potential Dc arising between the high concentration side (C1) and the low concentration side (C2) is introduced by summing up the Donnan potential DcDon and the diffusion potential DcDiff as follows: Dc ¼ DcDon1 þ DcDon2 þ DcDiff qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 2 ¯R RT C 2 C¯ R þ 4C 1 þ C qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ ln C1 ¯ 2 F ¯R C R þ 4C 22 þ C qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 ¯R C¯ R þ 4C 22 þ u¯ C RT u¯ ln qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 F ¯R C¯ R þ 4C 21 þ u¯ C DOI: 10.1016/S0927-5193(07)12004-0

ð4:1Þ

60

Ion Exchange Membranes: Fundamentals and Applications

C+

CR C1

C2 J+ = J−

Don2

Don1

diff x axis Cation exchange membrane

Figure 4.1

Ionic concentration and electric potential in an ion exchange membrane.

where u¯ ¼

u¯ þ u¯ u¯ þ þ u¯

(4.2)

¯ R is concentration of ion exchange groups in the membrane. u¯ þ and u¯ are the C mobility of cations and anions in the membrane, respectively. In Eq. (4.1), ionic activity coefﬁcients in a membrane phase and a solution phase and the ionic distribution coefﬁcient between both phases are assumed to be 1. Fig. 4.2 shows the relationship between C¯ R =C 1 and Dc obtained by substituting C2/C1 ¼ 0.1 in Eq. (4.1) and putting u¯ as parameter. Extrapolating C¯ R =C 1 to the inﬁnite and zero in Eq. (4.1), Dc converges as follows: lim

C¯ R =C 1 !1

Dc ¼

RT C 2 ln C1 F

(4.3)

61

Theory of Teorell, Meyer and Sievers (TMS Theory)

80 60 40

u = 0.6

∆ (mV)

20 0

0

-20 -0.6 -40 -0.9 -60 -80 10 - 3

10 - 2

10 - 1

1

10 1

10 2

C R /C 1

Figure 4.2

lim

Ion exchange group concentration vs. membrane potential (Hanai, 1981).

C¯ R =C 1 !0

Dc ¼

RT C2 u¯ ln C1 F

(4.4)

Comparing Eq. (4.1) with Eqs. (4.3) and (4.4), we know that the inﬂuence of the Donnan potential is predominated at C¯ R =C 1 ! 1; and that of the diffusion ¯ R =C 1 ! 0: Further, substituting the transport potential is predominated at C number of cations and anions deﬁned by Eq. (4.5) into Eq. (4.4), the Nernst equation (Eq. (4.6), cf. Eq. (3.39)) (Nernst, 1888, 1889) is introduced. u¯ þ u¯ þ þ u¯ u¯ t ¼ u¯ þ þ u¯ tþ ¼

(4.5)

RT C 2 (4.6) ln C1 F where t+ and t correspond to the transport number in a noncharged ion exchange membrane. Discussions mentioned above mean that the Nernst equation E ¼ ðtþ t Þ

62

Ion Exchange Membranes: Fundamentals and Applications

represents the diffusion potential and does not include the effect of the Donnan potential.

4.2.

DIFFUSION COEFFICIENT

Fluxes of cations J+ and anions J across a cation exchange membrane in Fig. 4.1 are introduced as follows: 8 >qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u¯ þ u¯ RT < 2 ¯ 2 þ 4C 2 C¯ R þ 4C 22 C Jþ ¼ J ¼ 1 R ð¯uþ þ u¯ Þd > : 9 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ > 2 2 ¯ ¯ C R þ 4C 2 þ u¯ C R = ¯u qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð4:7Þ ; ¯ 2R þ 4C 21 þ u¯ C¯ R > C where d is the thickness of the membrane. Ionic ﬂux is expressed as DðC 2 C 1 o0Þ J þ ¼ J40 ¼ d

(4.8)

From Eqs. (4.7) and (4.8), the diffusion constant D is introduced as 0 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u¯ þ u¯ RT 2 B ¯2 D¼ @ C R þ 4C 22 C¯ R þ 4C 21 ð¯uþ þ u¯ ÞðC 2 C 1 Þ 1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 2 ¯ ¯ C R þ 4C 2 þ u¯ C R C ¯ ln qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ ¯uC A ¯ 2R þ 4C 21 þ u¯ C ¯R C

ð4:9Þ

¯ R ¼ 0 in Eq. (4.9), D=DðC ¯ R ¼ 0Þ is Using DðC¯ R ¼ 0Þ obtained putting C indicated as 0 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ D 1 B ¯2 ¯ 2R þ 4C 22 ¼ @ C R þ 4C 21 C ¯ R ¼ 0Þ 2ðC 1 C 2 Þ DðC

¯R þ¯uC

1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 2 ¯ ¯ C R þ 4C 2 þ u¯ C R C ln qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ A 2 ¯R C¯ R þ 4C 21 þ u¯ C

ð4:10Þ

Fig. 4.3 is obtained by putting C2/C1 ¼ 0.1 in Eq. (4.10) and plotting D=DðC¯ R ¼ 0Þ against C¯ R =C 1 ; which shows suitably the feature of the diffusion

63

Theory of Teorell, Meyer and Sievers (TMS Theory)

2.5

D/D(CR=0)

2.0

1.5

-0.9 -0.6

1.0 0 u =0.6

0.5

0.0 10-2

10-1

101

1

102

103

C R /C 1

Figure 4.3

Ion exchange group concentration vs. diffusion constant ratio (Hanai, 1981).

¯ R ¼ 0Þ decreases with the increase constant. In this ﬁgure, we know that D=DðC ¯ R at u¯ ^0 (¯uþ ^¯u ). However, it increases with the increase of C¯ R and passes of C ¯ R at u¯ o0 (¯u 4¯uþ ): through the maximum and gets to zero at inﬁnite C lim

D

¯R C¯ R =C 1 !1 DðC

¼ 0Þ

¼0

(4.11)

¯ R ¼ 0Þ with the increase of C¯ R means that the The decrease of D=DðC diffusion velocity of counter-ions (cations) in the membrane is reduced by the co-ions (anions) and that the concentration of co-ions is decreased with the increase of C¯ R because of the Donnan exclusion and further that counterions never transfer when co-ionic concentration becomes zero owing to the ¯ R : The maximum of strongly developed Donnan exclusion at inﬁnite C ¯ D=DðC R ¼ 0Þ is due to the acceleration of counter-ions caused by co-ions exhibiting larger mobility as seen in u¯ o0 (¯u 4¯uþ ). Such an event is seen in the proton jump mechanism (Conway et al., 1956) induced by OH ions (co-ions) in a cation exchange membrane and H+ ions (co-ions) in an anion exchange membrane, and is applied in the recovery of acid and alkali in diffusion dialysis (cf. chapter 6 in Applications).

64

4.3.

Ion Exchange Membranes: Fundamentals and Applications

ELECTRIC CONDUCTIVITY

When a small electric current is passed across a cation exchange membrane placed in an electrolyte solution setting the electrolyte concentration on both sides of the membrane to be C, the electric conductivity k of the membrane is introduced as follows: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¯ þ þ u¯ 2 2 2u ¯ ¯ (4.12) k¼F C R þ 4C þ u¯ C R 2 ¯ R ¼ 0Þ as follows: From Eq. (4.12), we obtain k=kðC qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ k 1 2 ¯R C¯ R þ 4C 2 þ u¯ C ¼ 2C kðC¯ R ¼ 0Þ

(4.13)

k=kðC¯ R ¼ 0Þ is plotted against C¯ R =C setting u as parameter and is shown in Fig. 4.4, which is comparable with Figs. 3.5 and 3.6.

103

0 u=0 .6 .6

101

-0

.9

-0

(C R =0)

102

1

10-1 -2 10

10-1

101

1

102

103

C R /C1

Figure 4.4 1981).

Ion exchange group concentration vs. electric conductivity ratio (Hanai,

65

Theory of Teorell, Meyer and Sievers (TMS Theory)

4.4.

TRANSPORT NUMBER

Transport number of a cation exchange membrane ¯tþ immersed in an electrolyte solution of concentration C is obtained as follows: 0 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 2 2 ¯ ¯ u¯ þ B C R þ 4C þ C R C ¯tþ ¼ (4.14) @qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ A u¯ þ þ u¯ ¯ 2R þ 4C 2 þ u¯ C¯ R C ¯ R =C and ¯tþ is computed using Eq. (4.14) putting u¯ and Relationship between C the transport number in an uncharged cation exchange membrane t+ as parameter and is shown in Fig. 4.5, which is comparable with Figs. 3.3 and 3.4. ¯ R =C ! 0 as follows: ¯tþ converges at C¯ R =C ! 1 and C (4.15) lim t¯þ ¼ 1 C¯ R =C!1

u¯ þ 1 ¼ tþ (4.16) 2 Equation (4.16) means that the transport number in a cation exchange membrane becomes that of an uncharged membrane at C¯ R ¼ 0: lim ¯tþ ¼

C¯ R =C!0

1.0

0.8

u=0.6

t +=0.8

t+

0.6 0

0.5

-0.6

0.2

-0.9

0.05

0.4

0.2

0.0 10-2

10-1

1

101

102

CR/C 1

Figure 4.5

Ion exchange group concentration vs. transport number (Hanai, 1981).

66

Ion Exchange Membranes: Fundamentals and Applications

REFERENCES Conway, B. E., Bockris, J. O’M., Linton, H., 1956, J. Chem. Phys., 24, 834. Donnan, F. G., 1934, Die genaue thermodynamik der membrangleichgewichte, Z. Phys. Chem., A168, 369–380. Hanai, T., 1981, Membrane and Ions, Theory and Calculation of Mass Transport, Kagaku Dozin Co., Kyoto, Japan, pp. 221–244. Meyer, K. H., Sievers, J. F., 1936a, La permeabilite des membranes I, Theorie de la permeabilite ionique, Helv. Chim. Acta, 19, 649–664. Meyer, K. H., Sievers, J. F., 1936b, La permeabilite des membranes II, Essis avec des membranes selectives artiﬁelles, Helv. Chim. Acta, 19, 665–677. Nernst, W., 1888, Zur Kinetik der in losung beﬁndlichen korper, Z. Phys. Chem., 2(9), 613–679. Nernst, W., 1889, Die elektromotorische wirksamkeit der ionen, Z. Phys. Chem., 4(2), 129–181. Planck, M., 1890, Ueber die potentialdifferenz zwischen zwei verdunnten losungen binarer electrolyte, Ann Der Physik u Chemie, 40, 561–576. Teorell, T., 1935a, Transport process and electrical phenomena in ionic membrane, Prog. Biophys. Biophys. Chem., 3, 305–369. Teorell, T., 1935b, An attempt to formulate a quantitative theory of membrane permeability, Proc. Soc. Exp. Biol., 33, 282–385.

Chapter 5

Irreversible Thermodynamics 5.1. PHENOMENOLOGICAL EQUATION AND PHENOMENOLOGICAL COEFFICIENT Many theoretical approaches to the transport phenomena in a solution are based on the Nernst–Planck equation (Planck, 1890): J i ¼ C i ui

d m¯ i dx

(5.1)

where Ji is the ionic ﬂux, Ci the ionic concentration, ui the ionic mobility and m¯ i the electrochemical potential. Equation (5.1) is equivalent to J ¼ gX

(5.2)

where X is the driving force and g is the proportionality constant. In the discussion of ionic ﬂuxes in a solution dissolving two kinds of ions, we have to pay attention to the fact that both ions inﬂuence each other even if their charges are the same or different. Further, we have to notice that the ionic ﬂuxes affect solvent ﬂuxes. These phenomena mean that the ﬂuxes and driving forces are not independent and they are coupled together. The Nernst–Planck equation does not concern with these mutual effects (Kimizuka, 1988). The irreversible thermodynamics expressed these mutual effects by the following phenomenological equation (Kedem and Katchalsky, 1961): J i ¼ Li1 X 1 þ Li2 X 2 þ þ Lin X n ¼

n X

Lik X k

ði ¼ 1; 2; . . . ; nÞ

(5.3)

k¼1

where Xi is the force, Ji the ﬂux, Lik the phenomenological coefﬁcient and i and k are components. The matrix composed of the phenomenological coefﬁcients is symmetrical as suggested by the following Onsager’s (1931) reciprocal theorem: Lik ¼ Lki

ði; k ¼ 1; 2; . . . ; nÞ

(5.4)

Equation (5.3) is introduced on the assumption that the thermodynamic functions hold in a ﬁne irreversible space. This suggestion is termed ‘‘the assumption of partial equilibrium’’ and holds more strictly in the circumstance of being more close to equilibrium states. The actual electrodialysis system is not formed in the equilibrium process so that the irreversible thermodynamics exhibit only approximated meaning in the electrodialysis system. However, the irreversible thermodynamics is DOI: 10.1016/S0927-5193(07)12005-2

68

Ion Exchange Membranes: Fundamentals and Applications

Figure 5.1 Two-cell membrane system in which electrolyte solutions are partitioned by an ion exchange membrane.

considered to be applicable in the circumstances being apart to some extent from equilibrium states (Dunlop, 1957; Dunlop and Gosting, 1959). Fig. 5.1 shows a two-cell apparatus, in which electrolyte solutions are partitioned by an ion exchange membrane and the following system is realized: (1) The ion exchange membrane is placed in a boundary between cell I and cell II and forms a continuous interface. (2) The total system is closed, and there is no energy transfer between the closed system and the external one. (3) There is no appearance and disappearance of material caused by a chemical reaction. (4) The system is isothermal. In the circumstance described above, the entropy production s in the system is represented by the following equation (Staverman, 1952): dS X ¼ JiX i (5.5) s¼ dt i where Ji and Xi are the force and ﬂux of component i indicated as: Ji ¼

dM Ii dM II i ¼ dt dt

(5.6)

zi Dc þ vi DP þ Dmi Dm¯ i ¼ (5.7) T T where dM Ii and dM II i are the quantity changes of component i during dt in cells I and II, respectively. Dm¯ i ð¼ m¯ 0i m¯ 00i Þ and Dmi ð¼ m0i m00i Þ are an electrochemical potential difference and a chemical potential difference between the cells, respectively. DPð¼ P0 P00 Þ and Dcð¼ c0 c00 Þ are the pressure difference and potential difference between the cells. zi and vi are an electric charge number and Xi ¼

69

Irreversible Thermodynamics

partial molar volume of component i, respectively. The following dissipation function is introduced from Eqs. (5.5)–(5.7): X X J i Dm¯ i ¼ J i ðzi Dc þ vi DP þ Dmi Þ Ts ¼ i

i

¼ I Dc þ J DP þ

X

J i Dmi

ð5:8Þ

i

where I, J and Ji are an electric current, volume ﬂow of a solution and a mass ﬂux of component i, respectively. The entropy change dS in a closed system is expressed by the following Carnot–Clausius equation based on the second law of the thermodynamics: dQ þ diS (5.9) T Here, dQ is quantity of heat supplied to the system from the surroundings and deS the entropy change in the system caused by the heat supply indicating the reversible process. diS corresponds to the irreversible entropy change arising in the system and it is equivalent to the entropy production s deﬁned by Eq. (5.5). TdiS is equivalent to the dissipation function Ts (Eq. (5.8)). Accordingly, Eq. (5.8) expresses that the entropy production in the system is arisen by the electric current due to electromotive force, the mechanical ﬂow due to pressure difference and the diffusion due to chemical potential difference. Based on the irreversible thermodynamics, the phenomenological equation in the ion exchange membrane system is introduced starting from (5.8) as follows (Kedem and Katchalsky, 1963): X LEi Dmi (5.10) I ¼ LE Dc þ LEP DP þ dS ¼ d e S þ d i S ¼

i

J ¼ LPE Dc þ LP DP þ

X

LPi Dmi

(5.11)

Lik Dmi

(5.12)

i

J i ¼ LiE Dc þ LiP DP þ

X i

Further, the phenomenological equation is also introduced as follows from Eq. (5.8): X ðzk Lik Dc þ vk Lik DP þ Lik Dmk Þ (5.13) Ji ¼ i

where zk and vk are an electric charge number and partial volume of component k. The phenomenological equation introduced above is equivalent to Eq. (5.3) and the Onsager’s reciprocal theorem is realized between each phenomenological coefﬁcient. In the above ion exchange membrane system including cations i+ and anions i, the coupling of ionic ﬂuxes with ﬂuxes presented in the phenomenological equation (Eqs. (5.10)–(5.13)) is depicted in the model of Fig. 5.2 (Kimizuka, 1988).

70

Ion Exchange Membranes: Fundamentals and Applications

P

J i−

J i+

J

Figure 5.2

Fluxes, driving forces and membrane phenomena (Kimizuka, 1988, p. 162).

Further, the membrane phenomena are expressed as follows based on the phenomenological equation (Staverman, 1952; Sakai and Seiyama, 1956; Yamabe and Seno¯, 1964): (1) Permeability (a) Electric conductivity (permeability) Putting DP ¼ 0 and Dm ¼ 0 in Eqs. (5.10) and (5.13)

XX I 1X ¼ Lik zi zk zi J i ¼ Dc DP¼0;Dm¼0 E i k

LE ¼

(5.14) (b)

Hydraulic (mechanical) permeability Putting Dc ¼ 0 and Dmk ¼ 0; in Eqs. (5.11) and (5.13) LP ¼

J DP

¼ Dc¼0;Dm¼0

XX 1X vi J i ¼ Lik vi vk P i k

(5.15)

71

Irreversible Thermodynamics

(c)

Electric transport number of component i Putting DP ¼ 0 and Dm ¼ 0 in Eqs. (5.10) and (5.13) P P zi Lik zk zi Lik zk zi J i zi J i k k ¼ ¼ ¼ PP ti ¼ P zi J i DP¼0;Dm¼0 I LE Lik zi zk i

k

(5.16) (d)

Mechanical (hydraulic) transport number of component i Putting Dc ¼ 0 and Dm ¼ 0 in Eqs. (5.11) and (5.13) P P vi Lik vk vi Lik vk vi J i vi J i k k ¼ ¼ ¼ PP ti ¼ P vi J i Dc¼0;Dm¼0 J LP Lik vi vk i

k

(5.17) (2) Electrokinetic phenomena These are the phenomena appearing in a ﬂowing solution under an applied potential difference. When the concentrations on both sides of the membrane are the same (Dmi ¼ 0), the following equations are introduced from Eqs. (5.10) and (5.11): I ¼ LE Dc þ LEP DP

(5.18)

J ¼ LPE Dc þ LP DP

(5.19)

From Eqs. (5.18) and (5.19), the electrokinetic phenomena are expressed as follows: (a) Electroosmosis J LPE ¼ LE I DP¼0 (b)

ð5:20Þ

Streaming potential

Dc LEP ¼ DP I¼0 LE

ð5:21Þ

72

Ion Exchange Membranes: Fundamentals and Applications

Equation (5.20) shows a solution ﬂux caused by an electric current, and Eq. (5.21) shows a potential difference caused by a pressure difference. They are different at a ﬁrst glance, but these equations show the same phenomenon from the opposite view points. This suggestion is demonstrated by the Onsager’s reciprocal theorem, LEP ¼ LPE, and we have: PP Lik zi vk Dc J i k ¼ ¼ PP Lik zi zk DP I¼0 I DP¼0

i

(c)

(5.22)

k

Electroosmotic pressure

DP LPE ¼ LP Dc J¼0

(d)

(5.23)

Streaming current I LEP ¼ LP J DF¼0

(5.24)

Equation (5.22) shows a pressure difference caused by a potential difference, and Eq. (5.23) shows an electric current caused by a solution ﬂux. They show the same phenomenon because of the similar reason described above, so we have: PP Lik zi vk DP I i k P P ¼ ¼ Lik vi vk Dc J¼0 J Dc¼0

i

(5.25)

k

(3) Diffusion potential Putting I ¼ 0 and DP ¼ 0 in Eq. (5.10) and expressing the diffusion potential as Dc ¼ DcDiff, I ¼ LE DcDiff þ

X i

E Ei Dmi ¼ 0

(5.26)

73

Irreversible Thermodynamics

Accordingly, taking account of Eq. (5.16)

DcDiff ¼

1 X 1 XX LEi Dmi ¼ Lik zk Dmi LE i LE i k X ti Dmi ¼ zi i

ð5:27Þ

Equation (5.27) is a general expression of the Nernst equation (cf. Eq. (3.37)).

5.2.

REFLECTION COEFFICIENT

Assuming that an electrolyte solution is placed in cells I and II ðC 0i ¼ ¼ C i ; DC i ¼ 0Þ in Fig. 5.1 and that the solution in cell I is pressurized through a piston, then the water and solute i in cell I are transferred toward cell II. The ﬂuxes of water and solutes through the membrane in this system are expressed by Jwater and Jsolute. If the membrane in this system does not permeate the solute i at all (Jsolute ¼ 0) and permeates only water, the solute concentration in cell II becomes C 00i DC 00i ¼ ðC 00i V 00 Þ=ðV 00 þ DV 00 Þ: Here, DC 00i is solute concentration decrease and DV00 the volume increase in cell II. On the other hand, if Jwater is equivalent to Jsolute, C 00i does not change ðDC 00i ¼ 0Þ: The permselectivity of solutes against water in this system is deﬁned by the following reﬂection coefﬁcient si in the irreversible thermodynamics (Schultz, 1980): C 00i

si ¼ 1

C filtrate i C filtrand i

(5.28)

Here, we deﬁne the permselectivity coefﬁcient of solutes against water T solute water by the following equation, which is commonly applied in electrodialysis: T solute water ¼

J solute =J water C 0solute =C 0water

(5.29)

The relationships between Jwater, Jsolute, si and T solute water are shown as follows: J solute ¼ J water ; J solute oJ water ; J solute ¼ 0;

si ¼ 0; 0osi o1;

T solute water ¼ 1 T solute water 40

si ¼ 1;

T solute water

¼0

(5.30)

74

Ion Exchange Membranes: Fundamentals and Applications

In Fig. 5.1, the osmotic pressure p developed between cell I and cell II is represented by the following Van’t Hoff equation: p ¼ RTðC 0i C 00i Þ ¼ RT DC i

(5.31)

Equation (5.31) corresponds to p at Jsolute ¼ 0, si ¼ 1 and T solute water ¼ 0 in Eq. (5.30). Staverman (1951) deﬁned the effective osmotic pressure peff realized in all of the situations in Eq. (5.30) as follows: peff ¼ si p ¼ si RT DC i

5.3.

(5.32)

ELECTRODIALYSIS PHENOMENA

In this section, the ﬂux of ionic electrolytes across the membrane is discussed based on the approaches of Kedem and Katchalsky (1963). For simplicity, the ionic electrolytes are assumed to dissociate into monovalent cations and monovalent anions, and the phenomena are explained as follows (House, 1974; Schultz, 1980). We assume a two-cell electrodialysis system presented in Fig. 5.3 consisting of cells I and II and a cation exchange membrane. The concentrations of electrolytes i in cell I are assumed to be adjusted to C 0þ for monovalent cations and C 0 for monovalent anions, and those in cell II are adjusted to C 00þ for monovalent cations and C 00 for monovalent anions. Reversible electrodes are placed in both cells and an electric current is passed across the cation exchange membrane through the electrodes and electric potentials on both sides of the membrane are set at c0 and c00 ; respectively. The pressures in both cells are regulated by a piston to be P0 and P00 , respectively. The difference of electric

Figure 5.3 Two-cell electrodialysis system in which electrolyte solutions are partitioned by a cation exchange membrane.

75

Irreversible Thermodynamics

potential Dc, electrolyte concentration DCi, pressure DP and electrolyte chemical potential Dmi between both cells are deﬁned as: Dc ¼ c00 c0 DC i ¼ C 00i C 0i

(5.33)

DP ¼ P00 P0 Dmi ¼ m00i m0i

The dissipation function in the tertiary system consisting of three components, three ﬂows and three driving forces is represented by the following equation: T diS ¼ J þ Dm¯ þ þ J Dm¯ þ J W DmW dt

(5.34)

Dm¯ þ ¼ v¯ þ DP þ

RT DC þ þ F Dc C þ

(5.35)

Dm¯ ¼ v¯ DP þ

RT DC F Dc C

(5.36)

Here, the subscripts +, and W mean monovalent cations, monovalent anions and water (solvent), respectively. Dm¯ þ and Dm¯ are the electrochemical potential difference of+ions and ions. v¯ þ and v¯ are the partial molar volumes of these ions. C þ and C are the logarithmic mean concentrations Eq. 5.50 of these ions. From the electric neutrality in this system, we have C 0þ ¼ C 0 ¼ C 0i C 00þ ¼ C 00 ¼ C 00i

(5.37)

From Eqs. (5.34)–(5.37), the chemical potential difference of electrolytes i, Dmi ; is introduced as: Dmi ¼ Dmþ þ Dm ¼ v¯ i DP þ

v¯ i ¼ v¯ þ þ v¯

2RT DC i C i

(5.38)

(5.39)

If the electrode is reversible to anions, electromotive force E (volt) is expressed by the following equation indicating the deﬁnite relationship between E and Dc

76

Ion Exchange Membranes: Fundamentals and Applications

(Katchalsky and Curran, 1965): E¼

Dm RT ¼ Dln C þ DF F F

(5.40)

In this electrodialysis system, the transport number of a cation exchange membrane t+ integrated in the apparatus (Fig. 5.3) is expressed by the following equation because the ﬂux of cations J+ is equivalent to the ﬂux of electrolytes Ji: FJ þ FJ i ¼ I I

(5.41)

I ¼ F ðJ þ J Þ

(5.42)

tþ ¼

Substituting Eqs. (5.38) and (5.40) into Eq. (5.34), we get: T diS ¼ J W mW þ J i Dmi þ IE dt

(5.43)

From Eq. (5.43), the following phenomenological equations are introduced. J W ¼ LWW DmW þ LWi Dmi þ LWI E

(5.44)

J i ¼ LiW Dmi þ Lii Dmi þ LiI E

(5.45)

I ¼ LIW DmW þ LIi Dmi þ LII E

(5.46)

Equations (5.44)–(5.46) contain nine coefﬁcients (L). However, according to the Onsager’s reciprocal theorem, LWi ¼ LiW, LWI ¼ LIW and LiI ¼ LIi, so the coefﬁcients reduce to six. Equation (5.44) indicates that JW consists of the hydrodynamic term (LWW DmW), the osmotic pressure term (LWi Dmi) and the electroosmosis term (LWIE). Equation (5.45) indicates that Ji consists of ultra-ﬁltration term (LiW DmW), diffusion term (Lii Dmi) and electrophoresis term (LiIE). Equation (5.46) indicates that I consists of streaming current term (LIW DmW), diffusion stream term (LIi Dmi) and electromotive force term (LIIE). The phenomenological equation described above includes JW (Eq. (5.44)) which is difﬁcult to measure, so we try to change this parameter here to volume ﬂow JV applying DmW (Eq. (5.47)) and Dmi (Eq. (5.48)) to Eq. (5.43). DmW ¼ v¯ W ðP00 P0 Þ v¯ W RTðC 00i C 0i Þ ¼ v¯ W ðDP pÞ

Dmi ¼ v¯ i DP þ

RT DC i p ¼ v¯ i DP þ Ci Ci

(5.47)

(5.48)

77

Irreversible Thermodynamics

where Osmotic pressure; p ¼ RT DC i Logarithmic mean concentration; C i ¼

(5.49) DC i lnðC 00i =C 0i Þ

(5.50)

Consequently, Eq. (5.43) is converted to T diS J i ð1 C i v¯ i ÞRT DC i ¼ J V ðDP RT DC i Þ þ þ IE C i dt

(5.51)

In a diluted electrolyte solution we have C i 1

(5.52)

Taking account of Eq. (5.52) in Eq. (5.51), the following dissipation function is introduced: T diS J i RT DC i ¼ J V ðDP RT DC i Þ þ þ IE C i dt

(5.53)

Further, the following phenomenological equation is introduced from Eq. (5.53): J i ¼ LP ð1 si ÞC i ðDP RT DC i Þ þ oi RT DC i þ

I ¼ bGðDP RT DC i Þ þ

tþ I F

Gtþ RT DC i þ GE FC i

J V ¼ LP DP si LP RT DC i þ bI

(5.54)

(5.55)

(5.56)

We term the coefﬁcients in Eqs. (5.54)–(5.56) as follows: LP is the hydraulic conductivity, si the reﬂection coefﬁcient, b the electroosmotic permeability, oi the solute permeability, t+ the transport number and G the electric conductance. 5.4.

SEPARATION OF SALT AND WATER BY ELECTRODIALYSIS

A salt solution dissolving monovalent cations and monovalent anions is assumed to be partitioned by a cation exchange membrane in a two-compartment electrodialysis system. The concentrations of cations+and anions in one side

78

Ion Exchange Membranes: Fundamentals and Applications

compartment (cell I) and those in the other side of compartment (cell II) are II II assumed to be maintained to C Iþ ¼ C I ¼ C IS and C II þ ¼ C ¼ C S ; respectively. Passing an electric current through reversible electrodes immersed in both compartments across the membrane, cations in cell I are assumed to be transferred toward cell II. In this electrodialysis system, the ﬂux of electrolytes JS,K and that of a solution JS,V transported from cell I to cell II across the cation exchange membrane are expressed by the following phenomenological equations introduced from Eqs. (5.54) and (5.56): J S;K ¼ LP;K ð1 sK ÞC S ðDP RT DC S Þ þ oK RT DC S þ

J V;K ¼ LP;K DP sK LP;K DC S þ bK i

tþ Ki F

(5.57)

(5.58)

I II where i is current density. DC S ð¼ C IS C II S Þ and DP ( ¼ P P ) are the electrolyte concentration difference and the hydraulic pressure difference between cell I and cell II, respectively. tþ K is the transport number, oK the solute permeability, bK the electroosmotic permeability, LP,K the hydraulic conductivity and sK the reﬂection coefﬁcient (Staverman, 1951). These are the characteristics of the cation exchange membrane incorporated in this system. The basic principle of separation of salt and water by electrodialysis is expressed by a three-compartment (cells I, II and III) electrodialysis system, which consists of a central cell (cell II) and electrode cells (cells I and II). A cation exchange membrane (K) is placed between cell I and cell II, and an anion exchange membrane is placed between cell II and cell III. Supplying an electrolyte solution into cells I and III, current density i is applied and an electrolyte solution being collected in cell II is taken out by an overﬂow extracting system, until the electrolyte concentration in cell II reaches constant. The salt accumulation JS,K+JS,A and solution accumulation JV,K+JV,A in cell II are given by the following equations introduced from Eqs. (5.57) and (5.58):

i RT½ðoK þ oA Þ fLP;K ð1 sK Þ F ð5:59Þ þ LP;A ð1 sA ÞC S DC

J S;K þ J S;A ¼ ðtK þ tA 1Þ

J V;K þ J V;A ¼ ðbK þ bA Þi þ RTðsK LP;K þ sA LP;A ÞDC

(5.60)

A K A Here, we put DC ¼ C00 C0 ¼ DCS, tA þ þ t ¼ 1; tþ ¼ tK and t ¼ tA ; and neglect pressure difference driving force DP: DP ¼ 0. The subscript and superscript K and A mean a cation exchange membrane and an anion exchange membrane, respectively. The superscripts 0 and 00 mean desalting side (cells I and III) and concentrating side (cell II), respectively. C S is the logarithmic mean concentration

79

Irreversible Thermodynamics

as follows: C S ¼

C 00 C 0 lnðC 00 =C 0 Þ

(5.61)

Equations (5.57)–(5.61) represent electrodialysis phenomena in a solution dissolving monovalent ions, but they are applicable to the phenomena in the solution dissolving multivalent ions (cf. chapter 6). REFERENCES Dunlop, P. J., 1957, A study of interacting ﬂows in diffusion of the system rafﬁnose– KCl–H2O at 251C, J. Phys. Chem., 61, 994–1000. Dunlop, P. J., Gosting, L. J., 1959, Use of diffusion and thermodynamic data to test the Onsager reciprocal relation for isothermal diffusion in the system NaCl–KCl–H2O at 251C, J. Phys. Chem., 63, 86–93. House, C. R., 1974, Water Transport in Cells and Tissues, Edward Arnold, London, England. Katchalsky, A., Curran, P. F., 1965, Nonequilibrium Thermodynamics in Biophysics, Harvard Univ. Press, Cambridge, USA. Kedem, O., Katchalsky, A., 1961, A physical interpretation of the phenomenological coefﬁcients of membrane permeability, J. Gen. Phys., 45, 143–179. Kedem, O., Katchalsky, A., 1963, Permeability of composite membranes. Part 1. Electric current, volume ﬂow and ﬂow of solute through membranes, Trans. Faraday Soc., 59, 1918–1930. Kimizuka, H., 1988, Membrane Transport of Ions, Kyoritu Shuppan Co., Tokyo, Japan. Onsager, L., 1931, Reciprocal relations in irreversible process, Phys. Rev., 37, 405–426. Planck, M., 1890, Ueber die potentialdifferenz zwischen zwei verdunnten losungen binarer electrolyte, Ann. Der Physik u Chemie, 40, 561–576. Sakai, W., Seiyama, T., 1956, Electrochemical studies on ion exchanger. Application of non-equilibrium thermodynamics to ionic membrane system, J. Electr. Chem. Jpn., 24, 274–279. Schultz, S. G., 1980, Basic Principles of Membrane Transport, Cambridge University Press, Cambridge, England. Staverman, A. J., 1951, The theory of measurement of osmotic pressure, Rec. Trav. Chim., 70, 344–352. Staverman, A. J., 1952, Non-equilibrium thermodynamics of membrane process, Trans. Faraday Soc., 48, 176–185. Yamabe, T., Seno¯ , M., 1964, Ion-Exchange Resin Membrane, Giho Do Co., Tokyo, Japan.

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Chapter 6

Overall Mass Transport 6.1. OVERALL MEMBRANE PAIR CHARACTERISTICS AND MASS TRANSPORT ACROSS A MEMBRANE PAIR When an electrolyte solution is supplied to an electrodialyzer and an electric current is passed through it, ions and a solution in a desalting cell are transported to a concentrating cell across a cation and an anion exchange membrane. The quantity of ions JS and a solution JV transported across a pair of membranes per unit area and per unit time at current density i are expressed by the overall mass transport equation, Eqs. (6.1) and (6.2) (Tanaka, 2006). i ¼ C 00 J V ¼ li mðC 00 C 0 Þ ¼ li mDC (6.1) JS ¼ Z F J V ¼ fi þ rðC 00 C 0 Þ ¼ fi þ rDC

(6.2) 0

00

Z is current efﬁciency, F the Faraday constant, C and C electrolyte concentrations in a desalting and a concentrating cell, respectively, l the overall transport number, m the overall solute permeability, f the overall electro-osmotic permeability and r the overall hydraulic conductivity, and these parameters are termed the overall membrane pair characteristics altogether. The term ‘‘overall’’ means that the parameters are the sum of the contributions of a cation and an anion exchange membrane. It also means that the parameters are the sum of the contributions of many kinds of ions dissolving in an electrolyte solution. Parameters li and mDC in Eq. (6.1) stand for the electro-migration and solute diffusion, respectively, and parameters fi and rDC in Eq. (6.2) correspond to the electro-osmosis and concentration–osmosis. JS/i and JV/i against DC/i yield straight lines, so that l, m, f and r are obtained from the intercepts and the gradients of the lines based on the electrodialysis experiment as explained in Section 2.10. JS/i and JV/i vs. DC/i plots are obtained by repeating the electrodialysis by changing current density. The plots are not inﬂuenced by the concentration polarization and are obtained by the electrodialysis of seawater as shown in Fig. 6.1. On the basis of many electrodialysis experiments of seawater described above, the regularity in ion exchange membrane characteristics is found from the plot of l(eq C1), m(cm s1) and f(cm3 C1) against r(cm4 eq1 s1) as shown in Fig. 6.2. The plots for a 0.5 M NaCl solution electrodialysis are marked by asterisks in Fig. 6.2, indicating that the plotting is done on the same lines for seawater electrodialysis. DOI: 10.1016/S0927-5193(07)12006-4

82

Ion Exchange Membranes: Fundamentals and Applications

J S /i (10 -5 eqC -1 ) J V /i(10 -3 cm 3 C -1 )

5

4

=9.724 × 10-6eq C-1 =1.429 × 10-6cm s-1 =1.406 × 10-3cm3 C-1 =1.213 × 10-2cm4eq-1s-1 /i JV

3

2

JS/i

1

0 0.00

0.05

0.10

0.15

C/i (eq

Figure 6.1

0.20

0.25

0.30

A-1cm-1)

JS/i vs. DC/i plot and JV/i vs. DC/i plot (Tanaka, 2006).

Mizutani and Nishimura (1970) investigated microstructure of cation exchange membranes by converting them into porous inert membranes having no ion exchange component on treatment with hydrogen peroxide, and determined apparent pore size, tortuosity factor, number of pores and pore size distribution in the porous membranes. Fig. 6.3 gives the experimental result indicating the effects of porosity e on water content W and speciﬁc resistance v taking tortuosity factor s as a parameter, showing W and v to be zero and inﬁnite, respectively, at e-0. The phenomena described here means that the mass transport is increased with the porosity e, and the membrane loses electric conductivity at e ¼ 0 and becomes an insulator. Based on this experimental result, it is concluded that m, f and r are decreased with the decrease of e and approach zero at e-0, and that the membrane pair electrical resistance R is increased with the decrease of e and becomes inﬁnity at e-0, and further that the water content of the membrane W is decreased with the decrease of e and becomes zero at e-0, so we have the following equations: 1 ¼ lim W ¼ 0 (6.3) lim m ¼ lim f ¼ lim r ¼ lim !0 !0 !0 !0 R !0 Accordingly,

1 ¼ lim W ¼ 0 lim m ¼ lim f ¼ lim r!0 r!0 r!0 R r!0

(6.4)

83

Overall Mass Transport

(10-3cm3C-1)

2.0 1.8 1.6 1.4

(10-4cm s-1)

1.2 1.0 0.8

(10-5eq C-1)

0.6 0.4 0.2 0.0 -0.2 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

(10-2cm4eq-1s-1)

Figure 6.2

r vs. l, m and f (Tanaka, 2006).

Referring to Eq. (6.4), the plots in Fig. 6.2 are expressed by the following empirical equations (Tanaka, 2006). l ¼ l1 þ l2r m ¼ mr

l 1 ¼ 9:208 106

l 2 ¼ 1:914 105

m ¼ 2:005 104

f ¼ n1 r0:2 þ n2 r

n1 ¼ 3:768 103

(6.5) (6.6)

n2 ¼ 1:019 102

(6.7)

in which Eq. (6.4) is realized in Eqs. (6.6) and (6.7). r vs. membrane pair electric resistance R ( ¼ RK+RA, O cm2) and membrane pair water content W ( ¼ (WK+WA)/2, g H2O/g dry membrane) is indicated, respectively, in Figs. 6.4 and 6.5, expressed by the following empirical equations, in which Eq. (6.4) is satisﬁed. Subscripts K and A refer to a cation exchange membrane and an anion exchange membrane, respectively. R ¼ pr1

p ¼ 5:107 102

(6.8)

84

Ion Exchange Membranes: Fundamentals and Applications

500 3.8

(Ω cm)

400 2.4

300

=6.9 200 100 50 0.0

2.4

2.1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

W (%)

40 30 20 10 0 0.0

Figure 6.3 Effect of porosity on water content and speciﬁc electric resistance of ion exchange membranes (Mizutani and Nishimura, 1970).

W ¼ q1 r0:5 þ q2 r

q1 ¼ 3:785 q2 ¼ 6:375

(6.9)

The electrolyte concentration in a concentrating cell C00 is introduced from Eqs. (6.1) and (6.2) as follows: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 00 2 (6.10) C ¼ A þ 4rB A 2r A ¼ fi þ m rC 0

(6.11)

B ¼ li þ mC 0

(6.12)

Equations (6.5)–(6.7) indicate that r is a leading parameter and represents all of the overall membrane pair characteristics. l, m and f (and R, W) are computed by substituting r in Eqs. (6.5)–(6.7) (and (6.8), (6.9)). C00 is computed by substituting i and C0 in Eqs. (4.10)–(4.12). Accordingly, the electro-migration li, the solute–diffusion mDC, the electro-osmosis fi and the concentration–osmosis

85

Overall Mass Transport

10 9 8

R( Ω cm2)

7 6 5 4 3 2 1 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

(10-2cm4eq-1s-1)

Figure 6.4 Relationship between overall water permeability and membrane pair electrical resistance (Tanaka, 2006).

rDC are determined using Eqs. (6.5)–(6.7) and (6.10)–(6.12) by setting r, i and C0 as parameters. Here, we calculate the mass transport across a membrane pair JS, li, mDC, JV, fi and rDC based on the computation described above by setting r ¼ 1.00 102 cm4 eq1 s1 and C0 ¼ 6 104 eq cm3 and they are plotted against i. The results are presented in Fig. 6.6, indicating that mDC is negligible as compared to li, and that rDC is predominant at lower i and fi is predominant at larger i. JS, JV, C00 and Z are computed using Eqs. (6.1), (6.2), (6.5)–(6.7) and (6.10)– (6.12), i ¼ 3 A dm2 and C0 ¼ 0.6 eq dm3. They are plotted against r and are shown in Fig. 6.7, which means that the mass transport can be analyzed using r. 6.2. THE OVERALL MASS TRANSPORT EQUATION AND THE PHENOMENOLOGICAL EQUATION The phenomenological equation, Eqs. (5.59) and (5.60) and the overall mass transport equation, Eqs. (6.1) and (6.2) are substantially identical, so we

86

Ion Exchange Membranes: Fundamentals and Applications

0.6

W (gH2O/g dry m em br.)

0.5

0.4

0.3

0.2

0.1

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

(10-2cm4eq-1s-1)

Figure 6.5 2006).

Relationship between overall water permeability and water content (Tanaka,

have the following equations: J S;K þ J S;A ¼ J S

(6.13)

J V;K þ J V;A ¼ J V

(6.14)

From Eqs. (6.13) and (6.14), the overall membrane pair characteristics are represented by the following equations. tK þ tA 1 JS ¼ (6.15) l¼ i DC¼0 F m ¼ RT½ðoK þ oA Þ fLP;K sK ð1 sK Þ þ LP;A sA ð1 sA ÞgC S JS ¼ RT½ðoK þ oA Þ sð1 sÞðLP;K þ LP;A ÞC S ¼ DC i¼0 JV f ¼ b K þ bA ¼ i DC¼0

ð6:16Þ

(6.17)

87

Overall Mass Transport

10 (10-7eq cm-2 s-1)

(1) 8 6

JS

i

4 2 0 20

0

(2)

16

JV 12 8 4 0 0

2

4

6

8

10

12

i(A/dm2)

Figure 6.6 Electro-migration, solute diffusion, electro-osmosis and concentration osmosis in ion exchange membrane electrodialysis.

r ¼ RTðsK LP;K þ sA LP;A Þ ¼ RTsðLP;K þ LP;A Þ ¼

JV DC

(6.18) i¼0

Here, s is the membrane pair reﬂection coefﬁcient deﬁned for simpliﬁcation of the expression as follows: s¼

LP;K f1 sK ð1 sK Þg þ LP;A f1 sA ð1 sA Þg LP;K þ LP;A

(6.19)

6.3. REFLECTION COEFFICIENT r, HYDRAULIC CONDUCTIVITY LP AND SOLUTE PERMEABILITY x Yamauchi and Tanaka (1993) measured sK, LP,K and oK of commercially available cation exchange membrane Neocepta CL-25 T by means of pressuredriven dialysis of KCl supplied sucrose for generating pressure gradient. The experimental works were performed under the circumstances in which the

88

JS(10-7eq cm-2s-1) JV(10-5cm s-1) C"(eq dm-3)

Ion Exchange Membranes: Fundamentals and Applications

12

1.2

10

1.0

8

0.8 JV

6

0.6

4

0.4

C" JS

2

0 0.0

0.2

0.5

1.0

1.5

2.0

2.5

0.0 3.0

(10-2cm4eq-1s-1)

Figure 6.7 Effect of overall hydraulic conductivity on ionic ﬂux, volume ﬂux, electrolyte concentration in a concentration cell and current efﬁciency (Tanaka, 2006).

following equations hold: 1 J V;K sK ¼ DpS DPDpi ¼0 LP;K LP;K ¼

J V;K DP Dpi

J S;K oi ¼ DpS J V ¼0

(6.20)

(6.21) DpS ¼0

(6.22)

Here, DP is mechanical pressure difference, Dpi and DpS are osmotic pressure due to impermeable and permeable solutes, respectively. The results are presented in Table 6.1 indicating LP,K ¼ 1.62 1013 cm2 s mol g1 eq1, oK ¼ 0 s mol cm1 g1 and s ¼ 1. In order to analyze LP,K and oK in Table 6.1, the following equations are introduced from Eqs. (6.16) and (6.18): LP;K ¼

r 2RT sK

(6.23)

89

Overall Mass Transport

Table 6.1 Hydraulic conductivity, solute permeability and reﬂection coefﬁcient of a cation exchange membrane measured in the pressure dialysis of a KCl and a sucrose solution LP,K

1.62 1013

cm2s mol g1eq1

oK

0

S mol cm1 g1

sK

1

0.5 M sucrose/water system 0.01 M KCl/0.1 M KCl system 0.01 M KCl/0.1 M KCl+0.5 M sucrose system

Note: Neocepta CL-25 T 251C. Source: Yamauchi and Tanaka (1993).

oK ¼

m þ LP;K ð1 sK ÞC S 2RT

(6.24)

Here, m and r are divided by 2 because these are the membrane pair characteristics and the characteristics of a cation exchange membrane and that of an anion exchange membrane are assumed to be equivalent in this situation. The logarithmic mean concentration C S in Eq. (6.24) is calculated using Eqs. (5.61) and (6.10)–(6.12). Substituting m and r of Neocepta CL-25T/AVS-4T membrane evaluated in the electrodialysis experiment and sK ¼ 1 (Table 6.1) into Eqs (6.23) and (6.24), LP,K and oK are computed as shown in Table 6.2. LP,K in Table 6.2 is less to some extent than LP,K ¼ 1.62 1013 cm2 s mol g1 eq1 in Table 6.1, however, both give fairly good agreement. oK in Table 6.1 is evaluated to be zero, however, extremely small oK values are detected in Table 6.2. The argumentation described here demonstrates the overall mass transport equation to be in agreement with the phenomenological equations based on the irreversible thermodynamics. 6.4. PRESSURE REFLECTION COEFFICIENT AND CONCENTRATION REFLECTION COEFFICIENT:ELECTRIC CURRENT SWITCHING OFF CONCEPT Equations (6.15)–(6.18) show that sK and sA appear in m and r and do not appear in l and f. These events and Eqs. (6.1) and (6.2) mean that sK and sA do not exert an inﬂuence on mass transport with electric current passing. Accordingly, in order to understand the behavior of sK and sA in an electrodialysis process, it is necessary to create the image of zero current density. In other words, it is reasonable to image the electric current interruption (switch off) for a moment in the electrodialysis process operating under a constant electric current, and to assume the disappearance of the electro-migration and electroosmosis in this moment. Here, we assume further that DC and resulting solute

90

C0 (103 eq cm3)

m (106 cm s1)

r (103 cm4 eq1 s1)

LP,K (1013 cm2 s2 mol g1 eq1)

oK (1017 s mol cm1 g1)

0.294 0.577 1.132 1.920

1.458 3.208 0.908 3.575

6.354 6.788 7.566 7.691

1.27 1.35 1.51 1.53

2.90 6.38 1.81 7.11

Note: Neocepta CL-25T/AVS-4T 291C, seawater electrodialysis. Source: Tanaka (2006).

Ion Exchange Membranes: Fundamentals and Applications

Table 6.2 Hydraulic conductivity and solute permeability of a cation exchange membrane estimated from the overall membrane pair characteristics m and r

91

Overall Mass Transport

diffusion and solution concentration–osmosis exist as it is just after the interruption of an electric current. In order to discuss the behavior of the reﬂection coefﬁcient in an electrodialysis process, we express the volume ﬂow JV and exchange ﬂow JD in an ion exchange membrane pair by the following equation introduced by Schlogel (1964). J V ¼ ðLP;K þ LP;A ÞDP þ ðLPD;K þ LPD;A ÞRT DC ¼

JS JW þ C S C W

J D ¼ ðLDP;K þ LDP;A ÞDP þ ðLD;K þ LD;A ÞRTDC ¼

JS JW C S C W

(6.25)

(6.26)

DC and DP are pressure difference and concentration difference across the membrane, respectively. LP is the hydraulic conductivity and LD is the exchange ﬂow parameter. LPD is the osmotic volume ﬂow coefﬁcient and LDP is the ultraﬁltration coefﬁcient, between which the Onsager reciprocal relation LPD ¼ LDP (Onsager, 1931) is satisﬁed. JW is the ﬂux of water molecules, C S and C W are, respectively, logarithmic average concentration (Eq. (5.61)) of solutes and water (solvent) between a desalting cell and a concentrating cell. It should be noticed that Eqs. (6.25) and (6.26) are originally deﬁned in the pressure driven transport (pressure dialysis) of neutral species on the promise of no electric current. In a pressure driven process, putting DC ¼ 0 in Eqs. (6.25) and (6.26) get to the following equations being applicable in pressure dialysis. ðJ V ÞDC¼0 ¼ ðLP;K þ LP;A ÞDP

(6.27)

ðJ D ÞDC¼0 ¼ ðLDP;K þ LDP;A ÞDP

(6.28)

Staverman (1951) and Kedem–Katchlsky (Kedem and Katchalsky, 1958) deﬁne the reﬂection coefﬁcient s by Eq. (6.29) introduced from Eqs. (6.27) and (6.28). JD LDP;K þ LDP;A ¼ (6.29) s¼ J V DC¼0 LP;K þ LP;A s deﬁned by Eq. (6.29) is identical with the parameter included in Eqs (5.57) and (5.58). Here, we term s presented by Eq. (6.29) as ‘‘pressure reﬂection coefﬁcient’’, taking note that s exhibits a pressure difference DP driven phenomenon. In the electrodialysis process, DP is relatively low and possible to neglect, and at just after an electric current interruption situation, DC exists as it is. Putting DP ¼ 0 in Eqs. (6.25) and (6.26), we have the following equations being applicable to diffusion dialysis. ðJ V ÞDP¼0 ¼ ðLPD;K þ LPD;A ÞRTDC

(6.30)

ðJ D ÞDP¼0 ¼ ðLD;K þ LD;A ÞRTDC

(6.31)

92

Ion Exchange Membranes: Fundamentals and Applications

Here, we deﬁne another reﬂection coefﬁcient s0 by Eq. (6.32) introduced from Eqs. (6.30) and (6.31) which are deﬁned at just after an electric current interruption. JD LD;K þ LD;A 0 ¼ (6.32) s ¼ J V DP¼0 LPD;K þ LPD;A We term s0 presented by Eq. (6.32) as ‘‘concentration reﬂection coefﬁcient’’, paying attention that s0 expresses a concentration difference DC driven phenomenon. Regarding the Onsager reciprocal relation LPD ¼ LDP, in Eqs. (6.29) and (6.32): ss0 ¼

LD;K þ LD;A LP;K þ LP;A

(6.33)

Canceling J W =C W in Eqs. (6.25) and (6.26): JD ¼ 2

JS JV C S

(6.34)

From Eqs. (6.25), (6.32) and (6.34), s0 is introduced as follows:

s0 ¼ 1 2

1 C S

JS JV

¼12

JS C S JS JW þ C S C W

(6.35)

s0 deﬁned in Eq. (6.35) means the permselectivity between ions and water molecules at just after an electric current interruption. JS and JV are expressed as the following equations at just after an electric current interruption by putting i ¼ 0 in Eqs. (6.1) and (6.2), and canceling the minus sign of the second term in Eq. (6.1). J S ¼ mðC 00 C 0 Þ

(6.36)

J V ¼ rðC 00 C 0 Þ

(6.37)

Substituting Eqs. (6.36) and (6.37) into Eq. (6.35): m 1 0 s ¼12 r C S

(6.38)

s0 is calculated using Eqs. (6.38), (5.61) and (6.10)–(6.12) and substituting l, m, f and r measured by electrodialysis. The s0 of commercially available membranes is generally in the range of 0os0 o1, which is understandable from Eq. (6.35) that linear velocity of water molecules is larger than that of ions just after electric current interruption; JW JS 4 C W C S

(6.39)

s0 is plotted against current density i taking C0 as a parameter and as shown in Fig. 6.8 indicating that s0 increases with i. This phenomenon is understandable

93

Overall Mass Transport

Figure 6.8

i vs. s0 and LD,K+LD,A.

from Eq. (6.38) assuming C* increases with i and m/r is independent of i as shown in Figs. 6.1 and 6.2 and Eq. (6.6). 6.5. IRREVERSIBLE THERMODYNAMIC MEMBRANE PAIR CHARACTERISTICS From the pressure driven dialysis of a KCl solution (Section 6.3), the reﬂection coefﬁcient s of an ion exchange membrane is generally assumed to be 1. This is presumably owing to dense structure of an ion exchange membrane. So, the membrane pair characteristics deﬁned in the phenomenological equations are introduced from Eqs. (6.15)–(6.18) putting sK ¼ sA ¼ s ¼ 1 as follows. tK þ tA ¼ lF þ 1 oK þ oA ¼

m RT

bK þ bA ¼ f LP;K þ LP;A ¼

(6.40) (6.41) (6.42)

r RT

(6.43)

tK+tA, oK+oA, bK+bA and LP,K+LP,A are computed by substituting l, m, f and r measured by electrodialysis into Eqs. (6.40)–(6.43), and plotted against T, as shown in Fig. 6.9.

94

Ion Exchange Membranes: Fundamentals and Applications

(10-3cm3C-1) LP,K+LP,A(10-6mol cm4eq-1J-1s-1)

ω

ω

10 9 L P,K+L P,A

8 7 6 5 4 3

tK+tA

2 1 0 20

ω 30

40

ω

50

60

70

T(°C)

Figure 6.9

T vs. tK+tA, oK+oA and LP,K+LP,A (Tanaka, 2006).

P,

K+

L

D

P,

A)

10

,A )

=−

(L

D

8

,K +

L

PD

,A

+L D

K

L D,

K+

L

P,

A)

=− (

L

PD

6

P,

4

(L

LD,K+LD,A (10−13 cm2s mol g−1eq−1)

(LP,K+LP,A)=−(LPD,K+LPD,A)=−(LDP,K+LDP,A)

12

2

0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

(10−2cm4eq−1s−1)

Figure 6.10

Relationship between r and LP, LPD, LDP and LD (Tanaka, 2006).

95

Overall Mass Transport

Putting s ¼ 1 in Eqs. (6.29) and (6.43): sðLP;K þ LP;A Þ ¼ ðLP;K þ LP;A Þ ¼ ðLPD;K þ LPD;A Þ r ð6:44Þ RT LPD,K+LPD,A and LDP,K+LDP,A are calculated using LP,K+LP,A and Eq. (6.44), and are plotted against r in Fig. 6.10. From Eqs. (6.33) and (6. 43): ¼ ðLDP;K þ LDP;A Þ ¼

rs0 ¼ ðLP;K þ LP;A Þs0 (6.45) RT is calculated using s0 and Eq. (6.45), and plotted against i in

LD;K þ LD;A ¼ LD,K+LD,A Fig. 6.8.

REFERENCES Kedem, O., Katchalsky, A., 1958, Thermodynamic analysis of the permeability of biological membranes to non-electrolytes, Biochim. Biophys. Acta, 27, 229–246. Mizutani, Y., Nishimura, M., 1970, Studies on ion-exchange membranes. XXXII. Heterogeneity in ion-exchange membranes, J. Appl. Polym. Sci., 14, 1847–1856. Onsager, L., 1931, Reciprocal relations in irreversible processes, Phys. Rev., 37, 405–426. Schlogel, R. Z., 1964, Fortschritte der physikalischen Chemie, Band 9. Staverman, A. J., 1951, The theory of measurement of osmotic pressure, Rec. Trav. Chim., 70, 344–352. Tanaka, Y., 2006, Irreversible thermodynamics and overall mass transport, J. Membr. Sci., 281, 517–531. Yamauchi, A., Tanaka, Yasuko., 1993, Salt transport phenomena across charged membrane driven by pressure difference, In: Paterson, R. (Ed.), Effective Membrane Process – New Prospective, BHR Group Ltd., Information Press Ltd., Oxford, England, pp. 179–185.

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Chapter 7

Concentration Polarization 7.1.

CURRENT–VOLTAGE RELATIONSHIP

Concentration polarization has been widely studied based on the current (I)–voltage (V) curve. The following investigation is its pioneering work presented by Peer (1956). The I–V curve of a cation exchange membrane (Permutit C-10) indicated in Fig. 7.1 has an S-type shape including three characteristic regions: Region I shows Ohmic behavior, and it transforms as voltage is increased into Region II in which the current varies very slowly with voltage and exhibits a plateau presenting the limiting current density ilim. Region III is the overlimiting current sphere in which current increases gradually. The limiting current density equation is given by ilim ¼

FDC ð¯t tÞd

(7.1)

¯t and t are the transport number of counter-ions in an ion exchange membrane and in a solution. C is the electrolyte concentration in the solution, D the diffusion constant of electrolytes dissolving in the solution, F the Faraday constant and d the boundary layer thickness. Peer suggested that the current in excess of ilim was found to be carried partly by hydrogen ions but mostly by chloride ions. Spiegler calculated the current–voltage relationship for an anion exchange membrane placed in a 1,1 valent electrolyte solution based on the Nernst–Planck model, and introduced the potential drop across the membrane DE in an electrodialysis system in Fig. 7.2 as follows (Spiegler, 1971): ha i 1 þ ði=i Þ lim (7.2) DE ¼ ð2RS þ Rm Þi þ þ b g ln l 1 ði=ilim Þ where FD FD a¼ ¼ ¯t t ¯t t þ þ RT b¼ ð¯t ¯tþ Þ F RT ðt tþ Þ g¼ F Here, i is the current density, ilim limiting current density, Rs electric resistance of a solution, Rm electric resistance of a membrane, l equivalent conductance of a solution, ¯t ; ¯tþ transport number of anions and cations in a membrane, DOI: 10.1016/S0927-5193(07)12007-6

98

Ion Exchange Membranes: Fundamentals and Applications

200 180 160 i amps × 10 6

140

III

120

Membrane Area = 0.126 cm2

100

II

80 60 i lim

40 20 0

1

2

3

4

5

V=(Vi −iR i=0 ) volts

Figure 7.1

Current–voltage curve (Membrane area 0.126 cm2) (Peer, 1956).

C C

C C Cm

Concentrating side

Figure 7.2

Ion exchange membrane

Desalting side

Concentration polarization.

t–, t+ transport number of anions and cations in a solution, R Gas constant and T Absolute temperature. DE ( ¼ DE (total)) was plotted against i, obtaining Fig. 7.3 in which 1st term and 2nd term correspond to the terms in Eq. (7.2). Fig. 7.3 shows that upon increasing the voltage across the membrane, a current

Concentration Polarization

Figure 7.3

99

Current–voltage curve (Calculation) (Spiegler, 1971).

plateau is reached. The limiting current is realized when the electrolyte concentration reaches zero (Cm ¼ 0) in Fig. 7.2, however an overlimiting current seen in Fig. 7.1 does not appear in Fig. 7.3. Cowan and Brown expressed the current–voltage relationship (Cowan plot) by the following equation (Cowan and Brown, 1959). V ðV e þ V c þ V p Þ ¼Rþ (7.3) I I where Ve is the electrode potential, Vc concentration potential, Vp polarization potential and IR the Ohmic voltage. Equation (7.3) indicates that the intercept of a plot of V/I against I1 presents the resistance of the cell and the slope of the plot presents the cell voltage plus their derivatives. Polarization voltage manifest itself as a rapid change of slope as shown in Fig. 7.4 obtained for an anion exchange membrane. The pH of diluting stream begins to change at a current very near the value at which the resistance slope change and continue to decrease as current density increases. The pH change is attributed to the occurrence of water dissociation on the desalting surface of the anion exchange membrane. The point at which negative slope cuts positive slope shows the limiting current Ilim. Kooistra reported from the measurement of a I–V curve of a cell pair that the limiting current density of a cation exchange membrane ilim cation is less than that of an anion exchange membrane ilim anion placed in a 0.02 M NaCl solution (Fig. 7.5) (Kooistra, 1967). This is due to the transport number of Na+ ions to be less than that of Cl– ions in a NaCl solution.

100

Ion Exchange Membranes: Fundamentals and Applications

Figure 7.4

7.2.

Voltage/current–reciprocal current curve (Cowan and Brown, 1959).

CONCENTRATION POLARIZATION POTENTIAL

An ion exchange membrane is assumed to be immersed in a 1,1 valent electrolyte solution of electrolyte concentration C. Then, an electrodialysis system in Fig. 7.2 is formed by passing an electric current through the membrane. Next, the electric current is interrupted, and the potential across the membrane E just after the electric current interruption is measured. E is the concentration polarization potential, expressed by the following equation. RT ðC þ DCÞg1 (7.4) ð¯t tÞ ln E ¼ ED þ Em ¼ 2 ðC DCÞg2 F RT ðC DCÞg2 ð2t 1Þ ln (7.5) Diffusion potential : ED ¼ ðC þ DCÞg1 F RT ðC þ DCÞg1 Membrane potential : Em ¼ (7.6) ð2¯t 1Þ ln ðC DCÞg2 F g1 and g2 are the activity coefﬁcients of ions in solutions of the concentration C +DC and C–DC, respectively. DC is computed by substituting E observed

101

Concentration Polarization

3

E(V)

2

i lim, anion 1

i lim, cation 0

Figure 7.5

0

5 i (mA/cm2)

10

Current–voltage curve (Kooistra, 1967).

experimentally into Eq. (7.4). Further, we have the following equation by substituting i and DC into ilim and C in Eq. (7.1). DDC i ¼ ð¯t tÞ (7.7) d F d is obtained by substituting DC calculated above into Eq. (7.7). Onoue (1962) and Cooke (1961a) observed DC and d. Table 7.1 shows the data measured by Onoue for m-phenol sulfonic acid cation exchange membrane. 7.3.

CHRONOPOTENTIOMETRY

In order to obtain a clear picture of the mechanism of polarization and depolarization, Forgacs measured the potential differences between an ion exchange membrane during constant current transfer and after electric current interruption (Forgacs, 1962). The results are summarized in Fig. 7.6. In the ﬁrst instant of the application of a direct current through the solution–membrane

102

Ion Exchange Membranes: Fundamentals and Applications

Table 7.1

Concentration polarization of a cation exchange membrane

CNaCl (M)

i (A dm–2)

E (mV)

DC (M)

d 102 (cm)

0.1

0.25 0.50 0.75 1.00 1 2 4 6 1 2 3 6.67 2 4 6

21.3 38.0 70.0 95.0 8.5 15.2 28.5 40.0 3.2 6.0 8.4 15.0 2.9 5.1 9.5

0.037 0.060 0.080 0.095 0.075 0.13 0.24 0.31 0.10 0.18 0.25 0.44 0.13 0.23 0.40

3.0 2.4 1.9 1.9 1.4 1.3 1.1 1.0 2.1 1.9 1.8 1.4 1.4 1.2 1.0

0.5

1.5

2.5

Source: Onoue (1962).

system, a potential drop E0 is obtained. This potential increases nonlinearly, achieves a maximum value Em and decreases again to a steady value Es after time ts such that Es>E0. This was observed for all conditions of solution concentration, current densities and ﬂow conditions (static, stirred and continuously ﬂowing liquid). After the interruption of the current, the potential suddenly drops to a residual value Er which slowly disappeared with time. The value of Er depends upon the time of current application, but remains constant for times of current transfer greater than ts. When, instead of interrupting the current, the current is suddenly reversed, the following effects are obtained (Fig. 7.7). (1)

(2)

(3)

With the reversal of the current, there is a potential drop of reversed sign to a value which is a function of the time of current application, but achieves a constant value at time ts. The change in potential drop with continued application of the reversed current is similar to that occurring during the application of the direct (nonreversed) current. After the interruption of the reversed current, two types of depolarization curves may develop. If the duration of the reversed current is sufﬁciently long, the depolarization curve is the same as previously described (Fig. 7.6). But if the time of reversed current application is shorter, when this is stopped, the residual potential changes its sign, arrives at a maximum value, and disappears with time (Fig. 7.7). It is important to note that this maximum is achieved after a speciﬁc time lag and not immediately.

103

I (Applied current)

Concentration Polarization

+ 0 −

E (Potention drop on membrane)

Em Es +

Eo

Er

0 −

ts

Time

Figure 7.6

Potential–time curve (Forgacs, 1962).

The information provides proﬁtable aspects in electrodialysis reversal (DER) system (cf. Chapter 2 in Applications). Sistat and Pourcelly (1997) investigated the chronopotentiometric response of a cation exchange membrane as a function of the applied current density below the limiting one. Taking into account classical assumption such as the variation of concentration associated to the Teorell–Meyer–Sievers segmentation model, the concept of the Nernst layer model, the quasi-electro-neutrality condition within the diffusion boundary layer and the validity of the Donnan equation at the solution–membrane boundaries, theoretical values of the trans-membrane potential difference were obtained which ﬁt very well the experimental V–t responses. Moreover, this method allows the calculation of the diffusion boundary layer thickness. In addition, a decrease of the diffusion boundary layer thickness was observed when the current density increases. This result was attributed to the occurrence of convection effects inside the diffusion boundary layer. 7.4.

REFRACTIVE INDEX

When a ray of light shines on the interface between two solutions that have different refractive indexes, the light is refracted and the refractive index increases with the electrolyte concentration of the solutions. This phenomenon is

104

Ion Exchange Membranes: Fundamentals and Applications

+ I 0 −

+ E 0 −

Time

Figure 7.7

Potential–time curve (Forgacs, 1962).

the principle of the Schlieren-diagonal method, which was applied to measure the concentration polarization on the surface of an ion exchange membrane by Takemoto (1972). In this experiment, an Aciplex CK-2 cation exchange membrane or a CA-2 anion exchange membrane was integrated in the threecompartment optical glass cell. The effective membrane area and the distance between the membranes were maintained at 0.3 cm2 (1 cm height, 0.3 cm width) and at 0.2 cm, respectively. A NaCl solution (0.1 M or 0.05 M) was put in the central desalting cell, and in the electrode cells placed on both outsides of the central cell, and an electric current was passed through Ag–AgCl electrodes. The NaCl concentration changes were observed by the Schlieren diagonal method, changing the current density incrementally. Figs. 7.8 and 7.9 show the concentration distribution in a boundary layer formed on the cation exchange membrane and anion exchange membrane, respectively. In the 0.1 M NaCl solution, the limiting current density for the cation exchange membrane (2.93 A dm–2) was less than that for the anion exchange membrane (3.99 A dm–2). This difference is due to the lower mobility of Na+ ions (Na+ ion mobility uNa, zNauNaF ¼ 50 S cm2 mol–1) compared to Cl– ions (Cl– ion mobility uCl, zCluClF ¼ 76 S cm2 mol–1) and lower transport number of Na+ ions (Na+ ion transport number tNa ¼ 0.40) compared to Cl– ions (Cl– ion transport number tCl ¼ 0.60) in the NaCl solution. The boundary layer thickness d on the cation exchange membrane (0.0366 cm) was also less than that on the anion

105

Concentration Polarization

0.12

0.10

0.1M NaCl

2

m

d A/

3

1.1

0.08 2.1

C (M)

0

2.93A/dm 2 (LCD)

0.06 0.05MNaCl

4.30(over LCD) 0.04

8 2.2

0.02

0.00 0.00

(LC

D)

=0.0366 cm

0.01

0.02

0.03

=0.0580 cm

0.04

0.05

0.06

0.07

x (cm)

Figure 7.8 NaCl concentration distribution in a boundary layer. Cation exchange membrane (Aciplex CK-2) (Takemoto, 1972).

exchange membrane (0.0402 cm), and these are not affected by the current density. In the 0.05 M NaCl solution, however, the limiting current density for the cation exchange membrane (2.28 A dm–2) was larger than that for the anion exchange membrane (1.81 A dm–2). The thickness of the boundary layer on the cation exchange membrane (0.058 cm) was greatly increased compared to that on the anion exchange membrane (0.0362 cm). It was apparent in Fig. 7.8 that the NaCl concentration ﬂuctuated on the surface of the cation exchange membrane placed in the 0.05 M NaCl solution at the limiting current density within the range of the distance from the membrane surface xo0.01 cm. The concentration ﬂuctuation was found to propagate from the membrane surface toward the inside of the solution adjacent to the membrane. The velocity of the propagation was unstable, but it was estimated to be about 0.1 cm s–1. So, the frequency of ﬂuctuation was estimated to be 10 times s1. The overlimiting current phenomena seen in the cation exchange membranes are supposedly related the concentration ﬂuctuation. The concentration ﬂuctuation was not observed on the anion exchange membrane. Shaposhnik et al. used the three-frequency laser interferometry method for studying the concentration polarization of ion exchange membranes in wide range of current densities (Shaposhnik et al., 2000). The concentration and

106

Ion Exchange Membranes: Fundamentals and Applications

0.12

0.10

0.1M NaCl

2

m

d A/

3

1.1

0.08 2.1

C(M)

0

2.93A/dm 2 (LCD)

0.06 0.05M NaCl

4.30(over LCD) 0.04

8 2.2

0.02

0.00 0.00

(LC

D)

=0.0366 cm

0.01

0.02

0.03

=0.0580 cm

0.04

0.05

0.06

0.07

x(cm)

Figure 7.9 NaCl concentration distribution in a boundary layer. Anion exchange membrane (Aciplex CA-2) (Takemoto, 1972).

temperature ﬁelds of a solution involved in electrodialysis of sodium chloride are measured simultaneously. The proposed method makes it possible to measure absolute values of local concentration of acids and bases that form during water dissociation at the solution–membrane interfaces following an increase in the current density above the limiting value. According to an analysis of the concentration and temperature distribution in an electrodialyzer channel, maximum variations in the measured quantities occur near the interface. 7.5.

NATURAL CONVECTION

Under an applied electric current, a solution in a boundary layer ﬂows upward on the surface of the membrane because of the decrease in electrolyte concentration, and ﬂows downward because of the increase in electrolyte concentration. These phenomena (natural convection) occur owing to the decrease and increase in solution density in the boundary layer. Frilette observed the natural convection using the electrodialysis cell (Fig. 7.10) incorporated with two Permutit cation exchange membranes and equilibrated with a 0.0996 M NaCl solution (Frilette, 1957). A constant electric current was passed and was turned off after the predetermined time had elapsed by keeping total coulombs passed to be constant.

Concentration Polarization

107

Figure 7.10 Apparatus for measuring natural convection: (A) luicite end block; (B) graphite plate; (C) spacer; (D) membrane (Frilette, 1957).

After the completion of the experiment, the contents of the central chamber were drained off slowly and collected in two equal portions; the portion ﬁrst collected corresponded to the solution in the lower half of the central chamber. The two portions were analyzed for chloride ions. In all experiments it was found that a net movement of NaCl into the lower half of the chamber had occurred, with no signiﬁcant change in total electrolyte content of the chamber. The results of this experiment are shown in Table 7.2, which is characterized by a relatively large transfer of salt from the upper half into the lower half of the chamber. In order to determine the ascending ﬂow velocity vy caused by the natural convection on the desalting surface of an ion exchange membrane, Tanaka suspended ﬁne cellulose ﬁbers in a 0.5 M NaCl solution in a transparent polyethylene cell incorporated with a cation exchange membrane (Aciplex CK-2) and an anion exchange membrane (Aciplex CA-2) (Tanaka, 2004). Effective membrane area was adjusted to 4 cm2 (2 cm height, 2 cm width). The movement of the cellulose ﬁbers was observed with a microscope while applying an electric current through Ag–AgCl electrodes. The ﬂow velocity was plotted against current density and is presented in Fig. 7.11, which shows that vy on the cation exchange membrane is larger than vy on the anion exchange membrane. This event means that concentration polarization occurs more easily on the cation exchange membrane than on the anion exchange membrane. The ascending ﬂow supposedly produces the overlimiting current.

108

Table 7.2

Transfer of electrolytes in a cell owing to natural convection (Constant Current Timea)

Current (mA)

1.87 2.49 3.74 5.61 7.48 9.35 14.96

Time (min)

40 30 20 13 1/3 10 8 5

Source: Frilette (1957). a Total of 1.840 A min for all runs or 1.147 10–3 F.

Lost, Upper Layer (meq)

0.303 0.345 0.367 0.465 0.483 0.506 0.504

Gained, Lower Layer (meq)

0.310 0.310 0.365 0.457 0.488 0.493 0.511

Transferred Upper Layer (eq F–1)

Lower Layer (eq F–1)

–0.264 –0.301 –0.320 –0.406 –0.422 –0.442 –0.440

+0.270 +0.270 +0.318 +0.400 +0.426 +0.430 +0.446

Ion Exchange Membranes: Fundamentals and Applications

46 61.3 92 138 184 230 368

Current Density (A cm–2)

109

Concentration Polarization

16

14 r.

mb

12

e nm

tio

Ca

v y(10-2cm/s)

10

ion

br.

m me

An 8

6 4 2 0 0

1

2

3

4

5

6

7

i(A/dm2)

Figure 7.11 Ascending ﬂow velocity in a boundary layer (0.1 M NaCl, Aciplex CK-2/ CA-3) (Tanaka, 2004).

The natural convection occurring in the boundary layer had been discussed near a vertical electrode incorporated with an electrolyzer (Wagner, 1949; Tobias et al., 1952; Ibl and Muller, 1958). 7.6.

FLUCTUATION

Occurrence of ﬂuctuation of electric currents through ion exchange membranes is attributed to the depletion of salt on one side of the membrane, which creates a thin layer of high resistance. Joule heating in this depletion layer and ensuring temperature gradient, as well as the concentration gradient, give rise to buoyant forces, which may create a turbulent convection current. The turbulence mixes the depletion layer so that the electric resistance ﬂuctuates, and consequently the current ﬂickers (Lifson et al., 1978). Lifson suggests that the following experimental results support the above mentioned conjecture. (1)

Noise is coincident with the increase of the electric resistance by the depletion process.

110

(2)

(3) (4)

(5) (6)

Ion Exchange Membranes: Fundamentals and Applications

When the current density is reduced, it reaches a critical value, below which the convection current changes from turbulent to laminar, and the ﬂuctuation disappears. Fluctuation reduces with temperature, because the expansion coefﬁcient of water decreases with temperature and its viscosity increases. A nonionic water-soluble polymer added to the compartment on the side of the depletion layer reduces the ﬂuctuation, by increasing the bulk viscosity of the solution. Fluctuation depends on the membrane’s orientation in the gravitational ﬁeld. The convection current in the depletion layer can be observed directly, using a laser-beam, by adding latex particles, which create optical noise as they drift with the convection current across the beam. The optical noise is observed only coincidently with the current noise.

Krol et al. (1999) studied the overlimiting ion transport through a Neocepta CMX cation and AMX anion exchange membrane. This technique is used to characterize the ﬂuctuations in membrane voltage drop observed in the overlimiting current region. Above the limiting current the measurements show large voltage drop ﬂuctuation in time indicating hydrodynamic instability. The amplitude of this ﬂuctuation is increasing with increasing applied current density. The ﬂuctuation occurs when a set up is used where there is no forced convection and the depleted diffusion layer is stabilized by gravitation. Tanaka observed the voltage ﬂuctuation and water dissociation at over limiting current using an electrodialysis cell integrated with a cation exchange membrane (Aciplex K-172) and an anion exchange membrane (Aciplex A-172) (Tanaka, 2004). Effective membrane area was adjusted to 0.383 cm2 and a 5 mM NaCl solution was supplied into a desalting cell. An electric current was passed through Ag–AgCl electrodes, and the voltage ﬂuctuation was measured using a voltmeter. Current efﬁciencies for water dissociation arising on a cation exchange membrane ZH and those arising on an anion exchange membrane ZOH were calculated from the changes of pH and volume of a solution in the concentrating cell. Voltage ﬂuctuation on a cation and anion exchange membrane obtained by setting current density at 0.131 A cm–2 is shown in Fig. 7.12, which indicates that voltage ﬂuctuates on the cation exchange membrane but does not ﬂuctuate on the anion exchange membrane. ZH and ZOH were calculated as 0.041 and 0.336, respectively. Accordingly, water dissociation on the cation exchange membrane was conﬁrmed to be strongly suppressed compared to that on the anion exchange membrane. The mechanism of the ﬂuctuation is discussed in Section 7.8.5 in this chapter. Li et al. (1983) measured light scattering spectra from polystyrene latex near an Ionics Inc., #61-CZL-386 cation exchange membrane in 0.020 M HCl

Concentration Polarization

111

Figure 7.12 Voltage ﬂuctuation at overlimiting current density (5 mM NaCl, 0.131 A cm–2) (Tanaka, 2004).

and 0.020 M NaCl solution. For HCl, spectra on the depleted side showed evidence for turbulent ﬂow at and overlimiting current density. Spectra on the concentrate side showed similar spectra above approximately twice the limiting current density, although of lower intensity. For NaCl, depleted side spectra began at currents approximately twice the limiting value. On the concentrated side, at least six to seven times the limiting current density was needed for nonzero difference spectra. From these experimental results, they suggest that the electrical noise spectra correspond principally to ﬂuctuations induced by turbulent ﬂow on the depleted side of the membrane. 7.7.

OVERLIMITING CURRENT

In many investigations devoted so far to the limiting current density, considerable works are proceeded toward the elucidation of the mechanism of the overlimiting current. However, in spite of many discussions on the origin of the overlimiting current, a quantitative theory accounting for Region III in Fig. 7.1 observed in the current density–voltage curve for the cation exchange membrane is still lacking. Concentration polarization occurs easily on a cation exchange membrane than on an anion exchange membrane. This is because transport number of counter-ions in a solution is larger on a cation exchange

112

Ion Exchange Membranes: Fundamentals and Applications

membrane than on an anion exchange membrane. From this, it is estimated that water dissociation occurs easily on a cation exchange membrane than on an anion exchange membrane. At overlimiting current density, the deﬁcit of ions at a cation exchange membrane–solution interface is estimated to be compensated by generation of H+ ions and OH– ions caused by water dissociation in a boundary layer. However, contrary to this estimation, Rosenberg and Tirrell, and Cooke show that the water dissociation is rather difﬁcult to occur on a cation exchange membrane than on an anion exchange membrane (Rosenberg and Tirrell, 1957; Cooke, 1961b). Accordingly, water dissociation never prevents the deﬁcit of ions at the cation exchange membrane–solution interface and accordingly never contributes to generate ions at overlimiting current on the surface on the cation exchange membrane. Natural convection, voltage ﬂuctuation, concentration ﬂuctuation, optical ﬂuctuation described above are estimated to relate to the overlimiting current for the cation exchange membrane. However, the discussion on the mechanism of these phenomena is insufﬁcient. Here, we try to inspect another aspect concerning the overlimiting current in this section. 7.7.1

Co–Ion Leakage This idea is that the ionic transport is compensated by passing co-ions through an ion exchange membrane at overlimiting current. However, the permselectivity of counter-ions for commercially available membranes placed in a dilute salt solution was observed to be maintained at around 90–100%, and co-ion leakage was not arisen (Block et al., 1966). 7.7.2

Electro–Osmotic Convection Most studies on polarization are based on the Nernst diffusion model for the boundary layer, and little attention has been paid to the role of electroosmotic convection. In practice, electro-osmotic convection term is contained in the ﬂux equations. Frilette suggested that electro-osmotic streaming occur at the surface of the membrane, the Nernst layer would become thinner due to short range turbulence, and the electro-osmotic streaming would support conduction by transporting ions toward the membrane surface (Frilette, 1957). However, experimental and numerical simulation studies show that the electro-osmotic water transport does not support the overlimiting current (Mazanares et al., 1991). 7.7.3

Space Charge Rubinstein and Shtilman conﬁrmed that the water dissociation on the Selemion CMV cation exchange membrane at overlimiting currents is very small. At the same time the membranes remained highly permselective. Hence,

113

Concentration Polarization

an electric current many times greater than the limiting one was transferred exclusively by the salt cations. The computation in this study was proceeded based on the following Nernst–Planck–Poisson equation for a 1,1 valent electrolyte (Rubinstein and Shtilman, 1979; Rubinstein, 1981). @p ¼ divðgrad p þ p gradcÞ @t

(7.8)

@n ¼ divðgrad n n gradcÞ @t

(7.9)

Dc ¼ n p

(7.10)

p and n are dimensionless counter-ion concentration and dimensionless co-ion concentration respectively. e is a square ratio of the bulk Debye radius to the thickness of the unstirred layer. t is dimensionless time. c is dimensionless electric potential. The computed ion concentration proﬁle in an unstirred layer on a cation exchange membrane is illustrated in Fig. 7.13 which is distinguished by three distinct regions, Region I, II and III. Solid lines and dotted lines show

+ + + + + + + +

p I n

− − − − − − − − C+ < CR

II

III

x

Figure 7.13 Concentration proﬁles of cations and anions in an unstirred layer formed on the desalting surface of a cation exchange membrane (Rubinstein and Shtilman, 1979, Rubinstein, 1981).

114

Ion Exchange Membranes: Fundamentals and Applications

cation concentration and anion concentration respectively. In Region I, local electro-neutrality is preserved with high accuracy. Region II is a charged region developed in the course of concentration polarization. Its dimensions can exceed by orders of magnitude the equilibrium Debye radius. In this region the counter-ion (cation) concentration is much higher than that of co-ions, which is very low. The electric ﬁeld at the end of Region II is very high. Ion transport in this region is dominated by migration as opposed to diffusion. Region III is a boundary layer for counter-ions in which their con¯ þ within the cation centration rapidly approaches its high interface value C exchange membrane. Region III is comparable in thickness (though smaller) with the equilibrium Debye radius. If we assume here that the interface concentration of exchange groups within the cation exchange membrane in Fig. 7.13 is C¯ R ; in order to maintain the electric neutrality in a total system, ¯ R 4C¯ þ must hold and potential difference must be generated between a C solution and a membrane. 7.7.4

Hydrodynamic Convection The Nernst model assumes that there is no hydrodynamic convection, or mixing in the Nernst layer. However, Gavish and Lifson argued that this assumption cannot be strictly valid and suggested that hydrodynamic convection affects the current–voltage relationship in a way which is sufﬁcient to explain the overlimiting current behavior as follows (Gavish and Lifson, 1979). Turbulent convection in the depleted layer is the source of the current noise. The convection is attributed to the force of gravity acting on the depleted layer, where concentration gradients create density gradients, resulting in hydrodynamic convection current, which at high enough current densities becomes turbulent. The turbulent convection injects salt from the bulk of the solution into the depleted layer, thus reducing its resistance signiﬁcantly. The current separates the injected positive and negative ions, thus tending to rebuild the depleted layer against its destruction by the turbulent convection. The dynamic balance between these two opposing trends sets up a stationary state in which the depleted layer is only partially depleted. The phenomena mentioned above were discussed on the basis of the model illustrated in Fig. 7.14, consisting of two sublayers. One sublayer, in the range of 0oxod1, namely between the membrane surface and d1, is characterized by a ﬁxed concentration C¯ 1 : The other layer, like the Nernst diffusion layer, is characterized by a ﬁxed concentration gradient, C 0 . Thus, the concentration in the total depletion layer varies according to ¯ 1 ; for 0oxod1 CðxÞ ¼ C CðxÞ ¼ C 0 þ C 0 ðx dÞ; C 0 ¼

(7.11) ðC 0 C¯ 1 Þ ; for d1 oxod ðd d1 Þ

(7.12)

115

Concentration Polarization

Figure 7.14 Schematic description of the Nernst model for high current densities. (A) The concentration proﬁle. (B) The speciﬁc resistance proﬁle. DR is the net rise of resistance due to the formation of the depleted and enriched layer. (Gavish and Lifson, 1979).oComp: Change ﬁgure parts to uppercase ‘A’, ‘B’ in artwork.>

The width of the enriched layer, as well as that of depleted layer, remains d for all values of the current densities, as in the Nernst model. The surface concentration in the enriched layer continues to grow the same way as in the Nernst layer, namely its local concentration varies in the range –doxo0 according to CðxÞ ¼ C 0 þ C 0 ðx þ dÞ; C 0 ¼

¯ 1Þ ðC 2 C 0 Þ ðC 0 C ¼ d ðd d1 Þ

(7.13)

The voltage difference DV created solely by the formation of the Nernst layer is given by DV ¼ DV P þ JDR

(7.14)

DVP is the polarization potential established across the membrane. RT C2 (7.15) 2Dtþ ln DV P ¼ ¯1 F C R is the gas constant, T the absolute temperature, Dt+ difference of the transport numbers of the permeable cations between in the membrane and in the solution. J is electric current density deﬁned by J ¼ Jþ þ J ¼

DF C 0 Dtþ

(7.16)

116

Ion Exchange Membranes: Fundamentals and Applications

D is the diffusion constant of salt, F the Faraday constant. DR is the Ohmic resistance of the cell by an amount Z d Z d 1 1 dx rðxÞ r0 dx ¼ L1 DR ¼ C0 d d CðxÞ

(7.17)

where r(x) is the speciﬁc resistance at point x in the Nernst layer, and L is the equivalent conductance. They are related by r –1 ¼ LC. Using Eqs. (7.11)–(7.17) inclusive, the current–voltage relationship of the Nernst model may be transformed to dimensionless scale potential E and scaled current density I, deﬁned by E¼

F DV J C0d ¼ ; I¼ RT JL C0

(7.18)

JL is the limiting current density. The result is shown as follows putting ¯ 1 /C0. e¼C 1þI I ; for Io1 (7.19) E ¼ 2Dtþ þ ð2Dtþ Þ1 ln 1 I Dtþ 1þI I 1þ I E ¼ 2Dtþ þ ð2Dtþ Þ1 ln , þ 2tþ Dtþ for I41

ð7:20Þ

The transition between the two regimes of low and high current densities is smooth, in the sense that Eqs. (7.19) and (7.20) yield the same value of E at ¯ 1 and d1 ¼ 0. I ¼ 1 – e in the common boundary. At this point C1 ¼ C Gavish and Lifson compared the current–voltage relationship of the present model with the corresponding experimental results obtained by Cooke (1961a) in Fig. 7.15. 7.8.

MASS TRANSPORT IN A BOUNDARY LAYER (Tanaka, 2004)

Concentration polarization occurs because of the difference between the ion transport number in a solution and in an ion exchange membrane. The main subject to be studied in this ﬁeld must be to make clear ‘‘the mechanism of ionic transport in a depleted boundary layer’’. Concentration decrease in the depleted layer gives rise to the natural convection owing to the decrease in solution density as suggested by Gavish (Gavish and Lifson, 1979) (cf. Section 7.7.4). Accordingly, the mass transport in this region is analyzed based on the extended Nernst–Planck equation including convection term. In this section, we discuss the phenomena in the boundary layer formed on the desalting surface of an ion exchange membrane placed in

117

Concentration Polarization

0

0.5

1.0

1

40

1.5

2

3

40

30

30

20

20

E

slope = 1/ε

10

10

1- ε 0

0 0

0.5

1.0

1.5

I

Figure 7.15 Voltage plotted against current. (1) Nernst model; (2) Modiﬁed Nernst model (Eqs. (7.19) and (7.20)) with e ¼ 1/175; (3) Experimental curve according Cooke. (Note that all three curves coincide for 1o1–e) (Gavish and Lifson, 1979)

a NaCl solution as illustrated in Fig. 7.16, based on the investigation proceeded by Tanaka (2004). 7.8.1 The Equation of Material Balance, the Extended Nernst–Planck Equation, the Reduced Diffusion Coefﬁcient, the Reduced Transport-Diffusion Coefﬁcient Mass transport with natural convention in a boundary layer near the surface of a vertical membrane is a three-dimensional process shown in Fig. 7.17. The theory of three-dimensional free convection in a liquid is understandable from the equation of continuity and the equation of motion as expressed below. Equation of continuity: @ @ @ rvx þ rvy þ rvz ¼ 0 @x @y @z

(7.21)

118

Ion Exchange Membranes: Fundamentals and Applications

Anion exchange membrane

Cation exchange membrane C'

C'

J Na<0

J Na>0

J Cl>0

−

J Cl<0

i<0

i >0

VK<0

VA<0

d /dx >0

d /dx <0

dC/dx>0 C

+

dC/dx>0

o

Co x

Boundary layer

x Bulk

Boundary layer

Desalting cell

Figure 7.16 brane.

Boundary layer formed on a desalting surface of an ion exchange mem-

where r is the solution density. vx, vy and vz are x-, y- and z-components of solution velocity. Equation of motion: vx

@vx @vx @vx þ vy þ vz ¼0 @x @y @z

(7.22)

vx

@vy @vy @vy r r0 þ vy þ vz ¼g @x @y @z r

(7.23)

vx

@vz @vz @vz þ vy þ vz ¼0 @x @y @z

(7.24)

where r0 is the solution density in bulk and g the gravitational acceleration. Here, we separate the ﬂux of ions J in a boundary layer into x-component Jx, a y-component Jy and a z-component Jz, as shown in Fig. 7.17, and express the material balance of three components: J xjd þ J y;injxd þ J z;injxd ¼ J xjx þ J y;outjxd þ J z;outjxd

(7.25)

J xjx þ J y;inj0x þ J z;inj0x ¼ J xj0 þ J y;outj0x þ J z;outj0x

(7.26)

119

Concentration Polarization

y Jy,out | x-

Jy,out | 0-x l

C'

C Jz,out | 0-x Jx,m

Jz,out | x-

Jx | 0

Jx |

Jx | x Jz

Jz,in | 0-x

Jz,in | x-

Jy Jx z C

o

b x

x

0 Jy,in | 0-x Ion exchange

Boundary layer

Jy,in | x- Bulk

membrane

Figure 7.17 Ion ﬂux in a boundary layer formed on a desalting surface of an ion exchange membrane.

From the material balance of ionic ﬂuxes in the x-component: J xjd ¼ J xjx ¼ J xj0 ¼ J xjm

(7.27)

Each term in Eq. (7.27) concerns with an electric current, and Eq. (7.27) represents indirectly electric current balance in Fig. 7.17. Jx9m is ionic ﬂux across an ion exchange membrane, which corresponds to an electric current across an ion exchange membrane. The material balance in the y-component and the z-component is expressed by the following equations: J y;injxd ¼ J y;outjxd

(7.28)

J y;inj0x ¼ J y;outj0x

(7.29)

120

Ion Exchange Membranes: Fundamentals and Applications

1.2

(105s/cm2)

1.0 0.8 0.6 k

(eq/A • cm2)

0.4 0.2 0.0 -0.2 -0.4 0.0

A

0.1

0.2

0.3

0.4

0.5

C(10-3mol/cm3)

Figure 7.18 NaCl concentration vs. reduced diffusion coefﬁcient and reduced transportdiffusion coefﬁcient.

J z;injxd ¼ J z;outjxd

(7.30)

J z;inj0x ¼ J z;outj0x

(7.31)

Equations (7.28)–(7.31) do not concern them with an electric current and are excluded from the electric current balance. Eqs. (7.27)–(7.31) are one-dimensional expressions of three-dimensional mass transport phenomena in the boundary layer (Bird et al., 1960). They are equivalent to the equation of continuity (Eq. (7.21)) and the equation of motion (Eqs. (7.22)–(7.24)) and can be termed the equation of material balance. Based on Eq. (7.27), the transport of ion i at x in the boundary layer is expressed by Ji,x using the extended Nernst–Planck equation including the diffusion, migration and convection as follows: dC i FDi zi C i dc (7.32) þ C i vx dx RT dx where Ci is the concentration of ions i, c the electric potential, Di the diffusion constant of ions i, zi the ionic charge number of ions i, F the Faraday constant, R the gas constant and T the absolute temperature. In a NaCl solution Eq. (7.32) is expressed by Eq. (7.33). J i;x ¼ Di

121

Concentration Polarization

0.7

'(eq/A • cm2)

0.6

'K

0.5

0.4 'A

'(105s/cm2)

0.3 '

0.2

0.1

0.0 0.0

0.1

0.2

0.3

0.4

0.5

C(10-3mol/cm3)

Figure 7.19 NaCl concentration vs. reduced diffusion coefﬁcient and reduced transportdiffusion coefﬁcient.

dC Na FDNa C Na dc þ C Na v dx RT dx dC Cl FDCl C Cl dc þ þ C Cl v ¼ DCl dx RT dx

J Na ¼ DNa J Cl

(7.33)

In the electrodialysis of a NaCl solution, the electrical neutrality expressed by Eq. (7.34) is assumed to be satisﬁed in the boundary layer. C Na ¼ C Cl ¼ C

(7.34) +

–

The material balance of Na ions and Cl ions in an ion exchange membrane and in a boundary layer is expressed by Eq. (7.35) introduced from Eq. (7.27). i ¯tNa J Na ¼ J¯ Na ¼ F (7.35) i ¯tCl J Cl ¼ J¯ Cl ¼ F where ¯tNa and t¯Cl are the transport number of Na+ ions and Cl– ions in an ion exchange membrane.

122

Ion Exchange Membranes: Fundamentals and Applications

2.5 JCl,migr

Jdiff, Jmigr, Jconv(10-7mol/cm2 • s)

2.0 1.5 1.0 0.5

JCl =JCl,diff +JCl,migr +JCl,conv

0.0 -0.5

ff

, di

J Na

iff

l, d

JC

-1.0

J Na,migr

-1.5 J Na,conv = J Cl,conv

-2.0 -2.5

J Na =J Na,diff +J Na,migr+J Na,conv

-3.0 0.00

0.01

0.02

0.03

0.04

0.05

x(cm)

Figure 7.20 Diffusion ﬂux, migration ﬂux and convection ﬂux of Na+ ions and Cl– ions in a boundary layer (cation exchange membrane).

Using Eqs. (7.33)–(7.35), we obtain Eqs. (7.36) and (7.37). Equation of concentration gradient: dC ¼ avC bi dx Equation of potential gradient: dc RT i ¼ a 0 v b0 dx F C

(7.36)

(7.37)

where 1 1 1 a¼ þ 2 DNa DCl 1 b¼ 2F

¯tNa ¯tCl DNa DCl

(7.38)

1 1 1 a ¼ 2 DNa DCl 0

(7.39)

(7.40)

123

Concentration Polarization

2.0

J Na,migr

1.5

Jdiff, Jmigr, Jconv(10-7mol/cm2 • s)

1.0 J Na=J Na,diff+J Na,migr+J Na,conv 0.5 0.0

J Na,d

iff

-0.5

J Cl,di

ff

JNa,conv = J Cl ,co nv

-1.0 -1.5 -2.0

J Cl,migr

-2.5 -3.0 -3.5 -4.0 0.00

JCl = JCl,diff + JCl,migr + JCl,conv 0.01

0.02 x(cm)

0.03

0.04

0.05

Figure 7.21 Diffusion ﬂux, migration ﬂux and convection ﬂux of Na+ ions and Cl– ions in a boundary layer (anion exchange membrane).

b0 ¼

1 2F

¯tNa ¯tCl þ DNa DCl

(7.41)

a and a0 are termed the reduced diffusion coefﬁcient of NaCl, because they are another expression of DNa and DCl. b and b0 are termed the reduced transportdiffusion coefﬁcient, because they relate ¯tNa ; ¯tCl ; DNa and DCl. C vs. a, bK and bA, and C vs. a0 , b0 K and b0 A in a NaCl solution electrodialysis system are presented in Figs. 7.18 and 7.19 respectively. These parameters facilitate the computation in this chapter. 7.8.2

Ionic Flux in a Boundary Layer Substituting the equation of concentration gradient Eq. (7.36) and the equation of potential gradient Eq. (7.37) into the extended Nernst–Planck equation Eq. (7.33), the ﬂux of Na+ ions JNa and Cl– ions JCl are divided into the terms of diffusion Jdiff, electro-migration Jmigr and convection Jconv: J Na ¼ J Na;diff þ J Na;migr þ J Na;conv J Cl ¼ J Cl;diff þ J Cl;migr þ J Cl;conv

(7.42)

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Ion Exchange Membranes: Fundamentals and Applications

2 1 idiff

idiff, imigr(A/dm2)

0 -1 i migr

-2

i=i diff +i migr

1.13A/dm2

i=i diff +i migr

2.10

i migr i=i diff+i migr

2.93(LCD)

-3 i migr

-4 -5 -6 0.00

i=i diff+i migr

4.30(overLCD)

i migr

0.01

0.02

0.03

0.04

0.05

x(cm)

Figure 7.22 Diffusion current density and migration current density in a boundary layer (cation exchange membrane).

Here, on a cation exchange membrane: J Na;diff ¼ DNa ðavC bK iÞ J Cl;diff ¼ DCl ðavC bK iÞ

(7.43)

J Na;migr ¼ DNa ða0 vC b0K iÞ J Cl;migr ¼ DCl ða0 vC b0K iÞ

(7.44)

On an anion exchange membrane: J Na;diff ¼ DNa ðavC bA iÞ J Cl;diff ¼ DCl ðavC bA iÞ J Na;migr ¼ DNa ða0 vC b0A iÞ J Cl;migr ¼ DCl ða0 vC b0A iÞ

(7.45) (7.46)

and on a cation exchange membrane and an anion exchange membrane: J Na;conv ¼ J Cl;conv

(7.47)

125

Concentration Polarization

5

i=i diff + i migr

4

3.99(LCD) 3.75

i=idiff + imigr i migr

idiff, imigr(A/dm2)

i migr

3 i=i diff + i migr 2.27 2

i migr

i=i diff + i migr 1

1.19A/dm2

imigr idiff

0 0.00

0.01

0.02

0.03

0.04

0.05

x(cm)

Figure 7.23 Diffusion current density and migration current density in a boundary layer (anion exchange membrane).

Applying Eqs. (7.38)–(7.41) and Eqs. (7.43)–(7.47) to the concentration distribution in a boundary layer observed by means of the Schlieren-diagonal method (Figs. 7.8 and 7.9), ionic ﬂuxes in a boundary layer at the limiting current density are calculated. The ionic ﬂuxes on the cation exchange membrane placed in a 0.1 M NaCl solution are shown in Fig. 7.20, in which the absolute values of Jconv is recognized to be decreased, and the absolute values of Jdiff and Jmigr are increased. It is estimated that Jconv which does not carry an electric current converts to Jdiff and Jmigr, which carry an electric current instead of Jconv in the boundary layer. Gavish expressed the phenomenon mentioned above as ‘‘The turbulent convection injects salt from the bulk of the solution into the depleted layer, and the current separates the injected positive and negative ions, thus tending to rebuild the depleted layer against its destruction by the turbulent convection’’ (Gavish and Lifson, 1979) (cf. Section 7.7.4). Fig. 7.21 shows the ionic ﬂuxes on the anion exchange membrane, indicating that the absolute values of Jconv and Jmigr are decreased and Jdiff is increased. In this situation, Jconv converts to Jdiff but does not convert to Jmigr.

126

Ion Exchange Membranes: Fundamentals and Applications

18 16 14

-vx(10-3cm/s)

12 10 8 6 4

4.30(overLCD)

2.28(LCD)

2 0

2.93(LCD) 2.10 1.13A/dm2

0

1

2

3

4

5

6

x(10-2cm)

Figure 7.24

Solution velocity in a boundary layer (cation exchange membrane).

7.8.3

Current Density in a Boundary Layer Current density i is divided into the terms of diffusion current idiff, migration current imigr and convection current iconv: i ¼ idiff þ imigr þ iconv

(7.48)

idiff ¼ iNa;diff þ iCl;diff ¼ F ðJ Na;diff J Cl;diff Þ

(7.49)

imigr ¼ iNa;migr þ iCl;migr ¼ F ðJ Na;migr J Cl;migr Þ

(7.50)

iconv ¼ F ðJ Na;conv J Cl;conv Þ ¼ 0

(7.51)

Substituting Eqs. (7.43)–(7.46) into Eqs. (7.48)–(7.50), idiff and imigr are calculated for the Schlieren-diagonal experiment. The result for the cation exchange membrane placed in a 0.1 M NaCl solution is shown in Fig. 7.22. The sign of idiff (>0) on the cation exchange membrane is in the opposite to that of i (o0). Namely, idiff decreases i, and this is because 9JNa,diff9o9JCl,diff9 holds in Fig. 7.20. The absolute values of imigr on the cation exchange membrane are increased due to the conversion of Jconv to imigr and support an electric current. The result for the anion exchange membrane is shown in Fig. 7.23.

127

Concentration Polarization

3

-vx(10-3cm/s)

2

3.99(LCD

)

5

3.7

1.81(LCD)

1

2.27A/dm2 1.19

0

Figure 7.25

0

1

2

3 x(10−2cm)

4

5

Solution velocity in a boundary layer (anion exchange membrane).

vy,out y l

−vx,0

−vx

−vx+dx

z b 0

x 0

x

vy,in

v +dx

Figure 7.26 Convection of a solution in a boundary layer formed on an ion exchange membrane.

128

Ion Exchange Membranes: Fundamentals and Applications

12

8

0.1 M NaCl 1.13A/dm2 2.10 A/dm2 2.93 A/dm2(LCD) 4.30 A/dm2 (overLCD)

6

0.05 M NaCl 2.28 A/dm2(LCD)

-dvx /dx = (vy,out - vy,in) / l (s-1)

10

4

2

0

-2

0

1

2

3 x (10-2cm)

4

5

6

Figure 7.27 Solution velocity gradient in a boundary layer (cation exchange membrane).

7.8.4 (1)

Solution Velocity in a Boundary Layer x-component of convection velocity vx

The x-component of solution velocity vx is introduced from the equation of concentration gradient Eq. (7.36) as follows: 1 dC þ bi (7.52) vx ¼ aC dx The NaCl concentration distribution observed by the Schlieren-diagonal method (Figs. 7.8 and 7.9), a and b are substituted into Eq. (7.52) and nx is calculated (Figs. 7.24 and 7.25), showing vx on the cation exchange membrane to be larger than that on the anion exchange membrane. vx at x ¼ 0, vx,x ¼ 0 corresponds to the sum of electro-osmosis velosmo and concentration-osmosis vconosmo passing through an ion exchange membrane: vx;x¼0 ¼ velosmo þ vconosmo

(7.53)

129

Concentration Polarization

6

4

0.1 M NaCl 1.19 A/dm2 2.27 A/dm2 3.75 A/dm2 3.99 A/dm2(LCD)

3

0.05 M NaCl 2.28 A/dm2(LCD)

-dvx /dx = (vy,out-vy,in ) / l (s-1)

5

2

1

0

-1

0

1

2

3

4

5

6

x (10-2 cm)

Figure 7.28 Solution velocity gradient in a boundary layer (anion exchange membrane).

y-component of convection velocity vy

(2)

In Fig. 7.26, the convection velocity on y-axis in the range of x ¼ x to x+dx on x-axis is assumed to be vy,in at the bottom and vy,out at the top. Taking account of the material balance, we have blvxþdx þ bvy;in dx ¼ blvx þ bvy;out dx

(7.54)

from Eq. (7.54) dvx vy;out vy;in ¼ (7.55) dx l vx in Figs. 7.24 and 7.25 are differentiated and substituted into Eq. (7.55) to obtain (vy,out – vy,in)/l, which is shown in Fig. 7.27 (cation exchange membrane) and Fig. 7.28 (anion exchange membrane). Inspecting these ﬁgures, –dvx/dx ¼ (vy,out – vy,in)/l ¼ 0, that is vy,out ¼ vy,in is realized in almost whole region in the boundary layer. On the other hand, vy,out>vy,in (–dVx/dx>0) is seen near x ¼ 0 particularly at high current density. This phenomenon is attributed to that vx,0 is so little than vx that the velocity

130

Ion Exchange Membranes: Fundamentals and Applications

v

vy,out vx

vy,in

v Ion-exchange membrane

vx Boundary layer

Bulk

Figure 7.29 Convection velocity near an ion exchange membrane in a boundary layer (illustration).

excepting vx,0 is rejected to pass through the membrane and converted to vy,out. Convection velocity in this situation is illustrated in Fig. 7.29. When limiting current density is applied, vy,outovy,in (–dVx/dxo0) is recognized as shown in Figs. 7.27 and 7.28 at the point distant from the membrane to some extent. Convection velocity in this situation is illustrated in Fig. 7.30.

7.8.5

Fluctuation Phenomena in a Boundary Layer When the limiting current density is applied across the cation exchange membrane placed in a 0.05 M NaCl solution, the NaCl concentration ﬂuctuates on the membrane surface (Fig. 7.8). When the overlimiting current is applied across the cation exchange membrane placed in a 5 mM NaCl solution, the voltage ﬂuctuates (Fig. 7.12). These phenomena are supposedly due to the events represented in Fig. 7.31 consisting of the following steps: (1) (2)

Concentration velocity v near the membrane indicated in Fig. 7.30 is decreased. This event generates the optical noise (ﬂuctuation). Ionic ﬂux by the convection Jconv ¼ Cv is decreased.

131

Concentration Polarization

v

vy,out vx

C C C0 v vy,in C0

x vx

Cation exchange membrane Boundary layer

Bulk

Figure 7.30 Convection velocity and NaCl concentration ﬂuctuation in a boundary layer formed on a cation exchange membrane at limiting current density (illustration).

(3)

(4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

NaCl concentration near the membrane C is decreased. At the same time, dC/dx is increased. These events generate the concentration noise and voltage noise. Jconv is decreased further. C is decreased further. Jmigr is decreased and Jdiff ( ¼ JNa,diff+JCl,diff) is increased. imigr is decreased and idiff ( ¼ iNa,diff+iCl,diff) is decreased. Accordingly, i ( ¼ imigr+idiff) is decreased.1 v is increased for maintaining the material balance and electric current balance. This event generates the optical noise. Jconv is increased. C is increased and dC/dx is decreased. These events generate the concentration ﬂuctuation and voltage ﬂuctuation. Jconv is increased further. C is increased further. i is increased. v is decreased for maintaining the material balance and electric current balance.

132

Ion Exchange Membranes: Fundamentals and Applications

v decrease i increase

Jconv =Cv decrease Optical noise C decrease

Jdiff, Jmigr increase Concentration noise Voltage noise C increase

Jdiff, Jmigr decrease Optical noise Jconv=Cv increase

i decrease v increase

Figure 7.31 Mechanism of NaCl concentration ﬂuctuation in a boundary layer formed on a cation exchange membrane at limiting current density.

The process mentioned above is repeated 10 times per second on a cation exchange membrane placed in a NaCl solution, and do not get to steady state (cf. Section 7.4). Experimental and theoretical studies on ﬂuctuation presented so far (Lifson et al., 1978; Li et al., 1983; Krol et al., 1999; Tanaka, 2004) are understandable based on Fig. 7.31. 7.8.6

Potential Gradient in a Boundary Layer Potential gradient dc/dx is divided into the terms of Ohmic potential (dc/ dx)ohm and diffusion potential (dc/dx)diff: dc dc dc ¼ þ (7.56) dx dx ohm dx diff dc 1 (7.57) ¼ dx ohm k dc RT 1 dC ¼ ð2tNa 1Þ (7.58) dx diff F C dx

133

Concentration Polarization

35

(d/dx)diff , (d/dx)ohm(V/cm)

30

25

20

15

10

5

0 0.00

0.01

0.02

0.03 x (cm)

Cation exchange membrane 0.1 M NaCl 1.13 A/dm2; 2.10 A/dm2 ; 2

A/dm (over LCD),

0.04

0.05

2.93 A/dm2 (LCD);

4.30

open: ohmic gradient; filled: diffusion potential gradient.

Figure 7.32 Ohmic potential gradient and diffusion potential gradient in a boundary layer (cation exchange membrane).

where k is the speciﬁc electric resistance of a NaCl solution in a boundary layer. Equation (7.58) is the Henderson equation. In this electrodialysis system, the effect of the Donnan potential term is negligible. Substituting the Schlierendiagonal observation (Figs. 7.8 and 7.9) into Eqs. (7.56)–(7.58), (dc/dx)ohm and (dc/dx)diff are computed and shown in Fig. 7.32 (cation exchange membrane) and Fig. 7.33 (anion exchange membrane). (dc/dx)ohm on the cation exchange membrane is positive, and that on the anion exchange membrane is negative. (dc/dx)diff is positive both on the cation exchange membrane and on the anion exchange membrane. Integrating dc/dx vs. x plots, current density i vs. voltage drop DV in the boundary layer is calculated and shown in Fig. 7.34, in which the overlimiting current phenomenon generated in Region III in Fig. 7.1 is found. Note here that the overlimiting current is generated more easily (at lower voltage) on the cation exchange membrane than on the anion exchange membrane.

134

Ion Exchange Membranes: Fundamentals and Applications

10

(d/dx)ohm , (d/dx)diff (V/cm)

0

-10

-20

-30

-40

-50 0.00

0.01

0.02

0.03

0.04

0.05

x (cm) Anion exchange membrane 0.1 M NaCl 1.19 A/dm2; 2.27 A/dm2; (LCD),

3.75 A/dm2;

3.99 A/dm2

open: ohmic potential gradient; filled: diffusion potential gradient.

Figure 7.33 Ohmic potential gradient and diffusion potential gradient in a boundary layer (anion exchange membrane).

7.9. CONCENTRATION POLARIZATION ON A CONCENTRATING SURFACE OF AN ION EXCHANGE MEMBRANE Concentration polarization is usually discussed on the desalting surface of an ion exchange membrane as described in the preceding sections. In this section, however, we treat the phenomenon on the concentrating surface of the membrane. In order to observe the concentration distribution in a boundary layer formed on the concentrating surface of an ion exchange membrane, a threecompartment optical glass cell was set up with a central concentrating cell, desalting (electrode) cells put on both outsides of the central cell and ion exchange membranes (Aciplex CK-2/CA-2) (Takemoto, 1969). Effective membrane area was adjusted to 1.5 cm2 (1.5 cm height, 1 cm width). Distance between the membranes in the central concentrating cell was maintained at 2.6–2.8 mm. At 25 1C, 0.5 M NaCl solutions were put in the desalting cells and concentrating cell, and an electric current density of 2 A dm–2 was applied through Ag–AgCl electrodes. The changes of NaCl concentration distribution in the boundary

135

Concentration Polarization

6

5

i (A/dm2)

4

3 LCD 2

1

0

0.0

0.1

0.2

0.3 0.4 V (V)

: Cation exchange membrane 0.1 M NaCl

Figure 7.34

0.5

0.6

0.7

: Anion exchange membrane

Current density vs. voltage drop in a boundary layer.

layer formed on the concentrating surface of the membrane were observed by the Schlieren-diagonal method (cf. Section 7.4). The concentration changes in the boundary layer observed in this experiment are understandable on the basis of Fig. 7.35. In this experiment, ionic concentration in the cation exchange membrane is assumed to be larger than that in the anion exchange membrane. NaCl concentration in the concentrating cell is 0.5 M before electric current passing as shown by 0 in the ﬁgure. Applying an electric current, the concentrated counter-ions in the membrane ﬂows out into the concentrating cell and ﬂows down with concentrated co-ions along the membrane surface due to the electro-gravitational movement (Frilette, 1957). Successively, the concentration distribution is changed as 0-1-2-3, and ﬁnally attains to 4 in a steady state. Fig. 7.36 shows the concentration proﬁle corresponding to 4 in the steady state observed by Takemoto (1969), indicating that the NaCl concentration on the cation exchange membrane becomes larger than that on the anion exchange membrane. From the experiment described above, the mechanism of the concentration polarization occurring on the concentrating surface of the membrane is assumed to be not the same in principle to that occurring on the desalting surface of the membrane.

136

Ion Exchange Membranes: Fundamentals and Applications

C" 0K C" 0A 4 C"

3

2

electro-gravitation 1 0

Cation exchange membrane

Concentrating cell

Anion exchange membrane

0: before current passing, 1: just after current passing, 2,3: at a transitional state, 4: at a steady state

C (M)

Figure 7.35 Electrolyte concentration changes in boundary layers formed on the concentrating surface of ion exchange membranes.

x (mm)

Figure 7.36 NaCl concentration distribution on a concentrating surface of a cation and an anion exchange membrane in a steady state due to concentration polarization (Takemoto, 1969).

Concentration Polarization

137

NOTE 1. On the cation exchange membrane i (o0) ¼ idiff (>0)+imigr (o0) ¼ F(JNa,diff(o0) – JCl,diff(o0))+F(JNa,migr (o0) – JCl,migr (>0)) holds, and we have idiff > 0 because of 9JNa,diff9o9JCl,diff9. So,9i9is decreased owing to the increase of 9Jdiff9. On the other hand, on an anion exchange membrane, i (>0) ¼ idiff (>0)+imigr (>0) ¼ F(JNa,diff (o0) – JCl,diff (o0))+F(JNa,migr (>0) – JCl,migr (o0)) holds, and we have idiff > 0 because of 9JCl,diff 9>9JNa,diff9. So 9i9 is increased owing to the increase of 9Jdiff9. Accordingly, on the anion exchange membrane, the process represented in Fig. 7.31 is interrupted at step (4) and (5) and is never possible to continue (cf. Eqs. (7.48)–(7.50), Fig. (7.16) and Figs. (7.20)–(7.23)).

REFERENCES Bird, B. B., Stewart, W. E., Lightfoot, E. N., 1960, Transport Phenomena, Wiley, New York, London. Cooke, B. A., 1961a, Concentration polarization in electrodialysis–I, The electrometric measurement of interfacial concentration, Electrochim. Acta, 3, 307–317. Cooke, B. A., 1961b, Concentration polarization in electrodialysis–II, Systems with natural convection, Electrochim. Acta, 4, 179–193. Cowan, D. A., Brown, J. H., 1959, Effect of turbulence on limiting current in electrodialysics cells, Ind. Eng. Chem., 51(12), 1445–1448. Forgacs, C., 1962, Theoretical and practical aspects of scale control in electrodialysics desalination apparatus, Dechema Monographien, Band 47, NR 805–834. Frilette, V. J., 1957, Electrogravitational transport at synthetic ion exchange membrane surface, J. Phys. Chem., 61, 168–174. Gavish, B., Lifson, S., 1979, Membrane polarization at high current densities, J. Chem. Soc., Faraday Trans. I, 75, 463–472. Ibl, N., Muller, R. H., 1958, Studies of natural convection at vertical electrodes, J. Electrochem. Soc., 105(6), 346–353. Kooistra, W., 1967, Characterization of ion exchange membranes by polarization curves, Desalination, 2, 139–147. Krol, J. J., Wessling, M., Strathmann, H., 1999, Chronopotentiometry and overlimiting ion transport through monomer ion exchange membranes, J. Membr. Sci., 162, 155–164. Li, Q., Fang, Y., Green, M. E., 1983, Turbulent light scattering ﬂuctuation spectra near a cation electrodialysics membrane, J. Colloid Interface Sci., 91(2), 412–417. Lifson, S., Gavish, B., Reich, S., 1978, Flicker noise of ion-selective membranes and turbulent convection in the depleted layer, Biophys. Struct. Mech., 4, 53–65. Mazanares, J. A., Kontturi, K., Mafe, S., Aguilella, V. M., Pellicer, J., 1991, Polarization effects at the cation-exchange membrane–solution interface, Acta Chem. Scand., 45, 115–121. Onoue, Y., 1962, Polarization on the ion exchange membrane, J. Electrochem. Jpn., 30, 415–417. Peer, A. M., 1956, Discus. Faraday Sci., 21, 124 (communication in the membrane phenomena special issue). Rosenberg, N. W., Tirrell, C. E., 1957, Limiting current in membrane cell, Ind. Eng. Chem., 49(4), 780–784.

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Rubinstein, I., 1981, Mechanism for an electrodiffusional instability in concentration polarization, J. Chem. Soc., Faraday Trans. II, 77, 1595–1609. Rubinstein, I., Shtilman, L., 1979, Voltage against current curves of cation-exchange membranes, J. Chem. Soc., Faraday Trans. II, 75, 231–246. Shaposhnik, V. A., Vasil’eva, V. I., Reshetnikova, E. V., 2000, Concentration polarization of ion-exchange membranes in electrodialysics: An interferometric study, Russ. J. Electrochem., 36(7), 773–777. Sistat, P., Pourcelly, G., 1997, Chronopotentiometric response of an ion-exchange membrane in the underlimiting current-range. Transport phenomena within the diffusion layers, J. Membr. Sci., 123, 121–131. Spiegler, K. S., 1971, Polarization at ion exchange membrane–solution interface, Desalination, 9, 367–385. Takemoto, N., 1969, Concentration distribution in concentrating interface of membranes, Bull. Soc. Sea Water Sci. Jpn., 23, 54–59. Takemoto, N., 1972, The concentration distribution in the interfacial layer at desalting side in ion exchange membrane electrodialysics, J. Chem. Soc. Jpn., 1972, 2053–2058. Tanaka, Y., 2004, Concentration polarization in ion-exchange membrane electrodialysis. The events arising in an unforced ﬂowing solution in a desalting cell, J. Membr. Sci., 244, 1–16. Tobias, C. W., Eisenberg, M., Wilke, C. R., 1952, Diffusion and convection in electrolysis–A theoretical review, J. Electrochem. Soc., 99(12), 360C–365C. Wagner, G., 1949, The role of natural convection in electrolytic processes, Trans. Electrochem. Soc., 95, 161–173.

Chapter 8

Water Dissociation 8.1.

CURRENT–pH RELATIONSHIP

At an over limiting current, a sufﬁciently depleted layer is formed on the desalting surface of an ion exchange membrane, an electric current is carried by H+ and OH– ions (derived from the water dissociation) and the transport number of an ion exchange membrane is lowered. The water dissociation was ﬁrst observed by Kressman and Tye (1956) and Frilette (1956). Since then, this phenomenon is being widely investigated. Investigation based on the current–pH relationship was proceeded by Rosenberg and Tirrel (1957) using seven-cell assemblies indicated in Fig. 8.1. Cell 1 was bounded by an anode and an anion exchange membrane; cell 7 by a cathode and a cation exchange membrane; all other cells were bounded by membranes as shown. Water dissociation was studied in the central cell (cell 4) which was fed with 0.005–0.05 M NaCl solution. Other cells were fed with a salt

+

NaCl

Cl

1 2

Anode Anion memb.

Na Cl

Cation memb.

3 Anion memb. NaCl

4

Na Cl

5 6

Cation memb. Anion memb.

Na

Cation memb. 7 Cathode

– Figure 8.1

Cell assembly for studying polarization (Rosenberg and Tirrel, 1957).

DOI: 10.1016/S0927-5193(07)12008-8

140

Ion Exchange Membranes: Fundamentals and Applications

10 Cell 3

9 8 7

Cell 5

pH

6 5 4 Cell 4 3 Anion l lim 0.6

0.8

1.0

Cation l lim 1.2

1.4

Current (A)

Figure 8.2

Electric current–solution pH relationship (Rosenberg and Tirrel, 1957).

3–10 times more concentrated. At a series of increasing applied voltages, current, inﬂuent and efﬂuent concentrations in cell 4, and efﬂuent pH values in cells 3, 4 and 5 were determined. The cation exchange membranes were sulfonated divinylbenzene polystyrene types, and anion exchange membranes were quaternarized divinyl benzene pyridine types. A typical history of pH in cells 3, 4 and 5 is given in Fig. 8.2. As current increases, the interface between the anion membrane and a cell 4 solution becomes depleted sodium chloride. Transfer of hydroxyl ions from cell 4 to cell 3 causes pH of the efﬂuent to decrease in cell 4 and increase in cell 3. At this current, there is no indication of cation exchange membrane polarization. As the current is increased, however, the cation exchange membrane interface becomes depleted, hydrogen ion transfer from cell 4 to cell 5 occurs and the pH in cell 5 falls. However, the transfer of hydroxyl ions through the anion exchange membrane interface increases at a faster absolute rate, and the pH in cell 4 continues to fall. The mobility of Na+ ions is less than that of Cl– ions in a NaCl solution. Because of this fact, concentration polarization is generally recognized to occur more easily on the cation exchange membrane than that on the anion exchange membrane. Because of this reason, it is expected that the water dissociation occurs more easily on the cation exchange membrane than that on the anion exchange membrane. However, Fig. 8.2 shows that the water dissociation occurs more easily on the anion exchange membrane than that on the cation exchange

141

Water Dissociation

membrane. This phenomenon has been recognized in many investigations showing that the water dissociation is strongly suppressed on the cation exchange membrane. Accordingly, the pH in cell 5 might not decrease due to the water dissociation of the cation exchange membrane as described in this study, but would decrease due to the water dissociation of the anion membrane accompanied by hydrogen ion transfer from cell 4 to cell 5. Whether it is the truth or not, the mechanism of water dissociation is not yet clear. Many investigations introduced in this chapter will be concerned with this phenomenon. Water dissociation reaction is known to be related with the auto-catalytic nature of the functional groups in the membrane as will be described in the succeeding section in this chapter, although its mechanism is not perfectly clear at present. The difference between water dissociation phenomenon of a cation exchange membrane and that of an anion exchange membrane recognized by Rosenberg and Tirrel (1957) is closely related with the catalytic nature. 8.2.

DIFFUSIONAL MODEL

An ion exchange membrane is assumed to be placed in a strong 1, 1 valent electrolyte solution. When an over limiting current is passed across the membrane, unstirred boundary layer is formed on the desalting surface of the membrane and the following water dissociation is generated in the boundary layer: k1

H2 O 3 Hþ þ OH

(8.1)

k2

where k1 and k2 are the forward and reverse equilibrium constants, respectively. Rubinstein (1977) discussed the steady ion transfer based on the diffusional model by the following mass conservation with the electroneutrality using subscripts 1, 2, 3, 4 to represent, respectively, salt cations, salt anions, H+ ions and OH– ions. Mass conservation: dJ i ¼0 dx dJ i ¼ RW dx

or J i ¼ constant

ði ¼ 1; 2Þ

ði ¼ 3; 4Þ

(8.2) (8.3)

where RW is the generation rate of H+ and OH– ions in Eq. (8.1). The ionic ﬂuxes Ji are given by the Nernst–Planck equations: J i ¼ Di

dC i dF Di C i dx dx

ði ¼ 1; 3Þ

(8.4)

142

Ion Exchange Membranes: Fundamentals and Applications

dC i dF þ Di C i ði ¼ 2; 4Þ dx dx where F ¼ jzjF c=RT is the dimensionless electric potential. J i ¼ Di

(8.5)

Electroneutrality: C1 þ C3 ¼ C2 þ C4

(8.6)

Equations (8.2)–(8.5) were solved by supplementing the boundary conditions in which nonpenetrability for co-ions of an ideal ion exchange membrane is provided. The computation introduced the current–voltage relationship including the over limiting current regime, and the proﬁles of electric potential with the proﬁles of H+ and OH– ion concentrations in the unstirred layer. The conclusion introduced in this research does not explain the difference between water dissociation phenomenon of a cation exchange membrane and that of an anion exchange membrane. This is probably because the autocatalytic nature is not taken into account in RW (Eq. (8.3)).

8.3.

REPULSION ZONE

Patel et al. (1977) developed the theoretical model incorporated with ‘‘repulsion zones’’ in the solutions adjacent to the membrane surface. Here, the membrane is assumed to be ideally perm-selective, allowing the passage of only cations. In the repulsion zones, it is assumed that the repulsive forces exerted by the ﬁxed membrane charges upon co-ions dominate the situation. Outside the repulsion zones, the rest of the solution boundary layers Repulsion zone

Anode

Figure 8.3

Diluted boundary layer

Cation exchange membrane

Concentrated boundary layer

Cathode

Formation of repulsion zones on the membrane surfaces (Patel et al., 1977).

Water Dissociation

143

are present, and outside the boundary layers is the bulk solution phase (Fig. 8.3). The mass conservation Eqs. (8.2)–(8.5) are applied to the steady state electrodialysis system. The relationship between the space charge distribution and the electric potential gradient in the repulsion zones is given by the following Poisson’s equation: d 2c 4pRT ðC 1 þ C 3 C 2 C 4 Þ ¼ (8.7) 2 dx zF where e is the dielectric constant. However, away from the membrane surface large changes in the electric potential are not expected, so that the assumption of electroneutrality Eq. (8.6) is satisﬁed instead of Eq. (8.7). The generation rate of H+ and OH– ions is presented by Eq. (8.1). Using the above-mentioned equations and the Wien effect theory (cf. Section 8.5), the thickness of the repulsion zone rC, in which the recombination rate of H+ and OH– ions is strongly affected by the local electric ﬁeld, was computed. The results show that for cation exchange membranes, very high concentrations of H+ ions are built up at the membrane surface during polarization. The decrease in the recombination rate of H+ and OH– ions near the membrane is responsible for this. The feature of this research is that it takes into account of the Wien effect. However, the Wien effect theory does not include the concept of the autocatalytic effect, so the conclusion does not explain the difference between the water dissociation phenomenon of the cation exchange membrane and that of the anion exchange membrane. 8.4.

MEMBRANE SURFACE POTENTIAL

Ion exchange groups in an ion exchange membrane are electrically neutralized by counter-ions and the electroneutrality is satisﬁed in the membrane. At an over limiting current, however, the counter-ions combine with the ion exchange groups on the desalting surface of the membrane phase and dissolve into the solution phase. In the cation (anion) exchange membrane, the membrane surface is charged negatively (positively), the solution being adjacent to the membrane is charged positively (negatively) and the membrane surface potential is formed. The membrane surface potential is equivalent to the space charge (Rubinstein and Shtilman, 1979; Rubinstein, 1981) (cf. Section 7.7.3) and the repulsion zone (Patel et al., 1977) (cf. Section 8.3), and supposedly supplies counter-ions from the solution phase toward the membrane phase at an over limiting current. The membrane surface potential was measured as follows (Tanaka and Seno¯ , 1983a). The ionic types of ion exchange membranes, CMV, ASV and Aciplex K102, A-102, were adjusted suitably by immersing the membranes into 1 eq dm3

144

Ion Exchange Membranes: Fundamentals and Applications

Table 8.1

Ionic types and electrolyte solutions

Cation Exchange Membrane

Anion Exchange Membrane

Ionic Type

Electrolyte Solution

Ionic Type

Electrolyte Solution

H+ Na+ K+ NH4+ Mg2+ Ca2+ Ba2+ Ni2+ Co2+

HCl NaCl KCl NH4Cl MgCl2 CaCl2 BaCl2 NiCl2 CoCl2

OH– Cl– Br– I– NO–3 HCO–3 SO2– 4 SO2– 3 S2O2– 3

NaOH NaCl NaBr NaI NaNO3 NaHCO3 Na2SO4 Na2SO3 Na2S2O3

Source: Tanaka and Seno¯ (1983a).

electrolyte solution shown in Table 8.1. The membrane was incorporated with a set up illustrated in Fig. 8.4 with AgCl electrode E1 ﬁxed on the membrane surface. The potential of E1 is equivalent to that at p in the ﬁgure. Another electrode E2 (AgCl or Pt) was placed in a cell keeping the distance from the membrane at 1 mm. Supplying water or a 1 meq dm3 solution of the electrolyte in Table 8.1 into both cells in Fig. 8.4, the potential at p on the basis of E2 was measured while mixing the solution intermittently. From chronopotentiometric changes of the potential at p, V was detected as shown in Fig. 8.5. After that, the set up was reassembled removing the membrane, and V0 was measured without mixing. The membrane surface potential cm evaluated by cm ¼ V–V0 is listed in Table 8.2, showing that: (a) (b)

8.5.

The membrane surface potential is more increased when the membrane is placed in water than in electrolyte solutions. The membrane surface potential on the cation exchange membrane is larger than that on the anion exchange membrane.

WIEN EFFECT

The Wien effect is the phenomenon generated in an electrolyte solution under very strong electric potential ﬁelds of 106–107 V m1. In this circumstance, the ionic mobility is increased and Ohm’s law has only a limited range of validity (Wien, 1928). In the case of strong electrolytes, this effect has been successfully interpreted as a destruction of the ‘‘ionic atmosphere’’. The initial effect is proportional to the square of the ﬁeld intensity, and for very strong ﬁelds the equivalent conductance approaches a limiting value, which is not greater than the limiting equivalent conductance for small concentration.

145

Water Dissociation

E1 Potentiometer M p (b)

E2 1 mm

Z

E1 3 mm

E1

G

G M

E2

3 mm

i

S

20 mm

E2 Z-Z′ Z′ (a)

(c)

Figure 8.4 Experimental apparatus for measuring membrane surface potential (Tanaka and Seno¯ , 1983a).

Weak electrolytes, on the other hand, show much enhanced deviation from Ohm’s law; the conductance increases linearly over a considerable range of the ﬁeld intensity, and the limit of the increase, if any, corresponds to complete dissociation of the total amount of electrolyte present (Wien, 1931). It was considered an open question whether the prevailing theory for the electrostatic interaction of the ions could account for this increased dissociation of weak electrolytes. Onsager (1934) presented a result which was computed on the basis of the interionic attraction, and discussed its signiﬁcance based on theory of the Wien effect. The agreement with the available measurements of conductance in strong ﬁelds was considered satisfactory. In addition, the theory allowed some predictions concerning the rates of dissociation and recombination of the ions, and the considerations involved in this question were extended with equal ease to the case of high ﬁeld intensities. The computed relative increase of the dissociation

146

Ion Exchange Membranes: Fundamentals and Applications

Potential (mV)

∆V

V

V0 Time (min)

Figure 8.5 Chronopotentiometric change of membrane surface potential (Tanaka and Seno¯ , 1983a).

rate constant is given by the formula: k1 b2 b3 b4 b5 b6 þ þ þ ¼1þbþ þ þ k0 3 18 180 2700 56; 700

(8.8)

with b ¼ 0:09636

E r T 2

(8.9)

Here k1 and k0 are the forward equilibrium constant in Eq. (8.1) under the inﬂuence of an electric ﬁeld and that without an electric ﬁeld, respectively. E is the electric ﬁeld density (V m1), er the relative dielectric constant and T the absolute temperature. In the case of high ﬁeld intensities (E4108 V m1), Eq. (8.10) is introduced from Eq. (8.8) being used to calculate the effect of the electric ﬁeld on the dissociation rate constant. 1=2 1=2 k1 2 ¼ ð8bÞ3=4 eð8bÞ (8.10) k0 p

147

Water Dissociation

Table 8.2

Membrane surface potential (mV)

Concentration (meq dm3)

Counter–ion H+ Na+ K+ NH+ 4 Mg2+ 2+ Ca Ba2+ Ni2+ Co2+

Selemion CMV

Aciplex K-102

0

1

0

1

241.0 227.3 219.6 207.1 109.4 113.0 100.6 103.5 119.2

52.7 69.8 11.6 65.2 12.2 29.7 26.8 15.7 17.7

244.8 241.0 216.7 220.2 134.2 114.2 109.6 138.0 131.8

44.8 88.8 51.9 46.4 8.9 4.7 4.0 4.9 10.1

Selemion ASV 0 Counterion OH– Cl– Br– I– NO–3 HCO–3 SO2– 4 SO2– 3 S2O2– 3

+48.6 +11.7 +6.2 +9.6 +89.9 +55.4 +22.2 +32.7 +30.3

Aciplex A-102 1

0

1

+8.8 0.6 +0.6 +5.1 +3.7 +6.0 0 +1.7 +2.4

+100.4 +10.5 +22.1 +16.5 +149.3 +102.0 +47.1 +81.4 +77.0

+0.3 +0.1 +1.5 +1.1 +34.8 0 +16.3 +12.3 +63.2

Source: Tanaka and Seno¯ (1983a).

The discussion mentioned above is not concerned with the auto-catalytic water dissociation reaction but it is applicable to analysis of the mechanism of the water dissociation generated in the boundary layer adjacent to an ion exchange membrane. 8.6.

PROTONATION AND DEPROTONATION REACTIONS

Simons (1984, 1985) suggested that with anion exchange membranes the water dissociation is caused by the following catalytic reversible protonation and deprotonation reactions of weakly basic groups: k1

B þ H2 O 3 BHþ þ OH k1

k2

BHþ þ H2 O 3 B þ H3 Oþ k2

where B is a neutral base such as tertiary or secondary amine groups.

(8.11) (8.12)

148

Ion Exchange Membranes: Fundamentals and Applications

It has been known that when the applied electric ﬁeld is high enough, Ohm’s law is no longer valid and the conductance of electrolytes increases rapidly with the ﬁeld (Onsager, 1934). For weak electrolytes such as H2O, this phenomenon is known as ‘‘the second Wien effect’’, and the mechanism of catalytic water dissociation reaction described above is presented in two steps as follows (Simons, 1979): b

a

c

B þ H2 O 3 BHþ OH 3 BHþ þ OH

(8.13)

BHþ þ H2 O3B H3 Oþ 3B þ H3 Oþ

(8.14)

þ

þ

where BH OH and B H3 O are encounter pairs in the same solvent cage. a–b is a chemical transformation process and b–c a separation and encounter process. Applying the steady state approximation to the ! encounter pair, the expressions for the overall forward reaction rate constant k and the overall reverse reaction rate constant k are ! kab kbc ; k ¼ kba þ kbc

k ¼

kcb kba kba þ kbc

(8.15)

where kab and kba are, respectively, the forward and reverse reaction rate constants for the chemical transformations. kbc and kcb are, respectively, the forward and reverse rate constants for the separation and encounter processes. The chemical transformation is so fast that the diffusion-controlled process (separation and encounter process) is the rate-determining step, so that we have kba kbc (kba41012 s–1 while kbc is usually between 1010 and 1011 s–1). Thus, the overall reaction rate constants deﬁned by Eq. (8.15) are simpliﬁed as: ! kab kbc ; k ¼ kba

k ¼ kcb

(8.16)

Onsager suggested that only kbc increases with the electric ﬁeld, whereas kab, kba and recombination step kcb are independent of the ﬁeld (Onsager, ! 1934; Eigen and Maeyer, 1959). We understand from this suggestion that k increases with the electric ﬁeld, but k is not affected by the electric ﬁeld. We shall consider the following two ways by which the water dissociation reaction rate might be increased by the strong electric ﬁeld (Simons, 1979): (1)

(2)

In reaction (8.11), kbc depends on the strength of an external ﬁeld. In reaction (8.12), the site in B, for recombination with H3O+, is a lone pair, so that the charge product is effectively negative when the proton is sufﬁciently close to the reaction site. So, kbc would increase with the electric ﬁeld intensity for reaction (8.12) also. Actual proton transfer is very fast due to the Grotthuss protonic conduction (Barrow, 1973) as illustrated in Fig. 8.6. The rate-determining step seems to be the necessary reorientation of water molecules between

149

Water Dissociation

BH+

B

B

H+

H

H

H

O H

O H O

H

H

H

H

O H

O H O

H O

H

H

H

H

O

H O

H O

O

H

H

H H

O

H

H

H+

E

Figure 8.6 Deprotonation of amino group and proton conduction along a chain of oriented water molecules (Simons, 1979).

successive transfers (structural diffusion). When reaction (8.12) occurs, it is conceivable that there is a bridge of water molecules in the reaction layer, already favorably oriented for proton ! transfer by the strong electric ﬁeld, leading to the increase of kbc ( k ). Simons also suggested that quaternary ammonium groups do not bring about the reaction in Eqs. (8.11) and (8.12). However, the conversion of the quaternary amino groups into the tertiary form creates the reaction of Eqs. (8.11) and (8.12), and accelerates the water dissociation. Water dissociation at cation exchange membranes is generated when the membrane contains weakly acidic groups such as carboxylic acid according to the following catalytic reaction: k3

A þ H2 O 3 AH þ OH k3

k4

AH þ H2 O 3 A þ H3 Oþ k4

(8.17) (8.18)

where AH is a neutral acid group such as carboxylic acid. 8.7.

HYDROLYSIS OF MAGNESIUM IONS

Oda and Yawataya (1968) investigated water dissociation for Selemion CSG and CMG membranes in solutions of NaCl and MgCl2. Electric current–pH relationship in a concentrating cell is presented in Fig. 8.7 showing that a pH shift reaches as far as 1.3 in an MgCl2 solution; however, it was less than 4 in a NaCl solution. The pH changes in solutions containing Mg2+ ions are accompanied by a deposition of Mg(OH)2 near or on the desalting surface of the cation exchange membrane; the greater the pH shift, the more the deposit. The transport number for H+ ions through the membranes which are generated by the water dissociation was determined to be in the range of 10–1 to 100 in the MgCl2 solution.

150

Ion Exchange Membranes: Fundamentals and Applications

7 CMSG CMG-A, CMP-B CMS-A

6 5

CMG-A

3

CMP-B

pH

4

2 CMSG 1 0

CSG-A

0

10

20 30 Current density (mA/cm2)

40

50

Figure 8.7 pH change phenomena at cation exchange membranes in solutions of NaCl and MgCl2 (Oda and Yawataya, 1968).

This phenomenon is in contrast to the case in NaCl solutions, where no signiﬁcant pH change is recognized. They suggested the mechanism of water dissociation on the cation exchange membrane placed in the MgCl2 solution being caused by the following tendency toward catalytic hydrolysis of Mg2+ ions similar to the protonation and deprotonation reactions exhibited in Eqs. (8.11) and (8.12): k1

Mg2þ þ 4H2 O 3 MgðOHÞ2 þ 2H3 Oþ k1

k2

MgðOHÞ2 3 Mg2þ þ 2OH k2

(8.19) (8.20)

This fact indicates that Mg2+ ions become an acceptor of OH– ions generated from the water dissociation, accompanied by the successive water dissociation on the membrane surface. The pH shifts intensiﬁed in solutions of CaCl2 and NH4Cl are attributed to the hydrolysis character of the Ca2+ and NH+ 4 ions, though it is much weaker than that of the Mg2+ ions. Other heavy metal ions, such as Fe2+ and Cu2+, behave in a similar way in an electrodialysis process. 8.8. 8.8.1

EXPERIMENTAL RESEARCH ON THE WATER DISSOCIATION

Current Density–pH Relationship The apparatus in Fig. 8.8 incorporated with ion exchange membranes (Selemion CSG/ASG, Aciplex CK-2/CA-2, Neocepta CL-2.5T/AVS 4T) was

151

Water Dissociation

−

+ Vc

De : Desalting cell Con : Concentrating cell C : Cation exchange membrane A : Anion exchange membrane P : Partition (agar) + , − : Ag, AgCl electrode , : Potentiometer G : Gasket

G P

De

C Con P (a) −

+ VA

G P Con A De (b)

Figure 8.8

P

Cell arrangement (Tanaka, 1974).

assembled and water dissociation was observed from current–pH curves in Fig. 8.9, showing that the water dissociation is strongly suppressed on the cation exchange membrane (Tanaka, 1974). Accordingly, water dissociation in a NaCl solution never prevents the deﬁcit of ions at the cation exchange membrane/ solution interface and never contributes to generate H+ and OH– ions at the over limiting current on the surface of the cation exchange membrane. On the anion exchange membranes, however, the strong water dissociation is observed. This phenomenon is probably caused by the auto-catalytic water dissociation reaction of quaternary ammonium groups (Selemion AST, Neocepta AVS-4T) or quaternary pyridinium groups (Aciplex CA-3) in the anion exchange membranes in spite of the fact that the auto-catalytic mechanism is unknown. It is estimated further that the auto-catalytic water dissociation is not generated at the outside of the anion exchange membrane but it is generated at the inside of the anion exchange membrane because the reaction is caused by the functional groups (quaternary ammonium groups or quaternary pyridinium groups) existing in the anion exchange membrane. The apparatus in Fig. 8.10 was integrated with commercially available membranes (Tanaka, 1975). It consisted of a central concentrating cell (Con) partitioned into cells 1–4 by ﬁlter papers, desalting cells (De) and electrode cells bounded by the desalting cells. Effective area of the membranes was reduced to 0.367 cm2 using gaskets and 0.5 M NaCl solution was put in the electrode cells.

152

Ion Exchange Membranes: Fundamentals and Applications

8

Anion exchange memb.

(a)

Cation exchange memb.

6

4

(b)

Concentrating cell

pH

8 Desalting cell 6 Concentrating cell 4 Desalting cell (c) 8

6

4

0.1

0.2

0.3

i (A/cm2)

Figure 8.9

Electric current–solution pH relationship (Tanaka, 1974).

Further, 0.1 M NaCl solutions and 0.05 M NaCl solutions were put in the concentrating and desalting cells, respectively. After an electric current was passed through Ag–AgCl electrodes for 30 min, the solutions in cells 1–4 were taken out and pH was measured. The experiment was repeated by changing current densities.

153

Water Dissociation

F

Ar

G

A

Cathode

P

1

De

2

3 4

K

De

Con

P

Anode

Figure 8.10 Electrodialysis apparatus for measuring water dissociation (Tanaka et al., 1982). Table 8.3

pH changes of NaCl solutions in each cell (Neocepta CH-60T/AFS-4T)

Cell No., i (A cm2) 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.30 0.40

1

2

3

4

6.66 6.89 10.84 11.31 11.63 11.91 12.02 12.20 12.30 12.29 12.39 12.41

6.72 6.71 8.08 10.40 10.85 11.22 11.68 11.71 11.89 11.86 12.19 12.21

6.62 6.64 6.67 6.91 7.10 9.01 10.33 10.79 11.01 11.11 11.63 11.92

6.79 6.81 6.68 6.71 6.71 6.65 6.91 7.08 8.22 8.21 10.91 11.59

Source: Tanaka et al. (1982).

Table 8.3 shows the results obtained using Neocepta CH-60T/AFS-4T. It shows that the pH in cell 1 increases at ﬁrst due to water dissociation of the anion exchange membrane (Neocepta AFS-4T), and the pH in cells 2–4 also increases with increasing current density. The pH in cell 4 decreases slightly at ﬁrst owing to the water dissociation of the cation exchange membrane (Neocepta CH-60T). However, it begins to increase with the increase in current density due to the water dissociation of the anion exchange membrane. The accelerated water dissociation generated on the anion exchange membrane in this experiment is attributed to the auto-catalytic reaction of the quaternary ammonium groups in the anion exchange membrane.

154 Table 8.4

Ion Exchange Membranes: Fundamentals and Applications

pH changes of MgCl2 solutions in each cell (Neocepta CH-60T/AFS-4T)

Cell No., i (A cm2) 0.008 0.020 0.032 0.040 0.052 0.060 0.072 0.080 0.100 0.160 0.240

1

2

3

4

5.32 5.41 5.90 6.08 6.21 6.18 6.00 6.80 6.70 3.08 2.08

5.93 6.00 6.12 6.00 5.98 5.97 4.00 3.19 2.69 1.92 1.68

6.03 6.11 6.13 5.92 5.82 5.65 2.50 2.09 1.86 1.60 1.48

6.20 6.12 5.91 5.50 5.15 4.00 1.98 1.61 1.49 1.31 1.21

Source: Tanaka et al. (1982).

Next, in the above-mentioned experiment, 0.1 M MgCl2 solutions and 0.05 M MgCl2 solutions were put in the concentrating and desalting cells, respectively, and measured pH shifts in cells 1–4 as shown in Table 8.4. In this experiment, the pH in cell 4 declined to acidic due to the water dissociation of the cation exchange membrane (Neocepta CH-60T), and succeedingly the pH in cells 3 and 2 is also declined to acidic with increasing current density. The pH in cell 1 seems slightly declined to alkaline because of the water dissociation of the anion exchange membrane (Neocepta AFS-4T). However, it turns to acidic, being affected by the water dissociation of the cation exchange membrane. The water dissociation observed on the cation exchange membrane is brought about by the Mg(OH)2 precipitated on the desalting surface of the cation exchange membrane. This phenomenon demonstrates that the water dissociation occurs in the Mg(OH)2 layer formed at the outside of the cation exchange membrane and it is the auto-catalytic reaction observed by Oda and Yawataya (1968) in the electrodialysis for Selemion CSG and CMG cation exchange membranes placed in an MgCl2 solution (cf. Section 8.7). Finally, in the above-mentioned experiment, the ion exchange membranes were replaced by Selemion CMV/AST and 10 times as much as diluted seawater and seawater were put in the concentrating and desalting cells, respectively. The measured pH changes in cells 1–4 are presented in Table 8.5 showing that the pH in cells 1 and 2 declines to alkaline caused by water dissociation of the anion exchange membrane (Selemion AST). The pH in cell 4 is decreased at elevated current density due to the water dissociation of the cation exchange membrane (Selemion CMV). The pH in cell 3 is at ﬁrst increased owing to the water dissociation of the anion exchange membrane. However, it starts to decrease at elevated current density, being affected by the water dissociation of the cation exchange membrane. The water dissociation generated on the cation exchange membrane at elevated current density is caused by the auto-catalytic effect of

155

Water Dissociation

Table 8.5

pH changes of diluted seawater in each cell (Selemion CMV/ASV)

Cell No., i (A cm2) 0.01 0.02 0.036 0.05 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.15 0.17 0.20 0.21 0.22 0.24 0.25 0.26 0.27 0.28 0.30

1

2

3

4

7.75 8.36 8.46 9.88 10.47 10.08 10.14 10.51 10.15 10.62 12.02 12.25 12.43 12.65 12.55 12.63 12.94 12.78 12.03 12.93 12.24 12.73

7.73 7.86 7.88 7.91 8.37 9.36 8.95 9.86 9.54 9.88 9.73 9.94 10.30 10.35 9.95 10.10 10.23 9.77 11.00 11.23 10.05 10.06

7.67 7.78 7.86 7.74 7.67 7.59 7.46 7.50 7.86 8.05 7.86 7.95 8.20 8.22 9.18 9.33 9.74 1.15 9.86 9.75 1.65 1.16

7.52 7.23 7.32 7.33 7.14 7.13 6.85 6.67 7.11 7.16 6.83 7.00 6.96 6.65 7.42 7.16 7.47 0.84 6.23 7.36 1.25 0.95

Source: Tanaka (1975).

Mg(OH)2 precipitated on the cation exchange membrane and its effect is stronger than that of quaternary ammonium groups in the anion exchange membrane. 8.8.2 Inﬂuence of Ionic Electrolytes in a Solution on the Water Dissociation Reaction Fig. 8.11a and b illustrates the apparatus for measuring water dissociation of a cation exchange test membrane K* (Aciplex K-102) and an anion exchange test membrane A* (Aciplex A-102) integrated in the apparatus. The effective area of the test membranes was reduced to 0.264 cm2 by a gasket, so that water dissociation occurs more easily on K* and A* than that on the other membranes. D and C are the desalting and concentrating cells, respectively. A 0.1 eq dm3 solution of several chloride salts or sodium salts was supplied to D by a pump at the rate of 0.1 cm3 s1. The 1 eq dm3 solution of the same electrolytes which were supplied to D was added into D0 . A 1 eq dm3 NaCl solution was added into C (5 cm3) and D00 as well (Tanaka et al., 1982). After these preparations, an electric current was passed for 10 min between Ag–AgCl electrodes. When water dissociation takes place on the surface of K* or A* in D, H+ or OH ions generated are transferred into C. Solution pH in C was conﬁrmed to be almost steady 10 min after applying the electric

156

Ion Exchange Membranes: Fundamentals and Applications

Cathode

Anode K

A

K*

K

A

G

pHde

pHcon D′′

C

D

D′

(a)

Anode

Cathode A

K

A*

A

K

G

D′′

pHcon

pHde

C

D

D′

(b)

Figure 8.11 Electrodialysis apparatus for measuring water dissociation (Tanaka et al., 1982).

current. The electrodialysis experiment was repeated changing current densities incrementally. Current efﬁciencies for H+ ions ZH and OH ions ZOH were calculated from the pH changes in the solution in C. Experimental results are shown in Figs. 8.12 and 8.13 (cation exchange membrane; Aciplex K-102) and in Figs. 8.14 and 8.15 (anion exchange membrane; Aciplex A-102). The changes in these ﬁgures are illustrated in Fig. 8.16, indicating that the water dissociation does not occur between A and B, B presents the limiting current density ilim, and the water dissociation occurs between B and C. Inspecting the experimental results based on the illustration Fig. 8.16, the following phenomena are recognized: (a)

When the cation exchange membrane is placed in MgCl2 or NiCl2 solutions, ZH is increased largely at above limiting current density and violent water dissociation occurs. The violent dissociation generated at the cation exchange membrane is caused by the hydroxides precipitated

157

Water Dissociation

1

−1

10

−2

H

10

−3

10

−4

10

−5

10

−6

10

−2

−1

10

10

1 2

: NaCl,

i (A/cm ) : CaCl2, : MgCl2,

: BaCl2

: NiCl2

: KCl,

Figure 8.12 Current density vs. current efﬁciency of H+ ions. Cation exchange membrane, Aciplex K-102 (Tanaka et al., 1982).

(b)

on the cation exchange membrane. However, when the anion exchange membrane is placed in the same solutions, ZOH does not increase largely and the violent water dissociation is not detected. These phenomena mean that the intensity of the auto-catalytic water dissociation caused by quaternary pyridinium groups in the Aciplex A-102 anion exchange membranes is extremely weaker than that caused by metallic hydroxides precipitated on the Aciplex K-102 cation exchange membranes. When the cation and anion exchange membranes are placed in the other solutions, the violent water dissociation does not occur. In this situation, the water dissociation of the cation exchange membranes is more moderate (suppressed) than that of the anion exchange membranes, indicating that the sulfonic acid groups in the cation exchange membranes are seen not to generate the auto-catalytic water dissociation.

158

Ion Exchange Membranes: Fundamentals and Applications

10−1

10−2

H

10−3

10−4

10−5

10−6 10−1

10−2

1

i (A/cm2) : NaCl,

: Nal,

: Na2SO4

: NaBr,

: NaNO3

: Na2SO3

Figure 8.13 Current density vs. current efﬁciency of H+ ions. Cation exchange membrane, Aciplex K-102 (Tanaka et al., 1982).

The water dissociation arising on the cation exchange membrane in (b) is estimated to be caused by the Wien effect (cf. Section 8.5) which is generated under a strong potential drop in the repulsion zone (Patel et al., 1977) (cf. Section 8.3) or the depleted layer (Gavish and Lifson, 1979) (cf. Section 7.7.4) formed at the interface between the membrane and the solution. The potential drop is estimated to be caused by the space charge (Rubinstein and Shtilman, 1979; Rubinstein, 1981) (cf. Section 7.7.3). The membrane surface potential measurement suggests that the potential drop at the cation exchange membrane/ solution interface is larger than that at the anion exchange membrane/solution interface (Tanaka and Seno¯ , 1983a) (cf. Section 8.4). 8.8.3 Inﬂuence of Low Electrolyte Concentration and High Electric Potential Field on the Water Dissociation Reaction The depleted region formed on a desalting surface of a cation exchange membrane at an over limiting current is termed the depleted layer (Gavish and Lifson, 1979) or the repulsion zone (Patel et al., 1977). It carries a space charge

159

Water Dissociation

10−1

10−2

OH

10−3

10−4

10−5

10−6

10−2

10−1

1 2

i (A/cm ) : NaCI,

: CaCI2,

: MgCI2,

: KCI,

: BaCI2,

: NiCI2

Figure 8.14 Current density vs. current efﬁciency of OH– ions. Anion exchange membrane, Aciplex A-102 (Tanaka et al., 1982).

(Rubinstein and Shtilman, 1979; Rubinstein, 1981) or a membrane surface potential (Tanaka and Seno¯, 1983a). In this regime, the electrolyte concentration is decreased extremely, an electric potential ﬁeld is increased drastically and water dissociation is assumed to be accelerated under the inﬂuence of the Wien effect (Onsager, 1934). In order to make sure of the phenomena described above, water dissociation generated in diluted solutions was observed under a high electric potential ﬁeld as follows (Tanaka and Seno¯ , 1983b). An electrodialysis unit consisting of cells I and II was assembled as shown in Fig. 8.17. A polyvinyl chloride test plate T (Fig. 8.17a) in which a small hole (diameter 1 mm, length 1.2 mm) was bored at the center was put between cell I and cell II. A hole was bored in a polyvinyl chloride partition P (thickness 12 mm), and agar mixed with a 0.1 eq dm3 electrolyte solution was inserted in the hole, and then was allowed to solidify. These partitions P were put as shown in the ﬁgure. A total of 5 cm3 of the various diluted electrolyte solutions (10–2, 10–3, 10–4

160

Ion Exchange Membranes: Fundamentals and Applications

10−1

10−2

OH

10−3

10−4

10−5

10−6

10−2

10−1 i (A/cm2)

1

: NaCI,

: CaCI2,

: MgCI2,

: KCI,

: BaCI2,

: NiCI2

Figure 8.15 Current density vs. current efﬁciency of OH– ions. Anion exchange membrane, Aciplex A-102 (Tanaka et al., 1982).

and 10–5 eq dm3) was put in cells I and II with one or two droplets of pH indicators (methyl red and bromo thymol blue), and 1 eq dm3 NaCl solutions were added in the electrode cells. An electric current was passed applying 500 V to both ends of the small hole in the test plate. The potential gradient in the hole was estimated to be 4 105 V m1. These circumstances reproduce the situations at the cation exchange membrane/solution interface when an over limiting current is applied and the water dissociation occurring in the hole is observed from the color changes of the pH indicators. From the experiment mentioned above, intensities of water dissociation were classiﬁed and are listed in Table 8.6. When a 0.1 eq dm3 NaCl solution is added in cells I and II with methyl red, the color of the bottom of cell I turned to light pink after 2 min of passage of electric current. This is because H+ ions generated in the hole caused by the mild water dissociation transfer into cell II. When the NaCl solution with bromo thymol blue is electrodialyzed in the same way, the bottom of cell II turned to light blue, indicating OH– ion transfer due to the mild water dissociation.

161

Water Dissociation

10−1

H or OH

10−2

10−3

C

A

10−4 B 10−5

ilim

10−2

10−1

1 2

i (A/cm )

Figure 8.16

Current density vs. current efﬁciency of H+ or OH– ions. T : Test plate I : Chamber I II : Chamber II P : Partition Ar : Agar + : Anode − : Cathode

Notch

(a)

T

−

(b) +

1.2 mm

1mm φ Ar

P

I

T

II

P

Figure 8.17 Experimental apparatus for measuring water dissociation (Tanaka and Seno¯ , 1983b).

162 Table 8.6

Ion Exchange Membranes: Fundamentals and Applications

Intensities of water dissociation

Concentration of Electrolyte (meq dm3) MnCl2 CoCl2 MgCl2a NiCl2 MgCl2 AlCl3 Cr(NO3)2 CuCl2 ZnCl2 NaBr NaI NaNO3 Na2SO4 LiCl NaCl CaCl2 BaCl2 Na2S2O3 Fe(NO3)3 CH3 NH2 HCl CH3C6H4SO3Na KCl Na2SO3

102

101

1

10

& & & & & & & & & & & & & & & & & & & & & & &

J J J

J J J J

& D

D D D D D D D D D D D D

& & & & & & & & & & & & & & & D D D D D

J

J

Note: (J) Violent, (&) mild, (D) extremely mild and ( ) not occurred. Source: Tanaka and Seno¯ (1983b). a Before the experimental run, Mg(OH)2 was deposited on the surface in the hole of the test plate.

When a 0.1 meq dm3 MnCl2, CoCl2 or NiCl2 solution was added in cells I and II with methyl red, the bottom of the cell I turned to deep red just after the passage of electric current. When the same electrolyte solution was electrodialyzed with bromo thymol blue, the bottom of cell II turned to deep blue. It is estimated that mild water dissociation occurs at ﬁrst and precipitates Mn(OH)2, Co(OH)2 or Ni(OH)2 crystals in the hole, and then these hydroxides generate the auto-catalytic violent water dissociation. The phenomenon observed in the MgCl2 solution electrodialysis was slightly complicated. Namely, the water dissociation was moderate when inner surface of the hole in the test plate was washed with an aqueous HCl solution (MgCl2 in Table 8.6). However, when Mg(OH)2 was precipitated on the inner surface, the violent water dissociation was observed (MgCl2 a in Table 8.6). In the electrodialysis of other electrolyte solutions, violent water dissociation does not occur, but mild or extremely mild water dissociation takes place. The mild and extremely mild water dissociations observed in this experiment are presumably related to the Wien effect which describes the inﬂuence of a

163

Water Dissociation

strong electric potential gradient of 106–107 V m1 (cf. Section 8.5) (Onsager, 1934). The potential gradient 4 105 V cm1 appearing in the hole in this experiment is rather small compared to the values caused by the Wien effect. So, the phenomena in this experiment are assumed to be governed by the quasiWien effect. It is remarkable that the catalytic violent water dissociation occurs in MnCl2, CoCl2 and MgCl2 solutions under such a quasi-Wien effect. Further, it is noticed that the primary amine CH3NH2 HCl does not cause the violent water dissociation. The above experiment was achieved without ion exchange membranes. However, we can estimate the mechanism of water dissociation generated on the cation exchange membrane from the above experimental results as follows: (a)

(b)

Mild and extremely mild water dissociation reactions are the same as the phenomena already observed on the cation exchange membrane (Figs. 8.9, 8.12 and 8.13), and they are presumably caused by the second Wien effect in the circumstances of low-concentration and high-potential ﬁeld generated at the cation exchange membrane/solution interface. Violent water dissociation reactions are caused by the auto-catalytic reactions generated by the metallic hydroxides.

In order to make sure the mechanism in (b), the effect of metallic hydroxides on the water dissociation was observed using the apparatus in Fig. 8.17, where on the inner surface the test plate was notched in four points (Fig. 8.17b). Various insoluble hydroxides synthesized as shown in Table 8.7 were inserted in the notches. A total of 1 meq dm3 NaCl solutions was put in cells I and II and an electric current was passed as described above. The Table 8.7

Effect of insoluble salts on water dissociation

Insoluble Salts

Synthetic Method

Intensities of Water Dissociation

Mg(OH)2 Ni(OH)2 Co(OH)2 Mn(OH)2 Cu(OH)2 Fe(OH)3 Al(OH)3 MnCO3 Ca(OH)2 Zn(OH)2 CaSO4 BaSO4 CaCO3

Commercial NiCl2+2NaOH CoCl2+2NaOH MnSO4+2NaOH CuCl2+2NaOH Fe(NO3)3+3NaOH AlCl3+3NaOH MnSO4+NaHCO3 Commercial ZnCl2+2NaOH Commercial BaCl2+2NaOH CaCl2+NaHCO3

J J J J J J J J

Note: (J) violent and ( ) not occurred. Source: Tanaka and Seno¯ (1983b).

164

Ion Exchange Membranes: Fundamentals and Applications

intensities of the water dissociation are classiﬁed and listed in Table 8.7, showing that Mg(OH)2, Ni(OH)2, Co(OH)2, Mn(OH)2, Cu(OH)2, Fe(OH)2 and Al(OH)2 generate the violent water dissociation. MnCO3 is estimated to convert to Mg(OH)2 which arises the auto-catalytic violent dissociation in the notches.

8.8.4 Precipitation of Insoluble Metallic Hydroxides on the Membrane Surface and Generation of the Water Dissociation (Tanaka, 2007b) Mg(OH)2 was precipitated on the desalting surface of the cation exchange membrane K* (Selemion CMV) in the apparatus illustrated in Fig. 8.11a. Supplying a 0.1 M NaCl solution into D, an electric current was passed. Current density i vs. H+ ion current efﬁciency ZH exhibits stronger water dissociation on the cation exchange membrane as shown in Fig. 8.18. Next, Mg(OH)2 was precipitated on the desalting surface of the anion exchange membrane A* (Selemion ASV). Electrodialysis in this situation resulted in the generation of weaker water dissociation and the dissolution of Mg(OH)2. The mechanism of these phenomena is understandable from the illustration in Fig. 8.19, which shows that Mg(OH)2 layer on the cation exchange membrane is stable because OH ions generated by the water dissociation pass through the Mg(OH)2 layer. 0.5 Cation exchange membrane Selemion CMV

OH or H

0.4

0.3

0.2

0.1 Anion exchange membrane Selemion ASV 0.0 10-3

10-2

10-1

1

2

i (A/cm )

Figure 8.18 Precipitation of Mg(OH)2 on a membrane surface and generation of water dissociation.

165

Water Dissociation

OH−

H+

Cation exchange membrane

Mg(OH)2 layer

Water dissociation layer

OH−

H+

Mg(OH)2 layer

Anion exchange membrane

Figure 8.19 Illustration of Mg(OH)2 precipitation on the membrane surface and generation of water dissociation.

However, Mg(OH)2 layer formed on the anion exchange membrane dissolves because H+ ions pass through the Mg(OH)2 layer. In order to conﬁrm the inﬂuence of inorganic substances on the water dissociation on the cation exchange membrane (Aciplex K-102), the 0.02 M NaCl solutions suspending 0.1% (w/v) of Mg(OH)2, Ca(OH)2, Fe(OH)3, Al(OH)3, MgCO3, CaCO3, CaSO4 or SiO2 were fed into D in Fig. 8.11a. Passing an electric current for 10 min, ZH was measured in the same manner as described in Section 8.8.2. The results show that inorganic hydroxides, Mg(OH)2, Ca(OH)2, Fe(OH)2 and Al(OH)3, generate catalytic strong water dissociation; however, CaCO3, CaSO4 and SiO2 are conﬁrmed not to cause strong water dissociation. In this experiment, ZOH was evaluated on the anion exchange

166

Ion Exchange Membranes: Fundamentals and Applications

membrane (Aciplex A-102) feeding Mg(OH)2 into cell D; however, the accelerated water dissociation was not detected. Next, the cation exchange membrane (Aciplex K-102) was incorporated with D in the apparatus in Fig. 8.11a. Supplying a 0.02 M NaCl solution suspending 0.1% (w/v) Fe(OH)3 to D and ﬂowing 50 mA of an electric current for 5 min, Fe(OH)3 was attached to the desalting surface of the cation exchange membrane K*. After that, 0.02 eq dm3 NaCl, diluted seawater (Cl– ion concentration 0.02 eq dm3) or 0.02 eq dm3 MgCl2 was supplied into D and ZH was evaluated by applying current density i during 10 min. Plotting ZH against i indicated in Fig. 8.20 shows that ZH is increased due to the water dissociation caused by the Mg(OH)2 formed by the combining reaction between OH– ions generated in the Fe(OH)2 layer and Mg2+ ions dissolving in the feeding solution. Finally, Selemion CMV, Aciplex K-102 or Neocepta CH-45T cation exchange membrane was integrated with D in the apparatus in Fig. 8.11a. Supplying a 0.02 M NaCl solution suspending 0.1% (w/v) Fe(OH)3 and passing an electric current I for 5 min, Fe(OH)3 was deposited on K*. Then, feeding a 0.02 M NaCl solution and passing a 0.1 A cm2 of electric current, ZH was measured.

m3 M

gC

l2

1.0

/d

0.8

0.

H

02

eq

Sea water (diluted)

0.6

0.4 0.02 eq/dm3 NaCl 0.2

0

10−2

10−1

1 i (A/cm2)

Figure 8.20 Effect of Mg2+ ions on water dissociation generated on a cation exchange membrane.

167

Water Dissociation

0.5

H

0.4

0.3

0.2

0.1

0

0

20

40

60

80

100

Fe(OH)3 quantity (g/cm2) Selemion CMV

Aciplex K-102

Neocepta CH-45T

Figure 8.21 Precipitation of Fe(OH)3 on the surface of a cation exchange membrane and generation of water dissociation.

Further, disassembling the apparatus, the K* membrane was washed in a 1 M HCl solution with ultrasonic waves (35 kHz, 15 min). Fe components dissolved into the solution were analyzed using atomic absorption spectrometry. Changing the electric current I, the experiment was repeated. The relationship between ZH and the quantity of Fe(OH)3 attached to the membrane surface was measured as indicated in Fig. 8.21, which shows that ZH increases with Fe(OH)3 quantity.

8.8.5 Adhesion of Bacteria on the Membrane Surface and Generation of the Water Dissociation (Tanaka, 2007b) Spherical bacilli (C. bacillus, 1 mm diameter, forming white colony) were collected from the substances attached on the surface of the membrane integrated in the electrodialyzer operating in a seawater concentrating plant. The spherical bacilli were inoculated in a liquid medium (ORI culture medium), in which a cation exchange membrane (Aciplex K-102) and an anion exchange membrane (Aciplex A-102) were immersed to form bacteria layer on the

168

Ion Exchange Membranes: Fundamentals and Applications

H or OH

0.3

0.2

0.1

0 10−2

10−1

1

10

i (A/cm2) blank

bacteria attached

Aciplex K-102 Aciplex A-102

Figure 8.22 Bacteria attachment on the surface of an ion exchange membrane and generation of water dissociation.

membrane surfaces by means of vibration cultivation (281C, 24 h). The bacteria layer formed membranes were incorporated with D in Fig. 8.11. It was electrodialyzed for 10 min supplying 0.02 M NaCl and current efﬁciency for the water dissociation (ZH and ZOH) was measured. At the same time, ZH and ZOH for the bacteria layer nonformed membranes were measured in the same way. The experimental results are shown in Fig. 8.22. Inspecting Fig. 8.22, ZOH of the anion exchange membrane increases. This phenomenon is presumably caused by the promotion of concentration polarization in the bacteria layer and acceleration of auto-catalytic water dissociation reaction of quaternary pyridinium groups in the Aciplex A-102 membrane. However, ZH of the cation exchange membrane does not increase. This phenomenon indicates that sulfonic acid groups in the Aciplex K-102 membrane do not accelerate the auto-catalytic water dissociation reaction in spite of the promoted concentration polarization in the bacteria layer.

169

Water Dissociation

8.9. WATER DISSOCIATION ARISING IN SEAWATER ELECTRODIALYSIS (Tanaka, 2007b) In an electrodialyzer for concentrating seawater, water dissociation causes troubles such as current efﬁciency decrease, scale formation and membrane breakage. In this section, water dissociation associated with seawater electrodialysis operated in salt manufacturing plants in Japan is described with some experimental works performed to prevent the troubles. Water dissociation is detected by measuring voltage increases in a stack or pH changes in a solution. Observation in disassembled stacks shows that 91% of water dissociation starts at p on the desalting surface of a cation exchange membrane and expands toward an anode with OH– ion transfer as illustrated in Fig. 8.23 (Watanabe et al., 1984). Table 8.8 shows the constituents −

+

p

Figure 8.23 Illustration of water dissociation generation in an electrodialyzer (Watanabe et al., 1984). Table 8.8 100 g)

Constituents of substances attached to an ion exchange membrane (g per

Components

Cation Exchange Membrane

Anion Exchange Membrane

H2O Acid soluble Fe(OH)3 Cu(OH)2 Others Total Acid insoluble SiO2 Fe2O3 CuO Al2O3 Others Total Ignition loss

84.85

85.62

4.41 0.03 0.82 5.26

3.85 0.03 0.80 4.68

2.51 1.42 0.02 0.12 0.50 4.57 3.20

2.32 1.14 0.03 0.34 0.54 4.37 3.49

Source: Watanabe et al. (1980).

170

Ion Exchange Membranes: Fundamentals and Applications

of the substances attached to the desalting surface of the membrane which had been incorporated with an electrodialyzer in a salt manufacturing plant (Watanabe et al., 1980). From the experiment described in Section 8.8.4, Fe(OH)3 attached on the cation exchange membrane supposedly causes violent water dissociation. Membranes integrated in electrodialyzers operating in salt manufacturing plants were taken out, and water dissociation current efﬁciencies for a sulfonic acid type cation exchange membrane (Aciplex K-102) ZH and for a quaternary pyridinium type anion exchange membrane (Aciplex A-102) ZOH were measured in the same manner as described in Section 8.8.2. Plotting ZH and ZOH against operating period t of the membranes in the electrodialyzers gives Fig. 8.24, showing ZH to be less than ZOH at t ¼ 0 year; the water dissociation is hard to occur on the cation exchange membrane than on the anion exchange membrane 0.7 Cation exchange membrane

0.6

H (-)

0.5 0.4 0.3 0.2 0.1 0.0 0

2

4

6

8

10

12

14

12

14

Year 0.3

OH (-)

Anion exchange membrane

0.2 0. 1 0. 0

0

2

4 Plant A

6

8 Year Plant B

10

Plant C

Figure 8.24 Changes of ZH and ZOH of membranes integrated in electrodialyzers operating for long time in salt manufacturing plants.

Water Dissociation

171

at the beginning of the operation. This is supposedly because the water dissociation intensities in Aciplex K-102 membranes are weaker than the autocatalytic water dissociation of quaternary pyridinium groups in Aciplex A-102 membranes at t ¼ 0. However, ZH increases gradually at ﬁrst and increases extremely after t ¼ 6 years. This is presumably due to the auto-catalytic reaction of Fe(OH)3 deposited on the Aciplex K-102 membranes. It is concluded from this experiment that cation exchange membranes having been served for six years or more should be replaced with new ones to prevent water dissociation. Based on this suggestion, the membranes were replaced with new ones, and then the water dissociation was suppressed and stack disassembling frequencies were diminished from 200 to 40 stacks/month (Akoh Kaisui Co., 1984). Operating duration of an electrodialyzer during stack disassembling intervals is related to the frequencies of water dissociation occurrences. In this case, the operating duration was 20 days or less because the water dissociation occurred frequently as shown in Fig. 8.25 (1). Here, cation exchange membranes (Aciplex K-102) were replaced to new ones at ‘‘a’’ in the ﬁgure, resulting in an extension of operating duration to 40–80 days. Next, the operating duration was extremely shortened to one to three days as shown in Fig. 8.25 (2). Then, anion exchange membranes (Aciplex A-102) were replaced at ‘‘b’’ in the ﬁgure; however, the operating duration was unchanged. Thereupon, cation exchange membranes (Aciplex K-102) were replaced at ‘‘c’’, causing an extension of operation to 40 days. The experimental works described above demonstrate that the replacement of cation exchange membranes is effective to prevent water dissociation (Akoh Kaisui Co., 1984). In periodical disassembling works of an electrodialyzer in a salt manufacturing plant (cf. Section 1.5.3 in Applications), the membranes are taken out from the electrodialyzer and washed by hand using a sponge at an interval of usually three to four months. However, such an interval is decreased due to the occurrence of water dissociation. In order to examine the effect of washing for preventing the water dissociation, cation exchange membrane (Aciplex K-102) samples were cut in the disassembling works of an electrodialyzer in the salt manufacturing plant. The samples were sponge washed once or 10 times, and water dissociation was measured in the same manner as described in Section 8.8.2. The result showed that washing once is insufﬁcient but 10 times washing is effective. The cation exchange membrane samples were washed in a 5 M HCl solution for 16 h and substances attached to the membrane were removed. The effect of the HCl washing was not clear. The cation exchange membrane samples were washed for 1 and 16 h in a mixed solution of 0.1 M ammonium citric acid and 0.03 M EDTA. The washing effect was insufﬁcient (cf. Section 14.2.3).

172

Ion Exchange Membranes: Fundamentals and Applications

100

Operating durations (days)

(1) 80 60 40 20 0

Operating durations (days)

80

a (2)

60 40 20 0 b c a: Cation exchange membranes were replaced b: Anion exchange membranes werereplaced c: Cation and anion exchange membranes were replaced

Figure 8.25 Replacement of ion exchange membranes in a stack and the prevention water dissociation in an electrodialyzer (Akoh Kaisui Co., 1984).

The cation exchange membrane samples were washed in an HCl solution applying ultrasonic waves. The washing effect was remarkable. From the experiments mentioned above, Fe(OH)3 suspended in a feeding solution is estimated to invade into an electrodialyzer, ﬁx to cation exchange membranes (cf. Table 8.8) and form the water dissociation layers. In the water dissociation layers the extremely strong auto-catalytic water dissociation occurs caused by the Fe(OH)3. The Fe(OH)3 ﬁxes also to the anion exchange membrane, but it does not induce the strong water dissociation (Fe(OH)3 dissolves, cf. Fig. 8.19). The water dissociation on the anion exchange membrane is estimated to be caused by the auto-catalytic reaction due to the quaternary pyridinium (or ammonium) groups in the membrane. However, the intensity of the reaction is relatively weak comparing to the auto-catalytic reaction caused by Fe(OH)3 precipitated on the cation exchange membrane.

173

Water Dissociation

8.10.

MECHANISM OF WATER DISSOCIATION (Tanaka, 2007a)

8.10.1

Water Dissociation Reaction in the Water Dissociation Layer Under an unapplied electric potential ﬁeld, the water dissociation is an equilibrium reaction as shown in Eq. (8.21) (Eigen, 1954). ka

H2 O 3 Hþ þ OH , kb

ka ¼ 2 105 s1 ;

kb ¼ 1:5 1014 cm3 mol1 s1

ð8:21Þ

where ka and kb are, respectively, the forward and reverse equilibrium reaction rate constants. Under an applied electric potential ﬁeld, ka is assumed to increase with the electric ﬁeld due to the Wien effect (Wien, 1928, 1931) and the auto-catalytic reaction (Simons, 1984, 1985; Oda and Yawataya, 1968), whereas kb remains constant. From the experiment described in Section 8.8, it seems reasonable to estimate that the water dissociation occurs in the water dissociation layer formed near the membrane surface and the occurrence of the water dissociation is classiﬁed as follows assuming a cation exchange membrane (sulfonic acid type) or an anion exchange membrane (quaternary ammonium or quaternary pyridinium type) is placed in a NaCl or a MgCl2 solution: (1)

(2)

(3)

(4)

The phenomena generated in a cation exchange membrane placed in a NaCl solution. Sulfonic acid groups in the membrane generate the weak autocatalytic water dissociation. Water dissociation layer is formed at the inside of the membrance. The phenomena generated in an anion exchange membrane placed in a NaCl solution. Quaternary ammonium groups or quaternary pyridinium groups in the membrane generate the strong auto-catalytic water dissociation. The water dissociation layer is formed at the inside of the membrane. The phenomena generated on a cation exchange membrane placed in an MgCl2 solution. Mg(OH)2 layer is formed on the membrane and generates extremely strong auto-catalytic water dissociation. The water dissociation layer is formed at the inside of the Mg(OH)2 layer. The phenomena generated in an anion exchange membrane placed in an MgCl2 solution. Mg(OH)2 layer is not formed on the membrane, so the strong autocatalytic water dissociation does not occur. However, quaternary ammonium groups or quaternary pyridinium groups in the membrane generate strong auto-catalytic water dissociation. The water dissociation layer is formed at the inside of the membrane.

174

Ion Exchange Membranes: Fundamentals and Applications

On the other hand, from the seawater electrodialysis experiment described in Section 8.9, it is estimated that the ﬁxing of Fe(OH)3 suspended in feeding seawater to the cation exchange membrane generates the extremely strong autocatalytic water dissociation. Further, the ﬁxing of Fe(OH)3 to the anion exchange membrane does not induce the strong water dissociation, but the strong water dissociation occurs due to the quaternary pyridinium (ammonium) groups in the membrane. 8.10.2 Layer

Generation and Transport of H+ and OH– Ions in the Water Dissociation

When an over limiting current passes across an ion exchange membrane placed in an ionic solution, the water dissociation layer is formed near the membrane surface (the inside of the membrane or the metallic hydroxide layer) as described in Section 8.10.1. We assume here that H+ and OH– ions are generated and transported in the water dissociation layer as shown in Fig. 8.26. The generation rate of H+ ions sH at x ¼ 0–x is Z x sH ¼ ðka C H2 O kb C H C OH Þdx 0 Z x ¼ ka C H2 O x kb C H C OH dx ð8:22Þ 0

Water dissociation layer

JH

-JOH

Anode

Cathode

H

OH

x axis 0

x

l

Figure 8.26 Formation and transport of H+ and OH– ions in a water dissociation layer (Tanaka, 2002).

175

Water Dissociation

The generation rate of OH– ions sOH at x ¼ x–l is Z l sOH ¼ ðka C H2 O kb C H C OH Þdx x

Z

l

¼ ka C H2 O ðl xÞ kb

C H C OH dx

ð8:23Þ

x

where x is an axis drawn in the water dissociation layer, CH, COH and C H2 O the concentration of H+ ions, OH– ions and H2O at x, and l the thickness of the water dissociation layer. H+ and OH– ions generated are transported by electromigration and diffusion. The transport rate (ﬂux) of H+ ions JH and that of OH ions JOH at x are obtained from the Nernst–Planck equation as follows: J H ¼ DH

dC H FDH C H dc dx RT dx

(8.24)

dC OH FDOH C OH dc þ (8.25) dx RT dx where DH and DOH are the diffusion constants of H+ and OH– ions, F the Faraday constant, R the gas constant, T the absolute temperature and c the electric potential at x. From the material balance in Fig. 8.26, the following formulae hold between the generation and transport of H+ and OH– ions: i (8.26) Z sH ¼ J H ¼ F H i Z (8.27) sOH ¼ J OH ¼ F OH J OH ¼ DOH

where i is the current density, and ZH and ZOH the current efﬁciencies for H+ and OH ions, respectively. When the electrolyte solution dissolves cations A and anions B, total current efﬁciency for water dissociation reaction Z is Z ¼ ZH þ ZOH ¼ 1 ðZA þ ZB Þ

(8.28)

where ZA and ZB are current efﬁciencies for A and B ions, respectively. The following equations are obtained from Eqs. (8.22)–(8.28): Z l i Z ¼ ka C H2 O l kb C H C OH dx (8.29) F 0 i dC H FDH C H dc Z ¼ DH dx RT dx F dC OH FDOH C OH dc ð8:30Þ þ DOH dx RT dx

176

Ion Exchange Membranes: Fundamentals and Applications

8.10.3 Concentration Distribution of H+ and OH– Ions in the Water Dissociation Layer Multiplication of the concentrations of H+ and OH– ions (CH and COH) by diffusion constants (DH and DOH), respectively, is expressed by the distribution of the converted ionic concentrations XH and XOH as polynomials of x as follows: X H ¼ DH C H ¼

1 X

an xn

(8.31)

n¼0

X OH ¼ DOH C OH ¼

1 X

bn ðl xÞn

(8.32)

n¼0

From Eqs. (8.30)–(8.32) we obtain i dX H dX OH þ KX H þ þ KX OH Z¼ dx dx F

(8.33)

1 X i Z¼ Kfan xn þ bn ðl xÞn g F n¼0 ðn þ 1Þfanþ1 xn þ bnþ1 ðl xÞn g

ð8:34Þ

where K is the converted electric potential gradient given by F dc F ¼ ni (8.35) RT dx RT where n is speciﬁc electric resistance (O cm) of the water dissociation layer. Equation (8.34) indicates that (i/F)Z should be independent of x. Therefore, with the exception of the ﬁrst term, all other terms in the polynomials in Eq. (8.34) can be regarded as zero: setting n ¼ 0 in the ﬁrst term i (8.36) Z ¼ Kða0 þ b0 Þ ða1 þ b1 Þ F K ¼

Setting n ¼ 1, 2, 3, y in all other terms a2 x þ b2 ðl xÞ a3 x2 þ b3 ðl xÞ2 ¼3 a1 x þ b1 ðl xÞ a2 x2 þ b2 ðl xÞ2 n anþ1 x þ bnþ1 ðl xÞn ¼ ðn þ 1Þ ¼ an xn þ bn ðl xÞn

K ¼2

Substituting x ¼ l in Eq. (8.37), we arrive at a2 a3 anþ1 ¼3 ¼ ¼ ðn þ 1Þ ¼ K ¼2 a1 a2 an

ð8:37Þ

(8.38)

Water Dissociation

177

From Eq. (8.38), the coefﬁcients in the polynomials are obtained as follows: K K a1 ¼ a1 a2 ¼ 2 2! 2 K K a1 a3 ¼ a2 ¼ 3! 3 (8.39) n1 K K a1 an1 ¼ an ¼ n! n In the same way, substituting x ¼ 0 in Eq. (8.37), we get b2 b3 bnþ1 ¼3 ¼ ¼ ðn þ 1Þ ¼ K ¼2 b1 b2 bn K K b1 ¼ b1 2 2! K K b3 ¼ b2 ¼ b1 3 3!

(8.40)

b2 ¼

(8.41)

n1 K K b1 bn1 ¼ bn ¼ n! n Using Eqs. (8.39) and (8.41), Eqs. (8.31) and (8.32) are simpliﬁed as XH

a Kx K 2 x2 K n xn 1 þ þ ¼ a0 þ þ K 2! n! 1! a 1 ¼ a0 þ expðKxÞ 1 K b1 Kð1 xÞ K 2 ð1 xÞ2 K n ðl xÞn þ þ þ K 2! n! 1! b1 ½expfKðl xÞg 1 ¼ b0 þ K

ð8:42Þ

X OH ¼ b0 þ

ð8:43Þ

Equations (8.42) and (8.43) still include the polynomials a0, a1, b0 and b1. Further, the converted ionic concentrations XH and XOH and the converted potential gradient K must be restored to CH, COH and nl. The explanation of this process is present in the literature Tanaka (2007a), and we show only CH and

178

Ion Exchange Membranes: Fundamentals and Applications

COH introduced from Eqs. (8.42) and (8.43) as follows: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ DOH 0 0 F CH ¼ inl C H C OH exp DH 2RT

F F inl þ 1 exp inl exp RT RT

expfðF =RTÞinlxg 1 expfðF =RTÞinlg 1 rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ U OH 0 0 F inl ð2x 1Þ C H C OH exp ¼ UH 2RT C OH

rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ DH 0 0 F exp inl ¼ C C DOH H OH 2RT

F F inl þ 1 exp inl exp RT RT

expfðF =RTÞinlð1 xÞg 1 expfðF =RTÞinlg 1 rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ UH 0 0 F exp C C inl ð2x 1Þ ¼ U OH H OH 2RT

ð8:44Þ

ð8:45Þ

where x ¼ x/l, and C 0H and C 0OH are the concentrations of H+ and OH– ions at the outside of the water dissociation layer. 8.10.4

Electric Resistance of the Water Dissociation Layer When the solution pH reaches a steady value, the concentration of OH– ions and a pH value at x ¼ 0 in Fig. 8.26 are given by putting x ¼ 0 in Eq. (8.45) as: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ DH ðF =2RTÞinl e (8.46) C OHjx¼0 ¼ DOH pH ¼ 14 þ log C OHjx¼0

(8.47) 2

The electric resistance nl (O cm ) of the water dissociation layer formed near the anion exchange membrane is introduced from Eqs. (8.46) and (8.47) as nl ¼

pH 14 ð1=2Þ logðDH =DOH ÞC 0H C 0OH ; ðF =2RT Þi log e

i40

The formulae for a cation exchange membrane are as follows: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ DOH 0 0 C Hjx¼1 ¼ C C eðF =2RTÞinl DH H OH

(8.48)

(8.49)

179

Water Dissociation

pH ¼ log C Hjx¼1 nl ¼

(8.50)

pH þ ð1=2Þ logðDOH =DH ÞC 0H C 0OH ; ðF =2RT Þi log e

io0

(8.51)

8.10.5 Computation of Electric Resistance and H+, OH Ion Concentration in the Water Dissociation Layer Anion exchange membranes (Aciplex A-102) and cation exchange membranes (Aciplex K-102) were integrated in assemblies in Fig. 8.11 and a NaCl solution or an MgCl2 solution was supplied (cf. Section 8.8.2). pH values in a concentrating cell obtained by passing an over limiting current are substituted in Eqs. (8.48) and (8.51), and nl is computed as indicated in Fig. 8.27. The ﬁgure shows that in the NaCl solution, the nl in the cation exchange membrane is less than that in the anion exchange membrane. It is estimated that nl relates to the intensity of the water dissociation reaction. In the MgCl2 solution, the nl on the cation exchange membrane is increased considerably. This event is estimated to be due to the precipitation of Mg(OH)2 on the membrane surface and resultant acceleration of the water dissociation reaction in the Mg(OH)2 layer. 20 18 16

l ( Ω cm2)

14 12 10 8 6 4 2 0 0.0

0.2

0.4

0.6 0.8 1.0 1.2 i (A/cm2) Anion exchange membrane (Aciplew x A-102) ;0.1eq/dm3 NaCl, :0.1eq/dm3 MgCl2 Cation exchange membrane (Aciplex K-102) :0.1eq/dm3 NaCl,

Figure 8.27

:0.1eq/dm3 MgCl2

Electric resistance of a water dissociation layer (Tanaka, 2002).

180

Ion Exchange Membranes: Fundamentals and Applications

10-2 10-3 C

H

10-4

CH, COH(M)

10-5 10-6 10-7 10-8 10-9 CO H

10-10 10-11 10-12

0.0

0.2

0.4

0.6

0.8

1.0

(-) i (A/cm2)

0.083

0.235

0.568

0.871

1.140

l (Ω cm2)

2.950

1.343

0.678

0.502

0.388

Figure 8.28 Concentration distribution of H+ and OH ions in a water dissociation layer (anion exchange membrane in a NaCl solution).

Concentration distributions of H+ ions, CH, and OH ions, COH, in the water dissociation layer are calculated as follows using Eqs. (8.44) and (8.45) with nl obtained above. In the electrodialysis of a NaCl solution, CH and COH changes for an anion exchange membrane are larger than those for a cation exchange membrane (Figs. 8.28 and 8.29). In the electrodialysis of an MgCl2 solution, however, the CH and COH changes for a cation exchange membrane become larger than those for an anion exchange membrane (Figs. 8.30 and 8.31). 8.10.6 Current Efﬁciency of H+ and OH– Ions Generated in the Water Dissociation Layer For obtaining current efﬁciency of H+ and OH– ions, Z ¼ ZH+ZOH presented by Eq. (8.29), we must know CHCOH, which is introduced by multiplying Eq. (8.44) by Eq. (8.45) as the following simple constant value: C H C OH ¼ C 0H C 0OH

(8.52)

Substituting Eq. (8.52) into Eq. (8.29), Z is introduced as the following simple form, which is equivalent to an integrated form of Eq. (8.3) presented by

181

Water Dissociation

10-2

O

H

10-3 C

10-4

CH, COH (M)

10-5 10-6 10-7 10-8 10-9 CH

10-10 10-11 10-12

0.0

0.2

0.4

0.6

0.8

1.0

(-) i (A/cm2)

0.050

0.083

0.239

0.568

0.871

1.140

l (Ω cm2) 1.522

1.070

0.992

0.669

0.502

0.405

Figure 8.29 Concentration distribution of H+ and OH ions in a water dissociation layer (cation exchange membrane in a NaCl solution).

Rubinstein (1977): i Z ¼ ðka C H2 O kb C 0H C 0OH Þl F ka is given from Eq. (8.53) as follows. iZ 1 ka ¼ kb C 0H C 0OH þ Fl C H2 O

(8.53)

(8.54)

8.10.7 Electric Conductivity and Thickness of the Water Dissociation Layer and Potential Gradient in the Water Dissociation Layer Speciﬁc electric conductivity in the water dissociation layer l is given by the following equation assuming H+, OH, Na+ and Cl ions are dissolved in a solution. l ¼ lZ þ lð1 ZÞ

(8.55)

182

Ion Exchange Membranes: Fundamentals and Applications

10-2 10-3 C

H

10-4

CH,COH(M)

10-5 10-6 10-7 10-8 10-9

H

CO

10-10 10-11 10-12 0.0

0.2

0.4

0.6

0.8

1.0

ξ (-) i (A/cm2)

0.049

0.080

0.239

0.568

0.871

1.140

l (Ω cm2) 3.672

3.091

1.380

0.731

0.551

0.463

Figure 8.30 Concentration distribution of H+ and OH ions in a water dissociation layer (anion exchange membrane in an MgCl2 solution).

lZ and l(1Z) are respectively contribution of H+, OH ions and Na+, Cl ions to l, and they are respectively presented by the following equations. lZ ¼ F ðuH C H þ uOH C OH Þ

(8.56)

lð1 ZÞ ¼ F ðuNa C Na þ uCl C Cl Þ

(8.57)

Substituting Eqs. (8.44) and (8.45) into Eq. (8.56) gives qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2F F inl ð2x 1Þ l¼ uH uOH C 0H C 0OH cosh Z 2RT

(8.58)

l is the speciﬁc electric conductivity at x in the water dissociation layer, and the speciﬁc electric conductivity of the water dissociation layer L is introduced by integrating l within the range of x ¼ 01 as follows. Z 1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 4RT F inl (8.59) ldx ¼ L¼ uH uOH C 0H C 0OH sinh Zinl 2RT 0

183

Water Dissociation

1

C

O

H

10-2

CH, COH(M)

10-4 10-6 10-8 10-10 CH

10-12 10-14

0.0

0.2

0.4

i (A/cm2)

0.032

ξ (-)

0.6

0.056

0.8

0.120

0.240

l (Ω cm ) 18.241 10.994 5.367

2.910

2

1.0

Figure 8.31 Concentration distribution of H+ and OH ions in a water dissociation layer (cation exchange membrane in an MgCl2 solution).

Thickness of the water dissociation layer l is l ¼ Lnl

Ln ¼ 1

(8.60)

L and l are calculated by substituting nl obtained using Eqs. (8.48) and (8.51) into Eqs. (8.59) and (8.60). Potential gradient in the water dissociation layer is computed substituting i and L into Eq. (8.61). dV i ¼ dx L 8.10.8

(8.61)

Water Dissociation Reaction Generated in the Water Dissociation Layer. Based on the theory and experimental results using the apparatus shown in Fig. 8.11, L, l, dV/dx and the forward reaction rate constant ka are calculated using the following process. (a) (b) (c)

nl is calculated using Eqs. (8.48) or (8.51). L is calculated using Eq. (8.59). l is calculated using Eq. (8.60)

184

(d) (e) (f)

Ion Exchange Membranes: Fundamentals and Applications

dV/dx is calculated using Eq. (8.61). ka1 observed in the electrodialysis experiment is calculated using Eq. (8.54). ka2 caused by the second Wien effect is calculated using Eqs. (8.8) and (8.9) putting E ¼ dV/dx.

16

16

14

14

12

12

10

10

8

8

6

6

4

4

2

2

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Λ (10-3S/cm), l(10-5m), dV/dx(103V/m)

ka1(10-31/s),ka210-51/s)

Fig. 8.32 shows the current density dependence of the water dissociation reaction on the Selemion CMR cation exchange membrane and the ASR anion exchange membrane. It is seen in this ﬁgure that ka1 for both membranes is increased with current density. ka1 for the anion exchange membrane is larger than that for the cation exchange membrane. ka2 for both membranes is independent to current density and identical to 2.70 105 (s1) corresponding the forward reaction rate constant at i ¼ 0. This phenomenon means that the intensity of the second Wien effect is negligible for both membranes. In other words, the increase of the forward reaction rate constant ka1 observed in the electrodialysis is due to the auto-catalytic reaction of the functional groups (quaternary ammonium groups in the ASR membrane or sulfonic acid groups in the CMR membrane) and is not due to the second Wien effect, and further it means that the intensity of the auto-catalytic reaction of quaternary ammonium groups is stronger than that of sulfonic acid groups.

0 0.7

i (A/cm2) Figure 8.32 Water dissociation reaction generated in a water dissociation layer formed on a cation and an anion exchange membrane. JK: ka1, Wm: ka2, &’: L, BE: l, $%: dV/dx Open: Selemion CMR cation exchange membrane Filled: Selemion ASR anion exchange membrane 0.01 M NaCl.

Water Dissociation

185

L for the ASR anion exchange membrane is less than that for the CMR cation exchange membrane. l in both membranes is independent of current density. l in the anion exchange membrane (4.8 105 m) is less than that in the cation exchange membrane (8.4 105 m). dV/dx in both membranes tends to increase with current density, and the values in the anion exchange membrane are larger than those in the cation exchange membrane. It is estimated from the above calculation that the second Wien effect does not work because of low dV/dx values (103104 V/m) which is caused by large l values in the membrane.

REFERENCES Akoh Kaisui Co., 1984, Technical information. Barrow, G. M., 1973, Physical Chemistry, McGraw-Hill, New York. Eigen, M., 1954, Method for investigation of ionic reactions in aqueous solutions with half-times as short as 109s, application to neutralization and hydrolysis reactions, Discuss. Faraday Soc., 17, 194–205. Eigen, M., Maeyer, L. D., 1959, Hydrogen bond structure, proton hydration, and proton transfer in aqueous solution, In: The Structure of Electrolytic Solutions, Wiley, New York. Frilette, V. J., 1956, Preparation and characterization of bipolar ion-exchange membranes, J. Phys. Chem., 60, 435–439. Gavish, B., Lifson, S., 1979, Membrane polarization at high current densities, JCS Faraday Trans. I, 75, 463–472. Kressman, T. R. E., Tye, F. L., 1956, The effect of current density on the transport of ions through ion-selective membranes, Discuss. Faraday Soc., 21, 185–292. Oda, Y., Yawataya, T., 1968, Neutrality-disturbance phenomenon of membrane– solution systems, Desalination, 5, 129–138. Onsager, L., 1934, Deviation from Ohm’s law in weak electrolyte, J. Chem. Phys., 2, 599–615. Patel, R. D., Lang, K. C., Miller, I. F., 1977, Polarization in ion-exchange membrane electrodialysis, Ind. Eng. Chem. Fundam., 16(3), 340–348. Rosenberg, N. W., Tirrel, C. E., 1957, Limiting currents in membrane cells, Ind. Eng. Chem., 49(4), 780–784. Rubinstein, I., 1977, A diffusion model of ‘‘water splitting’’ in electrodialysis, J. Phys. Chem., 81(14), 1431–1436. Rubinstein, I., 1981, Mechanism for an electrodiffusional instability in concentration polarization, J. Chem. Soc., Faraday Trans. II, 77, 1595–1609. Rubinstein, I., Shtilman, L., 1979, Voltage against current curves of cation-exchange membranes, Faraday Trans. II, 75, 231–246. Simons, R., 1979, Strong electric ﬁeld effects on proton transfer between membranebound amines and water, Nature, 280, 824–826. Simons, R., 1984, Electric ﬁeld effects on proton transfer between ionizable groups and water in ion exchange membranes, Electrochim. Acta, 29(2), 151–158. Simons, R., 1985, Water splitting in ion exchange membranes, Electrochim. Acta, 30(3), 275–282. Tanaka, Y., 1974, Concentration polarization and dissociation of water in ion exchange membrane electrodialysis, J. Electrochem. Soc., Jpn., 42(9), 450–456.

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Ion Exchange Membranes: Fundamentals and Applications

Tanaka, Y., 1975, Concentration polarization and dissociation of water in the ion exchange membrane electrodialysis, J. Electrochem. Soc., Jpn., 43(10), 584–588. Tanaka, Y., 2007a, Water dissociation in reaction generated in a water dissociation layer formed on an ion exchange membrane, J. Membr. Sci., the article in submitting. Tanaka, Y., 2007b, Acceleration of water dissociation on ion exchange membranes, J. Membr. Sci., the article in submitting. Tanaka, Y., Matsuda, S., Sato, Y., Seno¯ , M., 1982, Concentration polarization and dissociation of water in ion exchange membrane electrodialysis III. The effects of electrolytes on the dissociation of water, J. Electrochem. Soc., Jpn., 50(8), 667–672. Tanaka, Y., Seno¯ , M., 1983a, The concentration polarization and dissociation of water in ion exchange membrane electrodialysis. V. The acceleration of ionic transport on the membrane surface, J. Electrochem. Soc., Jpn., 51(2), 267–271. Tanaka, Y., Seno¯ , M., 1983b, Concentration polarization and dissociation of water in ion exchange membrane electrodialysis. VI. The effects of insoluble inorganic materials on the dissociation of water under conditions of low concentration and high potential, J. Electrochem. Soc. Jpn., 51(6), 465–470. Watanabe, I., Morimoto, T., Kamaya, M., Tuzura, K., Kawate, H., 1984, Research on ion exchange membranes (Part 2), Investigation on water dissociation of ion exchange membranes, Presented at the 35th annual meeting, Society of Sea Water Science, JPM. Watanabe, T., Hiroi, K., Azechi, A., Tanaka, Y., Fujimoto, Y., 1980, Concentration process by ion exchange membrane method, Bull. Soc. Sea Water Sci. Jpn., 34(2), 61–90. Wien, M., 1928, Uber die abweichungen der elektrolyte vom Ohmschen gesetz, Phys. Zeits, 29, 751–755. Wien, M., 1931, Uber leitfahigkeit und dielektrizitatskonstante von elektrolyten bei hochfrequenz, Phys. Zeits, 32, 545.

Chapter 9

Current Density Distribution 9.1.

CURRENT DENSITY DISTRIBUTION IN AN ELECTRODIALYZER

9.1.1

Current Density Distribution Equation In an ion exchange membrane electrodialyzer, cation exchange membranes, anion exchange membranes, desalting cells and concentrating cells are arranged alternately. Electrolyte solutions are fed into every cell and an electric current is passed across the membranes. In this electrodialysis system, current density is decreased due to the electrolyte concentration decrease at the outlets of desalting cells. This phenomenon was discussed by Sonin and Probstein (1968) and Mas et al. (1970). While discussing the current density distribution in an electrodialyzer, attention should be paid to the fact that solution velocities in desalting cells vary because the friction factor of solutions ﬂowing in desalting cells is not uniform between the cells. This event gives rise to solution velocity distribution (cf. Section 11.6) and electrolyte concentration distribution. Further, electrolyte concentration distribution causes electric resistance and current density distributions (Tanaka, 2000, 2002). The current density distribution explained below is closely related to the limiting current density of an electrodialyzer, which is discussed in Chapter 11. An electrolyte solution is assumed to be supplied to entrances of desalting cells in a stack, passed through the cells and discharged at the exits of the cells in a one-pass ﬂow system. We deﬁne the velocity ratio x in desalting cells integrated in a stack in an electrodialyzer by Eq. (9.1): x¼

u u¯ u¯

(9.1)

where u* is the linear velocity in every desalting cell and u¯ the average linear velocity in a stack. The frequency distribution of x is equated by the normal distribution (cf. Section 11.6). The minimum of x and u* may be equated with 3s and u, respectively, where s is the standard deviation of the normal distribution and u the minimum value of linear velocities within all desalting cells in a stack. Putting x ¼ 3s and u* ¼ u in Eq. (9.1) gives Eq. (9.2): u ¼ u¯ ð1 3sÞ

(9.2)

An electrolyte solution is assumed to be transferred to the concentrating cells and discharged to the outside of a stack in an overﬂow discharging system. The current density distribution in the electrodialyzer is assumed to be approximated

DOI: 10.1016/S0927-5193(07)12009-X

188

Ion Exchange Membranes: Fundamentals and Applications

by the following quadratic equation expressed at x distant from the inlet of a desalting cell: i ¼ k 1 þ k 2 x þ k 3 x2

(9.3)

To determine k1, k2 and k3 in Eq. (9.3), three-dimensional simultaneous equations are set up as follows. When a large number of membrane pairs are integrated in an electrodialyzer, Eq. (9.4) is realized because electrical resistance and ohmic loss of electrodes incorporated in the electrodialyzer are negligible compared to the values between the electrodes. Equation (9.4) is the ﬁrst three-dimensional simultaneous equation, and it means that the voltage differences between the electrodes at the entrance of desalting cells Vin are equal to the values at the exits Vout (cf. Table 9.1): V in ¼ V out

(9.4)

V in ¼ A1 iin þ A2

(9.5)

V out ¼ B1 iout þ B2

(9.6)

A1 ¼ ðr0in þ rin;K þ rin;A þ r00 ÞN

(9.7)

Table 9.1

Voltage difference between electrodes in a stack

Experiment 1a I/S (A dm2) Vtop (V) Vbottom (V) Vtop/Vbottom Experiment 2b I/S (A dm2) Vtop (V) Vbottom (V) Vtop/Vbottom Experiment 3c I/S (A dm2) Vtop (V) Vbottom (V) Vtop/Vbottom

1 3.56 3.22 1.11

2 5.60 5.47 1.02

3 8.69 7.82 1.11

4 11.00 9.90 1.11

6 15.40 13.80 1.12

8 17.90 17.00 1.05

1.97 19.2 19.2 1.00

2.66 23.6 23.7 1.00

3.38 29.7 29.6 1.00

– – – –

– – – –

– – – –

2.50 104.3 103.4 1.01

2.50 104.1 103.6 1.00

– – – –

– – – –

– – – –

– – – –

Source: Tanaka (2005). S ¼ 5 dm2, N ¼ 20 pairs, Selemion CMV/ASV (Asahi Glass Co.), 20 pairs/stack 1 stack ¼ 20 pairs between electrodes. b S ¼ 200 dm2, N ¼ 87 pairs, Neocepta C66-5T/ACS (Tokuyama Inc.), 87 pairs/stack 12 stacks ¼ 1044 pairs between electrodes. c S ¼ 140 dm2, N ¼ 300 pairs, Aciplex K-172/A-172 (Asahi Chemical Co.), 300 pairs/ stack 6 stacks ¼ 1800 pairs between electrodes. a

189

Current Density Distribution

A2 ¼ 2ð¯tK þ ¯tA 1Þ

B1 ¼

N X

Y j r0out; j þ

1

00 00 RT g C N ln 0 0 gin C in F

N X 1

Y j rout;K; j þ

N X

Y j rout;A; j þ r00 N

(9.8)

(9.9)

1

! X RT N g00 C 00 B2 ¼ 2ð¯tK þ ¯tA þ 1Þ Y j ln 0 gout; j C 0out; j F 1

(9.10)

Here, C is electrolyte concentration, t¯ the transport number of counter-ions in the membrane, g the activity coefﬁcient, and subscripts j, in, out, K and A refer to group j, inlet of a desalting cell, outlet of a desalting cell, cation exchange membrane and anion exchange membrane, respectively. Superscripts 0 and 00 refer to desalting and concentrating cells, respectively. F is the Faraday constant. R is the gas constant. T is the absolute temperature. Yj is the number of desalting cells in group j within the range of (xj Dxj)oxjo(xj+Dxj), where Dxj is half of the velocity ratio x (deﬁned by Eq. (9.1)) of desalting cells in group j. In this theory, the distribution of Yj is assumed to be equated by the normal distribution in a stack incorporated with N desalting cells and the standard deviation of the normal distribution is assumed to be s. r0 ðr0in ; r0out Þ and r00 in Eqs. (9.7) and (9.9) are electric resistance (O cm2) of a desalting and a concentrating cell, respectively, given by the following deﬁnitions: r0 ¼

a 103 ð1 Þk0

(9.11)

r00 ¼

a 103 ð1 Þk00

(9.12)

where a is the thickness of the cell, k the speciﬁc conductivity of the solution (O cm) and e the current screening ratio of a spacer. The electric resistance of the concentrated solution r00 is assumed to be invariable in the system. rK (rin,K, rout,K) and rA (rin,A, rout,A) in Eqs. (9.7) and (9.9) are electric resistance (O cm2) of a cation and an anion exchange membrane, respectively, evaluated at a direct electric current (cf. Section 2.2(2)). The reasonability of Eq. (9.4) is conﬁrmed by the following seawater electrodialysis, in which the voltage difference at the top Vtop and that at the bottom Vbottom in a stack between electrodes is shown in Table 9.1 (Tanaka, 2005). Experiment 1 is for the small scale electrodialyzer in which the number of membrane pairs between electrodes is 20. Current density is changed incrementally and Vtop/Vbottom is in the range of 1.02–1.12. Experiments 2 and 3 are for the large scale electrodialyzers. Number of membrane pairs between

190

Ion Exchange Membranes: Fundamentals and Applications

electrodes is, respectively, 1044 in Experiment 2 and 1800 in Experiment 3, and in both experiments Vtop/Vbottom is 1.0. These experimental results show that Eq. (9.4) is realized when a large number of membrane pairs are integrated in an electrodialyzer. Using Eq. (9.4), the current density distribution equation is introduced as: x x2 (9.13) i ¼ a1 þ a 2 þ a3 l l I (9.14) a1 ¼ ðZ1 zout Þ þ Z2 S I 2Z 2 a2 ¼ 2 f3 ð2Z 1 þ 1Þzout g S

(9.15)

I a3 ¼ 3 f2 ðZ1 þ 1Þzout g Z2 S

(9.16)

Z1 ¼

B1 A1

Z2 ¼

(9.17)

A2 B2 A1

(9.18)

where l is the ﬂow-pass length in the desalting cell. I/S is the average current density in an electrodialyzer. zout is the outlet current density nonuniformity coefﬁcient deﬁned by: zout ¼

iout I=S

(9.19)

Under the situation in which Eq. (9.4) is realized, zout is expressed by zinout: zout ¼ zinout ¼

a1 þ a 2 p þ a3 p2 b1 þ b2 p þ b3 p2

(9.20)

I Z2 a1 ¼ S

(9.21)

I 2Z2 a2 ¼ 2 3 S

(9.22)

I Z2 a3 ¼ 3 2 S

(9.23)

191

Current Density Distribution

b1 ¼ Z 1

I S

(9.24)

I S I b3 ¼ 3ðZ 1 þ 1Þ S

b2 ¼ 2ð2Z 1 þ 1Þ

(9.25)

(9.26)

where p is the nondimensional distance x/l at which i ¼ I/S is satisﬁed. Next, the voltage difference between electrodes at inlets Vin is equal to Vp at the point x ¼ pl distant from the inlets of desalting cells. V in ¼ V p

(9.27)

Equation (9.27) is the second three-dimensional simultaneous equation, and Vp is expressed as: I þ C2 (9.28) V p ¼ C1 S C1 ¼

N X

Y j r0p;j þ

1

N X

Y j rp;K;j þ

1

N X

Y j rp;A;j þ r00 N

(9.29)

1

! X RT N g00 C 00 C 2 ¼ 2ð¯tK þ ¯tA 1Þ Yj 0 0 gp;j C p;j F 1

(9.30)

Under the situation in which Eq. (9.27) holds, zout is expressed by zinp: g 1 þ g2 p þ g 3 p2 ð2p 3p2 ÞðI=SÞ I þ Z4 g1 ¼ ðZ3 1Þ S I 2Z 4 g2 ¼ 2 ð3 2Z 3 Þ S I g3 ¼ 3 ðZ3 2Þ þ Z4 S zout ¼ zinp ¼

Z3 ¼

C1 A1

Z4 ¼

A2 C 2 A1

(9.31)

(9.32)

(9.33)

(9.34)

(9.35) (9.36)

192

Ion Exchange Membranes: Fundamentals and Applications

Finally, the third three-dimensional simultaneous equation is obtained from Eqs. (9.20) and (9.31) as follows: zinout ¼ zinp

(9.37)

Using the equations described above, we obtain zin, zout, p, a1, a2 and a3. zin is the inlet current density nonuniformity coefﬁcient deﬁned by: zin ¼

iin I=S

zin and zout are related to a1, a2 and a3 as follows: a1 zin ¼ I=S zout ¼

a 1 þ a2 þ a3 I=S

(9.38)

(9.39) (9.40)

9.1.2

Computation of Current Density Distribution We calculate here a1, a2 and a3 deﬁned in Eq. (9.13) using the equations introduced above and assuming the speciﬁcations of an electrodialyzer as S ¼ 1 m2, l ¼ 1 m, b ¼ 1 m, a ¼ 0.075 cm, I/S ¼ 3 A dm2 and the overall water permeability r ¼ 1 102 cm4 eq 1 s1 (cf. Chapter 6) for evaluating C00 in Eqs. (9.8) and (9.10). The current density distribution on an x-axis drawn along a ﬂow pass in a desalting cell is obtained as follows. Fig. 9.1 shows the current density distribution when the standard deviation of the normal distribution s of u given in Eq. (9.2) is altered as a parameter leaving uin and C 0in to be 5 cm s1 and 0.6 eq dm3, respectively. The current density changes are indicated by the project shaped curves and decreased drastically at the outlets of desalting cells when s is set at 0.292. In Fig. 9.2, uin is altered maintaining s and C 0in being 0.1 and 0.6 eq dm3, respectively. The current density also changed on the project shaped lines and decreased largely at the outlets of desalting cells when uin is kept to 0.925 cm s1. In Fig. 9.3, Cin is altered and s and uin are maintained at 0.1 and 5 cm s1, respectively. Here, the current density is changed on the concave lines and decreased sharply at C 0in ¼ 0:106 eq dm3 : 9.2. CURRENT DENSITY DISTRIBUTION AROUND AN INSULATOR AND ELECTRIC CURRENT SHADOWING 9.2.1

Equipotential Line Local electric current distributes around an insulator such as a partition, a reinforcement, a gasket and a spacer. It shadows an electric current, increases the local current density and causes an ohmic loss increase of an electrodialyzer.

193

Current Density Distribution

4.0 3.5 3.0

i (A/dm2)

2.5 2.0 1.5 1.0

: 0.1 : 0.2 : 0.292 : 0.29206

0.5 0.0 0.0

0.2

0.4

0.6 x (m)

0.8

1.0

1.2

Figure 9.1 Effect of standard deviation of solution velocity ratio on current density distribution.

4.5 4.0 3.5

i (A/dm2)

3.0 2.5 2.0 1.5 1.0

in : 5 cm/s :1 : 0.93 : 0.925

0.5 0.0 0.0

0.2

0.4

0.6 x (M)

0.8

1.0

1.2

Figure 9.2 Effect of solution velocity at the inlets of desalting cells on current density distribution.

194

Ion Exchange Membranes: Fundamentals and Applications

7 6

C ' in : 0.6 eq/dm3 : 0.2 : 0.12 : 0.106

i (A/dm2)

5 4 3 2 1 0 0.0

0.2

0.4

0.6 x (m)

0.8

6.0

1.2

Figure 9.3 Effect of electrolyte concentration at the inlets of desalting cells on current density distribution.

The electric current distribution is usually measured by drawing equipotential lines around an insulator, and depicting electric power lines perpendicular to the equipotential lines (Takeyama, 1968). In order to measure current density distribution, an insulator is placed between electrodes and an electric current is passed through the electrodes as illustrated in Fig. 9.4. The potential at the point x, y indicated in a two-dimensional plane is measured using a calomel electrode. From the potential obtained, equipotential lines are depicted and the electric current i around the insulator is measured using the following equation applied to Fig. 9.5: Dc (9.41) i¼k Dl where k is the speciﬁc conductivity, c the electric potential and l the distance on the electric force line. The measuring process of the current density distribution is as follows based on Fig. 9.5: (1) Electric potential at a point x, y is measured using a calomel electrode and equipotential lines are drawn from equipotential points. (2) The electrode surface is divided by n in the y-direction. Line 1 perpendicular to the equipotential line a is drawn at the point x, y. A circle in

195

Current Density Distribution

(x,y)

Insulator

Cathode

Electrodialyzer

Anode

Figure 9.4

Instrument for measuring current density distribution around an insulator.

Figure 9.5

Computing diagram of current density distribution.

contact with the equipotential line b being nearest to a is drawn on the basis of the point x, y. Line 2 perpendicular to the equipotential b is drawn at the contact point between the circle and the line b. The electric force line is obtained by linking the line 1 with the line 2.

196

Figure 9.6

Ion Exchange Membranes: Fundamentals and Applications

Current density distribution around an insulator (Saito, 1966).

(3) Dl and Dm are measured at every point x, y. Dl is the value in the range of Dm between A1 and A2. (4) Current density at the point x, y, ix,y, is calculated using the following equation:

ix;y ¼ ¯i

ð1=DlÞx;y n P ð1=nÞ ð1=DlÞx;y

(9.42)

y¼1

where ¯i is the average current density on the surface of the electrode. Saito (1966) measured the electric current distribution setting ¯i ¼ 1 A dm2 and changing the dimension of an insulator as shown in Fig. 9.6. 9.2.2

Equivalent Network Circuit The current density distribution is possible to be analyzed as follows by using the equivalent network circuit (Tanaka, 1984). We assume insulators to be arranged in an electrolyte solution as shown in the system of Fig. 9.7, in which an x-axis and a y-axis are drawn and electric currents are supplied from a

197

d

Current Density Distribution

l

y

0

d

l

d

x

Figure 9.7

Insulator in an electrolyte solution (Tanaka, 1984).

distance. We deﬁne an equivalent network circuit M N and current density im,n (1%m%M, 1%n%N) in the system (Fig. 9.8). Further, the current densities passing through the insulator are deﬁned to be zero as follows: iM;1 iM;R ¼ 0

(9.43)

Screening ratio r of the insulator at x ¼ 0 is d R ¼ (9.44) d þl N Applying the Kirchhoff equation to the network circuit in Fig. 9.8, the following M N-dimensional simultaneous equations are introduced: r¼

(1) m ¼ 1 For 1%n %N1:

2

n1 X n¼1

i1;n

n X n¼1

i2;n þ 3i1;n i1;nþ1 ¼ n

(9.45)

198

Ion Exchange Membranes: Fundamentals and Applications

l /2

y

iM,N

iM-1,N

im+1,N

im,N

i2,N

i1,N

iM,N-1

iM-1,N-1

im+1,N-1

im,N-1

i2,N-1

i1,N-1

iM,n+1

iM-1,n+1

im+1,n+1

im,n+1

i2,n+1

i1,n+1

iM,n

iM-1,n

im+1,n

im,n

i2,n

i1,n

iM,R+1 O iM,R

d /2

x

iM,2

iM-1,2

im+1,2

im,2

i2,2

i1,2

iM,1

iM-1,1

im+1,1

im,1

i2,1

i1,1

Figure 9.8

Equivalent network circuit (Tanaka, 1984).

For n ¼ N: N X i1;n ¼ N n¼1

(9.46)

199

Current Density Distribution

(2) 2%m%M1 For 1%n%N1: n X

im1;n 2

N¼1

n1 X n¼1

im;n þ

n X

imþ1;n 3m;n þ im;nþ1 ¼ 0

(9.47)

n¼1

For n ¼ N: N X

im;n ¼ N

(9.48)

n¼1

(3) n ¼ M For 1%n%R: im;n ¼ 0

Figure 9.9

Current density distribution on a y-axis (Tanaka, 1984).

(9.49)

200

Ion Exchange Membranes: Fundamentals and Applications

For R+1%n%N1: 2

n X

iM1;n 2

n¼1

n1 X

iM;n 3iM;n þ iM;nþ1 ¼ 0

(9.50)

n¼Rþ1

For n ¼ N N X

iM;n ¼ N

(9.51)

n¼Rþ1

In order to improve the precision, it is desirable to increase M and N as much as possible. The computation in this study was proceeded using a large-sized computer HITAC M-170 (Hitachi) with the aid of Gaussian elimination on the following source program setting M ¼ 20 and N ¼ 25.

3.0

2.5

x /d = 0

i

2.0

1.5

0.1

1.0

0.5

0.6

0.2

-0.4

-0.2

0

0.2 y/d

0.4

0.6

0.8

Figure 9.10 Current density distribution around an insulator. r ¼ 0.20 (Tanaka, 1984).

201

Current Density Distribution

Fig. 9.9 is an electric current distribution on a y/d-axis computed by putting x ¼ 0 and taking r as a parameter. This ﬁgure shows that i increases with decrease of y/d and increase of r. Current densities are plotted against y/d for r ¼ 0.20 taking x/d as a parameter and shown in Fig. 9.10, in which maximum

r : 0.08 0.20

1.6

0.32 0.40

1.4

0.52 0.60 1.2

y /d

1.0

0.8

0.6

0.4

0.2

0.2

0.4

0.6

0.8

1.0

1.2

x/d

Figure 9.11

Positions of maximum current densities (Tanaka, 1984).

Figure 9.12 Dimension of the insert used to evaluate electric current shadowing (Belfort and Gutter, 1972).

202 Table 9.2

Ion Exchange Membranes: Fundamentals and Applications

Qualitative estimate of percent shadowing

Current Density (mA cm2)

0.41 0.82 1.23 2.05 2.46

Width of Strap (in.) 0.05

0.10

0.20

0.40

0.60

0.80

0–1 0–3 5 0 0–1

5–10 10–15 10–15 5 5–10

20–25 20–25 20–25 10–15 20–25

40–45 45–50 40–50 50–60 40–45

80–90 80–90 85–90 80–90 75–85

90–95 90–95 90–100 90–95 90–95

Source: Belfort and Gutter (1972).

current density imax appeared at x/d>0 and electric current shadowing appeared at y/do0. The coordinates of imax are arranged on the same line as shown in Fig. 9.11. 9.2.3

Electric Current Shadowing Cross-section of spacer arms or struts and joints behaves as insulators because it shadows an electric current and causes increase in local current density and electric resistance in an electrodialyzer. Belfort and Gutter (1972) observed the electric current shadowing of insulators using a silver anode and a platinum cathode. In this experiment, Cl ions in a 1.0N NaCl solution migrate under an applied electric current for 1 min toward the anode through a shadower as shown in Fig. 9.12, and react with silver to form silver chloride. The shadowing effect is evaluated by observing the silver chloride precipitates on the anode. The shadowing set up in Fig. 9.12 is designed with varying strap dimensions of the Teﬂon shadower. From the qualitative results in Table 9.2, 90–95% shadowing occurs under the strap width ¼ 0.80 in. and percent shadowing decreases as the strap size decreases. REFERENCES Belfort, G., Gutter, G. A., 1972, An experimental study of electrodialysis hydrodynamics, Desalination, 10, 221–262. Mas, L. J., Pierrrd, P. M., Prax, P. A., 1970, Behavior of an electrodialysis unit cell, Desalination, 7, 285–296. Saito, H., 1966, Current density distribution around an insulator, Japan Monopoly Corporation Technical report S-20, pp. 129–134. Sonin, A. A., Probstein, R. F., 1968, A hydrodynamic theory of desalination by electrodialysis, Desalination, 5, 293–329. Takeyama, S., 1968, Theory of Electromagnetic Phenomena, Maruzen, Tokyo, Japan, p. 47. Tanaka, Y., 1984, Current density distribution around an insulator in an ion exchange membrane electrodialyzer, Bull. Soc. Sea Water Sci. Jpn., 37(5), 295–298. Tanaka, Y., 2000, Current density distribution, limiting current density in ion-exchange membrane electrodialysis, J. Membr. Sci., 173, 179–190.

Current Density Distribution

203

Tanaka, Y., 2002, Current density distribution, limiting current density and saturation current density in an ion-exchange membrane electrodialyzer, J. Membr. Sci., 210, 65–75. Tanaka, Y., 2005, Limiting current density of an ion-exchange membrane and of an electrodialyzer, J. Membr. Sci., 266, 6–17.

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Chapter 10

Hydrodynamics 10.1.

SOLUTION FLOW AND I–V CURVES

Sonin and Probstein (1968) developed the hydrodynamic theory of desalination electrodialysis for a multi-channel system with steady laminar ﬂow between plane parallel membranes. For sufﬁciently long channels, it was shown that there are two distinct regions: a ‘‘developing region’’ where the concentration diffusion layers are growing and a ‘‘developed region’’ where the diffusion layers ﬁll the channel as shown in Fig. 10.1. Parabolic and uniform velocity proﬁles were considered and self-consistent solution was derived for the distributions of salt concentration, electric ﬁeld and current density in the system, as well as for the total current. It was found that under a wide range of operating conditions, the solution for the total current is represented by the empirical formula 1=3 (10.1) I ¼ 1 expðC3 Þ where I and C are, respectively, dimensionless current and potential. Comparison was made of the calculated limiting total current with experiment. Mass et al. (1970) discussed the concentration distribution in a boundary layer based on the mass transport equation and the potential difference equation across the boundary layer. They show the concentration polarization and I–V curves as shown in Figs. 10.2 and 10.3. Curve 1 represents the concentration proﬁle and I–V relationship at the entrance of the desalting cell. Curves 2 and 3 represent the phenomena at increasing distance from the cell entrance. At curve 4 the concentration at the membrane surface is nearly zero. The solution velocity distribution in the desalting cell is assumed to be expressed by a parabolic line. 10.2.

EFFECT OF A SPACER ON SOLUTION FLOW (THEORETICAL)

10.2.1

Spacer Exerted Force The space between the membranes is ﬁlled with a ‘‘spacer’’ which has three major roles: (1) It keeps the membranes from touching each other; (2) It takes up any small mechanical force which may arise in the cell and which the membranes cannot support; and (3) It mixes the ﬂow and makes the concentration more homogeneous, which results in a better overall performance. The spacer may have many forms, ranging from extremely ﬁne porous media to coarse nets with holes of the size of the cell width. The ﬂow ﬁeld and the concentration ﬁeld depend on these forms. Pnueli and Grossman (1969) investigated the ﬂow between two parallel membranes in the presence of a spacer. A mathematical DOI: 10.1016/S0927-5193(07)12010-6

206

Ion Exchange Membranes: Fundamentals and Applications

Developing

Developed

∞ Length

Dialysate channel

Figure 10.1

Brine channel

Illustration of salt concentration in channels (Sonin and Probstein, 1968).

model for the spacer was introduced, which results in the momentum equation; an extension of the Darcy’s law, and was solved as follows to yield velocity proﬁles. The force Ku is assumed to act on the control volume through the pores inside it as illustrated in Fig. 10.4 and the following balance of forces are assumed to be realized. @u @2 u @P @u þ 2 dy dx P þ dx dy m dx Kudxdy ¼ 0 Pdy þ m @y @y @x @y (10.2) or @P @2 u ¼ Ku þ m 2 @x @y

(10.3)

207

Hydrodynamics

C

1 2 3 4 5 6

Y

Cationic membrane

Figure 10.2 Concentration proﬁles for the different distances from the compartment inlet (Mass et al., 1970).

and superposition of three components rP ¼ Kq þ mr2 q

(10.4)

Here, P is pressure, u the velocity on x-axis in ﬂow direction, m viscosity, x and y two Cartesian components, q velocity vector and K the constant in the extended Darcy’s law. The fully developed ﬂow considered here is completely described by Eq. (10.3) and the boundary conditions: u ¼ 0 at y ¼ d and at y ¼ d or by u ¼ 0 at y ¼ d and

@u ¼ 0 at y ¼ 0 @y

(10.5)

208

Ion Exchange Membranes: Fundamentals and Applications

1

2

I

3

4

5

6 V

Figure. 10.3 Current voltage characteristics for different distances from compartment inlet (Mass et al., 1970). P+

∂P dx ∂X

u

µ ∂u ∂y

x

Ku

µ(

2 ∂u + ∂ u2 dy) ∂y ∂y

y

P

Figure 10.4 Differential control volume containing some pores (Pnueli and Grossman, 1969).

209

Hydrodynamics

in which d is half cell width. On the scale of the model considered here the ﬂow is fully developed and continuity requires v¼w¼

@u @P @P ¼ ¼ ¼0 @x @y @z

(10.6)

in which v and w are the velocities on a y-axis and z-axis, respectively. Solving Eq. (10.3) with the boundary conditions, Eq. (10.5), the solution velocity u and the volume ﬂux Q are introduced as follows. coshðby=dÞ um 1 cosh b (10.7) u¼ tanh b 1 b Z

d

udy ¼

Q¼ d

2d dP tanh b 1 K dx b

(10.8)

um ¼ Q/2d is average solution velocity. b is a non-dimensional number and it characterizes the spacer by the following equation. b2 ¼

Kd 2 m

(10.9)

Some velocity proﬁles are shown in Fig. 10.5. By deﬁnition (see Eqs. (10.3) and (10.9)) b2 is a measure of the ratio of the ‘‘spacer exerted forces’’ to the ‘‘proﬁle shear exerted forces’’. The denser the spacer, the larger the b2 term becomes with a ﬂatter velocity proﬁle. For b ¼ 0 there is no spacer at all, and the well-known parabolic proﬁle is recovered from Eq. (10.7). For b-N the completely ﬂat proﬁle is obtained from Eq. (10.7). Existing systems operate with 3%b%30. Under these conditions, Eq. (10.7) can be approximated by the following simpler expression. h n b y oi 1 exp b 1 (10.10) u ¼ um b1 d 10.2.2

Flow Distribution Equation Miyoshi et al. (1982) derived the ﬂow distribution equation in an ion exchange compartment with a spacer by substituting the eddy viscosity of the spacer to the Navier–Stokes equation. The simulation in this research was proceeded based on the illustration in Fig. 10.6 showing that the solution ﬂows in the ion exchange compartment (IES) not only in a z-direction, but also in a y-direction colliding with a spacer network. In this study, at ﬁrst the ratio of the eddy viscosity ne against the molecular kinematic viscosity n is expressed as: ne me Rey ¼ n h

(10.11)

210

Ion Exchange Membranes: Fundamentals and Applications

=0

1.5

=5

=30

u/um

1.0

0.5

0.2

Figure 10.5

0.4

0.6 y/d

0.8

1.0

Velocity proﬁles in a ﬂow channel (Pnueli and Grossman, 1969).

in which, Re is the Reynolds number and me the eddy constant h is the half channel thickness of the compartment. Then, the ratio of the total viscosity nt against n is nt y ¼1þm n h

(10.12)

in which, m is the constant. Substituting Eq. (10.12) into the Navier–Stokes equation:

1þm

y d 2 u m du 1 Dp þ ¼ 2 h dy h dy n Dl

(10.13)

211

Hydrodynamics

2h

S

A

IES

K

u

z y

Figure 10.6 Solution ﬂow in an electrodialytic cell. A: anion exchange membrane, h: half channel thickness, IES: ion exchange compartment with spacer, K: cation exchange membrane, S: spacer and u: ﬂow velocity (Miyoshi et al., 1982).

where u is a component of the ﬂow velocity and Dp/Dl a pressure gradient in the ﬂow direction (on the z-axis). Boundary conditions are: u ¼ 0 at y ¼ 0 and y ¼ 2h du ¼ 0 at y ¼ h dy Solving Eq. (10.13) by taking account of Eq. (10.14) m ðm þ 1Þ lnðmY þ 1Þ mY U¼ ðm þ 1Þ2 lnðm þ 1Þ 1:5m2 m

(10.14)

(10.15)

in which U¼

u y and Y ¼ um h

(10.16)

and um ¼

h2 Dp ðm þ 1Þ2 lnðm þ 1Þ 1:5m2 m nm3 Dl

(10.17)

212

Ion Exchange Membranes: Fundamentals and Applications

The constant m in Eqs. (10.15) and (10.17) was evaluated as follows by measuring the pressure drop Dp between the pressure taps. 0:8 2:4 ð1 Þ2 m ¼ 2:1 10 nðt dÞ 3 5

(10.18)

in which, t is the thickness of the spacer, d the diameter of the ﬁber, n the number of the spacers and e the void fraction of the spacer. The solution velocity distribution is computed using Eqs. (10.15)–(10.18) taking m as a parameter and as shown in Fig. 10.7 (cf. Fig. 10.5). In Fig. 10.7, m ¼ 0 means n ¼ 0 (no spacer) in Eq. (10.18). m ¼ N means e ¼ 0 (no void) in Eq. (10.18).

m=0

1.5

101 102 104 ∞

U (−)

1.0

0.5

0

0

0.5 Y (−)

1.0

Figure 10.7 Flow distribution in an ion exchange compartment with spacer (Miyoshi et al., 1982).

Hydrodynamics

213

10.2.3

Mesh Step Model Mass transport in electrodialysis is governed by the ﬂow regime, which is determined by the presence of a spacer net (turbulizer). The ﬂow is characterized by the shedding of vortices at the discrete threads of the spacer net and these vortices produce convective mixing, which has a dominant inﬂuence on the process. Solan et al. (1971) proposed ‘‘mesh step model’’ representing the mass transfer process in a laminar concentration boundary layer whose development is periodically interrupted. In this theory, the cell length is divided into mesh steps of length Dx corresponding to the mesh of the spacer. The basic physical features in the mesh step model are: (a) the spacer produces partial mixing of the ﬂow and (b) it is characterized by a ﬁnite mesh size. At the beginning of the jth step, the concentration in bulk and the mixing cup average concentration are, respectively, denoted by Cb,j1 and Ca,j1 (subscripts b and a refer to bulk and average, respectively, and 1 means beginning), and the electric current density and the boundary layer thickness are, respectively, denoted by ij1 and dj1. At the end of the jth step the variables are denoted by, respectively, Cb,j2, Ca,j2, ij2 and dj2 (subscript 2 means end). In this situation, the bulk concentration at the beginning Cb,j1 is assumed to be equivalent to the value at the exit Cb,j2 C b;j1 ¼ C b;j2

(10.19)

Further, the concentration defect at the membrane surface at the end of the jth step is expressed by DC j2 ¼ C b;j2 C m;j2

(10.20)

in which subscript m refers to membrane. Here, the relationship between the concentration defect at the beginning of (j+1)th step and that at the end of the jth step is expressed by the following equation. DC ðjþ1Þ1 ¼ ð1 kÞDC j2

(10.21)

Here k is the mixing efﬁciency of the spacer. If k ¼ 1, the concentration proﬁle undergoes perfect mixing at the end of each discrete step Dx, while k ¼ 0 denotes the complete absence of mixing. Clearly, the mixing process leaves the average concentration unchanged, so that C a;ðjþ1Þ1 ¼ C a;j2

(10.22)

The phenomena mentioned above are schematically illustrated in Fig. 10.8, and analyzed by solving the basic laminar ﬂow equation for non-dimensional variables. Fig. 10.9 shows representative V/I vs. I curves obtained in this manner with experimental, indicating V/I to be decreased by the increase of k and by the decrease of d. Note here that Dx and d are the dimensionless values divided by the channel width.

214

Ion Exchange Membranes: Fundamentals and Applications

C b,j2 C b,(j+1)1 Ca,j2=Ca,(j+1)1 ∆C(j+1)1 ∆C j2 Cm,(j+1)1 Cm,j2

(j+1)1

Figure 10.8

j2

Concentration proﬁles before and after mixing (Solan et al., 1971). 3

EXPTL ∆x' = 10, k = 0.1 ∆x' = 10, k = 0.5 = 0.1

2 (V/i)/(V/i)i→0

= 0.2

1

0

Figure 10.9

1 i (amp/cm)

V/I vs. I curves (Solan et al., 1971).

2

215

Hydrodynamics

10.3.

EFFECT OF A SPACER ON SOLUTION FLOW (EXPERIMENTAL)

10.3.1

Solution Disturbing Effect A spacer is inserted in a desalting cell for mixing a solution ﬂowing in the cells. Hanzawa et al. (1965) evaluated the solution disturbing effects of the spacer using the assembly composed of one sheet of gasket (0.75 mm thick) and two sheets of transparent PVC plates (10 mm thick) illustrated in Fig. 10.10. A diagonal net spacer, a honeycomb net spacer or a crimp net spacer illustrated in Fig. 10.11 was incorporated with the gasket in which water was supplied. At the Transparent plate

A

Solution inlet

Solution outlet

A

Ink injecting hole

5

Slit

200

12.5

Frame

500

Frame

Ink inlet Spacer

Side frame Transparent plate A - A section

Figure 10.10 Assembly for observing stream lines around a spacer (Hanzawa et al., 1965).

216

Ion Exchange Membranes: Fundamentals and Applications

d

d′

A

A-A

θ A t Diagonal net d:3.5 mm

d′:0.6 mm

t:1.2 mm

e

t

Honeycomb net t:1.6 mm

d′

d

e:3.0 mm

t Crimp net d:20 mm

Figure 10.11

d′:1.5 mm

t:30 mm

Structure of spacers (Hanzawa et al., 1965).

217

Hydrodynamics

a b

X

C

X'

θ

u Y

Y

d

(a) Diagonal net

a

X u

b

Y

(b) Honeycomb net

Figure 10.12

Stream lines in a ﬂow pass (Hanzawa et al., 1965).

same time, coloring material was injected into the gasket from an injecting set up in Fig. 10.10. The ﬂow lines in the gasket were observed as presented in Fig. 10.12a for the diagonal net spacer and in Fig. 10.12b for the honeycomb net spacer or the crimp net spacer. The experiments show that the diagonal net disturbs the solution sufﬁciently, but the honeycomb net and crimp net do not. The streamlines around the diagonal net are presented in Photo 10.1. The ﬂow pattern for the diagonal net at the bottom of the ﬂow pass in the gasket and around an obstacle placed in the gasket are shown in Fig. 10.13a and b, respectively. This experiment shows that the structure of the spacer shape is also important to obtain a uniform solution distribution.

10.3.2

Mass Transport Effect Kuroda (1993) evaluated the limiting current density (mass transfer coefﬁcient) using the following oxidation–reduction reaction between ferrocy3 anide ion Fe(CN)4 6 and ferricyanide ion Fe(CN)6 in the simulation electrodialysis. 4 FeðCNÞ3 6 þ e ! FeðCNÞ6 ðCathodeÞ

(10.23)

3 FeðCNÞ4 6 ! FeðCNÞ6 þ e ðAnodeÞ

(10.24)

218

Ion Exchange Membranes: Fundamentals and Applications

Photo 10.1 Stream lines around a diagonal net spacer (Hanzawa et al., 1965). Y

Y′

(a)

(b)

Figure 10.13 Stream lines at the bottom of a ﬂow pass and at around of an obstacle with a diagonal net spacer (Hanzawa et al., 1965).

219

Hydrodynamics

The limiting current density in usual electrodialysis ilim,el (cf. Eq. 11.4) and the simulation electrodialysis ilim,sim are expressed by the following equations. ilim;el ¼

FDC ðt¯ tÞd

(10.25)

DCF (10.26) ¼ kL cF d C is the ionic concentration in a solution, D the diffusion constant of electrolytes, F the Faraday constant, ¯t and t the transport numbers of counter ions in a membrane and solution, respectively, d the thickness of a boundary layer and kL the mass transport coefﬁcient. Both equations are equivalent to each other from the respect that both are governed by kL if the ionic species and concentration are determined. In this experiment, spacer A, B, C or D in Table 10.1 was inserted in the ﬂow pass (150 mm width, 1540 mm length, 1 mm thickness) and an electrolysis solution (0.01 M K3Fe(CN)6, 0.01 M K4Fe(CN)6 and 2 M NaOH mixed solution) was supplied. Measuring the limiting current density ilim,sim by applying 500 mV between electrodes (Ni plate), kL and the following Sherwood number Sh were calculated using Eqs. (10.26) and (10.27). ilim;sim ¼

Sh ¼ kL Table 10.1

De D

Photograph and characteristics of spacers

Source: Kuroda (1993).

(10.27)

220

Ion Exchange Membranes: Fundamentals and Applications

Symbol

Spacer

d (m)

Sc (-)

A

1.0X10-3

480−2552

2.4X10-3

2552

B C

Sh Sc−1/3(−)

D

10

1/3 c 1/2 S

Re =k m

Sh

1

102

103 Re (−)

Figure 10.14

Sh/Sc1/3 Vs. Re (Kuroda, 1993).

in which De is the equivalent diameter ( ¼ 2dW(1eS)/(d+W)), d and W the thickness and width of the ﬂow pass, respectively, and eS the volume ratio of the spacer. From the above experiments, Sh/Sc1/3 (Schmidt number: Sc ¼ mL/rLD, mL: viscosity, rL: density) is plotted against Reynolds number Re ( ¼ DeULrL/ mL(1eS), UL: linear velocity) expressed by the following equation. Sh ¼ km Re1=2 Sc1=3

(10.28)

The plots are given in Fig. 10.14, which shows that the comparison of intensities of mass transport effect of each spacer is BACAD4A. The solution disturbing effect of a spacer is evaluated by the expanding degree of solution ﬂow sideward in the ﬂow pass (cf. Fig. 10.12 and Photo 10.1). 10.3.3

Flow Pattern Image Belfort and Gutter (1972) obtained a photographic image of a ﬂow pattern of liquid around the spacer. In this study, an exposed photographic ﬁlm (Kodak Panatomic X) was placed in an electrodialysis compartment (Fig. 10.15) in place of a membrane. The ﬁlm was exposed to saturation for two minutes in

221

Hydrodynamics

Photographic Developer In

Exposed Photographic Emulsion Spacer

Spent Developer Out

Figure 10.15 Surface ﬂow pattern experiment by Astropower photographic technique (Belfort and Gutter, 1972).

ordinary ﬂuorescent ceiling light. Photographic developer (22.2 ml/l Rodinal by Agfa) was then pumped through the cell compartment incorporated with the exposed ﬁlm. Under proper conditions, development of the ﬁlm occurred at a rate proportional to the rate at which the developer solution ﬂows over and mixes with the surface layer of the photographic emulsion. The photograph of typical mass diffusion contours is shown in Photo 10.2. The lighter areas represent faster ﬂowing regions or greater mass diffusion. The two dark strips on top and bottom of the photograph are the channel walls. Dark regular repeated patterns represent the location where spacer and surface touch, and irregular dark spots are air bubbles that remained in the stack during the 12-min developer run. All the light streaks can be thought of as a vortex screw-like ﬂow and

222

Ion Exchange Membranes: Fundamentals and Applications

Photo 10.2 Sectional photographic (positive) of the ﬁlm (negative) obtained from Astropower photographic technique (Belfort and Gutter, 1972).

can be followed along the ﬂow path in the ﬂow direction. In order to look at the photograph quantitatively, a vertical scan was carried out by the densitometer at a preselected position. Fig. 10.16 is an example of this scan for the expanded spacer (Exmet Corp. hexagonal net). The ordinate is a measure of mass diffusion toward the photographic ﬁlm. The empty channel (black) density–displacement curve is superimposed on the density–displacement curve for the spacer. Thus, any part of the spacer curve that drops below the maximum of the blank curve (optical density ¼ 0.67) can be considered dangerous for scale formation. 10.3.4

Dead Space Tanaka (2005) measured the limiting current density of an anion exchange membrane (Aciplex A-172, Asahi Chemical Co.) using the experimental apparatus incorporated with and without a diagonal net spacer in the desalting cell (0.075 cm thick). A NaCl solution in the range of 0.002–0.10 M was supplied into the cell at the linear velocity in the range of 1.6–13.6 cm s1. The limiting current densities measured with the spacer are plotted against the values measured without the spacer and presented in Fig. 10.17 showing that the spacer decreases the limiting current density. A spacer is usually considered to function as turbulence promoter. However, Fig. 10.17 shows that the spacer does not disturb the solution. It seems the spacer blocks the main stream of laminar ﬂow in a desalting cell and generates dead spaces between the spacer and a membrane as illustrated in Fig. 10.18. In the dead spaces, electrolyte concentration and solution density are estimated to be decreased, the solution ﬂows upward and the ﬂow forms branches. The dead spaces decrease the limiting current density,

223

Hydrodynamics

Spacer #8 Optical Density =1.27

Blank (Empty channel)

Optical Density =0.67

Scale Scale Formation formation danger

Base Line Density =0

Channel Width

Figure 10.16 Plot of density versus displacement across the width of the ﬁlm for a spacer and for the empty channel. Hexagonal expanded spacer, volume ﬂow rate: 44 ml/min and superﬁcial velocity: 5.05 cm/s (Belfort and Gutter, 1972).

and this event is supposedly accelerated when substances suspending in a feeding solution are adhered and accumulated in the dead spaces. In order to increase the limiting current density, the solution velocity and the Reynolds number must be increased and must create turbulence ﬂow, which promotes the main stream and suppresses the branch.

10.4.

LOCAL FLOW DISTRIBUTION IN A FLOW CHANNEL

Limiting current density of an electrodialyzer depends on a local ﬂow distribution of a solution in a desalting cell. Azechi et al. (1966) observed a local ﬂow distribution using a desalting cell model as follows. A stack of a practical scale unit-cell type electrodialyzer being operated for 10 months in a salt manufacturing plant was supplied for this investigation. The stack had been integrated with cross piece spacers manufactured by arranging strings (2 mm thick 2 mm width) at intervals of 25 mm. In this investigation, at ﬁrst, epoxy

224

Ion Exchange Membranes: Fundamentals and Applications

y

0.20

0.15

0.10

0.05

0.00 0.00

Figure 10.17

=

0.25

x

Limiting current density with a spacer (A/cm2)

0.30

0.05 0.10 0.15 0.20 0.25 Limiting current density with no spacer (A/cm2)

0.30

Effect of a spacer to the limiting current density (Tanaka, 2005).

Branch

Dead space Spacer string

Main stream

Branch Ion-exchange membrane

Figure 10.18

Desalting cell

Solution ﬂow around a spacer string (Illustration) (Tanaka, 2005).

resin (Three ronge AE and HW, Three bond Co.) was poured into the desalting cells in this stack and was hardened through a cross-linking reaction. The stack was then disassembled and the part of the hardened epoxy resin was taken out. The membrane deformation in this stack generated during 10 months operation

225

Hydrodynamics

Transparent plate

Middle plate

d

d'

n

io lut

w flo Base plate

So

Resin plate (epoxy)

Figure 10.19 Assembly for measuring solution velocity distribution in a channel (Azechi et al., 1966).

was reproduced exactly on the surface of the epoxy resin. A test plate presenting the uneven membrane deformation on the surface was cut down from the epoxy resin. The desalting cell model was assembled (Fig. 10.19), incorporated with the resin plate (epoxy resin), a transparent plate (PVC, 10 mm thick), a middle plate (PVC, d0 ¼ 3.4, 3.6, 4.0 or 4.4 mm thick) and a base plate (PVC, 15 mm thick). The distance between the transparent plate and the resin plate d corresponding to the local ﬂow-pass depth was determined by adjusting the thickness of the middle plate d0 . Next, water was supplied into the spaces formed between the test plate and transparent plate, and the stream lines were observed by pouring coloring material in the spaces (Fig. 10.20). The stream lines are shown by arrows originated at a0 , b0 , c0 ,y, k0 positioned on the right side in the ﬁgure. Reversed stream lines are also observed by supplying water in a reverse direction. Contour lines due to the membrane deformation are evaluated by d values presented at the bottom of the ﬁgure. Finally, local velocities u and the local ¯ and the relaﬂow-pass depth d at x, y are divided by their average u¯ and d; ¯ tionship between d=d and u=¯u is computed as indicated in Fig. 10.21 expressed by the following equation. 2 u d ¼ (10.29) u¯ d¯ The experiment in this study shows that the local solution velocity u depends only on the local distance d between a cation and an anion exchange membrane. In other words, it is necessary to avoid membrane deformation for preventing the irregularity of the local solution velocity.

226

285

140 120

k

k'

j

j'

i

h'

g

g'

80 f

f'

e

60

e'

d

40

c'

b

20

b'

10 5

a

1

2

3 di<0.3mm 0.3~0.5mm

Figure 10.20

d'

c

4

5

6

0.5~0.7mm 0.7~10mm

7

8 Section

1.0~1.5mm 1.5~2.0mm

Stream lines in a channel (Azechi et al., 1966).

a'

9

10

2.0mm (d'=3.4mm)

11

12

13

14

a~k, a'~k'--Coloring matter inlet

15

Ion Exchange Membranes: Fundamentals and Applications

Width of flow path

100

i'

h

227

Hydrodynamics

3.0 2.0

1.0

u u

0.5

0.2

d u = u d

d' mm 3.6 3.6 3.6 3.6 4.0 4.0 4.4 4.4 3.4

2

0.1

0.2

0.5

d mm 1.28 1.70 1.28 1.28 1.68 1.68 2.08 2.08 0.86 1

Q l/h 7.8 7.8 14.7 20.6 14.6 25.9 20.6 32.4 8.6

u cm/s 1.21(a~K) 0.91(a'~K') 2.28(a~K) 3.20( " ) 1.73( " ) 3.07( " ) 1.97( " ) 3.10( " ) 1.97( " ) 2

3

d d

Figure 10.21 Relationship between local ﬂow pass depth and local solution velocity in a channel (Azechi et al., 1966).

10.5. EFFECT OF SOLUTION FLOW ON LIMITING CURRENT DENSITY AND STATIC HEAD LOSS IN A CHANNEL Ichiki et al. (1976) assembles an electrodialysis cell incorporated with a cation exchange membrane (Selemion CMV, Asahi Grass Co.) and an anion exchange membrane (Selemion AMV). A hexagonal net spacer, a honeycomb net spacer and a diamond net spacer were integrated in the desalting cell. A 3000 ppm NaCl solution was supplied to a desalting cell at constant linear velocity u, and a constant electric current I was applied. Changing an electric current incrementally, the limiting current density ilim was determined from the inﬂection of I–V plots, at the same time the static head drop DH in the cell was determined. Changing u in the desalting cell incrementally, Reynolds number Re vs. DH and Re vs. ilim plots were obtained. The plotting of ilim and DH against Re in this investigation is illustrated by the model in Fig. 10.22 showing

228

Ion Exchange Membranes: Fundamentals and Applications

∆H

tur B rf

lo w

C

in a

ilim

m La

Log ilim

log ∆H

bu len t fl

ow

C

B

A A

Re

Figure 10.22

Re vs. DH and Re vs. ilim plots (illustration) (Ichiki et al., 1976).

that the ﬂow pattern of a solution is divided by the inﬂection point B, and further that A-B corresponds to the laminar ﬂow and B-C corresponds to the turbulent ﬂow. The relationship between Re and DH is expressed by the following equation including the constants m and n. DH ¼ mRen

(10.30)

Joining the above experimental result with another one, n is estimated to take the following values (Tanaka, 2004). n ¼ 1:0 1:6 ðlaminar flowÞ n ¼ 1:7 2:0 ðturbulent flowÞ

10.6.

(10.31)

AIR BUBBLE CLEANING

Electrodialyzers are subject to membrane fouling, which reduces limiting current density. In order to overcome such a problem, Hitachi Ltd. and Babcock-Hitachi K. K. developed an air bubble cleaning type electrodialyzer (Takahashi et al., 1979). The structure of an electrodialyzer is illustrated in Fig. 10.23. Air bubbles are introduced into the rectangular compartments by means of dispensers through conduits that are formed by holes – provided along the upper and lower edges of the frames and membranes – when the membranes

229

Hydrodynamics

Offgas Ion-exchange membrane

Brine

Compartment frame

Offgas

Air bubbles

Dilute Brine Air

Raw water

Air

Figure 10.23 Structure of an air bubble cleaning type electrodialyzer (Takahashi et al., 1979).

and frames are joined to construct the electrodialyzer. The bubbles clean the membrane surface and promote turbulence of the solution as illustrated in Fig. 10.24, so that suspended solids readily pass through the electrodialyzer. Raw water fed from one end of the compartment group is discharged as desalinated water from the other end, undergoing once-through treatment. Fig. 10.25 shows limiting current densities in a bubble agitation system (ﬂow rate: 2 cm s1) compared with those in a spacer agitation system observed in NaCl solution electrodialysis. The limiting current density by bubble agitation is constant regardless of ﬂow rate and shows a high level even at low ﬂow rates. Current shadowing by bubbles is lower than by spacers and has the effect of reducing the electric resistance of the electrodialyzer.

230

Ion Exchange Membranes: Fundamentals and Applications

Scale

Air bubble

Ion-exchange membrane

Figure 10.24

Principle of air bubble cleaning (Takahashi et al., 1979).

10.7. FRICTION FACTOR OF A SPACER AND SOLUTION DISTRIBUTION TO EACH DESALTING CELL (Tanaka, 2004) Fig. 10.26 illustrates the ﬂow system (Systems I and II) of a desalting solution in a stack of an electrodialyzer. The ﬂow system of an electrolyte solution to be desalinated is supplied from outside of a stack to an entrance duct, ﬂows through an entrance passageway, a current-passing section and an exit passageway and is discharged from an exit duct to the outside of the stack. Fig. 10.27 illustrates the static head of a solution in a desalting cell and a concentrating cell. A desalting solution is assumed to be supplied to a desalting cell by a one-pass ﬂow system. A concentrating solution is assumed to be collected by an overﬂow collecting system from the exit duct at point q corresponding to the static head of hex, as indicated in the ﬁgure. The static head difference DH between the entrance and the exit ducts of a desalting cell in Fig. 10.27 is given by Eq. (10.32). DH ¼ DH C þ 2DH W

(10.32)

where DHC is the static head difference between the entrance and the exit of a current-passing section. DHW is the static head difference between the entrance and the exit of a passageway. In Eq. (10.32), head loss caused by expansion, reduction and bending of ﬂow is neglected. Subscript C and W refer to a current-passing

231

Hydrodynamics

70

60

Limiting current density (A. l/dm 2.eq)

Air bubbling (2 cm/s)

50

40 Spacer 30

20

10 No bubbling, no spacer

0

Figure 10.25

0

5 Flow rate (cm/s)

10

Effect of air bubbling on limiting current density (Takahashi et al., 1979).

section and passageway, respectively. Using the Fanning equation, DHC and DHW are expressed by the function of friction head as: DH C ¼ H C;en H C;ex ¼

ff S l C ðaC þ bC Þu2C gaC bC

(10.33)

ff S ðaW þ bW Þu2W gaW bW

(10.34)

DH W ¼ H W;en H W;ex ¼

Here, f is the friction factor of a solution, fS the friction factor of a spacer, u the linear velocity of a solution, g the gravitational acceleration, a the ﬂow-pass depth, b the ﬂow-pass width and l the ﬂow-pass length. In hydrodynamics, friction factor is usually indicated only by f. In an electrodialyzer, however, a spacer in a ﬂowing solution causes friction loss and increases DH. This phenomenon is represented by fS in Eqs. (10.33) and (10.34).

232

Ion Exchange Membranes: Fundamentals and Applications

Q1 u1 Hex,1 uw1 way p

Exit duct

No.1 Current passing section

uC1

Q0

uw1 way p Entrance duct Q1 u1 Hen,1

u0 Hen,0

QN uN Hex,N u0*

Qx ux Hex,x uwx way p

Exit duct

uwN way p

No.x Current ucx passing section

No.N Current ucN passing section

uwx way p Entrance duct Qx ux Hen,x

uwN way p QN uN Hen,N

(a) System I (one-way flow system) u0* Hex,0

Q1 u1 Hex,1 way p

Q0 u0 Hen,0

Qx ux Hex,x

QN uN Hex,N

uwx way p Exit duct

uwN

No.1 Current uC1 passing section

No.x Current ucx passing section

No.N Current ucN passing section

uw1 way p

uwx way p

uwN way p

uw1

Exit duct

Entrance duct

Q1 u1 Hen,1

Entrance duct

Qx ux Hen,x

way p

QN uN Hen,N

(b) System II (Two-way flow system)

Figure 10.26

Desalting solution ﬂow system in a stack (Tanaka, 2004).

f is related to the Reynolds number Re in Eq. (10.35) because the solution ﬂowing in a current-passing section and in a passageway is approximated by laminar ﬂow. f ¼

16 Re

d eu Re ¼ ¼ w

(10.35) 2 ab u w aþb

(10.36)

where de is an equivalent diameter and w the kinetic viscosity of a solution. Substituting Eq. (10.36) into Eqs. (10.33) and (10.34) 8w a C þ bC 2 f l C uC DH C ¼ g S aC bC

(10.37)

233

Hydrodynamics

H w H c

H

Hc,en

Hen

Hw,en Hw,ex

Hc,ex

Exit duct

Hex

Hw q

Hw,en Hw,ex

hex

Exit way

Current passing section

Gasket

Entrance way

Entrance duct

Exit duct (concentrating cell)

Figure 10.27 Static head of a solution in a desalting cell and a concentrating cell (Tanaka, 2004).

DH W ¼

8w a W þ bW 2 fS l W uW aW bW g

Substituting Eqs. (10.37) and (10.38) into Eq. (10.32) ) ( 8w a C þ bC 2 aW þ b W 2 DH ¼ l C uC þ 2 l W uW f aC bC aW bW g S 8w aC þ bC 2 ¼ l C ð1 þ 2KÞf S uC aC bC g

2 aW þ bW lW uW aW bW lC uC 2 aC bC aW þ bW lW bC 1 ¼ n aC þ bC aW bW lC bW

K¼

(10.38)

ð10:39Þ

aC bC aC þ bC

ð10:40Þ

where K is the constant that relates to the structure of the current-passing section and n the number of passageways in the desalting cell at the entrance or the exit.

234

Ion Exchange Membranes: Fundamentals and Applications

Substituting DH distribution measured by an electrodialysis experiment into Eqs. (10.39) and (10.40), the distribution of fSuC and the average of fSuC, fSuC (average), are calculated. Further, fS is calculated from fSuC (average) and the average of uC, uC (average), in a stack using the following equation: fS ¼

f S uC ðaverageÞ uC ðaverageÞ

(10.41)

In the solution ﬂow system in the stack shown in Fig. 10.26, the amount of a solution Q0 supplied to the inlet of an entrance duct corresponds to the total amount of the solution distributed to current-passing sections in cell pair numbers 1 to N. Thus we have Eq. (10.42). Here, N is the number of all desalting cells in the stack. N X

aC bC uC;x ¼ Q0 ¼ u0 sn

(10.42)

x¼1

where uC,x is the linear velocity in a current-passing section in cell pair number x, u0 the linear velocity at the inlet of an entrance duct and s the sectional area of the duct. The amount of a solution Qx ﬂowing in a duct in cell pair number x is expressed by Qx ¼ Q0

x X

aC bC uC;x

(10.43)

x¼1x

The theoretical ratio of Qx to Q0 is deﬁned by

Qx Q0

x P

¼1 theo

aC bC uC;x

x¼1

Q0

(10.44)

Here, we deﬁne the approximate ratio of Qx to Q0 by

Qx Q0

appro

x y ¼ 1 N

(10.45)

where y is the distribution coefﬁcient of solution ﬂowing into each desalting cell. When y ¼ 1 holds, the linear velocity in each desalting cell becomes uniform. If the linear velocity is not uniform, y41 or yo1 holds. Here, we deﬁne the ratio of (Qx/Q0)appro to (Qx/Q0)theo by Eq. (10.46). y is computed by ﬁnding the

Hydrodynamics

235

circumstance in which the standard deviation of e distributed in a stack becomes minimum.

Qx Q0 appro ¼ Qx Q0 theo

(10.46)

Azechi and Fujimoto (1970) evaluated the performance of an electrodialyzer (Table 10.2) incorporated with cation exchange membranes Aciplex CK-2 and anion exchange membranes Aciplex CA-3 (Asahi Chemical Co.). The ﬂow system of the desalting solution in this investigation was classiﬁed as System I and System II (cf. Fig. 10.26). Seawater was supplied by a one-pass ﬂow system maintaining the average linear velocity in desalting cell uav (in a currentpassing section) at 2.88 cm s1, and electrodialyzed by applying constant current density 3.0 A dm2. The structures of the desalting cell and the concentrating cell are illustrated in Fig. 10.27. The static head in cell pair number x in an entrance desalting duct Hen,x and that in an exit duct Hex,x and their difference DHx were measured through manometers; they are shown in Fig. 10.28 (System I, one-way ﬂow system) and Fig. 10.29 (System II, two-way ﬂow system). In this experiment, Experiment 1 was achieved at ﬁrst, and then Experiment 2 was achieved after an electrodialytic operation during 300 h. The static head in cell pair number x in an entrance desalting cell Hen,x and that in an exit duct Hex,x and their difference DHx are plotted against x; these are illustrated in Fig. 10.28 (System I, Experiment 1) and Fig. 10.29 (System II, Experiment 1). An arrow in the ﬁgure shows the ﬂow direction of a solution in a duct. Hx reaches the lowest point DHmin at x ¼ N/2 ¼ 150, in Fig. 10.28 (System I) and becomes DHmin at x ¼ N ¼ 300 in Fig. 10.29 (System II). Solution velocities on each desalting cell u are proportional to DHx, so that in order to realize a uniform ﬂow rate distribution in desalting cells in a stack, it is preferable to adopt System I rather than System II and reduce the number of cells N in a stack. Substituting DHx shown in Figs. 10.28 and 10.29 into Eq. (10.39), fSuC is calculated. Substituting fSuC obtained above into Eq. (12.41), fS is evaluated (Table 10.3). Further, the solution distribution coefﬁcient y is obtained by setting the standard deviation of e (Eq. (10.46)) at the minimum (Table 10.3). Inspecting Table 10.3, it is found that fS in System I is the same as that in System II, and that yo1 holds in System I, and y41 holds in System II. If y ¼ 1 holds in System I, the solution velocity in desalting cells in a stack should be uniform. Such a condition is not realized in System II. fS in Experiment 2 is found to be larger than that in Experiment 1. This is probably because the substances suspended in the seawater feed accumulate on the surface of ion exchange

236 Table 10.2

Ion Exchange Membranes: Fundamentals and Applications

Speciﬁcations of an electrodialyzer and electrodialytic conditions

Membrane area S (106.5 cm 106.5 cm) Species of membranes Thickness of a cation exchange membrane CK-2 Thickness of an anion exchange membrane CA-3 Number of cell pairs in a stack N Flow-pass length of a current-passing section lC Flow-pass depth of a current-passing section aC Flow-pass width of a current-passing section bC Flow-pass length per unit-cell pair of a duct ( ¼ 0.023+0.021+2 0.075) Current density I/S Temperature in Experiment 1 Temperature in Experiment 2 (Desalting cell) Number of desalting cells in a stack Flow-pass length of a way lw Flow-pass depth of a way aw Flow-pass width of a way bw Dimension of a vertical of a duct a Dimension of a horizontal of a duct b Number of entrance or exit ducts (ways) of an electrodialyzer n Flow system in an electrodialyzer Solution volume at the inlet of entrance ducts Q0 Solution velocity at the inlet of an entrance duct v0 Solution velocity in a current-passing section vC (Concentrating cell) Number of concentrating cells in a stack Flow-pass length of a way lw Flow-pass depth of a way aw Flow-pass width of a way bw Diameter of a duct Number of entrance or exit ducts (ways) of an electrodialyzer n Flow system in an electrodialyzer Static head at the outlet of a concentrating exit duct hex

113.42 dm2 Asahi Chemical Co Aciplex CK-2, CA-3 0.023 cm 0.021 cm 301 106.5 cm 0.075 cm 106.5 cm 0.194 cm 3 102 A cm2 20.5–21.5 1C 15.4–18.1 1C 302 4.0 cm 0.075 cm 4.5 cm 3 cm 4 cm 10 One-pass ﬂow 25.00 m3 h1 57.87 cm s1 2.888 cm s1 301 4.0 cm 0.075 cm 1.8 cm 1.8 cm 4 Overﬂow collection 40 cm

Source: Azechi and Fujimoto (1970).

membranes or spacers during the operation of the electrodialyzer for 300 h. y in Experiment 1 is recognized to be the same as that in Experiment 2. 10.8. PRESSURE DISTRIBUTION IN A DUCT IN AN ELECTRODIALYZER (Tanaka, 2004) In Figs. 10.26 and 10.27, a solution is supplied to the inlet of an entrance duct at the ﬂow amount of Q0 and linear velocity of u0. In cell number x, the

237

Hydrodynamics

Figure 10.28 Distribution of static head of a solution in a desalting and a concentrating duct in a stack (System I) (Azechi and Fujimoto, 1970). 120

Hen,x, Hex,x, Hx, hex (cm)

100

80

Hen,x

60

H ex,x

hex

40

∆Hx 20 ∆Hmin 0

0

50

100

150

200

250

300

350

x

Figure 10.29 Distribution of static head of a solution in a desalting and a concentrating duct in a stack (System II). (Azechi and Fujimoto, 1970).

238

Ion Exchange Membranes: Fundamentals and Applications

Table 10.3 Spacer friction factor and solution distribution coefﬁcient in current-passing section in desalting cells Experiment

System

1

I

A B Average A B Average

II Average 2

I

A B Average A B Average

II Average

fs

y

6.00 6.16 6.08 5.95 6.01 5.98 6.03 7.91 7.50 7.71 7.65 7.76 7.71 7.71

0.930 0.889 0.910 1.056 1.044 1.050 0.980 0.952 0.921 0.937 1.015 1.033 1.024 0.980

Source: Tanaka (2004).

solution ﬂows in an entrance duct at the linear velocity of ux, ﬂows through a passageway (uW,x), ﬂows in a current-passing section (uC,x) and ﬂows out of an exit duct. At the outlet of the exit duct, the solution ﬂows out at the velocity of u0 : In this ﬂow system, the static head at point p in cell pair number x is Hen,x in an entrance duct and Hex,x in an exit duct, respectively. The changes of the static head, the velocity head and the friction head in an entrance duct and an exit duct are given using the Bernoulli theorem as follows. (1) In an entrance duct in ﬂow Systems I and II ux at a point p in a cell pair number x in an entrance duct is expressed by the following equation: x y ux ¼ u 0 1 N

(10.47)

The sum of the static head Hen,0 and the velocity head u20 =2g at the inlet of an entrance duct is equal to the sum of every head in the duct described below. (a) The static head at a point p in cell pair number x. (b) The velocity head at a point p in cell pair number x. (c) The total amount of friction head between the inlet and point p in cell pair number x.

239

Hydrodynamics

(d) The total amount of velocity heads of solutions ﬂowing through passageways between the inlet and point p in cell pair number x. The phenomena mentioned above are expressed by Eq. (10.48). 2 u20 u0 x 2y ¼ H en;x þ H en;0 þ 1 2g 2g N 2 X x x u2W;x u0 x 2y X þ ken;x 1 þ 2g x¼0 2g N x¼0

ð10:48Þ

where ken,x is the friction coefﬁcient of a solution in the entrance duct. (2) In an exit duct in a ﬂow System I ux is indicated by the following equation: ux ¼ u0

x y N

(10.49)

The relationship between the static head, the velocity head and the friction head in an exit duct are given by the same manner mentioned in (1) as follows: 2 2 u0 ðu0 Þ x 2y ¼ H ex;x þ H ex;N þ 2g 2g N 2 X x x x 2y X u2W;x ðu0 Þ ð10:50Þ þ kex;x þ 2g x¼0 2g N x¼0 where kex,x is the friction coefﬁcient of a solution in the exit duct. (3) In an exit duct in ﬂow System II Considering this in the same manner as described above, the following equations are introduced: x y ux ¼ u0 1 N

H ex;0 þ

(10.51)

2 ðu0 Þ2 ðu0 Þ x 2y ¼ H ex;x þ 1 2g 2g N 2 X x x u2W;x ðu0 Þ x 2y X ð10:52Þ þ kex;x 1 2g x¼0 2g N x¼0

240

Ion Exchange Membranes: Fundamentals and Applications

ken,x and kex,x in Eqs. (10.48), (10.50) and (10.52) are related to the friction factors in a duct, fen,x and fex,x by the Fanning equation as follows: ken;x ¼ 4f en;x

t Deq

(10.53)

kex;x ¼ 4f ex;x

t Deq

(10.54)

where t is ﬂow-pass length in a duct in a cell pair and Deq the equivalent diameter of a duct section. The shape of a duct section is rectangular, so that Deq is expressed as follows, using the dimension of the wetted perimeter, vertical and horizontal as L, a and b: Deq ¼ 4

s ab ¼2 L aþb

(10.55)

Substituting Eq. (10.55) into Eqs. (10.53) and (10.54) ken;x ¼ 2f en;x t

aþb ab

(10.56)

kex;x ¼ 2f ex;x t

aþb ab

(10.57)

The ﬂow pattern of a solution in a duct is laminar ﬂow, so that fen,x and fex,x are expressed as follows: f en;x ¼

16 Reen;x

(10.58)

f ex;x ¼

16 Reex;x

(10.59)

where Reen,x and Reex,x are the Reynolds numbers in an entrance and an exit duct, respectively, and they are shown to take account of Eq. (10.55) as follows: Reen;x

Deq x y u0 1 ¼ wen N

ab ¼2 aþb

1 x y u0 1 ðI and IIÞ wen N

ð10:60Þ

241

Hydrodynamics

Reex;x ¼

Deq x y ab 1 x y u0 u0 ¼2 ðIÞ wex N a þ b wex N

Deq x y u0 1 w N ex ab 1 x y ¼2 ðIIÞ u0 1 a þ b wex N

(10.61)

Reex;x ¼

ð10:62Þ

where wen and wex are the kinetic viscosities of a solution ﬂowing in an entrance and an exit duct, respectively. Taking account of Eqs. (10.53)–(10.62) in Eqs. (10.48), (10.50) and (10.52), we have the following equations. (1) In the entrance duct in ﬂow Systems I and II

u20 H en;0 þ 2g

u20 x 2y ¼ H en;x þ 1 N 2g X 2 x aþb u0 x y þ 16 wen t 1 2g x¼1 ab N þ

x X u2W;x x¼0

2g

ðI and IIÞ

ð10:63Þ

Eq. (10.63) is expressed by Eq. (10.64) H s;0 þ H v;0 ¼ H s;x þ H v;x þ H f;x þ H v;w;x

(10.64)

where s, v and f in subscripts refer to, respectively, the static head, the velocity head and the friction head in a duct. v, w refers to the velocity head in a passageway. (2) In the exit duct in ﬂow System I

H ex;N þ

2 2 ðu0 Þ ðu0 Þ x 2y ¼ H ex;x þ 2g 2g N X 2 x y aþb u x þ 16 wex t 0 2g x¼0 N ab þ

x X u2W;x x¼0

2g

ðIÞ

ð10:65Þ

242

Ion Exchange Membranes: Fundamentals and Applications

H s;N þ H v;N ¼ H s;x þ H v;x þ H f;x þ H v;w;x

(10.66)

(3) In the exit duct in ﬂow System II 2 2 ðu0 Þ ðu0 Þ x 2y ¼ H ex;x þ 1 H ex;0 þ 2g 2g N X 2 x aþb u x y þ 16 wex t 0 1 2g x¼0 ab N

x X u2W;x x¼0

2g

ðIIÞ

ð10:67Þ

H s;0 þ H v;0 ¼ H s;x þ H v;x þ H f;x H v;w;x

(10.68)

The static head difference DHx between point p in cell pair number x in an entrance duct and that in an exit duct is shown by Eq. (10.69). DH x ¼ H en;x H ex;x

(10.69)

120

(Hs,0+Hv,0)en

Hs Hs+Hv Hs+Hv+Hf (cm)

100

(Hv,w)en

Entrance duct 80

Exit duct

60

(Hs,N+Hv,N)ex (Hv,w)ex

40 (Hs)en (Hs+Hv)en (Hs+Hv+Hf)en

20

0

0

50

100

(Hs)ex (Hs+Hv)ex (Hs+Hv+Hf)ex

150

200

250

300

350

x

Figure 10.30 Pressure distribution in a desalting duct in a stack (System I) (Tanaka, 2004).

243

Hydrodynamics

120

Hs Hs+Hv Hs+Hv+Hf (cm)

100

(Hs,0+Hv,0)en Entrance duct

(Hv,w)en

Exit duct

(Hv,w)ex

80

60

40 (Hs)en (Hs+Hv)en (Hs+Hv+Hf)en

20

0

0

50

100

(Hs,0+Hv,0)ex (Hs)ex (Hs+Hv)ex (Hs+Hv+Hf)ex

150

200

250

300

350

x

Figure 10.31 Pressure distribution in a desalting duct in a stack (System II) (Tanaka, 2004).

The static head distribution in an entrance duct is computed using Eq. (10.63) and that in an exit duct is computed using Eqs. (10.65) and (10.67). Hs, Hs+Hv and Hs+Hv+Hf in an entrance duct and an exit duct are plotted against x and are illustrated in Fig 10.30 (System I) and Fig. 10.31 (System II). Hs, Hs,0+Hv,0 and Hs,N+Hv,N are observed values measured in the experiment described in Section 10.7 (Figs. 10.28 and 10.29). Hv,w is computed using the following equations obtained from Eqs. (10.64), (10.66) and (10.68). In the entrance duct in ﬂow Systems I and II ðH v;w Þen ¼ ðH s;0 þ H v;0 Þen ðH s þ H v þ H f Þen

(10.70)

In the exit duct in ﬂow System I ðH v;w Þex ¼ ðH s;N þ H v;N Þex ðH s þ H v þ H f Þex

(10.71)

In the exit duct in ﬂow System II ðH v;w Þex ¼ ðH s þ H v þ H f Þex ðH s;0 þ H v;0 Þex

(10.72)

Here, DHx in Eq. (10.69) corresponds to the following equation: DH ¼ ðH s Þen ðH s Þex

(10.73)

The changes of DH in a stack are found to depend largely on the changes of Hv,w as shown in Figs. 10.30 and 10.31. In order to operate an electrodialyzer stably,

244

Ion Exchange Membranes: Fundamentals and Applications

it is naturally desirable to realize a uniform distribution of DH. For this purpose, it is effective to decrease (Hv,w)en–(Hv,w)ex in Fig. 10.30 (System I), and this can be put into practice by keeping the distribution coefﬁcient of solutions ﬂowing into every desalting cell y at 1. REFERENCES Azechi, S., Fujimoto, Y., Yuyama, T., 1966, Studies on electrodialytic equipment with ion exchange membrane (XIII), Flow velocity distribution of the ﬂuid passing through the uneven ﬂat ﬂow path, Scientiﬁc Papers of The Odawara Salt Experiment Station, Japan Monopoly Odawara, Okayama, Japan, vol. 11, pp. 20–23. Azechi, S., Fujimoto, Y., 1970, Flow characteristics of the practical-scale electrodialytic apparatus of ﬁlter-press type, Bull. Soc. Sea Water Sci. Jpn., 23(4), 134–147. Belfort, G., Gutter, G. A., 1972, An experimental study of electrodialysics hydrodynamics, Desalination, 10, 221–262. Hanzawa, N., Azechi, S., Fujimoto, Y., Nagatsuka, S., 1965, Studies on the electrodialytic equipment with ion exchange membrane X, Comparison of spacer used for electrodialytic equipment, Scientiﬁc Papers of The Odawara Salt Experiment Station, Japan Monopoly Corporation, Odawara, Japan, vol. 10, pp. 16–25. Ichiki, T., Asawa, T., Hani, H., 1976, An experimental study of turbulance promoters in electrodialysics, Fifth International Symposium on Fresh Water from the Sea, vol. 3, pp. 89–96. Kuroda, O., 1993, Study for improvement of efﬁciency in electrodialyzer, Bull. Soc. Sea Water Sci., Jpn., 47(4), 248–258. Mass, L. J., Pierrard, P. M., Prax, P. A., 1970, Behavior of an electrodialysis unit cell, Desalination, 7, 285–296. Miyoshi, H., Fukumoto, T., Kataoka, T., 1982, A consideration on ﬂow distribution in an ion exchange compartment with spacer, Desalination, 42, 47–55. Pnueli, D., Grossman, G., 1969, A mathematical model for the ﬂow in an electrodialysics cell, Desalination, 6, 303–308. Solan, A., Winograd, Y., Katz, U., 1971, An analytical model for mass transfer in an electrodialysis cell with spacer of ﬁnite mesh, Desalination, 9, 89–95. Sonin, A. A., Probstein, R. F., 1968, A hydrodynamic theory of desalination by electrodialysics, Desalination, 5, 293–329. Takahashi, S., Arikawa, Y., Teraoka, Y., 1979, Air bubble cleaning type electrodialyzer and its high temperature process, Hitachi Rev., 28(6), 317–322. Tanaka, Y., 2004, Pressure distribution, hydrodynamics, mass transport and solution leakage in an ion-exchange membrane electrodialyzer, J. Membr. Sci., 234, 23–39. Tanaka, Y., 2005, Limiting current density of an ion-exchange membrane and of an electrodialyzer, J. Membr. Sci., 266, 6–17.

Chapter 11

Limiting Current Density 11.1. CONCENTRATION POLARIZATION, WATER DISSOCIATION AND LIMITING CURRENT DENSITY When an electric current is passed through an ion exchange membrane, salt concentration on a desalting surface of the membrane is decreased due to concentration polarization, and reduced to zero at the limiting current density. In this circumstance, there are no more salt ions available to carry the electric current. Thus, the voltage drop across the boundary layer increases drastically resulting in a higher energy consumption and generation of water dissociation. As described above, the limiting current density is closely related with the concentration polarization and water dissociation, and these phenomena were already discussed in Chapter 7 (Concentration polarization) and Chapter 8 (Water dissociation). In this chapter we discuss the mechanism of the limiting current density. 11.2.

DIFFUSION LAYER AND BOUNDARY LAYER

Tobias et al. (1952) discussed an electrode reaction between an electrode and a solution surrounding it, and suggested that in absence of ﬂuid turbulence, ions are transported from a solution to an electrode by three principal mechanisms: (a) migration, (b) diffusion and (c) convection. They illustrated the concentration proﬁle in the vicinity of an electrode during electrolysis showing the curved line as depicted in Fig. 11.1, in which the boundary layer (thickness d) is formed on the electrode. Diffusion layer (thickness d0 ) is deﬁned as the layer created from an intersection between the concentration line C0 in bulk and the concentration gradient line (dC/dx)x ¼ 0 at an electrode/solution interface. This theory is perfectly applicable to the phenomenon occurring on the surface of an ion exchange membrane. Referring to Fig. 11.1, the material balance of counterions in the membrane phase and at the membrane/solution interface (x ¼ 0) is represented by the following equation. i i dC ¯t ¼ t þ D (11.1) F F dx x¼0 dC C 0 C 00 ¼ (11.2) d0 dx x¼0 ¯t and t are transport numbers for counter-ions in the membrane and in the solution, respectively. C0 and C 00 are the ionic concentrations in bulk (desalting DOI: 10.1016/S0927-5193(07)12011-8

246

Ion Exchange Membranes: Fundamentals and Applications

(dC / dx) x = 0 C' Electrolyte concentration

C'

C'0

Diffusion layer Boundary layer

Distance from membrane

Figure 11.1 Concentration proﬁle in the boundary layer formed on the desalting surface of an ion exchange membrane (Tobias et al., 1952).

cell) and at x ¼ 0 (solution/membrane interface), respectively. D is the diffusion constant of an electrolyte dissolving in this system. In the absence of ﬂuid turbulence, the transport of ions i, Ji, in the boundary layer is generally described by the following extended Nernst–Planck equation. dC i FDi zi C i dc þ Civ (11.3) dx RT dx where Ci is the concentration of ions i, c the electric potential, Di the diffusion constant of ions i, zi the ionic charge number of ions i, v the solution velocity due to the natural convection, F the Faraday constant, R the gas constant and T is the absolute temperature. In this situation, the greater part of the ionic transport is due to the natural convection v, which is a horizontal component of ascending ﬂow produced by the decrease in the solution density in the vicinity of the membrane surface in the boundary layer (Tanaka, 2004). Under the forced ﬂowing circumstance in a desalting cell, the natural convection is suppressed and the solution velocity v in Eq. (11.3) is caused only by the electro-osmosis and concentration-osmosis passing through the membrane. In this situation, the convection term in Eq. (11.3) substantially disappears and the concentration distribution proﬁle in the boundary layer is approximated by a straight line (Tanaka, 2003). This event means that the J i ¼ Di

247

Limiting Current Density

diffusion layer thickness d0 in Fig. 11.1 becomes to be equivalent to boundary layer thickness d; d ¼ d0 , and the limiting current density equation of the membrane ilim is expressed by Eq. (11.4) introduced by putting C 00 ¼ 0 in Eqs. (11.1) and (11.2). Equation (11.4) is already suggested by Peer (1956) and Rosenberg and Tirrell (1957). FD dC FDC 0 ¼ (11.4) ilim ¼ ¯t t dx x¼0 ð¯t tÞd0 11.3. LIMITING CURRENT DENSITY EQUATION INTRODUCED FROM THE NERNST–PLANCK EQUATION Spiegler (1971) introduced the limiting current density equation in an electrolyte solution dissolving monovalent cations A and monovalent anions X from the Nernst–Planck equation as follows. dC FC dc þ (11.5) J þ ¼ Dþ dx RT dx dC FC dc (11.6) J ¼ D dx RT dx In the membrane, the numerical value of the ﬂux ratio, J+/J, is equal to the transport number ratio ¯tþ =¯t : ¯tþ ¯tþ Jþ ¼ ¼ ¯t J 1 ¯tþ

(11.7)

Here, in the membrane, J+ and J have opposite signs, while ¯tþ and ¯t are always taken positive. From Eqs. (11.5)–(11.7): Jþ ¼

J ¼

2Dþ dC Dþ ¯t dx 1 D ¯tþ D dC D ¯tþ dx 1 Dþ ¯t

(11.8)

(11.9)

It is often more convenient to express the ﬂuxes in terms of the diffusion coefﬁcient of the electrolyte, D, rather than the ionic diffusion coefﬁcients, D+ and D. Noting that in a free solution D þ tþ tþ ¼ ¼ D t 1 tþ

(11.10)

248

Ion Exchange Membranes: Fundamentals and Applications

Using the Nernst expression for the diffusion coefﬁcient of 1-1 electrolyte in a dilute solution D¼

2Dþ D ¼ 2Dþ ð1 tþ Þ Dþ þ D

(11.11)

Taking account of Eqs. (11.10) and (11.11), we rewrite Eqs. (11.8) and (11.9) as follows: Jþ ¼

D¯tþ dC ¯ ðtþ tþ Þ dx

(11.12)

J ¼

D¯t dC ð¯t t Þ dx

(11.13)

We can calculate the electric current density, i, from the Faraday law: i ¼ F ðJ þ J Þ

(11.14)

Substituting Eqs. (11.12) and (11.13) into Eq. (11.4) we obtain For a cation exchange membrane: i¼

FD dC ð¯tþ tþ Þ dx

(11.15)

For an anion exchange membrane: i¼

FD dC ð¯t t Þ dx

(11.16)

Since i, D and the transport numbers are constants, the concentration gradient dC/dx in Eqs. (11.15) and (11.16) is linear. The limiting current density ilim presented by Eq. (11.4) is introduced by substituting dC/dx ¼ C0 /d0 into Eqs. (11.15) and (11.16). Yamabe et al. measured the limiting current density ilim from an inﬂection of an electric current vs. electric potential curve under a ﬂowing circumstance in a desalting cell (Yamabe et al., 1967). The diffusion layer thickness d0 was calculated by substituting ilim into Eq. (11.4). Results are presented in Table 11.1. 11.4. DEPENDENCE OF LIMITING CURRENT DENSITY ON ELECTROLYTE CONCENTRATION AND SOLUTION VELOCITY OF A SOLUTION A drawback of Eq. (11.4) is that deﬁnite diffusion layer thickness d0 is not determined before hand, and further that the phenomenological meaning of d0 is obscure to some extent as deﬁned in Eq. (11.2). In order to determine the

249

Limiting Current Density

Table 11.1

Diffusion layer thickness

NaCl Concentration (M) 0.1

Solution Velocity (cm s1) 0.026 0.226 0.857 0.025 0.260 0.720 0.024 0.250 0.027 0.226 0.785

0.3 0.5 0.75

Diffusion Layer Thickness (102 cm) Selemion CMG-10

Selemion AMG-10

2.60 2.15 1.05 1.98 1.64 1.25 1.86 1.44 2.01 1.68 0.98

2.46 2.29 1.27 2.50 2.65 1.85 1.84 1.58

Source: Yamabe et al., 1967.

limiting current density of an ion exchange membrane, it is rather practically reasonable to measure directly the limiting current density and evaluate the effects of electrodialysis conditions on the limiting current density. An example of such an experiment (Tanaka, 2005) is introduced below. The experimental apparatus as shown in Fig. 11.2a was assembled incorporated with cation exchange membranes (Aciplex K-172, Asahi Chemical Co.) and anion exchange membrane (Aciplex A-172). The thickness of cell D was adjusted to 0.075 cm. Width and length of the ﬂow pass in cell D were adjusted to 1 and 2 cm, respectively (Fig. 11.2b). A diagonal net spacer was put into cell D. A 251C NaCl solution was supplied to cell D. Passing an electric current and changing the current density incrementally, the limiting current density ilim of a cation exchange membrane (K in the ﬁgure) was measured from the inﬂection of V/I vs. 1/I plot. The experiment was repeated by changing NaCl concentration C and solution velocity u in D step by step. ilim of an anion exchange membrane was measured in the same manner. ilim is plotted against C with u as a parameter, and shown in Fig. 11.3 (cation exchange membrane, ilim,K) and Fig. 11.4 (anion exchange membrane, ilim,A). The plots except for u ¼ 0 are expressed by the following equation: ilim ¼ mC n

(11.17)

m and n are expressed by the following functions of u (Fig. 11.5). For cation exchange membrane Aciplex K-172: m ¼ 83:50 þ 24:00u n ¼ 0:7846 þ 8:612 103 u

(11.18)

250

Ion Exchange Membranes: Fundamentals and Applications

G A

E

K

D'

K*

D

A

C

K

D'

E

(a) Cell arrangement

NaCl soln. (b) D

Figure 11.2 Apparatus for measuring limiting current density of an ion exchange membrane (Tanaka, 2005).

For anion exchange membrane Aciplex A-172: m ¼ 66:36 þ 14:72u n ¼ 0:7404 þ 3:585 103 u

(11.19)

11.5. LIMITING CURRENT DENSITY ANALYSIS BASED ON THE MASS TRANSPORT IN A DESALTING CELL Concentration polarization is a phenomenon occurring in a boundary layer formed on the desalting surface of an ion exchange membrane. The limiting current density is inﬂuenced by the solution ﬂow in a desalting cell and ionic transport in the boundary layer. This phenomenon is widely investigated by means of chemical engineering techniques, which are exempliﬁed in this section.

251

Limiting Current Density

i lim,K (A /cm2)

1 0

-1 10-1

-2 10-2

-3 10-3 10-6

10-5 C

Figure 11.3

10-4

10-3

(mol/cm3)

C vs. ilim,K plot (Aciplex K-172) (Tanaka, 2005).

11.5.1

Analysis Based on the Chilton–Coburn Transfer Factor Rosenberg and Tirrell (1957) applied the following Chilton–Coburn transfer factor jD for analyzing the boundary layer thickness d: 2=3 k m (11.20) jD ¼ u D where k is the mass transfer coefﬁcient, u the linear velocity in the desalting cell, m the viscosity and D the diffusion coefﬁcient of the salt. d is expressed as follows: D k jD in a ﬂat duct is presented as follows: d¼

For streamline ﬂow (Reynolds number Reo2100) 1=3 l j D ¼ 1:85 Re2=3 de

(11.21)

(11.22)

where l is path length over which the ﬂow is developed, de the equivalent diameter of the path.

252

Ion Exchange Membranes: Fundamentals and Applications

i lim,A (A /cm2)

1 0

-1 10-1

-2 10-2

-3 10-3 10-6

10-5

10-4

10-3

3)

C (mol/cm

Figure 11.4

C vs. ilim,A plot (Aciplex A-172) (Tanaka, 2005).

Using Eqs. (11.20)–(11.22) and taking account of Re ¼ deur/m(r ¼ 1), boundary layer thickness d ( ¼ diffusion layer thickness d0 ) is introduced as: 1 Dd e l 1=3 (11.23) d¼ 1:85 u Substituting Eq. (11.23) into Eq. (11.4), ilim/C is obtained as ilim FD u 1=3 ¼ 1:85 ¯t t Dd e l C

(11.24)

For turbulent ﬂow (Re>2100): j D ¼ 0:023 Re0:2

(11.25)

d and ilim/C are computed in a similar way as for the streamline ﬂow: 1=3 2=3 1 D m Re0:2 (11.26) d¼ u 0:023 2=3 ilim Fu D ¼ 0:023 Re0:2 ¯ C tt m

(11.27)

253

Limiting Current Density

1000 800 600 m 400

4.00u

.50 + 2

m = 83

200 .72u

m = 66.36 + 14

0 0

n

2

4

6

8

10

12

14

16

14

16

-3 n = 0.7846 + 8.612 × 10 u

1

-3 n = 0.7404 + 3.585 × 10 u

0 0

2

4

6

8 u (cm/s)

10

12

Figure 11.5 Coefﬁcients m and n in the limiting current density equation (Tanaka, 2005).

11.5.2

Analysis Based on the Frank–Kamenetskii Equation Cowan and Brown (1959) employed d introduced from the Frank– Kamenetskii equation: mRe1=8 (11.28) d¼a 0:395u

a is dimensionless constant. ilim/C is obtained by substituting Eq. (11.28) into Eq. (11.4): 7=8 ilim FD Re (11.29) ¼ 0:395 ¯t t C ad e 11.5.3 Analysis Based on the Stanton Number, Peclet Number and Potential Difference Number Kitamoto and Takashima (1967) expressed the mass transport and energy consumption in an electrodialysis system by the following Stanton number St,

254

Ion Exchange Membranes: Fundamentals and Applications

Peclet number Pe and potential difference number C. These parameters are deﬁned as follows: St ¼

i=F Cu

(11.30)

Pe ¼

au D

(11.31)

F Dc (11.32) RT Here, St stands for the dimensionless ratio of the material ﬂux transporting across the membrane i/F against that in the solution ﬂowing into the desalting cell Cu. Pe expresses the dimensionless solution velocity in the desalting cell u. a is the thickness of the desalting cell. D is the diffusion constant. C is the dimensionless potential difference between the potential at the cation exchange membrane surface and at the anion exchange membrane in the concentrating cell. Dc is approximated by the difference between the potential difference applied to a membrane pair Dcapplied and the membrane potential as follows: 2RT C con ade acon (11.33) ln ¼ þ þ rK þ rA i Dc ¼ Dcapplied C de kde kcon F C¼

where Cde and Ccon are electrolyte concentration in a desalting and a concentrating cell, respectively. ade and acon are the thickness of a desalting and a concentrating cell, respectively. kde and kcon are speciﬁc conductivity of electrolyte solution ﬂowing in a desalting and a concentrating cell, respectively. rK and rA are electric resistance of a cation and an anion exchange membrane, respectively. Plotting St against C/Pe was conﬁrmed to be expressed by the straight line as shown in Fig. 11.6 by means of the electrodialysis of a NaCl solution using the apparatus (effective membrane area; 5 50 or 8 24 cm2, thickness of a desalting cell; 0.71–5.6 cm) integrated with Selemion CMV-10/AMT-10 (Asahi Glass Co.) or Aciplex CK-1/CA-1, CA-2 (Asahi Chemical Co.) membranes with spacers and feeding a 103–0.6 M NaCl solution. Fig. 11.6 is presented by the following equation. C FD Dc St ¼ 1:04 ¼ 1:04 (11.34) Pe au RT Further, Kitamoto and Takashima (1968) measured the mass transport in a desalting cell applying the limiting current density (measured from I–pH or I–V curves) and obtained Fig. 11.7, which is presented by the following equation. c ¼ 0:09Pe0:65 lim C ¼ 0:09Pe0:35 Pe lim

(11.35)

255

Limiting Current Density

With spacer Key

Pe 1.5×105

10-2

D [cm]

Names of a pair of membranes

0.54

(+) CMV-10

9×104

0.54-0.55

(−) AMT-10

6.5×104

0.54-0.55

3×104

0.54-0.55

made by Asahi Glass Co., Ltd.

6×104

0.25

4×104

0.25

2×104

0.25, 0.075 (−) CA-1, CA-2 0.25, 0.075 Made by 0.25, 0.075 Asahi Chem. Ind. 0.075 Co., Ltd.

1.2×104 7×103 2×103

(+) CK-1

10-3

Key

10-4

Names of a pair of membranes

D [cm]

6×104

0.58-0.60 (+) CMV-10

1.5×105

0.58-0.60 (−) AMT-10

9.6×104

0.8-0.9

(+) CSG, (−) ASG

9.6×104

0.8-0.9

(+) CMG, (−) ASG

6×104

0.8-0.9

(+) CMG, (−) AMG made by Asahi Glass Co., Ltd. by Y. Oda20)

10-4

Figure 11.6

Pe

10-3

10-2

Relationship between St and C/Pe. (Kitamoto and Takashima, 1967)

Substituting Eq. (11.34) into Eq. (11.35), the limiting current density in a NaCl solution system is obtained as follows: Stlim ¼ 0:094Pe0:35

(11.36)

ilim ¼ 1:88 102 Cu0:65 D0:35

(11.37)

or

256

Ion Exchange Membranes: Fundamentals and Applications

103

lim

SO 2 Na

4

CI

102

Na

10 104

Figure 11.7

105 Pe

106

Relationship between Clim and Pe (Kitamoto and Takashima, 1968).

11.5.4

Analysis Based on the Sherwood Number Miyoshi et al. expressed the ionic electrolyte ﬂux Ji on a y-axis perpendicular to the membrane surface in a desalting cell incorporated with spacers by the following equation (Miyoshi et al., 1988). Ji ¼

t @C i þ De F @y

(11.38)

where t is the transport number of the ionic electrolytes and De the eddy diffusivity of the electrolytes in the solution. Based on Eq. (11.38) and the equation of continuity, the limiting current density ilim was introduced as in the form of the following Sherwood number Sh exhibiting the dimensionless ratio of current density i against electrolyte concentration in a desalting cell C: a i a a1=3 1=3 ð1þ2bÞ=3 1=3 lim ¼ M Re Sc (11.39) Sh ¼ ¯t t l C DF in which Sc is the Schmidt number ¼ n/D, M is a variable, a and b are the constants. Equation (11.39) was experimentally analyzed using the electrodialyzer (membrane area: 20 cm length 4 cm width, desalting cell thickness: 0.08– 0.40 cm) in which cation exchange membranes (Neocepta CL-25 T, Tokuyama Inc.) and anion exchange membranes (Neocepta AV-4 T) were incorporated with honeycomb net or pointed twill net spacers. Supplying a 0.005–0.10 eq dm3 NaCl solution or a 0.05 eq dm3 KCl, MgCl2, CaCl2, NaHCO3 or Na2SO4 solution into the electrodialyzer, ilim was measured from the inﬂection of V/I vs. 1/I plots. Based

257

Limiting Current Density

on the experiment mentioned above and Eq. (11.38), Sh was introduced as in the following equation, presented in Fig. 11.8: Sh ¼

ða=lÞ1=3 M 1=3

0:095

ð¯t tÞfnðd s d f Þg1=2 fð1 Þ2 =3 g1=5

Re1=2 Sc1=3

(11.40)

where ds is the thickness of a spacer, n and df are the number and ﬁber diameter of the spacer, e the void fraction of the spacer and M a spacer parameter represented by using the eddy viscosity parameter m originated by the spacer as follows: M¼

m3 ðm þ 1Þ lnðm þ 1Þ 1:5m2 m 2

5

m ¼ 2:1 10 fnðd s d f Þg

2:4

ð1 Þ2 3

(11.41)

0:8 (11.42)

11.5.5 Analysis Based on the Reynolds Number, Schmidt Number and Shape Factor Huang and Yu investigated the effects of Reynolds number, Schmidt number, and shape factor of the electrodialysis cell on the mass transfer rate in electrodialysis for various systems at limiting current density (Huang and Yu, 1988). In this study, the electrolyte concentration C in the electrodialysis cell was expressed by @C þ u rC ¼ rðDrCÞ (11.43) @t D is the molecular diffusion coefﬁcient of the electrolytes in a solution. Considering the ﬂow of an electrolyte solution through two ﬂat parallel ion exchange membranes at steady state, for ﬂow velocity in the x-direction nx and constant molecular diffusion coefﬁcient D, Eq. (11.43) is written on the coordinate along the membrane surface from the upstream end, x, and that normal to the membrane surface, y, as vx ¼

@C @2 C ¼D 2 @x @y

(11.44)

with the boundary conditions under limiting current density: C ¼ 0; C ¼ C0; 0

C¼C ;

x40; x ¼ 0;

y¼B BfyfB

x40;

y ¼ 1

(11.45)

Here, B is the half-thickness of the channel and C0 is the electrolyte concentration in bulk. If the Schmidt number is large, the thickness of the diffusion boundary layer will be smaller than that of the viscous boundary layer, so the velocity component nx can be expressed approximately by

258

Ion Exchange Membranes: Fundamentals and Applications

103 Run

102

1 2 3 4 5 6 7 8 9 10

Run 11 12 13 14 15

Run 16 17 18 19

101

102

Figure 11.8

103

Relationship between Re, Sc and Sh (Miyoshi et al., 1988).

y nx ¼ 3hui 1 (11.46) B Next, if the diffusivity in the solution of the cation is smaller than that of the anion, concentration polarization develops ﬁrst on the surface of the cation exchange membrane. In this situation, the dimensionless mass transfer rate, the Nusselt number Nu showing the dimensionless ionic ﬂux across the membrane N against the electolyte concentration in the desalting cell C on the cation exchange membrane is deﬁned as Nu ¼

N þ jy¼B d e C þ Dþ

(11.47)

ilim zþ @C ¼ nþ 1 Nþ ¼ Dþ zþ F z @y y¼B

(11.48)

N ¼ 0

(11.49)

Here, N+ and N are molar ﬂuxes of cations and anions, respectively. de is the equivalent diameter of the channel. n+ is the number of cations produced by the

Limiting Current Density

259

dissociation of one molecule of electrolytes in the solution. z+ and z are the valence of cations and anions, respectively. Solving Eqs. (11.44)–(11.48), Nu on the cation exchange membrane is introduced as follows: zþ ð4=3Þ1=3 Re Scd e 1=3 (11.50) Nu ¼ 1 z Gð4=3Þ x The average value of the Nu over the length L, (Nu)ave of the cation exchange membrane is introduced as Z 1 L zþ Re Scd e 1=3 Nudx ¼ 1:849 1 (11.51) ðNuÞave ¼ z L L 0 which is expressed by the function of the Reynolds number Re, Schmidt number Sc and dimension factor de/L. On the other hand, if the diffusivity in the solution of the anion is smaller than that of the cation, concentration polarization develops ﬁrst on the surface of the anion exchange membrane. In this case, (Nu)ave on the anion exchange membrane is expressed by the equation equivalent to Eq. (11.51), however Nu and N are expressed as follows: Nu ¼

N ¼

N jy¼B d e C 0 D ilim z F

(11.52)

(11.53)

The theory presented above was examined through the limiting current density measurement using the electrodialysis apparatus (effective membrane area; 20 cm2) incorporated with a desalting channel and an ion exchange membrane pair (Selemion CMV/AMV or Aciplex K-102/A-102). Supplying a CH3COONa, a NaCl, a CuSO4 or a NiSO4 solution or a mixed solution of H2SO4+glucose or xylose, into the channel, and passing an electric current, the limiting current density was determined from the ﬁrst inﬂection point of the current density vs. voltage curve. The relationship between the experimental Nusselt number (Nu)exp and Re, Sc and de/L was shown in Fig. 11.9, and was presented by the following equation, which is similar to the theoretical Eq. (11.51). ðNuÞexp ðfor cation exchange membraneÞ zþ 1 z ðNuÞexp ðfor anion exchange membraneÞ ¼ z 1 zþ 0:301 de ¼ 1:793 Re0:341 Sc0:329 L

ð11:54Þ

260

Ion Exchange Membranes: Fundamentals and Applications

130 120

CH3COONa NaCI

110

CuSO4 NiSO4

100

H2SO4 + 6% glucose 90

H2SO4 + 6% xylose + 1.8% glucose

(Nu)exp

80 70 60 50 40 30 20 10 0

0

20

40

60

1793Re 0.340

Figure 11.9

Sc 0.329

80

100

120

(de/L) 0.301

Relationship between Nu, Sc, de/L (Huang and Yu, 1988).

11.6. SOLUTION VELOCITY DISTRIBUTION BETWEEN DESALTING CELLS IN A STACK (Tanaka, 2005) Limiting current density of an electrodialyzer is strongly inﬂuenced by the distribution of solution ﬂow in desalting cells, which is discussed below. Seawater was supplied to desalting cells in an unit-cell type electrodialyzer (Table 11.2) incorporated with Selemion CMV/AST membranes and cross piece spacers, and electrodialyzed at the linear velocity of 3 cm s–1 and the current density of 2 A dm–2. The solution velocity distribution in stacks was evaluated by measuring the solution volume Q ﬂowing out of the stacks. After that, the stacks were disassembled and washed, and then the solution velocity distribution was measured again in the same manner. Frequencies of stacks Nstack are plotted ¯ Q; ¯ (Q: ¯ the average solution volume against solution volume ratio x ¼ ðQ QÞ=

261

Limiting Current Density

Table 11.2

Speciﬁcations of the electrodialyzer

Membrane

Selemion CMV/AMT

Numbers of stacks in the electrodialyzer Numbers of desalting cells in a stack Membrane area Distance between membranes in a desalting cell Spacer

44 12 0.96 m2 (98 cm 98 cm) 2 mm Cross piece

Source: Tanaka, 2005. 16

14

12

N stack

10

8

6

4

2

0 -0.4

-0.3

-0.2

-0.1

0.0

before disassembly Q = 23.7l/min

0.1

0.2

0.3

0.4

= 0.079

after washing and assembly Q = 28.9l/min

= 0.037

Figure 11.10 Velocity distribution of desalted solutions between stacks (Tanaka, 2005).

in a stack), and shown in Fig. 11.10 which is equated with the normal distribution. The standard deviation of the normal distribution s are measured as 0.037. Next, the solution velocity distribution in desalting cells in one of the stacks before assembly was evaluated by injecting coloring liquid into the inlets of each desalting cell and measuring elapsed time until the coloring liquid

262

Ion Exchange Membranes: Fundamentals and Applications

appears in the outlets of the desalting cells. The average linear velocity u¯ was adjusted to 3 cm s–1. The frequencies of desalting cells Ncell are plotted against the solution velocity ratio x ¼ ðu u¯ Þ=¯u; and shown in Fig. 11.11 which is also equated with the normal distribution and s is measured as 0.078. Seawater was supplied to desalting cells in a ﬁlter-press type electrodialyzer (Table 11.3) and electrodialyzed at the current density of 3 A dm–2. The electrodialysis was repeated changing the linear velocity of solutions in desalting cells incrementally. The solution velocity in each desalting cell u was evaluated by measuring the electrolyte concentration at the inlets Cin and the outlets Cout of cells. Ncell vs. x ¼ ðu u¯ Þ=¯u was conﬁrmed to be equated with the normal distribution. Standard deviation s of solution velocity ratio x is determined as presented in Table 11.4. s is distributed in the range of 0.017–0.222. Here, we deﬁne the solution velocity ratio x in desalting cells integrated in a stack in an electrodialyzer by Eq. (11.55) x¼

u u¯ u¯

(11.55)

20 18 16 14

N cell

12 10 8 6 4 2 0 -0.7

-0.5

-0.3

-0.1

0.1

0.3

0.5

0.7

=(u*- u ) / u u = 3 cm/s

Figure 11.11

= 0.078

Velocity distribution of desalted solutions between cells (Tanaka, 2005).

263

Limiting Current Density

Table 11.3

Speciﬁcations of the electrodialyzer

Membrane

Aciplex K-172/A-172

Numbers of stacks in the electrodialyzer Numbers of desalting cells in a stack Membrane area Distance between membranes in a desalting cell Spacer

1 36 0.15 m2 (96.6 cm 15 cm) 0.75 mm Diagonal net

Source: Tanaka, 2005. Table 11.4

Standard deviation of solution velocity ratio s in desalting cells

u (cm s1)

C 0in (eq dm3)

C 0out (eq dm3)

s

1.12 1.58 1.73 2.07 2.24 3.12 3.54 4.93

0.590 0.557 0.606 0.603 0.606 0.603 0.606 0.603

0.276 0.276 0.392 0.430 0.426 0.488 0.491 0.535

0.117 0.222 0.141 0.017 0.134 0.020 0.122 0.102

Source: Tanaka, 2005.

where u is the linear velocity in every desalting cell and u¯ the average linear velocity in a stack. The frequency distribution of x is equated by the normal distribution, so that the minimum of x and u may be equated with 3s and u, respectively, where s is the standard deviation of the normal distribution and u is the minimum value of linear velocities within all desalting cells in a stack. Putting x ¼ 3s and u ¼ u in Eq. (11.55) yields Eq. (11.56) u ¼ u¯ ð1 3sÞ

(11.56)

11.7. LIMITING CURRENT DENSITY OF AN ELECTRODIALYZER (Tanaka, 2005) 11.7.1

Limiting Current Density Equation When current density reaches the limit of an ion exchange membrane ilim at the outlet of a desalting cell in which linear velocity and electrolyte concentration are the least, the average current density applied to an electrodialyzer is deﬁned as its limiting current density (I/S)lim, in which I is the total electric current and S is the membrane area. (I/S)lim is strongly related to the circumstances distributing in an apparatus. Namely, (I/S)lim is inﬂuenced by the distribution of solution velocity (cf. Section 11.6). It is also inﬂuenced by the

264

Ion Exchange Membranes: Fundamentals and Applications

distribution of electrolyte concentration in desalting cells and an electric current in a stack (cf. Section 9.1). Further, it is naturally inﬂuenced by the limiting current density of an ion exchange membrane ilim (cf. Section 11.4). We discuss (I/S)lim in this section based on the suggestions mentioned above. Referring to Eqs. (11.17)–(11.19), ilim, is expressed by the function of electrolyte concentration C 0out and linear velocity uout at the outlet of the desalting cell in which the linear velocity is the least as follows: n þn2 uout

1 ilim ¼ ðm1 þ m2 uout ÞC 0 out

(11.57)

where m1, m2, n1 and n2 are the constant. uout is expressed by the following equation referring to Eq. (11.56): uout ¼ u¯ out ð1 3sÞ

(11.58)

The limiting current density of an electrodialyzer is deﬁned as follows using Eq. (9.19) I ilim ¼ (11.59) S lim zout Substituting Eq. (11.57) into Eq. (11.59): 1 þn2 uout I ðm1 þ m2 uout ÞC 0 nout ¼ zout S lim

(11.60)

Next, when the limiting current density (I/S)lim is applied to an electrodialyzer, the following material balance is realized in the desalting cell in which the linear velocity is the least: I aF ¼ (11.61) uav ðC 0in C 0out Þ S lim Zl a and l are, respectively, the thickness and ﬂow pass length of a desalting cell. F is the Faraday constant. uav is the average of linear velocity at the inlet and outlet of a desalting cell in which the velocity is the least. uin þ uout (11.62) uav ¼ 2 Z is the current efﬁciency in the desalting cell and indicated by the overall mass transport equation (cf. Chapter 6) as follows: F lðI=SÞlim mðC 00 C 0av Þ FJ S Z¼ ¼ (11.63) ðI=SÞlim ðI=SÞlim JS is the ﬂux of ions transported across a membrane pair (cf. Eq. (6.1)). C 0av is the average of electrolyte concentration at the inlet and outlet of a desalting cell in which the velocity is the least. C 0av ¼

C 0in þ C 0out 2

(11.64)

265

Limiting Current Density

C00 is the electrolyte concentration in concentrating cells and assumed to be invariable at every point in the cells because the concentrated solution is extracted through an overﬂow extracting system. On the other hand, the linear velocity uout at the outlet of desalting cell in which the velocity is the least is given using the overall mass transport equation (cf. Eq. (6.2)). S l I 00 0 J V ¼ uin f þ rðC C av Þ (11.65) uout ¼ uin ab a S lim uin ¼ u¯ in ð1 3sÞ

(11.66) 00

b is the ﬂow pass width of the desalting cell. C is introduced as follows using the overall mass transport equation (cf. Eqs. (6.10)–(6.12)). pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ A2 þ 4rB A 00 (11.67) C ¼ 2r l, m, j and r in Eqs. (11.67)–(11.69) are, respectively, the overall transport number, the overall solute permeability, the overall electro-osmotic permeability and the overall hydraulic conductivity, which are deﬁned in the overall mass transport equation. l, m and j are expressed by the functions of r (cm4 eq1 s1) as below (cf. Eqs. (6.5)–(6.7)): I A¼j þ m rC 0av (11.68) S lim I þ mC 0av B¼l S lim

(11.69)

lðeq C 1 Þ ¼ 9:208 106 þ 1:914 105 r

(11.70)

mðcm s1 Þ ¼ 2:005 104 r

(11.71)

jðcm3 C 1 Þ ¼ 3:768 103 r0:2 1:019 102 r

(11.72)

11.7.2 Procedure for Calculating the Limiting Current Density of an Electrodialyzer The limiting current density of an electrodialyzer (I/S)lim is computed using trial and error calculation as follows: 11.7.2.1 Process 1 The outlet current density uniformity coefﬁcient zout is calculated using the procedures described in Chapter 9 (Section 9.1.1), assuming appropriate

266

Ion Exchange Membranes: Fundamentals and Applications

s, uin, C 0in ; I/S, a, I and r. Here, l, m and j are computed using r and Eqs. (11.70)–(11.72).

11.7.2.2 Process 2 We adopt an approximated equation (11.73) for convenience uin ¼ uav ¼ uout uin ¼ uav ¼ uout u¯ in ¼ u¯ av ¼ u¯ out

(11.73)

Equation (11.73) means that the volume ﬂuxes transporting from desalting cells to concentrating cells are zero, so that computed result includes errors. Due to this approximation, Eq. (11.60) is presented by Eq. (11.74) using uin instead of uout: 1 þn2 uin I ðm1 þ m2 uin ÞC 0 nout ¼ (11.74) zout S lim The second term m(C00 –C0 ) in Eq. (11.63) is sufﬁciently small compared to the ﬁrst term l(I/S)lim, so that Z is expressed by canceling the second term as follows: Z ¼ Fl

(11.75)

Substituting Eq. (11.75) and uin ¼ uav in Eq. (11.73) into Eq. (11.61): a I ¼ (11.76) uin ðC 0in C 0out Þ S lim ll Setting as Eq. (11.74) ¼ Eq. (11.76): 1 þn2 uin C 0 nout ¼Z 0 C in C 0out azout uin Z¼ ll m1 þ m2 uin

(11.77)

(11.78)

Here, we calculate as follows: (a) (b) (c) (d) (e) (f) (g) (h)

Calculate uin by substituting uin and s into Eq. (11.66). Calculate C 0out 1 by substituting uin into Eqs. (11.77) and (11.78) and equating Eqs. (11.77) and Eq. (11.78). Calculate (I/S)lim 1 by substituting C 0out 1 into Eq. (11.74). Calculate C 0av 1 by substituting C 0out 1 into Eq. (11.64). Calculate C00 1 by substituting (I/S)lim 1 and C 0av 1 into Eqs. (11.67)–(11.69). Calculate uout 1 by substituting (I/S)lim 1 , C 0av and C00 1 into Eq. (11.65). Calculate uav 1 by substituting uin and uout 1 into Eq. (11.62). Calculate Z 1 using Eq. (11.75).

267

Limiting Current Density

11.7.2.3 Process 3 We calculate as follows: (a)

Calculate C 0out 2 by substituting (I/S)lim 1 and uout 1 into Eq. (11.79) introduced from Eq. (11.61). (11.79)

(b) Calculate C 0av 2 by substituting C 0out 2 into Eq. (11.64). (c) Calculate Z 2 by substituting C 0av 2 , C00 1 and (I/S)lim 1 into Eq. (11.63). (d) Calculate (I/S)lim 2 by substituting C 0out 2 and uout 1 into Eq. (11.60). (e) Calculate uav 2 by substituting uin and uout 1 into Eq. (11.62). (f) Calculate C00 2 by substituting (I/S)lim 2 and C 0av 2 into Eqs. (11.67)–(11.69). (g) Calculate uout 2 by substituting (I/S)lim 2 , C 0av 2 and C00 2 into Eq. (11.65). Process 3 is proceeded using correct equations, but the results are assumed to have errors due to the approximation (Eqs. (11.73) and (11.75)) adopted in Process 2. 20 18 16

(I/S) lim (A/dm2)

14 12 10 8 6 4 3 2 0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

u in = 5 cm/s, C'in = 0.6 eq/dm3, I/S = 3 A/dm2 a = 0.075 cm, b = 100 cm, l = 100 cm, S = 1 m2

Figure 11.12 Effect of standard deviation of solution velocity ratio on limiting current density of an electrodialyzer.

268

Ion Exchange Membranes: Fundamentals and Applications

11.7.2.4 Process 4 Repeat the calculation in process 3 until the errors becomes zero. Repeating two times is necessary and sufﬁcient.

11.7.3

Computation of the Limiting Current Density of an Electrodialyzer We calculate here the limiting current density of an electrodialyzer according to the processes described above and assuming the speciﬁcations of the electrodialyzer as S ¼ 1 m2, l ¼ 1 m, b ¼ 1 m, a ¼ 0.075 cm, I/S ¼ 3 A dm–2 and the overall water permeability r ¼ 1 102 cm4 eq1 s1 (cf. Chapter 6). In this calculation, we use the outlet current density uniformity coefﬁcient zout obtained by the process described in Section 9.1.1. Fig. 11.12 shows the relationship between s and (I/S)lim computed by setting uin ¼ 5 cm s–1 and C 0in ¼ 0:6 eq dm3. Taking account of that this apparatus is operating at I/S ¼ 3 A dm2, we can evaluate the limiting standard deviation of solution velocity slim ¼ 0.290, which corresponds to a permissible limit of s value. The relationship between uin and (I/S)lim is presented in Fig. 11.13, obtained by setting s ¼ 0.1 and C 0in ¼ 0:6 eq dm3. In this situation, 14

12

(I/S ) lim = (A/dm2)

10

8

6

4 3 2

0

u in, lim = 0.912cm/s

0

1

2

3

4

5

6

u in (cm/s)

Figure 11.13 Effect of solution velocity at the inlets of desalting cells on limiting current density of an electrodialyzer.

269

Limiting Current Density

14

12

(I/S)lim (A/dm2)

10

8

6

4 3 C'in,lim = 0.117eq/dm3

2

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

C'in(eq/dm3) = 0.1, uin = 5 cm/s, I/S = 3 A/dm2 a = 0.075 cm, b = 100 cm, l = 100 cm, S = 1 m2

Figure 11.14 Effect of electrolyte concentration at the inlets of desalting cells on limiting current density of an electrodialyzer.

the permissible limiting solution velocity is evaluated as uin,lim ¼ 0.912 cm s1. By setting s ¼ 0.1 and uin ¼ 5 cm s1, the relationship between C 0in and (I/S)lim is calculated as in Fig. 11.14. Here, the permissible limiting electrolyte concentration is recognized to be C 0in;lim ¼ 0:117 eq dm3. REFERENCES Cowan, D. A., Brown, J. H., 1959, Effect of turbulence on limiting current in electrodialysis cells, Ind. Eng. Chem., 51(12), 1445–1448. Huang, T. C., Yu, I. Y., 1988, Correlation of ionic transfer rate in electrodialysis under limiting current density conditions, J. Membr. Sci., 35, 193–206. Kitamoto, A., Takashima, Y., 1967, Mass transfer by electrodialysis using ion-exchange membranes–Studies on electrodialytic concentration of electrolytes, J. Chem. Eng., Jpn., 31(12), 1201–1207. Kitamoto, A., Takashima, Y., 1968, Studies on electrodialysis, maximum attainable concentration, limiting current density and on energy efﬁciency in electrodialysis using ion-exchange membranes, J. Chem. Eng., Jpn., 32(1), 74–82.

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Ion Exchange Membranes: Fundamentals and Applications

Miyoshi, H., Fukumoto, T., Kataoka, T., 1988, A method for estimating the limiting current density in electrodialysis, Sep. Sci. Technol., 23(6 & 7), 585–600. Peer, A. M., 1956, Discuss. Faraday Sci., 21, 124 (Communication in the membrane phenomena special issue). Rosenberg, N. W., Tirrell, C. E., 1957, Limiting currents in membrane cells, Ind. Eng. Chem., 49(4), 780–784. Spiegler, K. S., 1971, Polarization at ion exchange membrane-solution interfaces, Desalination, 9, 367–385. Tanaka, Y., 2003, Concentration polarization in ion-exchange membrane electrodialysis– the events arising in a ﬂowing solution in a desalting cell, J. Membr. Sci., 216, 149–164. Tanaka, Y., 2004, Concentration polarization in ion-exchange membrane electrodialysis. The events arising in an unforced ﬂowing solution in a desalting cell, J. Membr. Sci., 244, 1–16. Tanaka, Y., 2005, Limiting current density of an ion-exchange membrane and of an electrodialyzer, J. Membr. Sci., 266, 6–17. Tobias, C. W., Eisenberg, M., Wilke, C. R., 1952, Diffusion and convection in electrolysis– A theoretical review, J. Electrochem. Soc., 99(12), 359C–365C. Yamabe, T., Yamana, S., Yamagata, K., Takai, S., Seno, M., 1967, On the concentration polarization effect in the electrodialysis using ion-exchange membranes (IV) Concentration polarization effect multi-compartment electrodialysis cell, J. Electrochem. Soc., Jpn., 35, 578–582.

Chapter 12

Leakage 12.1.

ELECTRIC CURRENT LEAKAGE

12.1.1

Current Leakage Equation An electrodialyzer is assumed to be assembled by arranging desalting cells and concentrating cells (Fig. 12.1) alternately with ion exchange membranes, putting feeding and discharging cells and electrode cells on both ends of the electrodialyzer (Fig. 12.2). Desalting and concentrating solutions are assumed to be supplied to the feeding cell and further fed to each desalting and concentrating cell through ducts and slits incorporated in the bottom of the electrodialyzer. The solutions ﬂow upward in the desalting and concentrating cells, further pass through the slits and ducts incorporated in the head of the electrodialyzer and are discharged at the discharging cell to the outside of the electrodialyzer. In this ﬂow system, each desalting and concentrating cell is connected through the solutions passing across slits and ducts. Accordingly, when an electric current is supplied from the electrodes, an unavailable electric current (leakage), which does not pass through the effective area of membranes, is generated as shown by the arrows in Figs. 12.2 and 12.3 (Equivalent circuit). R is the electric resistance of an effective portion consisting of desalting cell rD, concentrating cell rC, cation exchange membrane rK and anion exchange membrane rA as follows. eM (12.1) R ¼ r D þ r C þ r K þ rA þ i in which eM is the sum of membrane potentials generated at the cation and anion exchange membranes, i the current density, RD and RC the electric resistances of slits integrated in the desalting and concentrating cells, respectively, ¯ D and R ¯ C the electric resistances of ducts corresponding to unit pair of deR ¯ D; R ¯ C the values salting and concentrating cells, respectively, RD, RC and R divided by the numbers of slits and ducts incorporated with the desalting and concentrating cells, respectively, and i0 the electric current supplied from electrodes. We put the number of desalting cells and concentrating cells as N+1 and N, respectively, in the electrodialyzer and draw a line l at the central position in the electrodialyzer as shown in Fig. 12.3. In this situation, the leakage currents i0n passing through desalting slit number n and i00n passing through concentrating slit number n from the anode are equivalent to the values at slit number n from the cathode. Accordingly, we are allowed to discuss the phenomena occurring only in the left half section of the circuit. DOI: 10.1016/S0927-5193(07)12012-X

272

Ion Exchange Membranes: Fundamentals and Applications

Figure 12.1

Desalting cell and concentrating cell.

Figure 12.2

Leakage current in an electrodialyzer.

273

Leakage

l RD

RD 1

i0

RD

RD

2 RD

3 RD

i' 1 R

i' 2 R

i' 3 R

i"

i"

1

RC

RC

1

RD

i' 3 R 3

RC

2 RC

RD

i"

2

RD

i' 2 R

i"

3

RC

RD

R

i"

2

RC

i"

i' 1 i0 1

RC

3 RC

RC

RC

Figure 12.3 Equivalent circuit of a leakage current in an electrodialyzer (Wilson, 1960).

Here, we deﬁne the overall electric resistance in the slits RL and in the ¯ L for simpliﬁcation as follows ducts R 1 1 1 ¼ þ RL RD RC

(12.2)

1 1 1 ¼ þ ¯L R ¯D R ¯C R

(12.3)

Further, we deﬁne the overall slit electric resistance ratio r and the overall duct electric resistance ratio d taking R as standard as follows: r¼ d¼

RL R ¯L R

(12.4)

R

The electric current in the left half circuit in Fig. 12.3 is simpliﬁed by applying Eqs. (12.2)–(12.4) and by assuming N to be extremely large as shown in Fig. 12.4, in which the number of both desalting and concentrating cells becomes N/2. in is the electric current passing across the membrane at desalting cell number n and concentrating cell number n. i0n is the sum of the leakage current passing through the slit in desalting cell number n and that in concentrating cell number n. Wilson applied the Kirchhoff equation to an equivalent network circuit in Fig. 12.4 and computed the electric current leakage as follows (Wilson, 1960). At ﬁrst, the electric current in circuit number n is expressed by applying the Kirchhoff equation as follows within the range of 1ono(N/2) 1 in1 r ¼ in ð2r þ d þ 1Þ inþ1 r i0 d

(12.5)

274

Ion Exchange Membranes: Fundamentals and Applications

i0

i' i0

i1

1

i2

=

i'

i1

i1

2

= i2

in

i'

i0

i1

=

in-1

r

r

n

iN/2-1

i2

in

i0

iN/2

i'N/2 =

No iN/2 Current

iN/2-1

r i0

iN/2

r in

r

r

i0 iN/2-1

i0 - iN/2

i0 - iN/2

Figure 12.4 Equivalent circuit of a leakage current in an electrodialyzer (Wilson, 1960).

For n ¼ N/2, substituting in ¼ in+1 into Eq. (12.5) iðN=2Þ1 r ¼ iðN=2Þ ðr þ d þ 1Þ i0 d

(12.6)

For n ¼ (N/2) 1, Eq. (12.5) becomes iðN=2Þ2 r ¼ iðN=2Þ1 ð2r þ d þ 1Þ iðN=2Þ r i0 d

(12.7)

Substituting Eq. (12.6) into Eq. (12.7) iðN=2Þ2 r ¼ iðN=2Þ

r2 þ 3ð1 þ dÞr þ ð1 þ dÞ2 3r þ d þ 1 þ i0 d r r

(12.8)

Comparison of the electric resistance of a slit with those of a membrane cell and a duct is expressed as r1

(12.9)

rd Taking account of Eq. (12.9) in Eq. (12.8), we have r2 þ 3ð1 þ dÞr ð1 þ dÞ2 3r 1 þ d So Eq. (12.8) becomes iðN=2Þ2 r ¼ iðN=2Þ fr þ 3ð1 þ dÞg 3i0 d

(12.10)

Next, for n ¼ (N/2) 2, Eq. (12.5) becomes as follows iðN=2Þ3 r ¼ iðN=2Þ2 ð2r þ d þ 1Þ iðN=2Þ1 r i0 d

(12.11)

Substituting Eqs. (12.6) and (12.10) into Eq. (12.11) iðN=2Þ3 r ¼ iðN=2Þ

r2 þ 6ð1 þ dÞr þ 3ð1 þ dÞ2 2r þ 1 þ d 3i0 d r r

(12.12)

275

Leakage

Taking account of Eq. (12.9) in Eq. (12.12) r2 þ 6ð1 þ dÞr 3ð1 þ dÞ2 2r 1 þ d So Eq. (12.12) becomes iðN=2Þ3 ¼ iðN=2Þ fr þ 6ð1 þ dÞg 6i0 d

(12.13)

Considering the coefﬁcients of 1+d and i0d in Eqs. (12.10) and (12.13) to be 3 ¼ 1+2 and 6 ¼ 1+2+3, respectively, we arrive at the following general equation. ( ) N=2 N=2 X X N N nþ1 i0 d nþ1 in1 r ¼ iðN=2Þ r þ ð1 þ dÞ 2 2 n¼n n¼n (12.14) Putting n ¼ 1 in Eq. (12.14) ! ( ) N=2 N=2 X X n ¼ iðN=2Þ r þ ð1 þ dÞ n i0 r þ d n¼1

(12.15)

n¼1

Now, the leakage current passing through slit number n in the circuit is expressed as follows. i0n ¼ in1 in

(12.16)

Substituting Eq. (12.14) into Eq. (12.16) ðN=2Þ n þ 1 r Substituting Eq. (12.15) into Eq. (12.17) i0n ¼ fiðN=2Þ ð1 þ dÞ i0 dg

i0n ¼

ððN=2Þ n þ 1Þi0 r þ ð1 þ

N=2 dÞSn¼1 n

¼

ððN=2Þ n þ 1Þi0 r þ ð1=8Þð1 þ dÞNðN þ 2Þ

(12.17)

(12.18)

Next, we discuss the leakage current ratio. In the circuit in Fig. 12.4, the leakage current i0n in slit number n passes through from duct numbers n to N/2. Accordingly, the leakage current in the electrodialyzer is expressed by iL,n iL;n ¼ i0n

ðN=2Þ n þ 1 N=2

(12.19)

The total leakage current iL in the electodialyzer is obtained by summing up from iL,1 in slit number 1 to iL,N/2 in slit number N/2 as follows iL ¼

N=2 X n¼1

iL;n ¼

N=2 X n¼1

i0n

ðN=2Þ n þ 1 N=2

(12.20)

276

Ion Exchange Membranes: Fundamentals and Applications

The leakage current ratio iL/i0 is introduced by substituting Eqs. (12.18) and (12.19) into Eq. (12.20) as follows N=2 P

iL ¼ i0

(

n2

n¼1

ðN=2Þ r þ ð1 þ dÞ

N=2 P

)¼

2ðN þ 2ÞðN þ 1Þ 24r þ 3ð1 þ dÞNðN þ 2Þ

(12.21)

n

n¼1

12.1.2

Computation of Leakage Current Ratio Here, we calculate the leakage current ratio in the electrodialyzer incorporated with the desalting cells and concentrating cells illustrated in Fig. 12.5 based on the following speciﬁcations. Number of cell pairs N: 300 Thickness of a cell pair t: 0.226 cm Electric resistance of a cell pair R: 0.001037 O Speciﬁc electric resistance of a desalted solution rD: 28.5 O cm Speciﬁc electric resistance of a concentrated solution rC: 5.0 O cm

Figure 12.5

Dimensions of a desalting cell and a concentrating cell.

277

Leakage

Dimensions of a desalting cell Effective thickness of a slit aD: 0.064 cm ( ¼ 0.075 0.85) Width of a slit wD: 4.0 cm Flow-pass length of a slit lD: 4.0 cm Diameter of a duct dD: 4.0 cm Number of slits and ducts in the cell nD: 10 2 Dimensions of a concentrating cell Effective thickness of a slit aC: 0.064 cm ( ¼ 0.075 0.85) Width of a slit wC: 2.4 cm Flow-pass length of a slit lC: 3.0 cm Diameter of a duct dC: 2.4 cm Number of slits and ducts nC: 3 2 In the speciﬁcation described above, the thickness of a cell pair was obtained from the length of a stack divided by the number of cell pairs incorporated in the stack N ( ¼ 300). The electric resistance of a cell pair was evaluated from cell voltage RI measured at 251C divided by an electric current I. The speciﬁc electric resistance of desalting solution rD and of concentrating solution rC were experimentally measured at 251C. The effective thickness of a slit in the desalting cell aD and in the concentrating cell aC were obtained by slit thickness void ratio ¼ 0.075 cm 0.85. The leakage current computation is as follows: RD ¼

rD l D 28:5 4:0 ¼ ¼ 22:27 O aD wD nD 0:064 4:0 2 10

RC ¼

rC l C 5:0 3:0 ¼ ¼ 16:28 O aC wC nC 0:064 2:4 2 3

RL ¼

1 ¼ 9:405 O ð1=RD Þ þ ð1=RC Þ

r¼

RL 9:405 ¼ ¼ 9070 R 0:001037

¯C ¼ R

rC t 5:0 0:226 ¼ 0:04163 O ¼ 2 ð1=4Þpd C nC ð1=4Þp 2:42 2 3

¯D ¼ R

rD t 28:5 0:226 ¼ 0:02563 O ¼ ð1=4Þpd 2D nD ð1=4Þp 4:02 2 10

¯L ¼ R

1 ¼ 0:01586 O ¯ CÞ ¯ ð1=RD Þ þ ð1=R

278

Ion Exchange Membranes: Fundamentals and Applications

¯L R 0:01586 ¼ ¼ 15:30 R 0:001037 The leakage current ratio is obtained by substituting the above-calculated values into Eq. (12.21) as follows. d¼

iL 2ð300 þ 2Þð300 þ 1Þ ¼ 0:039 ¼ i0 24 9070 þ 3ð1 þ 15:30Þ300ð300 þ 2Þ The leakage current described above corresponds to the internal leakage. In an actual electrodialysis system, however, the effect of external leakage passing through external liquid connections on both ends of the internal channel should be taken into consideration. Mandersloot and Hicks (1966) developed the theory of the leakage current including the effect of the external leakage. 12.2.

SOLUTION LEAKAGE (Tanaka, 2004)

12.2.1

Overall Mass Transport Equation and Solution Leakage When an electrolyte solution is supplied to a desalting cell and concentrating cell partitioned by a cation exchange membrane and an anion exchange membrane and an electric current is passed through them, ions and solutions are transported across the membranes. To analyze these phenomena, we have to focus on particular events occurring in a practical-scale electrodialyzer. That is to say, the dimensions of all parts of an electrodialyzer are not always consistent with the values in the speciﬁcations. Small pinholes can open in an electrodialyzer because the strength of ion exchange membranes is relatively low. Gaps may occur between the materials comprising the electrodialyzer (desalting cells, concentrating cells, ion exchange membranes and spacers) in the assembly works of an electrodialyzer. If a pressure difference between the desalting cells and concentrating cells exists in these circumstances, solutions leak through the pinholes in the membranes during the operation of the electrodialyzer. The size of the pinholes is extremely large compared to that of micro-pinholes in the membranes. When solutions leak, the ﬂux of ions JS and a solution JV across a pair of membranes are expressed by the following equation, which is introduced from the overall mass transport equation (cf. Chapter 6) by adding the terms of leakage. I mðC 00 C 0 Þ þ C 0 q0L C 00 q00L (12.22) JS ¼ l S I JV ¼ f (12.23) þ rðC 00 C 0 Þ þ q0L q00L S C 00 ¼

JS JV

(12.24)

279

Leakage

Here, I is electric current, S membrane area, I/S average current density, C0 and C00 electrolyte concentrations in a desalting cell and a concentrating cell, respectively, l the overall transport number, m the overall solute permeability, f the overall electro-osmotic permeability and r the overall hydraulic conductivity. These parameters are membrane pair characteristics. q0L is the solution leakage moving from a desalting cell to a concentrating cell, q00L is that moving from a concentrating cell to a desalting cell. Terms l(I/S), m(C00 C0 ) and C 0 q0L C 00 q00L in Eq. (12.22) stand for the migration, diffusion and leakage of ions, respectively. Terms f(I/S), r(C00 C0 ) and q0L q00L in Eq. (12.23) correspond to the electroosmosis, concentration–osmosis and leakage of solutions, respectively. Using Eqs. (12.22)–(12.24), q0L and q00L are introduced as follows: l fC 00 I 0 (12.25) qL ¼ ðm þ rC 00 Þ 00 0 C C S q00L

¼

l fC 0 C 00 C 0

I ðm þ rC 0 þ J V Þ S

(12.26)

q0L and q00L are known by evaluating the parameters included in Eqs. (12.25) and (12.26). 12.2.2

Measurement of Solution Leakage In order to measure q0L and q00L in a practical-scale electrodialyzer using Eqs. (12.25) and (12.26), the membrane pair characteristics l, m, f and r must be measured before hand in an experimental-scale electrodialyzer in which the solution leakage is conﬁrmed to be zero, under the same operating conditions of the practical-scale electrodialyzer. On the premise of the experimentation described above, the following results are obtained. Fig. 12.6 shows the effect of current density i on q0L and q00L in a practicalscale electrodialyzer. The speciﬁcations of the electrodialyzer are ion exchange membrane; Aciplex CK-2/CA-3, thickness of a desalting and a concentrating cell; 0.075 cm, effective membrane area; 113 dm2 and number of membrane pairs; 300. q0L and q0L =J V are recognized to decrease with the increase of i, but q00L and q00L =J V increase with the increase of i. These phenomena are estimated to occur because the increase of current density gives rise to an increase in solution density and static head in concentrating cells, and a resultant decrease in q0L and increase in q00L : Fig. 12.7 shows the inﬂuence of linear velocity u in desalting cells on q0L 00 and qL in a middle-scale electrodialyzer. The speciﬁcations of the electrodialyzer are ion exchange membrane; Aciplex K-172/A-172, thickness of a desalting cell and a concentrating cell; 0.075 cm, effective membrane area; 14.5 dm2 and number of membrane pairs; 36. q0L and q0L =J V are recognized to increase with the increase of u. However, q00L and q00L =J V decrease to some extent with the increase

280 12

0.6

10

0.5

0.4

6

0.3

4

q'L/q, q"L/q

q

8

/q q' L

q'L, q"L, q (10-5cm3/cm2 s)

Ion Exchange Membranes: Fundamentals and Applications

0.2 q"L/q

2

0

0

1

2

0.1

q"L

q'L

3 4 I/S(A/dm2)

5

6

7

0.0

Figure 12.6 Relationship between current density and solution leakage in an electrodialyzer.

0.6

q' L/J V

10

0.5

JV 8

0.4

0.3

6

q'L/JV

q' L 0.2

4

q"L

2

0

q'L/JV, q"L/JV

q'L, q"L, JV (10-5cm3 cm-2 s-1)

12

0

2

4

6

8

10 12 v(cm/s)

14

0.1

16

18

0.0 20

Figure 12.7 Relationship between linear velocity in desalting cells and solution leakage in an elecrodialyzer.

281

Leakage

of u. These changes are understandable because the increase of linear velocity in desalting cells brings about a static head increase in desalting cells. Presently, 1.3 million tons of edible salt per year is produced in Japan using ion exchange membrane electrodialyzers. The effective membrane area is 1–2 m2, and the numbers of membrane pairs incorporated are 200–300 in a stack and 2000–3000 between electrodes. The temperature of feed seawater changes with time in a year. Current density is maintained at a relatively higher level in a summer season and lower level in a winter season. The ﬂux of a solution across a membrane pair and the electrolyte concentration in a concentrated solution are changed under the inﬂuence of current density i and seawater temperature T. q0L and q00L were calculated by substituting the membrane pair characteristics l, m, f and r measured in an experimental electrodialysis and performance (i, T, C0 , C00 and JV) of electrodialyzers for concentrating seawater operating in salt-manufacturing plants (Japan Tobacco & Salt Public Corporation, 1993) into Eqs. (12.25) and (12.26). q0L ; q00L ; i, T, C00 and JV are plotted against operating time t. The plots for Plant E and Plant F are shown, respectively, in Figs. 12.8 and 12.9, for example. q00L s in electrodialyzers in every salt-manufacturing plant are plotted against q0L s and are shown in Fig. 12.10. q00L is recognized to increase along with the increase of q0L ; and both values in each plant are conﬁrmed to change within a large scope. The solution leakage is brought about by the pressure difference between desalting cells and concentrating cells. The pressure difference varies from place

50

10

45 JV

8

40

7

35

6

)

30 T

5

25

4

20 C"

3

15

i qL"

2

qL'

10 5

1 0

T(

qL', qL", JV (10-5cm3 cm-2 s-1)

i(A/dm2),C"(eq/dm3)

9

0

50

100

150

200 250 t(day)

300

350

400

0

Figure 12.8 Solution leakage in electrodialyzers operating a salt-manufacturing plant (Plant E) (Tanaka, 2004).

282

Ion Exchange Membranes: Fundamentals and Applications

50

10

45

JV

40

7

35

6

30

)

8

5

25

T

4

20

C"

10

qL'

1 0

15

i

3 2

5

qL" 0

50

100

150

T(

qL', qL", JV (10-5cm3 cm-2 s-1)

i(A/dm2),C"(eq/dm3)

9

200 250 t(day)

300

350

400

0

Figure 12.9 Solution leakage in electrodialyzers operating a salt-manufacturing plant (Plant F) (Tanaka, 2004).

2.00 1.75

q"L(10-5cm3/cm2s)

1.50 1.25 1.00 0.75 0.50 0.25 0.00

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

q'L(10-5cm3/cm2s)

Figure 12.10 Solution leakage in electrodialyzers operating in salt-manufacturing plants (Tanaka, 2004).

Leakage

283

to place in an electrodialyzer. In order to elucidate the details of the solution leakage, it is necessary to clarify the pressure distribution in an electrodialyzer. REFERENCES Japan Tobacco & Salt Public Corporation, 1993, Salt Production Technical Report. Mandersloot, W. G. B., Hicks, R. E., 1966, Leakage currents in electrodialytic desalting and brine production, Desalination, 1, 178–193. Tanaka, Y., 2004, Overall mass transport and solution leakage in an ion-exchange membrane electrodialyzer, J. Membr. Sci., 235, 15–24. Wilson, J. R., 1960, Demineralization by electrodialysics, Buther-worths Scientiﬁc Publication, London, p. 256.

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Chapter 13

Energy Consumption 13.1.

ENERGY REQUIREMENTS IN AN ELECTRODIALYSIS SYSTEM

The total energy that is needed to operate a practical electrodialysis (ED) system is the sum of the following factors: (1) energy required to ﬁlter solutions and supply them through desalting and concentrating cells, (2) potential drops associated with the electrodes and the electrode streams, (3) ohmic drops in the solutions and membranes and (4) the concentration potentials across the membranes (Shaffer and Mintz, 1966; Spiegler, 1971; Strathmann, 2004). We discuss the energy consumption in points (3) and (4) in this chapter (Tanaka, 2003). The principal identiﬁable factors in ohmic drops are (1) the resistance of the bulk solution in desalting cells Rde and in concentrating cells Rcon, (2) the resistance of the cation exchange membranes RK and anion exchange membranes RA, (3) boundary layer resistances Rbound. The concentration potential across the membranes consists from (1) membrane potential Vmemb, (2) junction potential Vjunk. In the above-mentioned factors, Rbound and Vjunk are inﬂuenced by the concentration polarization in the boundary layer, and the analysis of these phenomena is quite complex. The following computations are carried out disregarding Rbound, Vjunk and the effect of concentration polarization on Vmemb. Accordingly, the conclusions introduced in this chapter include errors particularly at under accelerated concentration polarization. 13.2.

ENERGY CONSUMPTION IN A STACK

13.2.1

Electrodialysis Program In a practical-scale electrodialyzer, solution velocities in desalting cells vary because the friction factor (cf. Section 10.7) of solutions ﬂowing in desalting cells is not uniform between the cells. This event generates solution velocity distribution (cf. Section 11.6) and electrolyte concentration distribution. Further, electrolyte concentration distribution generates electrical resistance distribution and current density distribution (cf. Section 9.1). We discuss the energy consumption in a practical-scale electrodialyzer on the assumption that the current density and solution velocity in desalting cells are distributed. The computation of energy consumption is carried out using the computer program (ED program) explained brieﬂy as below. The electrodes in an electrodialyzer are conductors, and their electrical resistance and ohmic loss are negligibly small compared to the values between the electrodes. The voltage difference between the electrodes is assumed to be the DOI: 10.1016/S0927-5193(07)12013-1

286

Ion Exchange Membranes: Fundamentals and Applications

same at every position in an electrodialyzer, and its value at the entrances of desalting cells Vin is equal to the value at the exits Vout (cf. Section 9.1): V in ¼ V out

(13.1)

V in ¼ A1 iin þ A2

(13.2)

V out ¼ B1 iout þ B2

(13.3)

A1 ¼ ðr0in þ rin;K þ rin;A þ r00 ÞN 00 00 RT g C N ln 0 0 A2 ¼ 2ð¯tK þ ¯tA 1Þ gC F X X X B1 ¼ Y j r0out;j þ Y j rout;K;j þ Y j rout;A;j þ R00 N

(13.4)

! X RT g00 C 00 Y j ln 0 B2 ¼ 2ð¯tK þ ¯tA 1Þ gout;j C 0out;j F

(13.5) (13.6) (13.7)

The above equations are identical to Eqs. (9.4)–(9.10). The reasonability of Eq. (13.1) is conﬁrmed by seawater ED (cf. Table 9.1). In Eqs. (13.2) and (13.3), the ﬁrst term stands for the ohmic potential drop in desalting cells, concentrating cells and membranes, and the second term corresponds to the membrane potential drop. Electric resistances r0in ; r0out and r00 appearing in Eqs. (13.4) and (13.6) are expressed by Eqs. (13.8)–(13.10), which are identical to Eqs. (9.11) and (9.12). Electric resistance at the inlet of a desalting cell a (13.8) r0in ¼ ð1 Þk0in Electric resistance at the outlet of a desalting cell a r0out ¼ ð1 Þk0out Electric resistance in a concentrating cell a r00 ¼ ð1 Þk00

(13.9)

(13.10)

where a is the thickness of the desalting cell and the concentrating cell, e the current screening ratio of a spacer and k0in ; k0out and k00 are speciﬁc conductivities at the inlets and the outlets of desalting cells and concentrating cells, respectively. The current density i at x distance from the inlets of desalting cells is approximated by the following quadratic equation, which is identical with Eq. (9.13): x x2 (13.11) i ¼ a1 þ a2 þ a2 l l

287

Energy Consumption

where l is the ﬂow-pass length in desalting cells. By applying three-dimensional simultaneous equation to Eq. (13.11), the coefﬁcients a1, a2 and a3 are calculated (cf. Section 9.1). Current density distribution in an electrodialyzer expressed in Eq. (13.11) is computed based on Eqs. (13.1)–(13.7) as explained in Section 9.1. In this calculating process, cell voltage applied to a membrane pair at the inlet Vcell,in and the outlet Vcell,out are introduced as follows. 00 00 RT g C 0 00 ¯ ¯ V cell;in ¼ ðrin þ rin;K þ rin;A þ r Þiin þ 2ðtK þ tA 1Þ ln 0 0 gin C in F

V cell;out ¼

X ( þ

Y j r0out;j þ

X

Y j rout;K;j þ

X

Y j rout;A;j

1

(13.12) þ r00 iout

N !) X 00 RT g00 C 1 2ð¯tK þ ¯tA 1Þ Y j ln 0 0 gout;j C out;j F N

ð13:13Þ Cell voltage Vcell is introduced taking account of Eq. (13.1) as: V cell ¼ V cell;in ¼ V cell;out

(13.14)

Energy consumption in a desalinating process Edes and in a concentrating process Econ is expressed as: V cell I (13.15) E des ¼ Qout E conc ¼

V cell I J SS

(13.16)

Electrolyte concentration of a desalted solution C 0out is expressed by the following equations. Zl I 1 0 0 (13.17) C out ¼ C in aF S u Electrolyte concentration of a concentrated solution C00 is introduced using the overall mass transport equation (cf. Section 6.1, Eqs. (6.10)–(6.12)) as follows. pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ A2 þ 4rB A 00 (13.18) C ¼ 2r I A¼f (13.19) þ m rC 0 S I B¼l þ mC 0 (13.20) S

288

Ion Exchange Membranes: Fundamentals and Applications

Equations (13.1)–(13.20) hold under the limiting current density. When current density reaches the limiting current density of the membrane ilim at the outlet of a desalting cell in which linear velocity and electrolyte concentration are the least, the average current density applied to an electrodialyzer is deﬁned as its limiting current density (I/S)lim in which I is the total electric current and S is the membrane area (cf. Section 11.7). ilim is expressed by the function of electrolyte concentration C 0out and linear velocity uout at the outlet of the desalting cell in which the linear velocity is the least as follows (cf. Section 11.4). 0

n1 þn2 uout ilim ¼ ðm1 þ m2 uout ÞC out

(13.21)

The limiting current density of an electrodialyzer is deﬁned as follows (cf. Eq. (11.59)). I ilim ¼ (13.22) S lim zout zout is the outlet current density non-uniformity coefﬁcient. 13.2.2

Computation of Energy Consumption in Electrodialysis In order to calculate Edes, C 0out and (I/S)lim in the desalting process and Econ, C00 and (I/S)lim in the concentrating process using the equations described above, the trial and error computation process based on the computer program (ED program) was developed. We introduce an example of the computation setting in the following situations. (1) Speciﬁcations of an electrodialyzer Flow-pass length l: 100 cm Flow-pass width b: 100 cm Effective membrane area S: 1 m2 Thickness of a desalting and concentrating cell a: 0.075 cm Number of membrane pair integrated in a stack N: 300 pairs Electric current screening ratio of a spacer e: 0.15 (2) Characteristics of an ion exchange membrane pair Overall transport number l: 9.399 106 eq A1 s1* Overall solute permeability m: 2.005 106 cm s1* Overall electro-osmotic permeability f: 1.398 103 cm3 A1 s1* Overall hydraulic conductivity r: 1.00 102 cm4 eq 1 s1* Transport number tK+tA: 1.9069** Altering current electric resistance ralter: 5.107/2 O cm2*** * These parameters were determined by substituting r ¼ 1.00 102 cm4 eq 1 1 s into the following equations (cf. Eqs. (6.5)–(6.7)). (1) l ¼ 9:208 106 þ 1:914 105 r

289

Energy Consumption

2.0

0.10 (I/S)lim=1.507A/dm2 3

I/S ) =(

1.020

0.06

I/S

1.2

0.07

lim

C ′ in

1.4

0.04

0.8

0.05 0. 06

1.0

0.02

0.4 0.2 0.0 0 0.0

0. 04

0.518

0.04 0.0

0.03 6

0.0

2

0.6

0.08

dm

eq/

06 = 0.

4

0.02 0.01

0.0 2

00.4

0.09

C'out (eq/dm3)

1.6

0.0

E des (kW h/m 3)

(I/S)lim (A/dm 2)

1.8

0.8

1.2

1.6

0.00 2.0

I/S (A/dm2) Energy consumption Salt concentration in a desalted solution Limiting current density

Figure 13.1 Energy consumption, salt concentration in a desalted solution and limiting current density.

m ¼ 2:005 104 r

(2)

f ¼ 3:768 103 r0:2 1:019 102 r

(3)

tK þ tA ¼ lF þ 1

(cf. Eq. (6.15)) 5:107 102 r1 ralter ¼ 2

(4)

(5)

(cf. Eq. (6.8)) Electric resistance of an ion exchange membrane under a direct current rdire was calculated by substituting ralter into the empirical equation obtained by the ED experiment (cf. Section 2.2 (2)). (3) ED conditions Standard deviation of normal distribution of linear velocity ratio s: 0.1.

290

Ion Exchange Membranes: Fundamentals and Applications

Solution velocity at the inlet of desalting cell uin: 5 cm s1. (4) Limiting current density Limiting current densities ilim and (I/S)lim were computed using Eqs. (13.21) and (13.22) setting m1 ¼ 83.50, m2 ¼ 24.00, n1 ¼ 0.7846 and n2 ¼ 8.612 103 for a cation exchange membrane Aciplex K-172 obtained in the ED of a NaCl solution (cf. Sections 11.4 and 11.7).

Fig. 13.1 shows I/S vs. Edes, C 0out and (I/S)lim in a saline water desalinating process in which salt concentration at the inlets of desalting cells C 0in is maintained at 0.06, 0.04 and 0.02 eq dm3. (I/S)lim of this process is obtained from the intersection between I/S vs. (I/S)lim plots and an I/S ¼ (I/S)lim line, and calculated as 1.507 A dm2 ðC 0in ¼ 0:06 eq dm3 Þ; 1.020 (0.04) and 0.518 (0.02). Fig. 13.2 shows I/S vs. Econ, C00 and (I/S)lim in a seawater concentrating process ðC 0in ¼ 0:6 eq dm3 Þ: The limiting current density is calculated as (I/ S)lim ¼ 13.46 A dm2. Figs. 13.1 and 13.2 are reasonable at lower current densities compared to the limiting current density; however, errors are increased particularly near the limiting current density.

100

20

90

18 (I/S) lim =13.46 A/dm 2

80

(I/S)lim

70 60

10

50

=( I/S

)l

im

12

8

40 n

E co

6

30

C ′′

4

20

2

10

0

0

2

4

6

Econ (Wh/eq)

14

I/S

C "(eq/cm3)

(I/S) lim (A/dm2)

16

8

10

12

14

16

18

20

0

I/S (A/dm2)

Figure 13.2 Energy consumption, salt concentration in a concentrated solution and limiting current density.

Energy Consumption

291

REFERENCES Shaffer, L.H., Mintz, M.S., 1966. Electrodialysis, In: Spiegler, K.S. (Ed.), Principles of Desalination, Academic Press, New York, pp., 200–289. Spiegler, K. S., 1971, Polarization at ion exchange membrane-solution interfaces, Desalination, 9, 367–385. Strathmann, H., 2004, Ion-Exchange Membrane Separation Processes, Membrane Science and Technology Series, vol. 9, Elsevier, Amsterdam, pp. 173–184. Tanaka, Y., 2003, Mass transport and energy consumption in ion-exchange membrane electrodialysis of seawater, J. Membr. Sci., 215, 265–279.

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Chapter 14

Membrane Deterioration 14.1.

MEMBRANE PROPERTY CHANGE WITH ELAPSED TIME

14.1.1

Membrane Characteristic Stability Against Various Agents The economic viability of electrodialysis plants depends on the life time of the membrane. In order to make the stability of the membrane clear, Kneifel and Hattenbach (1980) evaluated the membrane property change with elapsed time under several chemical environments. The ion exchange membranes were commercially produced mainly by companies in Japan and USA as follows: (1) Tokuyama Soda Co. Ltd. (Japan): anion exchange membrane AF-4T/ AFS-4T/AV-4T/AC-158 and cation exchange membrane C66-5T/CH-45T/ CH-2T/CL-25T. (2) Asahi Glass Co. Ltd. (Japan): anion exchange membrane AMV/ASV and cation exchange membrane CMV. (3) Asahi Chemical Ind. Co. Ltd. (Japan): anion exchange membrane A-111 and cation exchange membrane K-101. (4) Ionac Chemical Company (USA): anion exchange membrane MA 3148/ MA 3475 R/IM 12 and cation exchange membrane MC 3470. (5) Ionics Inc. (USA): anion exchange membrane 111BZL183/103PZL183/ 103QZL183 and cation exchange membrane 61 AZL 183/61 CZL 183. (6) Forschungsinstitut Berghof GmbH (Israeli): anion exchange membrane PEN 4/NPES A3 and cation exchange membrane NPES C2. (7) American Machine and Foundry (USA): cation exchange membrane AMF-C100/AMF-C311. (8) Rhone-Poulenc Chemie GmbH (Germany): anion exchange membrane ARP and cation exchange membrane CRP. The properties to be found in the literature and reference sheets of the membrane producers are not comparable with each other since measurements are often conducted under different methods and conditions. To obtain comparable values, the values of exchange capacity, water content, membrane resistance, thickness and permselectivity were determined and compiled under uniform conditions in Table 14.1 for the cation exchange membranes and in Table 14.2 for the anion exchange membranes. Here, the permselectivity P is given by P ¼ ð¯t tÞ=ð1 tÞ; where ¯t and t are transport number of counter-ions in the membrane and the solution, respectively, and ¯t was measured from membrane potentials. The results indicated in the tables are average values from tests DOI: 10.1016/S0927-5193(07)12014-3

294

Table 14.1 Properties of cation exchange membranes Membrane

Exchange Capacity (eq kg1)

Water Content (%)

Electric Resistance (1 N NaCl, 251C, O cm2)

Thickness (mm)

Permselectivity

1.0/0.5 N KCl 1.5 1.3 2.4 1.4 2.0 3.3 2.3 2.4 2.0 2.6 0.6 1.1 1.9 2.6

35 25 25 24 31 34 27 32 40 34 16 22 15–20 40

Source: Kneifel and Hattenbach, 1980.

6–10 20–30 2.9 2.1 2.9 1.5 2.1 2.2 4.5 7.2 4.8 3–7 6.3

0.6 0.22 0.15 0.24 0.18 0.16 0.17 0.17 0.6 0.7 0.3 0.22 0.4 0.6

0.68 0.65 0.95 0.91 0.81 0.89 0.92 0.86 0.62 0.81 0.84 0.77 0.91 0.65

0.1/0.05 N KCl

1.0/0.5 N KCl

0.1/0.05 N KCl

0.94 0.93 0.98 0.98 0.97 0.97

0.83 0.82 0.98 0.95 0.90 0.94 0.96 0.93 0.81 0.95 0.92 0.88 0.96 0.82

0.97 0.97 0.99 0.99 0.98 0.98

0.97 0.93 0.96 0.98 0.98

0.98 0.97 0.98 0.99 0.99

Ion Exchange Membranes: Fundamentals and Applications

MC 3470 MC 3142 CMV K 101 CL-25T C66-5T CH-45T CH-2T 61 AZL 183 61 CZL 183 AMF-C311 AMF-C100 NPES C/2 CRP

Transport Number

Membrane

Exchange Capacity (eq kg1)

Water Content (%)

Electric Resistance (1N NaCl, 251C, O cm2)

Thickness (mm)

Permselectivity

1.0/0.5 N KCl MA 3148 MA 3475 R IM 12 AMV ASV A 111 AF-4T AFS-4T AV-4T AVS-4T AC-158 111 BZL 183 103 PZL 183 103 QZL 219 PEN 4 NPES A/3 ARP

0.8 1.4 0.5 1.9 2.1 1.2 2.0 1.8 1.4 1.5

18 31 22 19 24 31 24 25 24 20

12–70 5–13 8 2–4.5 2.1 2–3 1.7 3.0 2.4 5.1 2.5

1.2 1.5 0.1–0.3 0.2–0.7 1.8

38 30 31 27 34

4.9 8.0 3–12 3–12 6.9

0.20 0.6 0.18 0.14 0.15 0.21 0.16 0.19 0.15 0.17 0.5 0.6 0.7 0.3 0.4 0.5

0.85 0.70 0.4 0.92 0.91 0.45 0.90 0.95 0.90 0.93 0.82 0.52 0.43 0.70 0.5–0.7 0.4–0.8 0.79

0.1/0.05 N KCl 0.98 0.94 0.70 0.99 0.99 0.91 0.98 1.00 0.98 0.99 0.98 0.95 0.90 0.85

Transport Number

1.0/0.5 N KCl 0.92 0.85 0.71 0.96 0.95 0.73 0.96 0.97 0.95 0.97 0.91 0.77 0.72 0.95 0.77 0.6–0.9 0.90

Membrane Deterioration

Table 14.2 Properties of anion exchange membranes

0.1/0.05 N KCl 0.99 0.97 0.85 0.99 0.99 0.95 0.99 1.00 0.99 1.00 0.99 0.97 0.95 0.98

Source: Kneifel and Hattenbach, 1980.

295

296

Ion Exchange Membranes: Fundamentals and Applications

of membranes from various membrane deliveries and hence possibly of different production charges. In this experiment, the membrane samples were subjected to the various agents at room and elevated temperatures for periods up to ﬁve years in the laboratory, and the membrane characteristics such as electric resistance, permselectivity and ion exchange capacity were measured during the test. Fig. 14.1 shows the electric resistance for six membrane types after having been subjected

t 1.0 Xt/X0

Xt/X0

1.0

0.5

0

C 66 5T

AF 4T 0 500 d

100

Xt/X0

Xt/X0

1.0

0.5

0.5

MA 3148 0 500

1000 d

MC 3142

1500

500

1.0

1000 d

1500

1.0 Xt/X0

Xt/X0

500 d

100

1.0

0

0.5

0.5

0.5 a)

0

CMV 0 500

1000 d

1500

AMV 500

1000 d

1500

Figure 14.1 Membrane resistance after exposure to various agents at room temperature (Kneifel and Hattenbach, 1980): (K) distilled water, (’) 0.2 N NaCl, (J) 0.1 N NaCl, (D) 0.1 N HNO3 and (m) 0.1 N NaOH. ‘a)’ indicates membrane destruction.

297

Membrane Deterioration

to different agents at room temperature. The strongest variations for most membranes are caused by the effect of a NaOH solution, especially applied to the heterogeneous membranes MA 3148 and MC 3142 (strong decrease in the resistance values) and the anion exchange membranes AF-4T (strong increase in the resistance values) and AMV (crumbled). Good stability is exhibited by the membrane C66-5T. The effect of the oxidizing solution on the electric resistance at room temperature is shown in Fig. 14.2, indicating particularly strong decrease in the resistance value of the membrane type CMV. All membranes with the exception of MC 3470 and MA 3475 R were destroyed at 851C. The dependence on duration test in 1 N NaCl at 851C of resistance is shown in Fig. 14.3, of permselectivity in Fig. 14.4 and of exchange capacity in Fig. 14.5. The strong increase in resistance of the membrane types AMV, AV4T, CMV, AF-4T and CH-45T is striking. The membrane types 103 QZL 219 and 61 CZL 183 showed no signiﬁcant changes. Variations in the permselectivities in trial of up to 100 days were slight with the exception of membrane type MA 3148. Longer duration however showed a marked decrease in values in the cases of membrane types AFS-4T, C66-5T, AF-4T, MA 3148, CRP

a)

xt/x0

a)

a)

t

1.0

a)

85 °C 0 MC 3470

AF - 4T

CMV

K 101

MA 3475 R

C66 - 5T

AMV

61CZL 183

1.0

25 °C 0 10-2

10-1

100

101

102

103

d

Figure 14.2 Membrane resistance after exposure to an oxidizing agent (Kneifel and Hattenbach, 1980). 0.1 N K2CrO4+1 N HCl+1 N NaCl. ‘a)’ indicates membrane destruction.

298

Ion Exchange Membranes: Fundamentals and Applications

2.0

61CZL 183

AMV

CMV

K101

AV - 4T

MA 3148

xt/x0

t 1.0

0 10-2

10-1

100

101

102

103

101

102

103

d

xt/x0

1.0

0

xt/x0

1.0

0 10-2

10-1

100 d

MC 3470 MA 3475R

MC 3142 103 QZL 219

AF - 4T

CH - 45T

CRP

C66 - 5T

1M - 12

ARP

Figure 14.3 Membrane resistance after exposure to 1 N NaCl at 851C (Kneifel and Hattenbach, 1980).

and ARP. The samples of types AF-4T and MA 3148 crumbled and type CMV shrank strongly. The values of exchange capacity, with one exception (IM 12) changed slightly for trial times up to 100 days. In longer trials the exchange capacities – with the exception of K 101 – were reduced to less than 60% of the initial values. Most experimental data at room temperature and 851C were obtained for membrane types AMV, CMV, AF-4T, C66-5T and K 101. Results for these membranes in long-term exposure tests in salt solution at room temperature indicated good stability. At 851C the membranes AMV, CMV and AF-4T showed low, type C66-5T fair and K 101 good stability, respectively.

299

Membrane Deterioration

Xt/X0

1.0 a) 103 QZL 219

MC 3142

CMV

61CZL 183

MA 3475R

0.5 10-2

100

10-1

101

103

102

d

Xt/X0

1.0 * AMV MC 3470

*

K 101

AF - 4T C66 - 5T

AFS - 4T

* *

a)

a)

MA 3148

0.5 10-2

100

10-1

101

103

102

d

Figure 14.4 Permselectivity after exposure to 1 N NaCl at 851C (Kneifel and Hattenbach, 1980). ‘a)’ indicates membrane destruction.

1.0 Xt/X0

t K101 CMV 0.2

C66 - 5T

Xt/X0

1.0 a) AFS - 4T AF - 4T

0.2 100

AMV IM 12 101

102

103

d

Figure 14.5 Exchange capacity after exposure to 1 N NaCl at 851C (Kneifel and Hattenbach, 1980).

14.1.2 Performance Change of Ion Exchange Membranes in Long-Term Seawater Electrodialysis Long-term seawater electrodialysis was carried out using a small-scale electrodialyzer (effective membrane area: 2 dm2) integrated with commercially

300

Ion Exchange Membranes: Fundamentals and Applications

available homogeneous ion exchange membranes and heterogeneous membranes produced in the laboratory (Hanzawa et al., 1966). The types of the membranes (cation exchange membrane/anion exchange membrane) applied in this experiment were: (1) Tokuyama Soda Co.: Neocepta CL-25T (St DVB PVC)/AVS-4T (St DVB VP PVC), including PVC ﬁber reinforcement. (2) Asahi Chemical Ind. Co.: Aciplex CK-2 (St DVB)/CA-3 (St DVB), including no reinforcement. (3) Asahi Glass Co.: Selemion CMV (St BD)/AST (St BD), including glass ﬁber reinforcement. (4) Japan Monopoly Corp.: Amberlite XE-69 PVC/Amberlite XE-119 PVC; heterogeneous membranes produced from strong acidic cation exchange resin Amberlite XE-69 and strong basic anion exchange resin XE-119, with PVC powder to form sheets including no reinforcement. The membranes described above are produced from the following materials: St, styrene; DVB, divinylbenzene; PVC, polyvinyl chloride; VP, vinylpyridine; BD, butadiene. Sand ﬁltered seawater was supplied into the electrodialyzer and electrodialyzed at current density of 1 A dm2 for periods of up to four years. Electrolyte concentration in a concentrating cell C00 (Baume’s solution density Be0 ), volume ﬂux across a membrane pair q, current efﬁciency Z and feeding seawater temperature T are plotted against running time t. The plots are shown in Fig. 14.6 (Neocepta CL-25T/AVS-4T), Fig. 14.7 (Aciplex CK-2/CA-3), Fig. 14.8 (Selemion CMV/AST) and Fig. 14.9 (Amberlite XE-69 PVC/XE-119 PVC), showing periodical changes of C00 and q caused by the seasoning change of seawater temperature T. After t ¼ 25,000 h, chlorine gas was unfortunately contaminated into the feeding seawater. Due to this trouble, Z is recognized to be decreased during this period. Except the data affected by this trouble, the performance of the homogeneous membranes (Figs. 14.6–14.8) was quite stable. However, C00 , q and Z of heterogeneous membrane (Fig. 14.9) are decreased with time. In parallel with the experiment mentioned above, long-term seawater electrodialysis was performed setting the current density at 2–4 A dm2. However, the performance and durability were not evaluated because the membranes were destroyed due to the precipitation of CaCO3 and CaSO4 on the membrane surfaces. 14.2. 14.2.1

SURFACE FOULING

Mechanism of Surface Fouling Surface fouling is usually caused by deposits of macromolecules or colloidal matter from the feed solution. Grossman and Sonin (1973) discussed the

301

Membrane Deterioration

C'' (°Be')

21 20

15°C

t

19

20°C

18

25°C

q (ml/h)

17 18

25°C

16

20°°CC 15

14

(%)

90 80 70

T (°C)

30 20 10 0

5000

10000

15000 20000 t (h)

25000

30000

Figure 14.6 Seawater electrodialysis test for a long term (Neocepta CL-25T/AVS-4T) (Hanzawa et al., 1966).

mechanism of the surface fouling as follows by assuming that the membranes are covered with thin surface ﬁlms of the deposited material. Fig. 14.10 shows the salt concentration distribution in a desalting and a concentrating cell (thickness: a). The linear concentration distribution in the diffusion layers is an approximation which results from the Nernst diffusion model for the convective–diffusion process. In the Nernst diffusion model, the salt ions are assumed to arrive at the membrane surface by diffusion across hypothetical diffusion layers of thickness d. Using Eqs. (11.1) and (11.2), one obtains the salt concentration C0 at the desalting surface of the membrane as follows: C0 ¼ C

¯t t id FD

(14.1)

where i is current density, C the salt concentration in the desalting cell outside the diffusion layer, D the salt diffusion coefﬁcient in the solution, ¯t and t the transport numbers of counter-ions in the membrane and the solution, respectively, and F

302

C'' (°Be')

Ion Exchange Membranes: Fundamentals and Applications

14 13

15°C 20°C

t

12

25°C

11

q (ml/h)

30 25°C 20°C 15°C

28 26

(%)

24 90 80

T (°C)

70 30 20 10 0

5000

10000

15000 20000 t (h)

25000

30000

Figure 14.7 Seawater electrodialysis test for a long term (Aciplex CK-2/CA-3) (Hanzawa et al., 1966).

the Faraday constant. Here, it should be noticed that the phenomenological meaning of d is exhibited by the salt concentration gradient at the membrane/ solution interface (x ¼ 0) as follows (cf. Section 11.1, Eq. (11.2)): d¼

C C0 ðdC=dxÞx¼0

(14.2)

The limiting current density ilim is introduced by substituting C0 ¼ 0 into Eq. (14.1) as follows, which was already expressed in Eq. (11.4): ilim ¼

FDC ðt¯ tÞd

(14.3)

When a surface ﬁlm is present on the membrane as shown in Fig. 14.11, the material balance in the diffusion layer is expressed based on the Nernst diffusion model introduced from Eq. (14.1) as C C ¼

¯t t id FD

(14.4)

303

C'' (°Be')

Membrane Deterioration

14

15°C 20°C

t

13 12

25°C

11

q (ml/h)

30

25°C 20°C 15°C

28 26 24

(%)

90 80 70

T (°C)

30 20 10 0

5000

10000

15000 20000 t (h)

25000

30000

Figure 14.8 Seawater electrodialysis test for a long term (Selemion CMV/AST) (Hanzawa et al., 1966).

The material balance in the ﬁlm is expressed by C C0 ¼

¯t t iD FDf

(14.5)

where C is salt concentration at the interface between the diffusion layer and the ﬁlm, D the ﬁlm thickness, Df the salt diffusion coefﬁcient in the ﬁlm and t the transport number in the ﬁlm. In Eq. (14.4), materials composing the surface ﬁlm are assumed to be uncharged (neutral), so t in the ﬁlm (in Eq. (14.5)) is approximated by t in the solution (in Eq. (14.4)). At limiting current density, substituting i ¼ ilim and C0 ¼ 0 into Eqs. (14.4) and (14.5) leads to C C ¼

C ¼

¯t t ilim d FD

¯t t ilim D FD

(14.6)

(14.7)

304

Ion Exchange Membranes: Fundamentals and Applications

C'' (°Be')

15 14

t

15°C 20°C C 25°

13 12

q (ml/h)

11

22 20

25°C 20°C 15° C

18

(%)

70 60 50

T (°C)

30 20 10 0

5000

10000

15000 20000 t (h)

25000

30000

Figure 14.9 Seawater electrodialysis test for a long term (Amberlite XE-69 PVC/XE119 PVC) (Hanzawa et al., 1966).

Canceling C from Eqs. (14.6) and (14.7), the limiting current density of the membrane having the ﬁlm is introduced as follows: FDC 1 (14.8) ilim ¼ ð¯t tÞd 1 þ fp Here, fp is the fouling parameter deﬁned by Eq. (14.9), which is dimensionless and indicates the effect of the ﬁlm on the limiting current density. fp ¼

DD Df d

(14.9)

It is clear from Eqs. (14.8) and (14.9) that a fouling ﬁlm depresses the limiting current density only if the quantity fp is comparable with unity or larger, that is, when the ﬁlm thickness is comparable with the Nernst diffusion layer thickness and/or the ﬁlm diffusion coefﬁcient is small compared with the diffusion

305

Membrane Deterioration

a i

C'

C0

C0

x

Concentrating cell

Anion exchange membrane

x

Desalting cell

Cation exchange membrane

Concentrating cell

Figure 14.10 Salt concentration distribution in electrodialysis channels according to Nernst diffusion model (Grossman and Sonin, 1973).

coefﬁcient in the solution. fp represents the ratio of the ohmic resistance of the ﬁlm to the ohmic resistance of the ﬂuid within the Nernst diffusion layer. Since in many practical cases the diffusion layer is quite thin (cf. Table 11.1) compared with the thickness of the desalting cell (a in Fig. 14.10), fp can be of order unity even if the ohmic resistance of the fouling layer is quite small compared with that of the desalting cell. In other words, the ﬁlm may bring about a signiﬁcant reduction in the limiting current density, and yet contribute negligibly to the ohmic resistance of the system as a whole. However, if D is comparable with the thickness of the desalting cell, or if Df is very small, a ﬁlm capable of depressing the limiting current would also increase the resistance of the system. 14.2.2

Formation of Films on the Membrane Surface Surface fouling discussed above is caused by deposition of suspended matters in a feeding solution on the membrane surfaces to form ﬁlms. Small particles suspended in a feeding solution are usually removed using sand ﬁltration, membrane ﬁltration, coagulation sedimentation ﬁltration, etc. However,

306

Ion Exchange Membranes: Fundamentals and Applications

Surface film

i

C'

C*

C0 Desalting Diffusion cell layer

Cation exchange membrane

Diffusion Concentrating layer cell

Figure 14.11 Salt concentration distribution with surface ﬁlms on a cation exchange membrane (Grossman and Sonin, 1973).

extremely small particles pass through the ﬁlter, enter into an electrodialyzer and deposit on the membranes. Constituents of the substances attached to the membrane surface are shown in Table 8.8. Attention should be given to the fact that microorganisms passing through the ﬁlter enter into an electrodialyzer and breed at the membrane surface. Ohwada et al. (1981) measured viable bacteria count, chlorophyll a and organic components in the substances attached to the membranes integrated into the electrodialyzer operating in salt manufacturing plants (Table 14.3).

Membrane Deterioration

307

Table 14.3 Deposition of substances on ion exchange membranes and microorganisms in the deposit (Ohwada et al., 1981).

14.2.3

Removal of Films on the Membrane Surface The deposit is removed by (1) stack disassembling (cf. Section 1.5.3 in Applications), (2) periodic current reversal (cf. Section 2.6 in Applications) and (3) washing with a chemical reagent. We discuss (3) in this section. Urabe and Doi (1987) washed the membranes with a mixed solution of alkalis, mineral salts and organic solvents. In this research, cation exchange membrane CL-25T and anion exchange membrane ACH-45T were integrated into an electrodialyzer (effective membrane area: 0.25 m2, number of membrane pairs: 500). Seawater was supplied and desalinated passing an electric current. In the course of the electrodialysis operation, cell voltage was increased from 0.7 to 1.2 V due to the precipitation of ﬁne substances to the membrane surfaces. So, the 25–301C washing solution mixed with tap water (500 l) and methanol (500 l) dissolving NaCl (90 kg) and NaOH (40 kg) was circulated through the desalting and concentrating cells for 3 h. Then, the cell voltage was restored to original 0.7 V without the decrease of the current efﬁciency, permselectivity and strength of the membranes. In the washing operation, NaCl, NaOH and methanol are estimated to dissolve the substances precipitated in the membrane into the external solution. Yamashita (1976) (Tokuyama Soda Co.) washed the membranes with ammonia water dissolving citric acid and EDTA. In this study, ﬁltrated industrial waste water was supplied to an electrodialyzer (effective membrane area: 5 dm2, number of membrane pairs: 20) maintaining the solution velocity and static head loss, respectively, at 40 l min1 and 154 mmHg, respectively. After 166 m3 of the solution was electrodialyzed, it became difﬁcult to operate the apparatus because the static head is increased to 452 mmHg due to the adhesion of suspended substances in the feeding solution to ﬂow paths in the electrodialyzer. So, a 301C aqueous solution dissolving 2% citric acid and 1% EDTA was supplied to the electrodialyzer at the ﬂow velocity of 40 l min1, keeping pH at 4.5 by adding ammonia water. The static head was decreased to 162 mmHg after 45 min, and then after operating further 15 min, the electrodialyzer was

308

Ion Exchange Membranes: Fundamentals and Applications

disassembled, and it was found that the attached substances disappeared. Finally the electrodialyzer was assembled again and the operation was proceeded supplying the solution at the static head of 162 mmHg. In this experiment, complex forming agents such as citric acid and EDTA dissolved the substances attached to the membrane at a reasonable pH value. Ueno et al. (1980) supplied seawater to an electrodialyzer incorporated with Selemion CMV and Selemion ASV. Static pressure at the inlet of the apparatus was 0.6 kg cm2 G1 at ﬁrst. In the course of operation, the pressure was gradually increased due to the attachment of slime to the membrane surfaces in desalting cells, and eventually it became impossible to operate because the pressure attained the limiting value of 1.2 kg cm2 G1. In order to avoid the trouble, 900 ml of an aqueous solution dissolving 0.5% Neoplex Paste (Kao Atlas Co., anion-surfactant, effective component: sodium dodecyl benzene sulfate) and 0.5% hydrazine was supplied into 1 m3 of water in a washing line, and was circulated through the circulating tank and the electrodialyzer for 30 min. Next, adding 25.7 kg of 35% hydrogen peroxide into the circulating tank, the washing solution was circulated through the electrodialyzer for 3 h keeping the temperature at 25–301C. Consequently, the pressure was decreased to 0.6 kg cm2 G1 and it became possible to operate the electrodialyzer again. After the experiment, the apparatus was disassembled and it was conﬁrmed that the slime was removed perfectly. Electric resistance of the ion exchange membranes was not altered by the washing.

14.3. 14.3.1

ORGANIC FOULING

Organic Fouling Phenomena Organic fouling of ion exchange membranes is one of the major problems in electrodialysis. It is caused by the precipitation of colloids on the membranes and because most of the colloids present in natural water are negatively charged, it is almost always the anion exchange membranes which are affected. Korngold et al. (1970) examined experimentally the process of organic fouling using multicompartment electrodialysis cells and humate as the fouling agents as follows. Fouling is deﬁned as the voltage rise across anion exchange membranes due to fouling agents. The apparatus used for the experiments was a multicompartment cell series with forced circulation. Two measuring electrodes were inserted in each cell member so that they were near the membrane surfaces adjoining the members. The membranes were clamped tightly between two cell members. Fig. 14.12 shows the fouling curves of AMF anionic membranes in 0.1 N KCl solutions containing 1.0 and 0.1% humate, respectively. Reversal of the current immediately reduced the voltage on the membrane to its original values,

309

Membrane Deterioration

40

0.1% humate

35

15 10

Current original sign

20

Current reversal Current original sign

Mechanical cleaning of the surface

V (Volt)

25

Current reversal

1.0% humate

30

5 0

0

1

2

3

4

5

t (h)

Figure 14.12 Fouling of AMF A-63 membranes in a mechanically stirred apparatus by Na-humate containing 0.1 N KCl solutions. i ¼ 19 mA/cm2; V ¼ voltage across the membrane (Korngold et al., 1970).

but its reversal to its original direction raised it again almost instantaneously as high as it had been before reversal. Mechanical cleaning of the membrane surface also helped for only a very short time. There was, of course, much more humic acid precipitated in the 1% solution. Fig. 14.13 shows the inﬂuence of current density on the organic fouling. The abscissa is not the time but the amount of electricity passed across a set of eight consecutive AMF A-63 membranes in the multicell apparatus. Fouling is given on the ordinate as the average voltage drop across these membranes. Fig. 14.14 shows the result of experiments in which the fouling has been performed in solutions of increasing KCl concentration, keeping all other parameters unchanged. It is clear that fouling increases quickly with decreasing KCl concentration. It was found in the following experiment that fouling acidiﬁes the solution on the side of the anionic membrane on which humic acid precipitates and makes the solution on its other side alkaline. In this experiment using a six compartment cell, an AMF anionic membrane was put between cells 3 and 4 with voltage measuring electrodes near its surface (Fig. 14.15). Both cells were separated by cationic AMF membranes from their adjoining compartments which contained 0.1 N NaCl to insulate them from the cells with the current electrodes. HCl was added to the cathode cell (pH2) and NaOH to the anode cell (pH11). The electrolyte in the measuring cells 3 (desalting cell) and 4 (concentrating cell) was 0.1 N in each cell in the control experiment, and cell 3

310

Ion Exchange Membranes: Fundamentals and Applications

V (volt)

10

20 mA/cm2

5

0 10

10 mA/cm2

100

5 mA/cm2

1000

5000

Coulombs

Figure 14.13 Inﬂuence of current density on fouling (Korngold et al., 1970). AMF A-63 membranes. 0.04 N KCl containing 1000 ppm Na-humate. Flow velocity 1.8 cm s1. pH 8.4.

30

0.1 N KCI 20 V (volt)

0.03 N KCI

10 0.04 N KCI

0 0.1

1

10

100

t (h)

Figure 14.14 Inﬂuence of KCl concentration on fouling (Korngold et al., 1970). AMF A-63 membranes. 1000 ppm Na-humate. 10 mA cm2. Flow velocity 1.8 cm s1. pH 8.4.

311

Membrane Deterioration

HCl

NaOH

Cathode

Anode

0.1N NaCl

0.1N NaCl

0.1N NaCl

0.1N NaCl

0.1N NaCl

0.1N NaCl

+ H+OH− 0.06% sodium humate Cell 1

A

Cell 2

K

Cell 3 desalt.

A*

Cell 4

K

Cell 5

A

Cell 6

concent.

A: anion exchange membrane

desalt.: desalting cell

A*: test anion exchange membrane

concent.: concentrating cell

K: cation exchange membrane,

Figure 14.15 Six compartment cell for measuring pH changes caused by organic fouling (Korngold et al., 1970).

received an amount of 0.06% sodium humate in the main experiment. A current of 60 mA (i ¼ 19 mA cm2) was passed through the system in both experiments and the voltage across the membrane and the pH in both measuring compartments was measured as a function of time. NaCl was added every 10 min to cell 3 to compensate for what was being lost by electrodialysis. The pH in cells 2 and 5 was determined every 10 min to ensure that they did not change and they isolated the experimental cells from the electrode compartments. Cells 3 and 4 were stirred mechanically at constant speed. Table 14.4 shows the results. It is clear that fouling causes changes of pH on both sides of the membrane. The results mentioned above indicate that fouling by anionic colloids of insoluble colloid acids is auto-catalytic process, triggered by polarization on the anionic membrane and increasing the polarization on it so as to increase fouling more rapidly after an incubation period. The underlying chemical process must be the precipitation of humic acid on the membrane. The layer of this ‘‘cation-active’’ colloid on the anion-active membrane gives rise to a composite, ‘‘sandwich’’ membrane which becomes depleted of salt ions from both sides because it receives the current in this ‘‘closing’’ direction. Thus, an increasing part of current conduction is taken over by the ions of water, making the humate side (desalting side) acidic and the other side (concentrating side) alkaline. The H+ ions entering the humate solution auto-catalytically increase the precipitation of humic acid so that fouling increases rapidly once it has started.

312

Ion Exchange Membranes: Fundamentals and Applications

Table 14.4 Acid is generated on the cathode side of an anion exchange membrane and alkali is generated on its anode side Time (min.)

Control: No Humate V

0 5 17 30 40 63 80 95 110 130 150 165

2.2 2.2 2.3 2.3 2.3 2.3 2.4 2.5 2.5 2.5 2.5 2.5

pH in cell 3 (desalt.)

pH in cell 4 (concent.)

5.5 5.4 5.2 5.1 5.0 4.8 4.5 4.5 4.5 4.6 4.6 4.5

5.5

5.6

6.3 6.3

With Humate V 2.5 4.5 7.5 8.2 8.7 9.0 10.5 10.7 11.8 12.5 12.2 14.0

pH in cell 3 (desalt.) 6.6 5.7 5.5 5.5 5.5 4.2 3.4 3.2 3.0 2.9 2.8 2.7

pH in cell 4 (concent.) 5.5 6.0 6.0 6.0 6.5 7.0 7.0 10.9 11.1

Note: desalt., desalting cell; concent., concentrating cell. 600 ppm humate in 0.1 N NaCl 19 mA/cm2 (mechanical stirring). Source: Korngold et al., 1970.

14.3.2 Anti-Organic Fouling Membranes 14.3.2.1 Macroreticular Anion Exchange Membrane In order to prevent organic fouling, Kusumoto et al. (1976) developed the following macroreticular (macroporous) anion exchange membrane. Namely, a syrupy monomer solution was prepared by mixing styrene-divinylbenzene with polybutadiene rubber (viscosity increasing agent) and t-amylalcohol (macroporous structure forming agent). The macroreticular membrane was obtained by coating the mixed solution to a polypropyrene reinforcement and polymerizing under pressure. In this investigation, the membranes were synthesized by changing the ratio of t-amylalcohol as shown in Table 14.5. Fig. 14.16 gives the inﬂuence of amylalcohol ratio to electric resistance, transport number and diffusion constant of the membranes synthesized above, showing that the macroporous structure develops with the increase of tamylalcohol content. The anti-organic fouling performance was measured using a two-cell electrodialysis unit ﬁlling with a 0.05 N NaCl+100 ppm dodecylbenzene sulfonate solution in the cathode chamber (desalting side) and a 0.05 N NaCl solution in the anode chamber (concentrating side). Passing an electric current of 2 mA cm2, electric resistance change due to the organic fouling of the membrane was evaluated as shown in Fig. 14.17 by measuring the potential difference Vm across the membrane. The result shows that the electric resistance increase due to the organic fouling is suppressed with the development of macroporous structure.

313

Membrane Deterioration

Table 14.5

Composition of monomer mixed solutiona

No.

Stb

DVBc

PBd

t-AmOHe

1 2 3 4

0.7 0.7 0.7 0.7

0.3 0.3 0.3 0.3

0.1 0.1 0.1 0.1

0.4 0.5 0.8 1.0

Source: Kusumoto et al., 1976. a Weight. b Styrene. c Divinylbenzene. d Polybutadiene. e t-Amylalcohol.

RA (Ω cm2)

6 4 2 0

t (−)

0.9 0.8 0.7

D (cm2h−1)

8 6 4 2 0 0.2

0.4 0.6 0.8 1.0 (t-AmOH)/(St + DVB) (wt. Ratio)

Figure 14.16 Electrochemical properties of a macroreticular anion exchange membrane (Kusumoto et al., 1976). RA: electric resistance (251C, 0.5 N NaCl), ¯t: transport number (251C, 0.5 N/2.5 N NaCl) and D: NaCl diffusion constant (251C).

314

Ion Exchange Membranes: Fundamentals and Applications

No.1

Vm (volts)

2

1

No.2

No.3 No.4 0

0

2

4

6 Time (h)

8

10

Figure 14.17 Anti-organic fouling of a macroreticular anion exchange membrane (Kusumoto et al., 1976).

Hodgdon and Sudbury (1971) applied for a patent of ‘‘Ion exchange membranes having a macroporous surface area’’, in which the membranes were fabricated with a polymeric macroporous surface lessening the tendency to foul when employed in the electrodialysis of solutions containing fouling constituent.

14.3.2.2 Formation of Thin Cation Exchange Layer on the Anion Exchange Membrane Another anti-organic fouling membrane was developed by sulfonating the surface of an anion exchange membrane and forming thin cation exchange layer on the anion exchange membrane (Kusumoto and Mizutani, 1975). The synthetic process starts from sulfuric acid treatment of styrene-divinylbenzene base membrane and the modiﬁed membrane is obtained via chloromethylation and amination (Fig. 14.18). Table 14.6 shows the electric resistance RA and transport number ¯t to be not inﬂuenced by sulfuric acid treatment time t. Fig. 14.19 gives the inﬂuence of t to the potential difference Vm in the electrodialysis experiment caused by the organic fouling due to dodecyl-sulfonic acid showing that the antiorganic fouling performance of membrane no. 4 (t ¼ 3.0 h) and no. 5 (t ¼ 5.0 h)

315

Membrane Deterioration

Styrene.divynylbenzene base membrane

Sulfuric acid treatment

Washing and drying Washing by 80 % H2SO4, 40 % H2SO4, H2O

Chloromethylation CH2OCH2Cl 1 part, CCl4 2 parts, SnCl4 25 °C, 4h

Amination 15 % trimethyl amine room temperature, 6 h

Modified anion exchange membrane

Figure 14.18 Synthetic process of a modiﬁed anion exchange membrane (Kusumoto and Mizutani, 1975).

Table 14.6

Sulfuric acid treatment and membrane characteristics

No.

ta (h)

A Sb (meq per Gram Dry Membrane)

RAc (O cm2)

1 2 3 4 5

0 0.5 1.25 3.0 5.0

– Not detected Trace 0.01 0.08

2.2 2.3 2.3 2.3 2.4

Source: Kusumoto and Mizutani, 1975. a Treating time in 98% sulfuric acid. b Sulfonic acid concentration. c Electric resistance: 0.5 N NaCl, 251C. d Transport number: 0.5 N NaCl/2.5 N NaCl, 251C.

¯td 0.91 0.91 0.91 0.91 0.91

316

Ion Exchange Membranes: Fundamentals and Applications

10

Vm (volts)

No.1 No.2

No.3

1

No.4,5 0.1

0

1

2

6

Time (h)

Figure 14.19 Anti-organic fouling of a modiﬁed anion exchange membrane (Kusumoto and Mizutani, 1975).

is excellent. The anti-organic fouling mechanism of this membrane is similar to the divalent ion permeability decreasing mechanism across the ion exchange membrane discussed in Sections 3.6 and 3.7.

REFERENCES Grossman, G., Sonin, A. A., 1973, Membrane fouling in electrodialysis: A model and experiments, Desalination, 12, 107–125. Hanzawa, N., Yuyama, T., Suzuki, K., Nakayama, M., 1966, Studies on durability of ion exchange membrane (IV): Long term electrodialytic concentration test, Scientiﬁc Papers of the Odawara Salt Experiment Station, Japan Monopoly Corporation, Odawara, Japan, No. 11, pp. 1–13. Hodgdon, R. B., Sudbury, Jr., 1971, Ion exchange membranes having a macroporous surface area, UA Patent, 3,749,655. Kneifel, K., Hattenbach, K., 1980, Properties and long-term behavior of ion exchange membranes, Desalination, 34, 77–95. Korngold, E., Korosy, F. D. E., Rahav, R., Taboch, M. F., 1970, Fouling of anionselective membranes in electrodialysis, Desalination, 8, 195–220. Kusumoto, K., Mizutani, Y., 1975, New anion-exchange membrane resistant to organic fouling, Desalination, 17, 121–130.

Membrane Deterioration

317

Kusumoto, K., Ihara, H., Mizutani, Y., 1976, Preparation of macroreticular anion exchange membrane and its behavior relating to organic fouling, J. Appl. Polym. Sci., 20, 3207–3213. Ohwada, K., Shimizu, U., Taga, N., 1981, Microorganism and organic matter deposited on the ion exchange membrane, Bull. Sea Water Sci. Jpn., 34(6), 367–372. Ueno, K., Ozawa, T., Ooki, H., Ishida, T., Nakajima, K., Sudo, T., 1980, Washing method of ion-exchange membranes, JP Patent, S55-33662. Urabe, S., Doi, K., 1987, Washing method of ion-exchange membranes, JP Patent, S62-52624. Yamashita, I., 1976, Removing method of fouling substances in an electrodialyzer, JP Patent, S51-131477.

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Applications

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Chapter 1

Electrodialysis 1.1.

OVERVIEW OF TECHNOLOGY

Industrial application of ion exchange membranes started at ﬁrst in the ﬁeld of electrodialysis (ED) (cf. Preface) and it induced the development of the fundamental theory. This fact is easily understandable from those phenomena explained in Fundamentals, which are described by taking the ED into account. The development of the fundamental theory led to further development of the ED technology. After that ion exchange membrane technology developed in the succeeding technology such as electrodialysis reversal (EDR), bipolar membrane electrodialysis (BP), electrodeionization (EDI), electrolysis (EL), fuel cell (FC) etc. describing in the succeeding chapters. Looking over these historical details, we notice that the ED becomes the fundamental technology and it is applied to the succeeding technologies based on the ion exchange membranes. In this chapter, we discuss the main subjects such as the structure of electrodialyzer, ED process, practical application of ED etc.

1.2.

ELECTRODIALYZER

1.2.1

Structure of an Electrodialyzer The basic structure of the vertical sheet-ﬂow type module consists of stacks in which cation exchange membranes, anion exchange membranes, gaskets (desalting cells and concentrating cells) are arranged alternately (Fig. 1.1). Fastening frames are put on both outsides of the stack which is fastened up together through cross bars setting in the frames. The deformation of the membranes is prevented by regulating hydrostatic pressure in the fastening frames. Inlet manifold slots and outlet manifold slots are prepared at the bottoms and heads of the gaskets, respectively. Spacers are incorporated with the gaskets to prevent the contact of cation exchange membranes with anion exchange membranes. Many stacks are arranged through the fastening frames. Electrode cells are put on both ends of the electrodialyzer, which are fastened by a press putting on the outsides of electrode cells (Fig. 1.2). An electrolyte solution to be desalinated is supplied from solution feeding frames to entrance manifolds, ﬂows through entrance slots, current passing portions and exit slots, and discharged from exit manifolds to the outside of the stack (Figs. 1.1 and 1.2). A concentrated solution is usually supplied to concentrating cells in a circulating ﬂow system, and discharged to the outside of the stack through an overﬂow extracting system. DOI: 10.1016/S0927-5193(07)12015-5

322

Ion Exchange Membranes: Fundamentals and Applications

k

e

l

g

k

e

h

l

−

+

l

j

f d

a

i

j

b

c

f

Figure 1.1 Structure of a stack (ﬁlter-press type). a, Desalting cell; b, concentrating cell; c, manifold; d, slot; e, fastening frame; f, feeding frame; g, cation exchange membrane; h, anion exchange membrane; I, spacer; j, feeding solution; k, desalted solution; l, concentrated solution (Azechi, 1980).

Fastening frame Anode chamber

Feeding frame

Feeding frame

Press (fix)

Press (move)

Stack

Figure 1.2

Cathode chamber

Stack

Filter-press type electrodialyzer (Azechi, 1980).

Electrodialysis

323

Effective membrane area is in the range from less than 0.5 m2 to about maximum 2 m2. In order to reduce energy consumption, it is desirable to decrease the electric resistance of the membrane and gasket thickness. Gasket material is selected from synthesized rubber, polyethylene, polypropylene, polyvinyl chloride and ethylene–vinyl acetate copolymer etc. The spacer is usually incorporated with the gasket and a solution ﬂows dispersing along the spacer net. 1.2.2

Parts of an Electrodialyzer The electrodialyzer is composed of the parts as follows (Urabe and Doi, 1978). 1.2.2.1 Fastening Frame Maximum 2000 pairs of membranes are arranged between electrodes in an electrodialyzer, so as to let disassembling and assembling works be easy. The membrane array is divided further into several stacks consisting of 50–400 pairs. Fastening frames are ﬁxed by bolts on both ends of the stack. The fastening frame is usually served as a solution feeding frame, so that a desalting and a concentrating solution are supplied to each gasket cell from the feeding frame incorporated in every stack. Material of the fastening frame is selected from polyvinyl chloride, polypropylene and rubber-lining iron etc. 1.2.2.2 Solution Feeding Frame A solution feeding frame is integrated for feeding solutions to each desalting and concentrating cell. Manifold holes are prepared at corresponding positions of the holes ﬁtted in the gasket. Solutions are usually supplied through the manifolds to each stack, but as the case may be supplied to each plural stack. 1.2.2.3 Gasket The shape of the gasket is presented in Fig. 1.3. A solution is supplied from the inlet manifold put at the bottom, ﬂows through the slot and is fed into the current passing portion. Then the solution is discharged through the outlet slot to the manifold ﬁtted to the head. The gasket has the following functions: (1) prevents solution leakage from the inside to the outside of the electrodialyzer, (2) adjusts the distance between a cation exchange membrane and an anion exchange membrane, (3) prevents solution leakage between a desalting cell and a concentrating cell occurring at slot sections. In order to prevent the solution leakage, it is desirable to adopt a soft material for the gasket. On the other hand, it is desirable to adopt a hard and stable material to avoid dimension changes during long-term operation. The material of the gasket is selected from rubber, ethylene–vinyl acetate copolymer, polyvinyl chloride, polyethylene etc. The thickness of the gasket is in the range of 0.5–2.0 mm.

324

Ion Exchange Membranes: Fundamentals and Applications

Manifold

Gasket Spacer

Slot Manifold

Figure 1.3

Gasket (Urabe and Doi, 1978). Deformation of a membrane

Membrane Gasket

Slot

Figure 1.4

Deformation of an ion exchange membrane (Urabe and Doi, 1978).

(a)

Figure 1.5

(b)

(c)

Structure of slots (Urabe and Doi, 1978).

1.2.2.4 Slot It is important to reduce the inside solution leakage (cf. Section 12.2 in Fundamentals), which arises through pinholes and cracks in the membranes or through gaps due to the membrane deformation at the slot as shown in Fig. 1.4. In order to prevent these troubles, a lot of devices are proposed as exempliﬁed in Fig. 1.5 in which (a) decrease the width of the slot, (b) bend the slot, (c) insert the support in the slot.

325

Electrodialysis

(a) Expanded PVC

(c) Diagonal net

Figure 1.6

(b) Wave porous plate

(d) Mikoshiro texture

(e) Honeycomb net

Structure of spacers (Urabe and Doi, 1978).

1.2.2.5 Spacer The function of a spacer is to keep the distance between the membranes. In addition, the spacer increases the limiting current density due to solution disturbance (cf. Sections 10.2 and 10.3 in Fundamentals). The spacer is selected taking account of the requirement such as; (1) low friction head loss, (2) low electric current screening effect, (3) easy air discharge, (4) less blocking of ﬂowpass caused by the precipitation of ﬁne particles suspended in a feeding solution. The structures of a spacer are classiﬁed in Fig. 1.6 as (a) expanded polyvinyl chloride, (b) wave porous plate, (c) diagonal net, (d) mikosiro texture and (e) honeycomb net.

1.2.2.6 Electrode and Electrode Chamber Platinum plated titanium, graphite or magnetite is used for anode material and stainless or iron is used for cathode material. The shape of electrodes is classiﬁed into net, bar and ﬂat. A partition is inserted between an electrode chamber and a stack for preventing the mixing of solutions. In an anode chamber, oxidizing substances such as chlorine gas evolve. An ion exchange membrane is easily deteriorated by contact with the oxidizing substances, so it is necessary to use two sheets of partitions and put a buffer chamber between the two partitions. Material of the partition is an ion exchange membrane, an asbestos sheet or a battery partition.

326

Ion Exchange Membranes: Fundamentals and Applications

An acid solution is added into a cathode solution and the electrodialyzer is operated under controlling pH of the cathode solution for preventing the precipitation of magnesium hydroxides in the cathode chamber. A feeding solution or a concentrated solution is supplied into the electrode chamber. The concentration of oxidizing substances in the anode solution is reduced by adding sodium sulﬁte or sodium thiosulfate into the solution being discharged. Sometimes, a sodium sulfate solution is supplied to an anode and a cathode chamber, achieving the neutralization by mixing the efﬂuent of both chambers. 1.2.2.7 Press An oil pressure press is usually used adjusting the pressure to be 5–10 kg cm2. 1.2.3

Requirements for Improving the Performance of an Electrodialyzer In order to improve the performance of an electrodialyzer, membrane characteristics should be naturally improved. At the same time, the circumstances in an electrodialyzer in which the membranes work should be better. Here, we describe the deﬁnite problems lowering the circumstances in an electrodialyzer and requirements for improving the circumstances and performance of an electrodialyzer (Urabe et al., 1978). 1.2.3.1 Solution Velocity Distribution between Desalting Cells In an electrodialyzer, ion exchange membranes and desalting and concentrating cells are arranged alternately and a solution is supplied into desalting cells. In this ﬂow system, the solution velocity distribution in desalting cells does not become uniform. This phenomenon causes the concentration distribution and current density distribution in the electrodialyzer, and gives rise to the decrease of the limiting current density of the electrodialyzer (cf. Sections 9.1, 11.6 and 11.7 in Fundamentals). In order to operate the elctrodialyzer stably, it becomes necessary to make the solution velocities between the desalting cells uniform. 1.2.3.2 Solution Leakage in an Electrodialyzer The dimensions of all parts of an electrodialyzer are not always consistent with the values in the speciﬁcations. Small pinholes can open in an electrodialyzer because the strength of ion exchange membranes is relatively low. Gaps may occur between the materials composing the electrodialyzer in the assembly works of an electrodialyzer. If a pressure difference between the desalting cells and concentrating cells exists in these circumstances, solutions leak through the membranes and lower the performance of the electrodialyzer (cf. Section 12.2 in Fundamentals). In order to avoid these troubles, we have to remove the pinholes and gaps in the electrodialyzer and control the pressure difference between desalting cells and concentrating cells.

Electrodialysis

327

1.2.3.3 Distance between the Membranes Decrease of the distance between the membranes brings about the decrease of electrical resistance and energy consumption. On the other hand, it brings about the increase of friction loss of solution ﬂow, blocking of the materials suspended in a feeding solution and the increase of pumping motive power. Accordingly, it becomes necessary to realize the optimum distance between the membranes. The optimum distance is decided further taking account of electric resistance of ion exchange membranes and that of electrolyte solution in desalting and concentrating cells. 1.2.3.4 Spacer Main functions of a spacer in to create space between a cation exchange membrane and an anion exchange membrane. When solution velocity and the Reynolds number are decreased, hydrodynamic pattern exhibits laminar ﬂow, which means that disturbing effect of the spacer is low. In order to increase the limiting current density, turbulent ﬂow should be induced by increasing the Reynolds number (cf. Sections 10.3.4 and 10.5 in Fundamentals). 1.2.3.5 Electric Current Leakage A part of an electric current ﬂows through slots and manifolds causing ineffective current leakage. Current leakage is increased by the increases of the numbers of cell pairs integrated in a stack and the increase of sectional area of slots and manifolds (cf. Section 12.1 in Fundamentals). These events, however, related with the solution velocity distribution between the cells described in Section 1.2.3.1. 1.2.3.6 Simplicity of Structure of an Electrodialyzer Disassembling and assembling work is peculiar characteristics in operating an electrodialyzer (cf. Section 1.5.3 in Applications). Excellent durability of ion exchange membranes is owing to careful treatment in this work. So, the simplicity of the structure is a requirement for performing this work. 1.3.

ELECTRODIALYSIS PROCESS

The ED process had been explained in detail in several articles (Mintz, 1963; Shaffer and Mintz, 1966; Itoi et al., 1978; Yawataya, 1986; Tanaka, 1993). The following is overall description of the process. 1.3.1

One-Pass Flow Process An electrolyte solution is fed to an electrodialyzer and desalted solution is discharged to the outside of the process (Fig. 1.7). When the concentration of the feeding solution is invariable, the performance of the system becomes stable. Joining the process in Fig. 1.7 to the succeeding process, a one-pass ﬂow

328

Ion Exchange Membranes: Fundamentals and Applications

Concentrated discharge

Feeding solution

Concentrating cell Desalted solution Ion-exchange membrane

Desalting cell Feeding solution

Figure 1.7

Pump

One-pass ﬂow process (Tanaka, 1993).

C out b

a

l

C-dC C

x+dx x

C in 0

Figure 1.8

Electrolyte concentration change in a desalting cell (Tanaka, 1993).

multiple continuous system suitable for a large-scale plant is formed. The desalination in Fig. 1.7 is proceeded as below. In the desalting cell shown in Fig. 1.8, a, b and l are the ﬂow-pass depth (distance between membranes), the ﬂow-pass width and the ﬂow-pass length, respectively. Cin and Cout are the electrolyte concentration at the inlet and the outlet of the desalting cell. Passing an electric current across the membranes, ions in the desalting cell are transferred toward the concentrating cell. Assuming the transport of water to be negligible across the membranes under an electric current passing, the material balance between at x and x+dx in Fig. 1.8 is

Electrodialysis

329

indicated by the following equation, including current density i, linear velocity in a desalting cell u, current efﬁciency Z and electrolyte concentration at x distant from the inlet of a desalting cell C. 1 Z i dC ¼ dx (1.1) C FC Voltage applied to a membrane pair (cell voltage) consists of a membrane potential and Ohmic loss of a cation exchange membrane, an anion exchange membrane, a desalting cell and a concentrating cell. In the desalting process, Ohmic loss of a desalting cell iRde (Rde: electric resistance of desalting cell) is dominant in the cell voltage and voltage difference between electrodes is independent of x (cf. Section 9.1 in Fundamentals). Accordingly, iRde in the desalting cell is estimated to be invariable in the range of x ¼ 0l in Fig. 1.8. Further, Rde is inversely proportional to C, so that i/C is assumed to be nearly constant and we can integrate Eq. (1.1) as follows: Z C out Z 1 Z i l ua dx (1.2) dx ¼ C FC 0 C in au

Solving Eq. (1.2) C out lZ i ¼ exp C in aFu C Desalting ratio a is deﬁned as follows: C out lZ i a¼1 ¼ 1 exp C in aFu C

(1.3)

(1.4)

¯ instead of i/C (Yawataya, 1986) in Eq. Here, we can adopt the average value ¯i=C (1.4) as follows: ¯i i 2¯i ¼ ¼ ¯ C C C in þ C out

(1.5)

From Eqs. (1.4) and (1.5) i 2¯i ¼ C C in ð2 aÞ Substituting Eq. (1.6) into Eq. (1.4) 2Z¯i a ¼ 1 exp aF C in ðu=lÞð2 aÞ

(1.6)

(1.7)

a is calculated using Eq. (1.7), assuming a ¼ 0.1 cm, Cin ¼ 0.05 eq dm3, Z ¼ 0.90, and plotted against u/l taking ¯i as parameter (Fig. 1.9). l vs. u is computed setting a ¼ 0.90 (Fig. 1.10) indicating u is proportional to l. In a practical-scale sheet-ﬂow electrodialyzer, ﬂow-pass length l is from less than

330

Ion Exchange Membranes: Fundamentals and Applications

1.0 0.9

2.5

0.8

2.0

0.7

1.5

0.6 0.5

1.0

0.4 0.3

i =0.5

A / dm 2

0.2 0.1 0.0 0.00

Figure 1.9 ratio.

0.01

0.02

0.03 0.04 u/l(s-1)

0.05

0.06

Inﬂuence of linear velocity, ﬂow-pass length and current density to desalting

40 35

u (cm s-1)

30

2.

25

5 0

2.

20 1.5

15 1.0

10

2

A / dm

i =0.5 5 0 0

Figure 1.10

1

2

3

4

5 6 l (m)

7

8

9

10

Flow-pass length and linear velocity in a desalting cell.

331

Electrodialysis

1–2 m, and linear velocities in desalting cells u are 3–10 cm s1. In a tortoise-ﬂow type electrodialyzer, however, l and u are larger than those in the sheet-ﬂow type (cf. Section 2.2 in Application). 1.3.2

Batch Process In Fig. 1.11, the feeding solution is prepared in the circulation tank at ﬁrst. Next, open valve V1, close valve V2 and circulate the solution between the tank and the electrodialyzer. The solution is electrodialyzed applying constant voltage until electrolyte concentration of a desalted solution attains a deﬁnite value, and then the desalted solution is discharged. The process mentioned above is repeated periodically. This system is usually adopted in a small-scale plant and the desalination is proceeded as follows. A deﬁnite volume V of electrolyte solution is assumed to be circulated between the circulating tank and the electrodialyzer and it is electrodialyzed applying a constant voltage between the electrodes. An electric current I and electrolyte concentration C of the solution decrease with elapsed time t, but I/C does not change with t, because Ohmic loss IRdil is dominant in a cell voltage and roughly inversely proportional to C. Setting numbers of cell pairs integrated in the electrodialyzer M, the electrolyte concentration in a feeding solution CF and in a desalted product solution CP, and an operating time in an unit batch cycle t, and assuming the transport of water to be negligible across Concentrated discharge

Feeding solution

Feeding solution

V1 Desalted solution V2

Circulation tank

Figure 1.11

Batch process (Tanaka, 1993).

332

Ion Exchange Membranes: Fundamentals and Applications

the membranes under an electric current passing, the material balance in a desalting cell in this batch system (Fig. 1.11) is expressed by the following equation. Z Z CP dC MZ 1 t ¼ dt (1.8) V F C 0 CF C Integrating Eq. (1.8) CP MZ I t ¼ exp FV C CF

(1.9)

Expressing an electric current I as I ¼ bli and the solution volume V as V ¼ QPt, (Qp is product solution volume, water transport across the membranes is assumed to be neglected) in Eq. (1.9), the desalting ratio a in the batch system is introduced as follows: CF MblZ i ¼ 1 exp (1.10) a¼1 CP FQP C Accordingly, numbers of cell pairs M integrated in the electrodialyzer is M¼

FQP lnðC F =C P Þ blZði=CÞ

(1.11)

Here, we estimate M in the following case: QP ¼ 1 m3 h1 ¼ 106/3600 cm3 s1, CF/CP ¼ 10, a ¼ 1CP/CF ¼ 0.90, b ¼ 50 cm, l ¼ 50 cm, Z ¼ 0.90, ¯i ¼ 0:01 A cm2 ; CF ¼ 5 105 eq cm3, F ¼ 96,500 C eq1. From Eq. (1.6), i/C is calculated as: i 2¯i ¼ 364 ¼ C C in ð2 aÞ Substituting these values into Eq. (1.11), we obtain M ¼ 75 pairs. 1.3.3

Partially Circulation (Feed and Bleed) Process An electrodialyzer is operated at constant current density supplying a deﬁnite amount of solution and circulating a part of feeding solution (Fig. 1.12). Joining Fig. 1.12 to the succeeding process, a multiple partially circulation system (Fig. 1.13) suitable for a middle-scale plant is formed. The desalination in Fig. 1.13 is achieved as below. Assuming the linear velocity in desalting cells u, current efﬁciency Z and i/C to be constant in each electrodialyzer, Cout/Cin in each electrodialyzer is expressed using Eq. (1.3) as follows: ðC out Þ1 ðC out Þ2 ðC out Þn C out ¼ ¼ ¼ ¼ ¼b ðC in Þ1 ðC in Þ2 ðC in Þn C in

(1.12)

333

Electrodialysis

Concentrated discharge

Feeding solution

Desalted solution

Feeding solution

Figure 1.12

Partially circulation process (Tanaka, 1993).

QF=Q QR (Cin)1

Figure 1.13

QR-Q

QR-Q

QR-Q

(Cout)1

(Cout)2

(Cout)n

Q

1

QR

Q

2

QR (Cin)n

(Cin)2

QP=Q

n

CP=(Cout)n

QR

QR

QR

(Cout)1

(Cout)2

(Cout)n

Multiple partially circulation process (Tanaka, 1993).

From the material balance in Fig. 1.13 C F QF þ ðC out Þ1 ðQR QÞ ¼ ðC in Þ1 QR ðC out Þ1 Q þ ðC out Þ2 ðQR QÞ ¼ ðC in Þ2 QR .. .

(1.13)

ðC out Þn1 Q þ ðC out Þn ðQR QÞ ¼ ðC in Þn QR Substituting Eq. (1.12) to Eq. (1.13) C F QF ¼ ðC in Þ1 fQR bðQR QÞg ðC in Þ2 fQR bðQR QÞg ðC in Þ1 ¼ bQ .. . ðC in Þn ðC in Þn1 ¼ fQR bðQR QÞg bQ

(1.14)

334

Ion Exchange Membranes: Fundamentals and Applications

Putting Eq. (1.14) together C F QF ¼

ðC in Þn fQR bðQR QÞgn ðbQÞn1

(1.15)

Substituting QF ¼ QP ¼ Q, CP ¼ (Cout)n (water transport across the membranes is neglected) and Eq. (1.12) into Eq. (1.15), and rearranging the equation n CF QR C in ¼ 1 þ1 (1.16) CP QP C out Desalting ratio a of the process is introduced as follows from Eq. (1.16). n CP QR C in a¼1 ¼1 1 þ1 (1.17) CF QP C out In one-path ﬂow system, QR ¼ QP holds, so Eq. (1.17) becomes CF C in n ¼ CP C out

(1.18)

A large-scale plant is realized by assembling a multi-stage multiple partially circulation process arranging in each stage N units of electrodialyzer incorporated with M cell pairs as indicated in Fig. 1.14. The amount of solution QR circulating in each stage is QR ¼ abuMN

(1.19)

N

N

N

2

2

2

1

1

1

QR (Cin)1 QF=Q

QR (Cout)1 (Cin)2 Q

QR (Cout)2 (Cin)N

Q

Q

CF

CP=(Cout)N QR-Q

Figure 1.14

(Cout)N

QR-Q

QR-Q

Multi-stage multiple partially circulation process (Tanaka, 1993).

335

Electrodialysis

Table 1.1 process

Arrangement of electrodialyzers in a multi-stage multiple partially circulation

n

QR (cm3 s1)

1 2 3 4 5 6

514,530 123,617 65,999 44,494 33,438 26,744

N

nN

25.7 6.2 3.3 2.2 1.7 1.3

1 26 26 33 42 52 61

We estimate the numbers and arrangement of electrodialyzer in a multi-stage multiple partially circulation process (Fig. 1.14) putting the following parameters: a ¼ 0.1 cm, b ¼ 100 cm, l ¼ 100 cm, u ¼ 5 cm s1, i/C ¼ 364 A cm eq 1, CF/CP ¼ 10, QP ¼ 200 m3 h1 ¼ 200 106/3600 cm3 s1, Z ¼ 0.9, M ¼ 400 pairs, F ¼ 96,500 Ceq1. At ﬁrst, Cin/Cout is computed as follows: C in lZ i 100 0:90 364 ¼ exp ¼ 1:9718 ¼ exp C out aFu C 0:10 96500 5 Using Eq. (1.16), CF/CP is n n CF QR C in QR ð1:9718 1Þ þ 1 ¼ 1 þ1 ¼ CP QP C out 200 106 =3600 ¼ 10 Accordingly, QR is expressed as follows: QR ¼ ð101=n 1Þ

200 106 =3600 cm3 s1 0:9718

(1)

From Eq. (1.19), numbers of cell pairs per unit stage are MN ¼ 400N ¼

QR QR ¼ abu 0:1 100 5

So, we have N as follows: N¼

QR 20000

(2)

Changing the values of n, QR, N and nM are computed as indicated in Table 1.1 using Eqs. (1) and (2).

336

Ion Exchange Membranes: Fundamentals and Applications

C′′ q ′′

Desalted solution

Concentrated

q 0 C′out q′

C ′in q ′ Feeding solution

Figure 1.15

C0 q0

Concentration or separation process.

1.3.4

Concentration Process Fig. 1.15 gives a single-stage concentration unit process. The output of a multi-stage multiple process X is expressed by the following equation. i blZMnN (1.20) X¼ F

Here, we calculate numbers of electrodialyzers in the process for concentrating seawater by ED and crystallizing NaCl by evaporation. Putting as NaCl output in the evaporation process: 200,000 t y1, operating time of electrodialyzers: 8000 h y1, NaCl yield rate in the evaporation process: 0.97 and NaCl molecular weight: 58.5, we obtain: X¼

200000 ¼ 122:38 eq=s 8000 3600 0:97 58:5

Substituting X ¼ 122.38 eq s1, i ¼ 0.03 A cm2, b ¼ 100 cm, l ¼ 100 cm, e ¼ 0.92, Z ¼ 0.90, M ¼ 2000 pairs and F ¼ 96,500 C eq1 into Eq. (1.20), nN ¼ 23.8 is obtained. Accordingly, the numbers of the electrodialyzers in this multi-stage multiple processes are known to be 24. Electrolyte concentration in a concentrated solution C 00 is expressed by the following equation introduced from the overall mass transport equation (cf. Section 6.1 in Fundamentals). qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 A2 þ 4rB A C 00 ¼ 2r (1.21) A ¼ fi þ m rC 0 B ¼ li þ mC 0

337

Electrodialysis

6

5

C" (eq dm-3)

4 C' (eq dm-3) 1 3 5 7 9

3

2

1

0

0

1

2

3

4

5

6

7

8

9

10

i (A dm-2)

Figure 1.16

Dependence of C00 on i and C0 .

The overall transport number l, the overall solute permeability m and the overall electro-osmotic permeability f are expressed by the following empirical equations of the overall hydraulic conductivity r (cf. Section 6.1 in Fundamentals). l ¼ l1 þ l2r m ¼ mr

l 1 ¼ 9:208 106

l 2 ¼ 1:914 103

(1)

m ¼ 2:005 104

f ¼ n1 r0:2 þ n2 r

n1 ¼ 3:768 103

(2) n2 ¼ 1:019 102 2

4

(3) 1

1

Here, we calculate l, m and f by substituting r ¼ 1 10 cm eq s into m ¼ 2.005 106 cm s1, Eqs. (1)–(3) as; l ¼ 9.399 106 eq C1, 3 3 1 00 f ¼ 1.398 10 cm C . Dependence of C on i for this membrane pairs is computed as shown in Fig. 1.16 by substituting current density i, electrolyte concentration in a feeding solution C0 , l, m, f and r into Eq. (1.21). 1.3.5

Separation Process An ion exchange membrane shows the permselectivity between ions having the same charged sign, which is deﬁned by the permselectivity coefﬁcient Eq. (1.22) for ion A against ion B, T BA (cf. Section 3.2 in Fundamentals). T BA ¼

ðC 00B =C 00A Þ ðC 0B =C 0A Þ

(1.22)

338

Ion Exchange Membranes: Fundamentals and Applications

C 00i ; is concentration (eq dm3) of ion i in a concentrating cell and it is assumed to be invariable in the cell. Concentration of ion i in a desalting cell C 0i is the average of the values at the inlet and the outlet as follow: 1 C 0i ¼ ðC 0i;in þ C 0i;out Þ 2

(1.23)

C 0i;in and C 0i;out are concentrations of ion i at the inlet and outlet of a desalting cell. Ion A is separated from ion B by applying the permselectability of the membrane in the separation process indicated in Fig. 1.15. Here, we deﬁne the separation factor of ion B against ion A, in a desalted 0 00 solution S AB and in a concentrated solution S AB by the following equations. 0

S AB ¼

00

S AB ¼

ðC 0B;out =C 0A;out Þ ðC 0B =C 0A Þ ðC 00B =C 00A Þ ðC 0B =C 0A Þ

(1.24)

(1.25)

C 0A ; C 0B : Concentration of ion A and ion B in a feeding solution. Desalting ratio of ion i (ai) in Fig. 1.15 is deﬁned as: C i;out ¼ ð1 ai ÞC 0i

(1.26)

The material balance of ion i in Fig. 1.15 is shown by the following equations assuming q0 q00 hold. C 0i q0 ¼ C 0i;out q0 þ C 00i q00

(1.27)

C 0i;in q0 ¼ C 0i;out q0 þ C 00i q00

(1.28)

q0 is the amount of feeding solution to the process, q0 the amount of a desalting solution being supplied to the electrodialyzer and q00 the amount of a concentrating solution ﬂowing out from the electrodialyzer. Following equations are introduced from Eqs. (1.22)–(1.28): 00

S AB ¼

00

1 aB ð1 ðq0 =2q0 ÞÞ 1 aA ð1 ðq0 =2q0 ÞÞ 0

S AB ¼ SAB T BA ¼

1 aB ð1 ðq0 =2q0 ÞÞ B T 1 aA ð1 ðq0 =2q0 ÞÞ A

(1.29)

(1.30)

When q0 q0 hold, Eqs. (1.29) and (1.30) become 0

S AB ¼

1 1 aA ð1 T BA Þ

(1.31)

339

Electrodialysis

00

0

S AB ¼ SAB T BA ¼

T BA 1 aA ð1 T BA Þ

(1.32)

In Eqs. (1.31) and (1.32), the following phenomena are found: when T BA 41 when T BA ¼ 1 T BA o1

when

0

00

SAB o1

S AB oT BA

0

00

SAB ¼ 1 0

S AB ¼ T BA

(1.33)

00

S AB 41

S AB 4T BA

Equation (1.33) means that the separatability is inferior to the permselectability. Further, we ﬁnd the following events in Eqs. (1.31) and (1.32): 0

lim S AB ¼ 1

aA !0

00

lim S AB ¼ T BA

aA !0 0

0

lim SAB ¼

aA !1

1 T BA

(1.34)

00

lim SAB ¼ 1

(1.35)

aA !1

00

aA vs. SAB and SAB is computed using Eqs. (1.31) and (1.32) and shown in Fig. 1.17, in which the relationships in Eqs. (1.33)–(1.35) are conﬁrmed. 102

101 10

B

TA

S ′AB S′′AB

4

.01 =0

0.4

1

10

0.4 4 10

10-1

0. 01 10-2 0.0

0.2

0.4

A

0.6

0.8

1.0

Figure 1.17 Relationship between permselectivity coefﬁcient, desalting ratio and sep0 00 aration factor. Open, SAB ; ﬁlled, S AB :

340

1.4.

Ion Exchange Membranes: Fundamentals and Applications

ENERGY CONSUMPTION AND OPTIMUM CURRENT DENSITY

In multi-stage multiple partially circulation system (Fig. 1.14), rectiﬁers are assumed to be put in each stage, in which an electric current I is supplied to electrodialyzers through a parallel circuit. I is expressed as follows: I (1.36) ZMN ¼ QRfðC in Þn ðC out Þn g F Voltage V applied to an electrodialyzer is indicated by the following equation putting the voltage in the electrode cell as VP. V ¼ MV cell þ V P

(1.37)

Vcell is cell voltage as follows (cf. Section 13.2 in Fundamentals): V cell ¼ IðRK þ RA þ Rdil þ Rconc Þ þ E M

(1.38)

RK and RA are electric resistance of a cation and an anion exchange membrane. Rdil and Rconc are electric resistance of a desalting and a concentrating cell. RM is membrane potential. A reasonable estimate of the optimum current density is introduced by assuming that the major costs are divided into three categories: those directly proportional to current density, those inversely proportional to current density, and those independent of current density (Eq. (1.39)). b (1.39) Z ¼ ai þ þ c i where Z is total cost, and a, b, c are the relative proportionality constants. The optimum current density iopt is deﬁned by the minimum of Eq. (1.39), so it is introduced by differentiating Eq. (8.37); dZ/di ¼ 0 and expressed as (Leitz, 1986): 1=2 P (1.40) iopt ¼ QR P is depreciation cost ($/m2s), Q the energy cost ($/Ws) and R the cell pair electric resistance (O m2). 1.5. 1.5.1

SURROUNDING TECHNOLOGY

Filtration of a Feeding Solution Fine materials such as sand, clay, iron components, humus soil and miscellaneous inorganic and organic colloid are usually suspended in a raw feeding solution. In order to avoid invasion of these materials into an electrodialyzer, a feeding solution is ﬁltrated using sand, ﬁbers or cohesive agent and turbidity of the solution is decreased less than 0.1–0.2 ppm. First of all, the following valveless sand ﬁlter is broadly applicable (Tsunoda, 1994). In Fig. 1.18, a raw feeding

341

Electrodialysis

H3 10 9

H2

6

5

8

H1 7 11

2

1

3 4

Figure 1.18 Valve-less ﬁlter. 1, Feeding solution inlet; 2, ﬁltrating chamber; 3, sand ﬁlter; 4, collecting chamber; 5, ﬁltrate ﬂow out pipe; 6, ﬁltrate outlet; 7, connecting duct; 8, washing chamber; 9, siphon pipe; 10, siphon breaker; 11, control valve (Tsunoda, 1994).

solution is supplied into the ﬁltrating chamber, ﬁltrated through the sand ﬁlter and collected in the collecting chamber. The ﬁltrate ﬂows out through the ﬂowout pipe and supplied to an electrodialyzer at solution level H2. At the same time, a part of ﬁltrate ﬂows through the connecting pipe into the washing chamber put on the ﬁltrating chamber and is accumulated there at H2. Proceeding with the operation, solution level in the siphon pipe goes up with the increase of ﬂow resistance in the sand ﬁlter. When the level surpasses H3, the solutions in the ﬁltrating chamber, the collecting chamber and the washing tank are discharged to the outside of the process at one stroke through the siphon pipe due to the siphon function. In this instance, sand is washed and the level in the washing tank goes down to H1.

1.5.2 Scale Trouble Prevention 1.5.2.1 Acid Dosage Total carbonic acid dissolved in brine is equilibrated to CO2 gas (3 104 atm.) in air. Total carbonic acid concentration in seawater is 2–5 102 mol dm3 at pH ¼ 7.0 –7.4. 15–30% of this total value is carbonic acid molecules (CO2 and H2CO3), and the remainders are ionic carbonic acid 2 consisting of HCO 3 (more than 95%) and CO3 (less than 5%). In a concen trating cell in an electrodialyzer HCO3 ions decompose as follows and combine

342

Ion Exchange Membranes: Fundamentals and Applications

with Ca2+ ions to form CaCO3 precipitation. 2 2HCO 3 3CO3 þ H2 O þ CO2 "

(1)

2þ ! CaCO3 (2) CO2 3 þ Ca In order to avoid CaCO3 precipitation, HCO3 ions are decomposed into CO2 gas by dosing with an HCl or a H2SO4 solution into concentrating cells. þ HCO (3) 3 þ H ! CO2 " þH2 O

1.5.2.2 Precipitation Controlling Agent Dosage Small amount of precipitation controlling agents such as condensed sodium phosphate Na2[Na4(PO3)6] are dosed into a concentrating cell, resulting with the absorption of crystalline nuclei to the agents and dissolution of CaSO4 or CaCO3 due to the following chelate reaction. Na2 ½Na4 ðPO3 Þ6 þ CaX ! Na2 ½Na2 CaðPO3 Þ6 þ Na2 X CaX : CaSO4 or CaCO3

(4)

Carboxyl methyl cellulose (CMC) or poly-acrylic acid is also available instead of condensed sodium phosphate. 1.5.3

Disassembling and Assembling Works In spite of the ﬁltration described in Section 1.5.1, a very small quantity of ﬁne particles passes through a ﬁlter and invades into an electrodialyzer. Sometimes, ﬁne organisms pass through the ﬁlter and breed in an electrodialyzer. The ﬁne particles are adhered on the surface of membranes and spacers in desalting cells (cf. Section 14.2.2 in Fundamentals), causing the increase of ﬂow resistance of a solution in the desalting cell with acceleration of concentration polarization on the membrane surface (cf. Section 14.2.1 in Fundamentals). In order to avoid these troubles, an electrodialyzer is usually disassembled and washed periodically. The disassembling and washing process is generally as follows (Tanaka, 1987): (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

Electric current interruption Solution feeding interruption Solution discharge Stack extraction Stack disassembling Membrane surface washing Desalting cell, concentrating cell and spacer washing Stack assembling Leak test Integrating stack into an electrodialyzer Solution feeding Electric current passing.

343

Electrodialysis

1.6.

PRACTICE

1.6.1

Potable Water Production from Brackish Water Residents in an isolated island suffer from serious water shortage because of their high dependence on rainwater. In order to solve this problem, Asahi Chemical Co. constructed the ED plant (2500 m3/day) illustrated in Fig. 1.19 in 1990 in Ohshima island, Tokyo (Fukuhara et al., 1993). Ohshima Town supplies potable water to the residents even now. The speciﬁcations of this plant are shown in Table 1.2. Raw brackish water pumped up from wells is fed to the suspended solid ﬁlter (SSF), and then it is supplied to the ﬁrst stage electrodialyzer unit (EDUA1 and EDU-B1) through the ﬁrst stage desalination tank (DST-1). A part of the ﬁltrated solution is supplied to the concentrated solution tank (CST). The desalted solution in DST-1 is further desalted at the second stage electrodialyzer unit (EDU-A2 and EDU-B2) to be about 400 ppm, and then supplied to the water cleaning tank (WCT).

ACS-A FS-A CS-A ACS-B FS-B CS-B

DS-A 1

+ EDU-A 1 − + EDU-A 2 −

P

P

P

P

P

P

DS-B 1 CCS-A DS-A 2 DS-B 2 CCS-B

+ EDU-B 1 − + EDU-B 2 −

P

P

P

P

P

P Wells

ST

SSF

CST

AT

EST

DST-1

DST-2 PWT

WCT

DR

Figure 1.19 Saline water desalting process (Ohshima island). ACS, Anode compartment solution; AT, acid tank; CCS, cathode compartment solution; CS, concentrated solution; CST, concentrated solution tank; DR, distributing reservoir; DS, desalinated solution; DST, desalination tank; EDU, electrodialyzer unit; EST, electrode solution tank; FS, frame solution; PWT, product water tank; SSF, suspended solid ﬁlter; ST, stock tank; WCT, water cleaning tank (Fukuhara et al., 1993).

344 Table 1.2

Ion Exchange Membranes: Fundamentals and Applications

Speciﬁcations of the electrodialysis plant

Site

Ohshima, Tokyo

Capacity, product water

2500 m3/day, from 1200 ppm TDS raw water 1000 m3/day, from 3000 ppm TDS raw water 4 brackish wells TDS: 450 ppm or less Chloride ions: 150 ppm or less Asahi Chemical SS-0 1780 m3 (318 pairs/stack, 4 stack) Dilution compartment: 0.5 mm Concentration compartment: 0.5 mm Dual-train, two steps per line automatic, continuous

Raw water source Product water Electrodialyzers Conductive area Thickness Mode of operation Source: Fukuhara et al. (1993).

Table 1.3

Operational results

Production rate Product water Electric consumption

2610 m3/day, from 1200 ppm TDS raw water TDS: 440 ppm Chloride ions: 145 ppm pH: 6.8 0.8 kWh m3

Source: Fukuhara et al. (1993).

Organic fouling due to organic acid including in raw brackish water is avoided by integrating anti-fouling anion exchange membranes Aciplex A-201 into the electrodialyzer instead of standard type Aciplex A-101 membranes (cf. Section 14.3.2 in Fundamentals). Operational results are shown in Table 1.3. Analysis of raw and product water are shown in Table 1.4. The values listed in both tables meet the potable water standard established by the Ministry of Welfare, Japan. Actual operating cost is determined based on the plant operation in a year as indicated in Table 1.5. 1.6.2 Electrodialysis Desalination System Powered by Photo-Voltaic Power Generation Babcock-Hitachi K.K. and Hitachi Ltd. established ED system combined with sunlight photo-voltaic power generation in Oshima island and at Sakiyama, Nagasaki (Inoue and Kuroda, 1993). In this system, the electrodialyzer was operated using direct current power generator using solar batteries and produced potable water. Fig. 1.20 gives the system in Oshima island, showing a two-stage seawater desalting process for producing 103/day of potable water. In the ﬁrst stage, if it is ﬁne, seawater (35,000 mg l1-TDS) is desalted during the daytime to obtain an

345

Electrodialysis

Table 1.4

Analysis of raw and product water Raw Watera

Product Water

Visual Inspection

Colorless, Transparent

Colorless, Transparent

Turbidity (1) Color (1) pH Electrical conductivity (mS cm1) Total hardness (CaCO3, ppm) Calcium hardness (CaCO3, ppm) Evaporation residue (ppm) Silica (SiO2, ppm) Chloride ion (Cl, ppm) Sulfuric ion (SO4, ppm) Hydrocarbonate ion (HCO3, ppm) Calcium ion (Ca, ppm) Potassium ion (K, ppm) Magnesium ion (Mg, ppm) Sodium ion (Na, ppm)

o1.0 o1.0 7.2 2500 685 406 1631 43 632 262 210 51 17 48 368

o1.0 o1.0 7.3 650 83 33 418 42 131 40 82 14 3 12 94

Source: Fukuhara et al. (1993). a From single well.

Table 1.5

Operating cost Units

Volume of product water Raw water TDS Water recovery Electric consumption Stering agents Membrane replacement Total

m3/day mg l1 % yen m3 yen m3 yen m3 yen m3

Projected

Actual

1950 1600 80.0 27.82 0.38 11.80 40.00

1853 1250 86.5 10.04 3.73 13.77

Source: Fukuhara et al. (1993).

intermediately desalted solution (5000 mg l1-TDS) and at the same time, electric power surpluses are stored in batteries (STB). In the second stage, the intermediately desalted solution is further desalted to obtain potable water (400 mg l1-TDS) in the rainy or cloudy daytime or in the nighttime using the stored electric power. Fig. 1.21 shows the system in Sakiyama for producing 200 m3/day of potable water from brackish water. In this system, electric consumption for pumping up raw brackish water is larger. So, in the ﬁne daytime, raw brackish water (1500 mg l1-TDS) is pumped up and is desalted to obtain potable water (400 mg l1-TDS). At the same time, brackish water and electricity are stored in

346

Ion Exchange Membranes: Fundamentals and Applications

SOB t

CBO

STB

DAT FIL −

DST

+

IST

FST SWP Sea

DSP

ED

CSPCST

PWT Brine

Product water

Sea

Figure 1.20 Seawater desalination process powered by solar generation (Oshima island). CBO, Control board; CSP, concentrated solution pump; CST, concentrated solution tank; DAT, direct/altering current transducer; DSP, desalted solution pump; DST, desalted solution tank; ED, electrodialyzer; FIL, ﬁlter; FST, ﬁltrated solution tank; IST, intermediately concentrated solution tank; PWT, product water tank; SOB, solar battery; STB, storage battery; SWP, seawater pump (Inoue and Kuroda, 1993).

the ﬁne daytime for operating the electrodialyzer in the rainy or cloudy daytime and in the nighttime. The speciﬁcations of both systems are shown in Table 1.6. An electric power consumption pattern of the Oshima plant is illustrated in Fig. 1.22. In a batch desalting system, electric power consumption is large at beginning and it decreases with elapsed time. So, when a large amount of electric power is generated in the ﬁne daytime, seawater is electrodialyzed to obtain intermediately desalted solution, which is temporarily stored in a tank (highconcentration operation). At the same time, electric power surpluses are stored in STB. In the cloudy or rainy daytime and in the nighttime, the stored solution is further desalted to obtain potable water (low-concentration operation) passing the stored electric power. Fig. 1.23 shows an electric power consumption pattern of the Sakiyama plant, which is automatically controlled with a sunlight photo-voltaic power generation system, a storage battery system and an ED system. An electric power generated in the solar system is directly consumed in the electrodialyzer, and the electric power surpluses charge the battery. Operating performance of both plants are indicated in Table 1.7.

347

Electrodialysis

SOB t CBO

STB

Alternating current ACL

DAT

FST to CST

DCL

Direct current

ECM

FIL

from FST −

PWT

+

DST CST

ED WEL SWP Saline water

DSP

Product water

CSP Sea

Figure 1.21 Saline water desalination process powered by solar generation (Sakiyama). ACL, Altering current load; CBO, control board; CSP, concentrated solution pump; CST, concentrated solution tank; DAT, direct/altering current transducer; DCL, direct current load; DSP, desalted solution pump; DST, desalted solution tank; ECM, electroconductivity meter; ED, electrodialyzer; FIL, ﬁlter; FST, ﬁltrated solution tank; PWT, product water tank; SOB, solar battery; STB, storage battery; SWP, seawater pump; WEL, well (Inoue and Kuroda, 1993).

1.6.3 Electrodialytic Recovery of Wastewater from a Metal Surface Treatment Process Electrodialysis is applicable to recovering wastewater and nickel in a metal surface treatment process. The process was developed by Asahi Glass Co. as follows (Itoi et al., 1986). A nickel plating process includes several rinsing processes. In this process, Ni concentration in the efﬂuent from the ﬁrst rinsing stage is high. So that the efﬂuent is usually returned to the electro-plating bath and the efﬂuent from the ﬁnal rinsing stage is discharged. The ED process is designed to collect Ni ions in the ﬁrst rinsing stage and return them to the electro-plating bath for the purpose of increasing recovery ratio of Ni and decreasing Ni content in the waste from the ﬁnal rinsing stage. Fig. 1.24 is a continuous process operating in the car components manufacturing factory. The process includes two stages of rinsing baths and one unit

348

Ion Exchange Membranes: Fundamentals and Applications

Table 1.6

Speciﬁcations of the desalting process

Solar generator Type Capacity Module number Storage battery Type Capacity Voltage Electrodialyzer Capacity Raw water Type Gasket dimension Effective membrane area Distance between membranes Number of cell pair System control

Oshima

Sakiyama

Silicon single crystal 25 kW 64 W 390 module

Silicon single crystal 65 kW 47 W 1380 module

Lead storage battery 115 kWh 96 V

Lead storage battery 230 kWh 192 V

10 m3/day Seawater (35,000 mg l1-TDS) Filter-press 185 2000 mm 0.238 m2

200 m3/day Saline water (1500 mg l1TDS) Filter-press 370 2000 mm 0.476 m2

0.8 mm

0.8 mm

250 3 modes operation 1. High-concentration operation 2. Low-concentration operation 3. Stand by operation

600 4 modes operation 1. Pump up+desalting operation 2. Pump up operation 3. Desalting operation 4. Stand by operation

Source: Inoue and Kuroda (1993). Electrodialysis

Solar battery output

Electric current (A)

Intermediately concentrated solution production

Potable water production

Auxiliary machine 6

8

10

12

14

16 Time

18

20

22

24

Figure 1.22 Electric power consumption pattern of the seawater desalination plant (Oshima island) (Inoue and Kuroda, 1993).

349

Electrodialysis

Solar battery output

Electric current (A)

Pump up current

Electrodialysis current Auxiliary machine current

Desalination + Pump up

Desalination

6

8

10

Stand by

12 14 Time

16

18

20

Figure 1.23 Electric power consumption pattern of saline water desalination plant (Sakiyama) (Inoue and Kuroda, 1993).

Table 1.7

Operating performance of the electrodialyzer Oshima

2

Sunlight quantity (kWh m ) Generation quantity (kWh/day) Water production (m3/day) Electric power consumption (kWh m3)

Sakiyama

1986

1987

1988

1900

1901

3.60 49.3 3.45 14.3

3.73 50.6 3.44 14.7

3.86 57.0 4.04 14.1

4.08 162 229 0.71

3.60 145 194 0.75

Source: Inoue and Kuroda (1993).

of electrodialyzer, which is designed to maintain the Ni concentration in the ﬁrst stage rinsing bath to about 5 g l1 when the concentration in the Ni plating bath is about 84 g l1. The speciﬁcations of the electrodialyzer are presented in Table 1.8. The limiting current density for NiSO4 or NiCl2 is extremely low comparing to that for Na2SO4 or NaCl. So, it is important to control the current density to prevent the precipitation of Ni(OH)2 caused by water dissociation. Further, the organic substances in the solution added into the electro-plating bath possibly give rise to generate the organic fouling of anion exchange

350

Ion Exchange Membranes: Fundamentals and Applications

Chemical dosing

* EPB

1st RIT

2nd RIT CXC

AXC

PRT +

−

ED

*

FIL 1st RIW

DIL

CON

ELR

2nd RIW

DEW

Figure 1.24 Electrodialysis Ni2+ electro-plating wastewater recovery process. AXC, Anion exchange column; CXC, cation exchange column; CON, concentrate; DEW, demineralyzed water; DIL, diluate; ED, electrodialyzer; ELR, electrode rinse; EPB, electro plating bath; FIL, ﬁlter; PRT, pretreatment; RIT, rinse tank; RIW, rinse waste (Itoi et al., 1986). Table 1.8

Speciﬁcations of the electrodialysis plant

Electrodialyzer Ion exchange membrane Size of membrane Effective membrane area Number of membrane pairs Distance between membranes Flow velocity Current density Maximum voltage

Model DU-111 Selemion CMV/AMV 0.49 0.98 m 0.336 m2 40 pairs 2.0 mm 3.0 cm s1 1.0 A dm2 50 V

Source: Itoi et al. (1986).

membranes. So, it is necessary to remove the organic substances by means of a special pretreatment. Material balance of Ni2+ ions and water in the process is indicated in Fig. 1.25 showing that the recovery ratio is larger than 90% and a diluted solution is perfectly recycled to the ﬁrst stage rinsing bath. Current efﬁciency and electric power of ED were, respectively, greater than 90% and 2 kWh kg1 Ni ion. Cost estimation is presented in Table 1.9.

351

Electrodialysis

Take out from plating bath 13 l/h (Ni2+ 84.2 g/l)

1 st stage Rinsing tank

Take out to 2nd stage 13 l/h (Ni2+ 5g/l)

Feed to ED 3 m3/h (Ni2+ 5g/l) Concentrated stream To plating bath 12.4 l/h (Ni2+ 83 g/l)

Figure 1.25

Electrodialyzer

Diluate stream 3 m3/h Ni2+ 4.65 g/l

Ni2+ and water balance in the electrodialysis process (Itoi et al., 1986).

Table 1.9 Cost estimation of electrodialytic recovery of rinsing waste in the nickel electroplating process Nickel recovery rate (as NiSO4 6H2O) Electricity consumption (as NiSO4 6H2O)

3460 kg month1 0.7 kWh kg1

Equipment installation cost Electricity unit cost Purchasing price of nickel salt (as NiSO4 6H2O)

15 million yen1 10 yen kWh1 360 yen kg1

Proﬁt of Nickel salt recovery 360 yen kg1 3460 kg month1 ¼ Runnig cost Electricity 10 yen kWh1 0.7 kWh kg1 3460 kg month1 ¼ Maintenance and consumable item (annually 3%) 15,000,000 0.03/12 month ¼ Amortization (7 years) 15,000,000 yen (7 year 12 month)1 ¼ Interest (annually 9%) 15,000,000 yen 0.09/12 month ¼ Running cost total Proﬁt

1,245,600 yen month1 24,220 yen month1 37,500 yen month1 178,570 yen month1 112,500 yen month1 352,790 yen month1 892,810 yen month1

Source: Itoi et al. (1986).

1.6.4

Reuse of Wastewater by Electrodialytic Treatment Ion exchange membrane ED technology is applicable to wastewater treatment for realizing resource saving and protection of environment. Tokuyama Inc. developed the technology to establish a closed system by means of

352

Ion Exchange Membranes: Fundamentals and Applications

Process

HCl, H2SO4

Acid waste

NaOH

Neutralization

Flocculant

Clarifier

Filter

Electrodialysis

Desalted solution

Concentrated solution

Traider receiving Designed process is surrounded by the dotted line.

Figure 1.26

Electrodialytic treatment process of industrial waste (Matsunaga, 1986).

Solution Circulating solution Concentrated solution

Na Ca 0.255N 13 ppm 3.870 220

Cl SO4 0.168 N 0.087 N 3.329 0.541

to process

ED

from clarifier

SAF MIT

DST

CHF

HCl

1 CST

2

Concentrated solution 65.4 l /h

Figure 1.27 Electrodialytic treatment process of industrial waste. CHF, Check ﬁlter; CST, concentrated solution tank; DST, desalted solution tank; ED, electrodialyzer; MIT, middle tank; SAF, sand ﬁlter (Matsunaga, 1986).

Electrodialysis

353

electrodialytic reuse of wastewater in a plating process as shown in Figs. 1.26 and 1.27 (Matsunaga, 1986).

Typical components of a raw feeding solution in this system. pH: 9.5, NaCl: 17.6 g l1, Na2SO4: 7.1 g l1, Ca: 48 mg l1, SS: 20 mg l1. Main component: Fe(OH)3. The others: Fe, Cu, Zn, P etc. Conditions of electrodialytic treatment. Quantity of a desalted solution: 10 ton/month. Degree of desalination: maximum. Degree of concentration: maximum. Temperature: normal. Operating time: 24 h/day, 30 days/month, 12 months/year. Operating system: partially circulation. Ion exchange membrane: Neocepta C5S-8 T (monovalent cation selectively permeable cation exchange membrane) and Neocepta ACH-45 T (anion exchange membrane). Operating results. Current density: 3.0 A dm2. Cell voltage: 0.5 V/pair (18–20 1C). Electrolyte concentration in a desalted solution: Cde,Na ¼ 0.25–0.32 eq dm3, Cde, Ca ¼ 13–15 mg l1. Electrolyte concentration in a concentrated solution Ccon,Na ¼ 3.80– 4.02 eq dm3, Ccon,Ca ¼ 220–240 mg l1. Quantity of a concentrated solution: 60–66 l h1 (1.44–1.58 m3/day). Quantity of a desalted solution 10.9– 12.1 ton/month. Running cost. Electric power: 262 kWh/day 15 yen/kWh ¼ 3930 yen/day Labor: 0.2 people/day 15,000 yen/people ¼ 3,000 yen/day The others (Ion exchange membrane, HCl, electrode, ﬁlter): 1330 yen/day Total: 8260 yen/day.

1.6.5 Simultaneous Treatment of Wastewater by Electrodialysis and Reverse Osmosis Yunichica Ltd. developed a treatment process of wastewater including toxic metallic ions discharged from a semi-conducting material manufacturing process (Ishibashi, 1986). The process is illustrated in Fig. 1.28 consisting from the following system. 1.6.5.1 High-Concentration System HS gas dissolving in the wastewater is deaerated and neutralized adding NaOH. Fine particles suspending in the wastewater are removed using a microosmosis ﬁlter. Then, a clear salt solution is supplied to an ion exchange membrane ED unit and concentrated to 3.5–4.0 M. The concentrated solution is evaporated using a vacuum evaporator (EV) to obtain Na2SO4 and NaCl crystals, which are reused after re-puriﬁcation. The desalted solution obtained from the ED unit is further desalted using a reverse osmosis (RO) unit. Concentrated

354

Ion Exchange Membranes: Fundamentals and Applications

Concentrated solution

High concentration system

Low concentration system

TDS 36g/l

TDS 240g/l

Separated salt 570 kg/day

EV

TDS 1.5g/l

ED

RO TDS 0.1g/l

Polishing

IX

Pure water Heigh pure water

Process ED: Electrodialysis RO:Reverse osmosis IX: Ion exchange EV:Evaporation

Figure 1.28 Simultaneous treatment process of wastewater by electrodialysis and reverse osmosis (Ishibashi, 1986).

solution from the RO unit is returned to the ED unit. The speciﬁcations of both units are as follows:

Electrodialysis unit Tokuyama TS-25-160 type integrated with Neocepta C66-5T/AFS Batch wise operating system Desalting performance 18 m3/day Concentration of a desalted solution 1.5 g l1 Reverse osmosis unit Middle pressure hollow ﬁber B-9 Desalting performance 15 m3/day Concentration of a desalted solution 100 ms

1.6.5.2 Low-Concentration System After deaeration, the solution is ﬁltered passing through a carbon ﬁlter and neutralized using weak basic ion exchange resins. Then the solution is supplied to a cation exchange and an anion exchange column to obtain pure water. The pure water is fed to the semi-conducting material manufacturing process

355

Electrodialysis

Anion exchange layer

Mn+

+

H+ Anode

Cation exchange membrane

+ + + + + +

− − − − − −

− − − − −

− H+ Cathode

Figure 1.29 H+ ion permeable cation exchange membrane. Mn+, n valent metalic ion (Katayama, 2004).

directly or via a polishing column ﬁlled up with cation and anion exchange resins and nonionic resins. 1.6.6

Electrodialytic Recovery of Acid Acid is recovered from a waste acid applying a H+ ion permselective cation exchange membrane placed an anion exchange layer on a cation exchange membrane as illustrated in Fig. 1.29. Here, multivalent cations Mn+ do not pass through the membrane due to repulsive effects between the cations and the anion exchange layer. The concept mentioned above is applicable to recover an acid from an aqueous solution dissolving for instance Fe(NO3)3 with HNO3 as shown in Fig. 1.30. In this system, cation exchange membranes correspond to the membrane illustrated in Fig. 1.29, and they permeate H+ ions selectively and do not permeate Fe3+ ions. On the other hand, anion exchange membrane permeate NO ions selectively rather than H+ ions. Consequently, HNO3 is recovered in the concentrating chamber and Fe(NO3)3 is remained in the desalting chamber. Table 1.10 shows the material balance in an electrodialyzer (effective membrane area: 90 m2) developed by Tokuyama Inc., which treated a wasted acid solution (0.54 M acid solution including H2SO4 and HCl with 0.30 M of Al3+ ions) generated in an etching process of aluminum products (Katayama, 2004). Acid concentration in a recovered acid is 1.90 M including 0.01 M of Al3+ ions. Acid recovering ratio and leak ratio are, respectively, 88% and 0.6%. Energy consumption and current efﬁciency are, respectively, 12 kW and 55%. 1.6.7

Seawater Concentration for Salt Production Electrodialysis is applied to concentrating seawater for producing salt in Japan. The seawater concentrating process is illustrated in Fig. 1.31 (Tomita, 1995). Seawater pumped up from sea is ﬁltered and supplied to the electrodialyzer via the ﬁltered solution tank. Concentrated seawater is circulated

356

Ion Exchange Membranes: Fundamentals and Applications

Recovered acid HNO3 De-acidified solution Fe(NO3)3 C

A NO3−

+

H+

H+

C NO3−

A NO3−

H+

C NO3−

H+

−

H+

Fe3+

Fe3+ Anode

Cathode Water Waste acid HNO3 Fe(NO3)3

Figure 1.30 Acid recovery by means of ion exchange membrane electrodialysis. C, H+ ion permselective cation exchange membrane; A, H+ ion low-permselective anion exchange membrane (Katayama, 2004).

Table 1.10

Material balance in an electrodialyzer for acid recovering

Solution

Waste acid (before electrodialysis) Deacid solution (after electrodialysis) Water Recovered acid

Solution Quantity (l h1)

Composition H+ (M)

Al3+ (M)

SO2 4 (M)

Cl (M)

742

0.54

0.30

0.65

0.16

671

0.07

0.33

0.50

0.08

115 186

0 1.90

0 0.01

0 0.79

0 0.35

Source: Katayama (2004).

between the concentrated seawater tank and the electrodialyzer, and its gain is supplied to an evaporating process to obtain salt crystals. CaCO3 scale precipitation in concentrating cells is prevented by adding hydrochloric acid to the 2 concentrated seawater to decompose HCO 3 and CO3 ions (cf. Section 1.5.2 in Applications). A part of ﬁltrated seawater is supplied to anode chambers. Titanium is adopted as the anode material. In order to avoid membrane destruction due to Cl2 and HClO generated by an anode reaction, a perﬂuorinated ion exchange membrane is integrated between the cathode chamber and the

360

Ion Exchange Membranes: Fundamentals and Applications

Table 1.11 Performance of an electrodialyzer for concentrating seawater (plant A, 1987) Current density (A dm2) Temperature (1C) Cl current efﬁciency (%) Na current efﬁciency (%) Energy consumption (kWh t1 NaCl) Concentrated solution puritya (%) Constitution of concentrated solution NaCl (g dm3) Cl (eq dm3) SO4 (eq dm3) Ca (eq dm3) Mg (eq dm3) K (eq dm3) Na (eq dm3)

2.66 25.3 88.6 80.8 178.6 90.90 190.6 3.568 0.015 0.064 0.169 0.095 3.256

Source: Tanaka (1991). NaCl(g)/Total electrolyte (g).

a

The operating performance and energy consumption in a salt manufacturing plant were investigated for an ion exchange membrane ED system to which discharged brine from a RO plant is supplied as follows (Tanaka et al., 2003). The salt manufacturing process (NaCl production capacity: 200,000 ton/year) is illustrated in the dotted frame in Fig. 1.35. Discharged brine (electrolyte concentration: 1.5 eq dm3) from a RO plant is assumed to be supplied to an ion exchange membrane electrodialyzer. The concentrated solution obtained from the electrodialyzer is supplied to a multiple-effect EV, in which salt is crystallized. The salt obtained from the evaporator is supplied to an ion exchange membrane electrolytic bath, in which sodium hydroxide and chlorine are produced. Energy consumption in the salt manufacturing process is assumed to be supplied by a simultaneous heat-generating electric power unit consisting of a boiler and a back-pressure turbine. Fig. 1.36 shows the ﬂows of electricity and steam in a salt manufacturing plant. Boiler steam is introduced to a turbine and generates electricity, which is distributed to electrodialyzers, etc. The back-pressure of a back-pressure turbine is supplied to a heater in a No. 1 evaporator in multiple-effect evaporators. Evaporated steam in a No. 1 evaporator is supplied in turn to the following evaporators. Pressure and temperature of boiler steam are set as 6 Mpa and 4801C in this study. The temperature difference between heating steam and evaporated steam is ﬁxed to 201C at each evaporator. The number of evaporator is kept to a minimum, but the quantity of electricity does not exceed the electric power consumption in this salt manufacturing plant. An electric power shortfall is assumed to be made up by purchased electric power, which is generated by a condensing turbine.

357

Electrodialysis

C

9 10

+

−

7

6

8

2

3

4

5

1

Figure 1.31 Electrodialytic seawater concentration process. 1, Diluted seawater tank; 2, cathode solution tank; 3, concentrated seawater tank; 4, washing solution tank; 5, HCl tank; 6, ﬁltrated seawater; 7, concentrated seawater output; 8, HCl; 9, electrodialyzer; 10, anode solution (Tomita, 1995).

adjacent stack. The wasted solution from the anode chamber is mixed with the ﬁltrated seawater to suppress the growth of microorganisms in seawater. Cathode material is plated with Pt. An HCl solution is supplied to the cathode chamber to neutralize OH ions generated by the cathode reaction. A washing system is provided for washing the inside of desalting cells by acid or chemical reagents and dissolving adhered substances (cf. Section 14.2.3 in Fundamentals). When the turbidity of raw seawater is 2 ppm, it is decreased to about 0.05 ppm by ﬁltering through two-stage sand ﬁlters (cf. Section 1.5.1 in Applications). In spite of such ﬁltration, ﬁne particles pass through the ﬁlter and invade into the electrodialyzer and precipitate on the membrane surfaces. Fe(OH)3 components precipitated on the membrane possibly give rise to water dissociation (cf. Sections 8.8.4 and 8.9 in Fundamentals). Sometimes, ﬁne organisms pass through the ﬁlter and breed in the electrodialyzer. These troubles are avoided by disassembling and washing the electrodialyzer at the interval of 4–6 months (cf. Section 1.5.3 in Applications). In order to increase current efﬁciency and avoid CaSO4 scale precipitation, membrane surfaces are treated to give monovalent ion permselectivity (cf. Section 3.7 in Fundamentals).

358

Ion Exchange Membranes: Fundamentals and Applications

Figure 1.32 Composition of an electrodialyzer (Tokuyama). 1, Fastening bolt; 2, fastening and feeding frame; 3, concentrated seawater inlet; 4, diluted seawater inlet; 5, diluted seawater outlet; 6, concentrating cell; 7, desalting cell; 8, desalting cell manifold; 9, concentrated seawater outlet; 10, cation exchange membrane; 11, anion exchange membrane; 12, concentrating cell manifold (Tomita, 1995).

Compositions of electrodialyzers developed by Tokuyama Inc., Asahi Glass Co. and Asahi Chemical Co. are illustrated in Figs. 1.32–1.34 (Tomita, 1995). Typical performance of an electrodialyzer is exempliﬁed in Table 1.11 (Tanaka, 1991). 1.6.8 Salt Production Using Brine Discharged from a Reverse Osmosis Seawater Desalination Plant Concentrated brine is discharged from a RO seawater desalination process. It seems advantageous to use this brine as raw material for salt production.

Electrodialysis

359

Figure 1.33 Composition of an electrodialyzer (Asahi Glass Co.). 1, Cathode chamber; 2, anode chamber; 3, cathode plate; 4, anode plate; 5, intermediate frame; 6, desalting cell; 7, concentrating cell; 8, cation exchange membrane; 9, anion exchange membrane; 10, packing cell frame; 11, intermediate packing; 12, blind cell frame (Tomita, 1995).

Figure 1.34 Composition of an electrodialyzer (Asahi Chemical Co.). 1, Diluted seawater; 2, special gasket; 3, concentrating cell; 4, turn-Buckle; 5, desalting cell; 6, concentrated seawater; 7, fastening frame; 8, cation exchange membrane; 9, anion exchange membrane (Tomita, 1995).

361

Electrodialysis

Seawater 0.6 eq/dm3

Desalted solution

Discharged brine C′in=1.5 eq/dm3 RO C′′ C′out ED Cl2 T

B

EV NaOH NaCl crystals IM

Salt manufacturing process H2O

Figure 1.35 RO-ED combined salt manufacturing process. RO, Reverse osmosis; ED, electrodialyzer; EV, evaporation; IM, ion exchange membrane electrolysis; B, boiler; T, turbine. Diagonals in RO, ED and IM unit box represent the membranes (Tanaka et al., 2003).

The energy required for producing salt F is plotted against current density I/S in both cases of RO discharged brine ED and seawater ED. The plots are shown in Fig. 1.37, which indicates that the energy consumption in a salt manufacturing process using RO discharged brine is 80% of the energy consumption in the process using seawater. The optimum current density at which the energy consumption required in the salt manufacturing process being minimized is 3 A dm2 for both RO discharged brine ED and seawater ED. 1.6.9

Desalination of Amino Acid and Amino Acidic Seasonings Amino acid is an amphoteric electrolyte, and its behavior is different from that of usual electrolytes. Itoi and Utsunomiya (1965) electrodialyzed aqueous solutions of methionine and glysine containing sodium formate as follows; (a) methionine 25 g l1, HCOONa 20 g l1. (b) glysine 70 g l1, HCOONa 20 g l1. The solution was supplied to the electrodialyzer (membrane pairs: 9, effective membrane area: 209 cm2) incorporated with Selemion CSG and AST. Changing pH and maintaining cell voltage at 15 V (average current density: nearly 1 A dm2), amino acid permeation ratio (the ratio of amino acid

362

Ion Exchange Membranes: Fundamentals and Applications

Purchsed electric power

∆G

Ggen+∆G=Etotal × PNaCl RO

H*S*

Discharged brine 1.5 eq/dm3solution

Generated electric power Ggen B

ED

BPT

W = w × PNacl 70°C

50°C

30°C

St

Qcond EV NO1

EV NO2

EV NO3

Tcond=90°C Hcond Scond

Figure 1.36 Energy ﬂow in a salt manufacturing process. B, Boiler; BPT, back-pressure turbine; EV, evaporator; ED, electrodialyzer; RO, reverse osmosis unit (Tanaka et al., 2003).

transported across a membrane pair against that dissolving in a feeding solution) was measured and shown in Fig. 1.38, indicating that the amino acid permeation ratio becomes minimum near the isoelectric point of amino acid. Changing current density and keeping pH near the isoelectric point of the amino acid, the amino acid permeability (quantity ratio of amino acid transported across a membrane pair against electricity) was measured and shown in Fig. 1.39. Inspecting Fig. 1.39 and the limiting current density measured for an HCOONa solution, it is concluded that the amino acid permeability becomes minimum by applying the limiting current density. Concentration changes of NaCl and essence in the batch system ED of soy sauce are indicated in Tables 1.12 and 1.13.

363 60

1.2

50

1.0

40

0.8

30

0.6

20

0.4

10

0.2

0 0

1

2

3

4 5 6 I/S (A/dm2)

7

8

9

(RO discharged brine electrodialysis)/ (seawater electrodialysis)

(103M cal/h)

Electrodialysis

0.0 10

: RO discharged brine electrodialysis : Seawater electrodialysis : RO discharged brine electrodialysis / Seawater electrodialysis

Figure 1.37

1.6.10

Energy consumption in a salt manufacturing plant (Tanaka et al., 2003).

Desalination of Natural Essences In an extraction process of natural essences, several kinds of salt, acid and alkali are added. Accordingly salt is obtained as a by-product in a ﬁnal stage. Salt content in the natural essences is expected to be controlled for maintaining a taste and human health. Tokuyama Inc. developed the following desalination processes of natural essences (Ideue, 1986; Yamamoto, 1993). An ED system was set up using ion exchange membranes met the food hygiene standard established by the Ministry of Welfare, Japan, and incorporated with polyvinyl chloride or polypropylene materials suitable for food production. It was further necessary to pay attention to prevent solution stagnation and cultural contamination. Further cleaning in place (CIP) was necessary to operate the apparatus stably. The electrodialyzer was operated in a batch system using ED system indicated in Fig. 1.40, in which a conductivity control indicator was set at an exit of the electrodialyzer for detecting the concentration of a desalted solution. The solution feed and solution discharge were automatically controlled by switch valves operating with the conductivity control indicator. Natural essences include meat essences, seafood essences, ﬂesh essences etc. They were extracted with the aid of a NaCl solution. Salt added in the extraction process was desalinated by means of ED mentioned above. Constituent changes in desalination of extracted meat essences, ﬁsh essences and fruit

364

Ion Exchange Membranes: Fundamentals and Applications

80

Cell voltage : 15 V

Glycine

60

ionin

e

50 40

Meth

Amino acid permentation ratio (%)

70

30 20 10 0

0

2

4

6

8

10

12

14

pH Glicine 70 g/l, HCOONa 20 g/l Methionine 25 g/l, HCOONa 20 g/l

Figure 1.38 Relationship between solution pH and amino acid permeation ratio through ion exchange membranes (Itoi and Utsunomiya, 1965).

ﬂesh essences are shown in Table 1.14. Speciﬁcations of an electrodialyzer for seafood essences are shown in Table 1.15. 1.6.11 Electrodialysis of Milk and Whey 1.6.11.1 Composition of Milk and Whey (Ideue, 1986; Tomita et al., 1986) Whey is obtained as a by-product of a cheese production process. The output of whey amounts to nine times of that of cheese, so it is an important subject in the dairy industry to utilize the whey effectively. The effective utilization of permeates derived from an ultra-ﬁltration process of milk and whey is also a big problem in the dairy industry. The composition of milk, whey and ultraﬁltration permeates is indicated in Table 1.16. Ash content in dry matter of the whey and permeate is so high that it is expected to reduce their ash content by ED. Powdered milk for baby rising is prepared using cow milk as main raw materials. The constituents of breast milk and cow milk are not same as shown in Table 1.17. Total ash and casein compositions of cow milk are, respectively, 3.4 and 4.4 times of those of the breast milk. Accordingly, baby rising powdered

365

Electrodialysis

3.0 pH: 6.3-6.9

ine yc

2.0

Gl

1.5

nin

e

1.0

et

hio

Amino acid permeability (g/Ah)

2.5

0

M

0.5

0

0.5

1.0

1.5

2.0

Average current density (A/dm2) Glycine 70 g/l, HCOONa 20 g/l Methionine 25 g/l, HCOONa 20 g/l

Figure 1.39 Relationship between current density and transport rate of amino acid (Itoi and Utsunomiya, 1965).

Table 1.12

Electrodialytic demineralization of soy sauce Start

Solution quantity (l) NaCl concentration (g l1) Essence concentration (g l1) pH Density Current efﬁciency (%)

11.6 191 163 4.7 1.181

End 31 191 4.7 1.103 90

Note: Effective membrane area: 209 cm2; Numbers of membranes: 10 pairs; Current density: 3.5 A dm2; Applied voltage: 25–58 V. Source: Itoi (1983).

366

Ion Exchange Membranes: Fundamentals and Applications

Table 1.13

Concentration changes of components in electrodialysis of soy sauce

Component

Ratio (Before ED/After ED)

NaCl Total amino acid Glutamic acid Aspartic acid Lysine Leucine Isoleucine Alanine Phenylalanine Valine Total nitrogen Essence part

0.800 0.94 0.93 0.95 0.98 0.98 0.98 0.96 0.87 0.95 0.96 1.009

Source: Itoi (1983).

milk is prepared by adding whey to cow milk. Before this mixing operation, however, it is necessary to extract excessive ash from the milk or whey by ED. 1.6.11.2 Limiting Current Density in Electrodialysis of Milk and Whey (Nagasawa et al., 1973; Nagasawa et al., 1974) In ED of a dairy product solution, protein is condensed and attached on the desalting surface of an anion exchange membrane at above limiting current density due to occurrence of water dissociation. At the same time, insoluble salt such as calcium phosphate etc. precipitates on the concentrating surface of the anion exchange membrane. Accordingly, it is important to increase the limiting current density to operate a practical electrodialyzer stably. Nagasawa et al. evaluated the limiting current density as follows. In ED of a skim milk solution, limiting current density was evaluated based on the relationship between current density and voltage. The relationship between conductivity of the skim milk solution k and the limiting current density ilim was expressed by ilim ¼ 1.08 103k. (i/k)lim was known to be proportional to the 0.6th power of solution velocity of skim milk V. (i/k)lim/V0.6 vs. temperature T and dry matter content of skim milk S is given in Fig. 1.41 which indicates that (i/k)lim/V0.6 decreases with the increase of T and S. Flow length and distance between the membranes did not inﬂuence to ilim. From the investigation mentioned above, the following limiting current density equation was introduced as 0:1

ilim ¼ QS1=6 ð1:01665S ÞT V 0:6 k

(1)

Q is a constant. S, T and V can be voluntarily ﬁxed, so the above equation is expressed by the following equation. ilim ¼ Rk

(2)

VI

Electrodialysis

AI

8 CCI

10

_

+

7 9

F1

F1

LA P1

LC

1

2

P1

P1

F1

F1

P1

6 LA

3

4 3

5 3

367

Figure 1.40 Electrodialysis process of natural essences. 1, Raw solution tank; 2, desalted solution tank; 3, drain; 4, concentrated solution tank; 5, concentrated waste solution; 6, electrode solution tank; 7, water supply; 8, ammeter; 9, electrodialyzer; 10, desalted solution; Vi, voltage indicator; Ai, ampere indicator; Fi, ﬂow indicator; Pi, pressure indicator; CCi, conductivity control indicator, LC, level control; LA, level alarm (Yamamoto, 1993).

368 Table 1.14

Ion Exchange Membranes: Fundamentals and Applications

Desalination of ﬁsh essences Raw Essence

Conductivity Viscosity Ash Na K Ca Mg Cl

15.4 mS cm 4 cp

1

2975 ppm 241 ppm 38 ppm 45 ppm 3299 ppm

Desalted Essence

Desalting Ratio

1

2.74 mS cm 6.4 cp

82.2%

560 ppm 19 ppm 2.4 ppm 1.9 ppm 583 ppm

81.2% 92.1% 93.7% 95.8% 82.3%

Source: Yamamoto (1993).

Table 1.15

Speciﬁcations of an electrodialyzer for desalinating seafood essences

Requirement Raw solution NaCl Protein Speciﬁc gravity Viscosity pH Treating amount

14 g l1 100 g l1 1.05 4.0 cp 5.5 0.5 t h1

Speciﬁcations Effective membrane area Number of membrane pair Ion exchange membrane Model Operating system

256 m2 200 pairs Neocepta CM-1, AM-1 TS-25-200 Automatic batch system

Running cost

1517 yen t1

Source: Yamamoto (1993).

Table 1.16

Typical composition of milk and UF-permeate Fat (%)

Cow milk Cheese whey Permeate derived from UF of milk

3.3 0.3 0

Source: Tomita et al. (1986).

Protein (%) 2.9 0.7 0.2

Lactose (%)

Ash (%)

4.5 4.5 4.4

0.7 0.6 0.5

Water (%) 88.6 93.7 94.8

Ash/Dry Matter (%) 6.1 9.5 9.6

369

Electrodialysis

Table 1.17

Comparison of composition between breast milk and cow milk Water (%)

Breast milk Cow milk

88.0 88.6

Ash (%)

Whey Protein (%)

0.2 0.7

0.68 0.69

Casein (%) 0.42 2.21

Fat (%) 3.5 3.3

Lactose (%) 7.2 4.5

Source: Tomita et al. (1986).

(i/)lim/V0.6 x 102

10

5

2 0 S%

10 : 0.3,

20 30 Temperature (°C) : 8.3,

: 16,

40

: 25

Figure 1.41 Effects of temperature and total solid content on (i/k)lim/V0.6 (Nagasawa et al., 1974).

R is a constant. We know ilim from k, and it was conﬁrmed that the electrodialyzer is operated stably at under ilim estimated from Eq. (2). 1.6.11.3 Ion Exchange Membrane (Okada et al., 1975) for the Demineralization of Milk or Whey In the demineralization of skim milk or whey including rich proteinaceous materials or other organic matters, conventional membranes applied to the treatment of saline water are not feasible because the life span of the membranes is shortened and the performance is deteriorated. In order to make membranes applicable to the demineralization process of milk or whey, the investigation was performed to give the following characteristics to the membranes. Anti-Organic Fouling The speciﬁc conductance of various membranes k was determined in a demineralization experiment of Gouda cheese whey. The membranes are, Aciplex K-101 (conventional cation exchange membrane, Asahi Chemical Co.), A-101 (conventional anion exchange membrane) and A-201 and A-211 (both are

370

Ion Exchange Membranes: Fundamentals and Applications

Remaining specific conductance(%)

100 K-101

80 A-211 A-201

60 40 20 0

A-101 0

2000 4000 6000 Operating time (hr)

8000

Figure 1.42 Membrane conductivity changes with operating time (Okada et al., 1975).

newly developed anion exchange membranes). k of K-101 is not changed largely with running time as indicated in Fig. 1.42. k of A-101 shows very rapid decrease. However, k of A-201 and A-211 membranes does not change signiﬁcantly for 6000 h. A-201 and A-211 membranes show excellent anti-fouling (cf. Section 14.3.2 in Fundamentals). Anti-Alkaline Circumstance Organic fouling due to deposition of proteinaceous materials or fatty substances from the dairy products is cleaned by washing in an alkaline detergent by means of CIP method. Exposure of the membrane to OH ions generated from water dissociation vitiates its performance. Therefore, life span of the membrane is shortened without the durability against a basic solution in contact. Fig. 1.43 shows the durability evaluated by measuring speciﬁc conductance k of the membranes immersed in a 1% NaOH solution. k of conventional cation exchange membrane K-101 does not change, however, that of anion exchange membrane A-101 decreases remarkably with immersing duration. On the other hand, decrease of k is suppressed for anti-organic fouling anion exchange membrane A-201 and A-211. Particularly, A-211 membrane exhibits excellent anti-alkaline performance. Permeability to Larger Organic Ions of an Anion Exchange Membrane An anion exchange membrane which does not permeate larger organic anions causes pH lowering in demineralization of dairy products. This is because OH ions caused by water dissociation generated on a desalting surface of an anion exchange membrane permeate the membrane instead of the larger organic anions toward a concentrating cell. This phenomenon induces pH increase in the concentrating cell and gives rise to the precipitation of inorganic salts such as Ca3(PO4)2, CaCO3, CaSO4 etc. On the other hand, pH in the desalting cell is

371

Electrodialysis

100

K-101 A-211

Remaining specific conductance(%)

90 80 70 A-201

60 50 40 30 20 10

A-101 0

0

100

200 300 400 Immersing duration (hr)

500

Figure 1.43 Membrane conductivity changes with time in alkaline circumstances. 1 % NaOH at 371C (Okada et al., 1975).

estimated to be lowered because H+ ions are remained in the desalting cell. Fig. 1.44 shows pH changes upon 90% ash reduction of Gouda cheese whey using three types of anion exchange membranes. A-211 membrane scarcely brings about the decrease in pH. This is because pore radius in A-211 membrane is large enough (cf. Section 14.3.2.1 in Fundamentals), so that organic acids such as citric acid, lactic acid, amino acid as well as phosphoric acid easily permeate the membrane and that water dissociation does not easily occur. From the experiment described here, it is concluded that A-211 is the most suitable anion exchange membrane. CIP operations of an electrodialyzer incorporated with A-211 membranes realize 90% ash reduction and life span extension.

1.6.11.4 Electrodialysis System (Okada et al., 1975) for the Demineralization of Milk or Whey Fig. 1.45 illustrates the four stack ED process MED SV1/2 4-4 developed by Morinaga Milk Industry Co. The speciﬁcations and operating conditions of this system are shown, respectively, in Tables 1.18 and 1.19. In Fig. 1.45, the

372

Ion Exchange Membranes: Fundamentals and Applications

A-211 7

A-201 (and A-101)

pH

6

5

4

Figure 1.44

0

10

20

30 40 50 60 70 Relative deashing rate [%]

80

90

pH changes of whey in demineralization (Okada et al., 1975).

pump P1 feeds the whey to the balance tank WB-1. Succeedingly, the whey is supplied to the 1st stack of the ED system, demineralized to some extent and overﬂows from WB-1 to WB-2. The whey in WB-2 circulates through pump P3 and second stack, then part of which overﬂows into WB-3. In the similar way, the whey ﬂows via P4, third stack, WB-4, fourth stack, WB-5, and ﬁnally demineralized whey ﬂows out via P6 and supplied to the succeeding process such as pasteurization, evaporation and drying. At each balance tank, the conductivity of the whey is monitored to control the desalting rate. The feed rate of the whey to this system is automatically controlled by means of conductivity measurement in the efﬂuent of demineralizing stream. 1.6.12

Desalination of Sugar Liquor The sugar manufacturing system is classiﬁed into the cane sugar–ﬁne sugar manufacturing system and the beet sugar manufacturing system. The raw material for the former is sugar canes and that for the latter is beet sugar. In the sugar manufacturing process, the greater part of organic nonsugar components in raw sugar is removed by means of defecation, carbonation, adsorption (bone char, active carbon, ion exchanger etc.). In these treatments, inorganic components are not removed and transferred to an evaporation process, in which residual organic nonsugar components are separated from sugar crystals and remained in molasses. In the course of repeating evaporation and separation, the inorganic and organic nonsugar components are gradually accumulated in the

CB-5

CB-4

P11

for anode frame (one pass & waste)

P10

I1

V1

CB-3

P9

Con

Con

1st

2nd

DC Dil

CB-2

I2

Dil

V2

V3 DC DC

Water

CB-1

P8

I3

Electrodialysis

Va1

H2SO4

P7

Con

Con

3rd

4th

I4

V4 Rinse solution for fastening frame & cathode frame

DC Dil

Dil P12

P2 Whey

P3

P4

P5

P1

WB-1

WB-2

WB-3

WB-4

PB-5

Demineralized whey P6

1st : Stack - 1 2nd : '' -2

DC : Rectifier

3rd :

''

-3

I1-4 : Amperage meter

4th :

''

-4

Con. : Concentrating compartments Dil. : Diluting compartments

V1-4 : Voltage meter

373

Figure 1.45 Flow diagram of Morinaga continuous electrodialysis process (Okada et al., 1975).

374 Table 1.18

Ion Exchange Membranes: Fundamentals and Applications

Speciﬁcations of MED SV1/2 4-4

1. Center-press 2. Stack 3. Electrode 4. Cell pair 5. Distance between membranes 6. Effective membrane area 7. Spacer 8. No. of channel 9. Width of the channel 10. Length of the channel

1 4 4 pairs 150 cell pairs/stack 0.75 mm 50 dm2/cell Sheet-ﬂow type 1 500 mm 1000 mm

Source: Okada et al. (1975).

Table 1.19

Operating conditions of demineralization of whey (Morinaga ED system)

1. Quality of whey to be treated 1.1 Total solids 1.2 Ash content 1.3 Speciﬁc conductance 1.4 Sediment test (200 ml, 1000 G)

20% 1.60% 0.013 S cm1 less than 0.1 ml

2. Operating conditions 2.1 Level of applied d-current density 2.2 Linear velocity in the compartment 2.3 Operating temperature

3000 ka (mA cm2) 12 cm s1 201C

Source: Okada et al. (1975). k: Speciﬁc conductance.

a

molasses and ﬁnally they are discharged to the outside of the system as waste molasses. The waste molasses includes considerable amount of sugar components, so it is utilized as raw materials for fermentation or animal food, however, its economical value is extremely low comparing to that of sugar itself. Because of the background described above, the technology development was expected for preventing sugar component transfer to waste molasses and increasing sugar recovering ratio. Further desalting technology by means of ion exchange membrane ED came to be attracted because the sugar recovering ratio is inﬂuenced by residual inorganic components in syrup. Application of ED in sugar manufacturing industry was investigated from the latter half of 1950s. However, it was difﬁcult to put this program into practice. This is because water dissociation and organic fouling are apt to occur on anion exchange membranes (cf. Section 14.3 in Fundamentals). In order to avoid these troubles, Taito Co. and Asahi Chemical Co. developed the technology using neutral membranes consist of polyvinyl alcohol instead of anion exchange membranes (Sugiyama et al., 1982; Kokubu et al., 1983). The

375

Electrodialysis

advantages and disadvantages of this method (Transport depletion method) are as follows. 1.

Advantages (a) Neutral membranes do not deteriorate due to organic fouling. (b) Sugar does not decompose, because pH decrease caused by water dissociation does not occur on the neutral membrane. (c) Current density can be increased, because water dissociation does not occur. 2. Disadvantages (a) Removing efﬁciency of anions is low. (b) Current efﬁciency Z is low, because transport number of anions of a neutral membrane ¯tA A0:5: If we assume the transport number of a cation exchange membrane ¯tK ¼ 1:0; Z ¼ ¯tK þ ¯tA 1 ¼ 0:5:

In the ﬁrst stage in a sugar manufacturing process, raw molasses (original syrup) is treated to remove organic materials and evaporated to obtain A sugar Table 1.20

Effect of electrodialysis on pretreatment for molasses

Desalting ratio (%) Current efﬁciency (%) Current density (A dm2) Molasses volume (l) Molasses concentration (oBx) Molasses purity (%) pH

Ash (% on solid) CaO MgO K2O Cl SiO2 SO3 P2O5 CO2 Sulfate ash

I

II

66.18 43.55 3.04

63.60 34.01 3.07

III 2.58 9.54 0.03

Start 10.00 51.35

End 9.76 46.85

Difference D 0.24 D 4.50

Start 10.00 50.45

End 9.76 46.45

Difference D 0.24 D 4.00

0.00 D 0.50

51.70 6.35

59.01 6.35

7.31 0.00

52.66 6.40

58.45 6.40

5.79 0.00

1.52 0.00

Start

End

Desalting ratio

Start

End

Desalting ratio

0.19 0.74 5.47 3.99 0.41 0.69 0.18 0.19 12.42

0.06 0.33 1.59 0.15 0.33 0.41 0.19 0.14 4.73

68.42 55.41 70.93 96.24 19.51 40.58 D 5.56 26.32 61.92

0.22 0.72 5.98 3.65 0.44 1.22 0.21

0.13 0.42 2.01 0.19 0.41 1.00 0.18

40.91 41.67 66.39 94.79 6.82 18.03 14.29

27.51 13.74 4.54 1.45 12.69 22.55 D 19.84

12.78

5.19

59.39

2.53

Note: I: Duple-stage centrifuging after CaCl2 adding; II: Duple-stage centrifuging without CaCl2 adding. Source: Kokubu et al. (1983).

376

Ion Exchange Membranes: Fundamentals and Applications

2nd boiling

B sugar

B molasses

Ca(OH)2

CaCl2

Mixing Water

Steam Heating

1st centrifuging

1st sludge

1st centrifuged molasses Steam

Water 2nd centrifuging 3rd centrifuging 2nd sludge

2nd centrifuged molasses

Separated molasses Final sludge Refrigerator Seawater Discharged water

Electrodialyzer

Water

Desalted molasses (C molasses)

3rd boiling

Figure 1.46

C sugar

Desalination of B molasses (Kokubu et al., 1983).

and A molasses. In the next stage, B sugar and B molasses are obtained from A molasses through the similar process. Finally, C sugar and C molasses are obtained from B molasses. Table 1.20 shows ED experiment of B molasses, which is centrifuged two times after adding CaCl2 (Case I) and without adding CaCl2 (Case II). The experiment indicates that desalting ratio and current efﬁciency in Case I are increased comparing those in Case II. This is because the minerals such as CaO, SiO2, SO3, P2O5 etc. are removed by the CaCl2 treatment in Case I. Based on the experiment described above, Taito Co. designed the ED treatment process of B molasses as shown in Fig. 1.46. In this process, B

377

Electrodialysis

Table 1.21

Bacterial strains and media for cell count

Strains

Media (Agar)

Staphylococcus aureus Salmonella heidelberg Escherichia coli K-12 Pseudomonas aeruginosa Proteus vulgaris Klebsiella pneumoniae Bacillus subtilis

Mannitol salt Deoxycholate Deoxycholate Deoxycholate Deoxycholate Deoxycholate Nutrient

Source: Sato (1989).

+

C

I

A

II

III

FS

−

A

C

IV

V

FS

Anode

Cathode

P

P

P

AS

BSS

CS

Figure 1.47 Schematic diagram of an electrodialytic disinfection diagram. C, Cation exchange membrane (Selemion CMV); A, anion exchange membrane (Selemion AMV); CS, cathode solution; AS, anode solution; BSS, bacteria cell suspending solution; distance between the membranes, 1 cm; membrane area, 18.4 cm2 (Sato, 1989).

molasses is treated at ﬁrst by defecation mixing with Ca(OH)2 and CaCl2. After heating and two stages of centrifugation, the second centrifuging molasses is supplied to the electrodialyzer via the refrigerator to obtain desalted molasses (C molasses). C sugar is crystallized in the evaporation of C molasses. By integrating the ED step mentioned above in the sugar manufacturing process, it became possible to obtain D sugar from C molasses.

378

Ion Exchange Membranes: Fundamentals and Applications

100 90

Cell viability (%)

80 70 60 50 40 30 20 10 0

0.54

0.81

1.08

1.35

1.65

Current density (A/dm2) : S. aur.,

: Sal. heid,

: K. pneu.,

: B. sub (spore).

: E. coli,

:Ps. aerug.,

:Pr. vulg.,

Figure 1.48 Relation between bacteria cell viability and current density. Flow rate, 3 cm3/min; duration time, 60 min (Sato, 1989).

1.6.13

Electrodialytic Disinfection Sato et al. (1984) investigated water disinfection by means of ion exchange membrane ED. The merits of this method are as follows. (1) (2) (3)

The operation is proceeded at normal temperature. Comparing to chlorine disinfection, the electrodialytic disinfection is more powerful and proceeded during shorter time. The process is not harmful to human body.

Bacterial strains in Table 1.21 were cultivated at 371C for 18 h. The cultivated solution suspending 108 cells cm3 of bacteria cells was supplied into the desalting chamber (chamber III) in an ED system in Fig. 1.47 and electrodialyzed for 60 min. Viability of the cells is plotted against current densities and shown in Fig. 1.48. Here, limiting current density is 0.81 A dm2. Bacteria viability is seen to be decreased with the increase of current density in a range of over limiting current densities and becomes zero at 1.63 A dm2. Electron

379

Electrodialysis

E. coli cell Water dissociation

OH

H

+

H+

Anode

Cathode

Anion exchange membrane

Figure 1.49

Desalting chamber

Cation exchange membrane

Mechanism of disinfection in electrodialysis (Sato, 1989).

microscope observation revealed that bacteria cell conformation is shrank under applying over limiting current density. The mechanism of electrodialytic disinfection in this study is estimated as follows. In Fig. 1.49, Escherichia coli cells are suspended in a solution in the desalting chamber (Chamber III). Passing over limiting current in this system, the electrolyte concentration in the desalting chamber is decreased and electric resistance of the solution is increased. In this situation, water dissociation is generated on the anion exchange membrane (cf. Section 8.8.1 in Fundamentals) and H+ ion concentration in the desalting chamber is increased. An E. coli cell is an electron conducting substance, so H+ ions pass through the E. coli cells. This phenomenon is similar to that in electrodeionization (cf. Chapter 4, Fig. 4.8 in Application). E. coli cells are estimated to be destroyed by H+ ions passing through the cells. The investigation described here should be analyzed from the biological effects of alkaline electrodialyzed water at the cellular level (Takahashi, 2006; Kikuno, 2006). REFERENCES Azechi, S., 1980, Electrodialyzer, Bull. Soc. Sea Water Sci., Jpn., 34(2), 77–83. Fukuhara, K., Hamada, M., Azuma, I., 1993, Efﬁcient desalination of brackish water by electrodialysis, Industrial Application of Ion Exchange Membranes, vol. 2. Research group of electrodialysis and membrane separation technology, Soc. Sea Water Sci., Japan, pp. 159–167. Ideue, K., 1986, Desalination with ion exchange membranes in food industry, Food Dev., 21(7), 54–59.

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Ion Exchange Membranes: Fundamentals and Applications

Inoue, S., Kuroda, O., 1993, Electrodialysis desalination system powered by photovoltaic power generation, Industrial Application of Ion Exchange Membranes, vol. 2. Research group of electrodialysis and membrane separation technology, Soc. Sea Water Sci., Japan, pp. 151–157. Ishibashi, T., 1986, Simultaneous treatment of waste water by electrodialysis and reverse osmosis, Industrial Application of Ion Exchange Membranes, vol. 1. Research group of electrodialysis and membrane separation technology, Soc. Sea Water Sci., Japan, pp. 177–180. Itoi, S., 1983, Electrodialytic demineralization of soy sauce and amino acid seasonings, Food Industry and Membrane Utilization, Saiwai Shobo Inc., Tokyo, pp. 157–162. Itoi, S., Komori, R., Terada, Y., Hazama, Y., 1978, Basis of electrodialyzer design and cost estimation, Ind. Water, No. 239, pp. 29–40. Itoi, S., Nakamura, K., Kawahara, T., 1986, Electrodialytic recovery of waste water from metal surface treatment process, Industrial Application of Ion Exchange Membranes, vol. 1. Research group of electrodialysis and membrane separation technology, Soc. Sea Water Sci., Japan, pp. 206–211. Itoi, S., Utsunomiya, T., 1965, Electrodialysis of aqueous solution of amino acid containing electrolyte by ion exchange membrane, Asahi Glass Res. Report, 15, 171–178. Katayama, S., 2004, Waste water treatment and recovering of useful substances, In: Seno, M., Tanioka, A., Itoi, S., Yamauchi, A., Yoshida, S. (Eds.), Functions and Applications of Ion Exchange Membranes, Industrial Publishing & Consulting Inc., Tokyo, Japan, pp. 151–169. Kikuno, R., 2006, Microbicidal effect of strong alkaline electrolyzed water, 2005 Alkaline Electrodialyzed Water Symposium, Tokyo, Kitasato University, September 3, 2006. Kokubu, T., Yamauchi, T., Miyagi, S., 1983, Application of electrodialysis in sugar industry, Food Ind., 9, 26–31. Leitz, F. B., 1986, Measurements and control in electrodialysics, Desalination, 381–401, presented at the International Congress on Desalination and Water Re-use, Tokyo (1977). Matsunaga, Y., 1986, Reuse of waste water by electrodialytic treatment, Industrial Application of Ion Exchange Membranes, vol. 1. Research group of electrodialysis and membrane separation technology, Soc. Sea Water Sci., Japan, pp. 188–196. Mintz, M. S., 1963, Criteria for economic optimization are presented in the form of comparative performance equations for various methods of operation, Ind. Eng. Chem., 55, 19–28. Nagasawa, T., Okonogi, S., Tomita, M., Tamura, Y., Mizota, T., 1973, Demineralization of skim milk by means of electrodialysis with ion permselective membrane, I. Relationship between limiting current density and speciﬁc conductivity of demineralizing solution, Jap. J. Zootech. Sci., 44(8), 426–431. Nagasawa, T., Okonogi, S., Tomita, M., Tamura, Y., Mizota, T., 1974, Demineralization of skim milk by means of electrodialysis with ion selective membrane, II. The effects of linear velocity, temperature and total solid content etc. on the limiting current density, Jap. J. Zootech. Sci., 45(11), 578–584. Okada, K., Tomita, M., Tamura, Y., 1975, Electrodialysis in the treatment of dairy products, Symposium ‘‘Separation processes by membranes, ion-exchange and freezeconcentration in food industry’’, Paris, March 13–14. Sato, T., 1989, Investigation on water disinfection applied ion exchange membrane electrodialysis and production of pyrogen-free water, Thesis, Yokohama National University, Yokohama, Japan.

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Sato, T., Tanaka, T., Suzuki, T., 1984, Disinfection of a colon bacillus by means of ion exchange membrane electrodialysis, J. Electrochem. Jpn., 52, 239–243. Shaffer, L. H., Mintz, M. S., 1966, Electrodialysis, In: Spiegler, K. S. (Ed.), Principles of desalination, Academic Press, New York, London, pp. 200–289. Sugiyama, M., Takatori, Y., Touyama, R., Nakamura, A., Yamauchi, T., Kawate, H., Yamaguchi, A., 1982, On the desalination process of sugar solutions by electrodialysis using neutral membranes, J. Sugar Reﬁning Technology, 30, 26–32. Takahashi, R., 2006, Basic analysis of biological effects of potable alkaline electrodialyzed water at the cellular level, 2005 Alkaline Electrodialyzed Water Symposium, Tokyo, Kitasato University, September 3, 2006. Tanaka, Y., 1987, Concentration of seawater using electrodialysis, In: Kawasaki, J., Kunime, T., Sakai, K., Hakuta, T. (Eds.), Membrane Separation Technology Hand Book, Science Forum, Tokyo, pp. 211–215. Tanaka, Y., 1991, Membrane separation, In: Seno, M., Abe, M., Suzuki, T. (Eds.), Ion Exchange, Kodansya Scientiﬁc Co., Tokyo, pp. 211–227. Tanaka, Y., 1993, Electrodialysis, In: Sakai, K. (Ed.), Theory and Design of Membrane Separation Process, Industrial Publishing & Consulting Inc., Tokyo, pp. 69–107. Tanaka, Y., Ehara, R., Itoi, S., Goto, T., 2003, Ion exchange membrane electrodialytic salt production using brine discharged from a reverse osmosis seawater desalination plant, J. Membr. Sci., 222, 71–86. Tomita, A., 1995, Electrodialyzer, In: Ogata, N. (Ed.), Engineering in Salt Manufacturing, vol. 2, Electrodialysis, Japan Salt Industry Foundation, Tokyo, pp. 85–101. Tomita, M., Tamura, Y., Mizota, T., 1986, Electrodialysis of milk and whey, Industrial Application of Ion Exchange Membranes, vol. 1. Research group of electrodialysis and membrane separation technology, Soc. Sea Water Sci., Japan, pp. 147–158. Tsunoda, S., 1994, Present status and latest trends of deep bed ﬁltration, Bull. Soc. Sea Water Sci., Jpn., 48, 27–37. Urabe, S., Doi, K., 1978, Electrodialyzer, Ind. Water, 239, 24–28. Yamamoto, Y., 1993, Desalination of natural essences by electrodialysis, Industrial application of ion exchange membranes, vol. 2. Research group of electrodialysis and membrane separation technology, Soc. Sea Water Sci., Japan, pp. 181–188. Yawataya, T., 1986, Ion Exchange Membranes for Engineers, Kyoritsu Shuppan Co. Ltd., Tokyo, pp. 94–98.

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Chapter 2

Electrodialysis Reversal 2.1.

OVERVIEW OF TECHNOLOGY

In 1952, Ionics Inc. invented Electrodialysis (ED) and offered a way to desalt brackish water. In 1953, ED became commercially viable when Ionics supplied an oil ﬁeld campsite in Saudi Arabia with their ﬁrst ED system. Many more ED units followed that one. By January 1970, 208 ED units had been installed, including Coalinga, CA (1958), Buckeye, AZ (1962), Port Mansﬁeld, TX (1965), White Sands Missile Range, NM (1969) and many others. For practical purposes, Reverse Osmosis (RO) was commercialized in 1969. Electrodialysis reversal (EDR) and RO competed on many projects as follows (Reahl, 2004). EDR was developed with ED technology as the basis in 1974. The same membranes were used to provide a continuous self-cleaning ED process, which uses periodic reversal of the DC polarity to allow systems to run at higher recovery rates. DC electric ﬁeld was alternatingly reversed to drive salt scale off the membranes before those materials become permanently attached. DC ﬁeld reversal eliminated the need to feed either acid or antiscalant chemicals into the desalination process. Not having to feed chemicals at remote water treatment sites was a major advantage of EDR over RO. In the mid-1980s RO made a dramatic process improvement through the development of new thin-ﬁlm-composite (TFC) membranes. Acid was no longer needed in RO feed water, RO operating pressures were signiﬁcantly reduced, and membranes had more consistent salt rejections over a longer period of time. New families of antiscalant chemicals made it possible to increase RO water recovery. In 1997, Ionics reinvented EDR technology with improved membrane spacers, system design and operating efﬁciency, as will be discussed in the succeeding sections. With a greater ability to remove salts, EDR was applied to preferentially remove selected ionic species from public water supplies, such as nitrates. EDR was sold to reclaim tertiary treated wastewater for irrigation reuse. EDR ﬂow was expanded extensively and it proved to be 25% less costly than MF or RO. Since silica does not affect EDR performance, numerous EDR plants are now producing drinking water from sources with 100 ppm+silica in the feed. Combining EDR with antiscalant addition increases the allowable concentration of these scale forming entities even further. As an electrically driven process, product water quality from EDR can be varied by controlling the voltage input into the membrane stack, and by controlling how many stacks in DOI: 10.1016/S0927-5193(07)12016-7

384 Table 2.1

Ion Exchange Membranes: Fundamentals and Applications

Feed water constituents which limit the process performance

Inﬂuent Feed Water Factor

EDR Limits

RO Limits

Well or surface supply

Flow through system is unaffected by source 15 (5 min SDI) Up to 15 ppm Unlimited to saturation Up to 1 ppm Up to 2 NTU 0.3 ppm 0.1 ppm Up to 1 ppm 40–1001F

Reduced ﬂux on surface water of wastewater 5 or less (15 min SDI) Up to 2–5 ppm Depend on water recovery Zero 0.1–1 NTU 0.3 ppm 0.1 ppm No limit if not mixed with O2 40–1001F

0.5 ppm continuous with spikes to 15–20 ppm+ 2.0–11.0

None, Cl2 will destroy TFC membranes 2.0–12.0

Silt density index TOC Silica Oil and grease Turbidity Iron (Fe2+) Mn2+ H2 S Normal temperature range Free chlorine Feed pH Source: Reahl (2004).

series (or stages) are used. Salt removal rates can be altered to speciﬁcally meet optimum conditions on any project. EDR is not affected by as many feed water constituents as RO, which limit that processes performance. This is illustrated in Table 2.1. Project costs are usually measured in terms of combined capital and longterm operation and maintenance (O&M) costs (cf. Table 2.12). On 800 to 2000 ppm waters the combination of capital (equipment, installation and building required) along with long-term O&M can favor EDR. This is especially true on applications requiring high water recovery. EDR systems operate with up to a 60% total dissolved solids (TDS) reduction per stage, depending on the speciﬁc constituents in the water. EDR is usually most competitive when a one- or two-stage system is used to desalt raw water sources. However, threestage and four-stage EDR systems have also been shown to be more cost effective than RO when certain combinations of feed water constituents are present with the need for high water recovery. EDR is capital competitive or slightly higher in cost compared with RO. Normally, building required will be larger than that for RO. Offsetting this is EDR’s lower O&M cost with reduced (or no chemical) feed, with reduced pretreatment/posttreatment costs, and with reduced long-term membrane replacement costs. On lower TDS waters (less than 1500 ppm), the EDR electrical power consumption can be less than RO. When ‘‘ancillary costs’’ such as raw water pumping, and waste brine disposal are added in, the O&M cost consideration often times outweighs the higher capital costs for EDR.

Electrodialysis Reversal

2.2.

385

SPACER (von Gottberg, 1998)

The ion ﬂux across the membrane is strongly inﬂuenced by the boundary layer formed at the membrane/solution interface. The boundary layer thickness is a function of velocity and ﬂow spacer geometry, and it may be minimized by promoting turbulent ﬂow, and thus increasing the limiting current density (Belfort and Guter, 1972; Chiapello and Bernard, 1993; Zhong et al., 1983). The amount of turbulence promotion is a function of the velocity in the ﬂow spacer – the higher the velocity, the greater the turbulence. The operating velocity in an ED stack is limited by the pressure drop along the ﬂow spacer and through the stack. There is a maximum inlet pressure at which membrane stack should be operated to prevent external leakage. If the pressure drop is too high, then the number of stages that can be utilized in series is limited. Hence, it is desirable to ﬁnd a turbulence promoter that optimizes the performance by maximizing limiting current density and minimizing pressure drop. The type of ﬂow spacer that has had the most commercial success in terms of the total installed capacity of ED/EDR plants is the tortuous path spacer. This spacer is manufactured by using two sheets of low-density polyethylene with die-cut ﬂow channel. The two sheets of polyethylene are glued together to form an under/over ﬂow path that creates turbulence. Since the under/over straps that create the turbulence are fairly infrequent, the amount of turbulence promotion is limited. At higher velocities, however, the turbulence is sufﬁcient to obtain reasonable limiting current densities. The pressure drop per unit length of this design is low, so a long ﬂow path can be used without having excessive pressure drops. By utilizing a long tortuous ﬂow path and operating at velocities in the 20–40 cm s–1 range, this design optimizes turbulence promotion and stack pressure drop. The disadvantage of this approach is that the tortuous design has signiﬁcant membrane area wasted as sealing area. In a typical commercial design, 36% of the membrane area is shadowed by sealed area, so only 64% of the membrane area is usable for desalting. Fig. 2.1 illustrates a tortuous path ﬂow spacer, designated Mark III by the manufacturer. For practical long-term operation of large ED systems, the thickness tolerances of ﬂow spacers are critical. Since a thousand or more spacers are piled on top of one another in an ED stack, even slight variations in component thickness can lead to large variations in the stack heights. The thickness of the sealing area around the ﬂow path must be very close to the thickness of the ﬂow spacer. If the sealing area is thicker than the turbulence promoters, the turbulence promoters do not touch the membrane surface. This can cause laminar ﬂow at the membrane surface, which in turn reduces limiting current density signiﬁcantly. Several manufacturers of ED equipment have employed screen spacers to promote turbulence. In these spacers, woven or nonwoven netting is used in the ﬂow path to create turbulence, and the performance of the screen spacer is found

386

Ion Exchange Membranes: Fundamentals and Applications

Cathode −

1

4

2

3

1

Diagram of a tortuous-path spacer for an electrodialysis stack.

Anode + 1. 2. 3. 4.

Figure 2.1

Anion-selective membrane Dilution stream Concentrating stream Cation-selective membrane Spacer for the diluting compartment Spacer for the concentrating compartment

Tortuous ﬂow path spacer (Mark III) (Lacey and Loeb, 1972).

to be better than that of the tortuous path spacer. Further, in the 1990s, with the development of the spiral-wound RO element, the technology for manufacturing nonwoven netting has improved dramatically. These achievements have become useful to take a new look at screen spacers for EDR systems and urged to develop the following advanced versions of the spacer. At ﬁrst, Ionics manufactured bench scale screen spacers and their performance in terms of limiting current density and pressure drop was measured in the laboratory for a NaCl solution at 701F. Fig. 2.2 shows a graph of limiting current density vs. solution velocity for conventional tortuous path spacers and a screen spacer manufactured with nonwoven netting. For a given velocity, the limiting current density for the screen spacer is about three times that of the tortuous path spacer. The pressure drop per unit length is much greater for the screen spacer than the tortuous path spacer, as shown in Fig. 2.3. Since the frequency of turbulence promoters much higher for the screen spacer than for the tortuous path spacer,

387

Electrodialysis Reversal

(i /C)lim (mA /cm2) / (eq/l )

3000 2500 2000 Screen Spacer 1500 1000 Tortuous Path Spacer

500 0 0

Figure 2.2

5

10

15 20 25 Velocity (cm /s)

30

35

40

(i/C)lim vs. solution velocity (von Gottberg, 1998). 0.18

Pressure drop (psi/cm)

0.16 0.14 0.12

Screen Spacer

0.10 0.08 0.06 0.04

Tortuous Path Space

0.02 0 0.0

10.0

20.0

30.0

40.0

50.0

Velocity (cm /s)

Figure 2.3

Pressure drop per unit length vs. solution velocity (von Gottberg, 1998).

these results are not surprising. To minimize the pressure drop, the optimum velocity for the screen spacer is in the 6–12 cm s1 range, and a short ﬂow path length is selected. The outside dimensions of 1800 4000 for the high performance screen spacer were based on the dimensions of preexisting ion exchange (IE) membrane production lines and the requirement for membranes and spacers to be easy to handle by one person for stack maintenance. A U-shaped ﬂow path was developed to ﬁt the optimum ﬂow path length and width into the 1800 4000 conﬁguration. This spacer design, known as the Mark IV, has about 74% usable area in contrast to 64% for the Mark III spacers (see Fig. 2.4). The screen spacer

388

Ion Exchange Membranes: Fundamentals and Applications

A

B C D

U-shaped ﬂow path spacer (Mark IV) (von Gottberg, 1998).

Power Consumption

Figure 2.4

Tortuous Path Spacer

Screen Spacer

Number of Cell Pairs

Figure 2.5

Power consumption vs. number of cell pairs (von Gottberg, 1998).

thickness is 0.03000 vs. 0.04000 for the conventional tortuous path spacers. The maximum stack height of a Mark III stack was 500 cell pairs. This height is determined by the maximum safe DC voltage that can be applied to a stack and the dimensions of a standard shipping container which the stack can ﬁt. With the new spacer, the maximum stack height is 600 cell pairs. The combination of more usable area per membrane and more cell pairs per stack has led to an increase of 38% usable membrane area in an ED stack. The increase in membrane area per stack combined with the increased current density that can be applied to a stack means that fewer stacks are required to desalt a given volume of water. This leads to capital and building cost savings for the customer. In ED plant design, there is a trade off between power consumption and capital cost. For any particular spacer, the greater the number of cell pairs, the lower the DC power consumption and vice versa (Fig. 2.5). In developing the new spacer, it was important to make sure that capital cost savings from using

389

Electrodialysis Reversal

fewer stacks and cell pairs were not accompanied by increases in power consumption. The use of the thinner spacer means that the electrical resistance of each cell pair is reduced, so that the overall DC power consumption for a given number of cell pairs decreases. Therefore, at constant DC power, fewer cell pairs can be used with the screen spacer, providing savings in capital cost without increase in operating costs. The overall system pressure drop is lower since fewer stages are required, and this in turn reduces pumping power. Use of the new spacer offers signiﬁcant savings in capital costs and can reduce the overall power consumption of an EDR system.

2.3.

WATER RECOVERY

The source water feed to an EDR system is divided into three streams as shown in Fig. 2.6. The largest ﬂow is the dilute feed, which passes through the stacks once and exists as desalted product. The second stream, termed concentrate makeup, is fed to a concentrate stream being re-circulated through the stacks. At the exit from the stacks there is an overﬂow to waste. The third stream is electrode compartment ﬂush water, which on most system is 1% of the dilute ﬂow. Normally, this water is directed to waste after it passes through the stacks. This system enhances the water recovery in the process as follows (Allison, 1993). A small amount of the dilute stream water ﬂow is transferred to the concentrate stream as it passes through the stack. First, water is transferred through the membrane with the passage of ions. This ‘‘water transfer’’ amounts to 0.15–0.45% of the dilute ﬂow per 1000 mg l–1 of salts removed. Internal leakage also occurs between the dilute stream and the concentrate stream which is approximately 0.25–0.50% per stage. The concentrate stream is normally operated about 1 psi lower in pressure than the dilute stream so that this solution leakage will be from the dilute stream to the concentrate stream. Water transfer and cross leakage do not reduce water recovery. These ﬂows are calculated as part of the concentrate makeup ﬂow in the plant design.

Electrode Flush Dilute Feed

Electrode Waste Water Transfer

Cross Leak

Product Off-Spec Product

Concentrate Makeup

Concentrate Blowdown

Concentrate Recycle

Figure 2.6

EDR ﬂow diagram (von Gottberg, 1998).

390

Ion Exchange Membranes: Fundamentals and Applications

The periodic reversal of the DC power polarity interchanges the solutions in the individual spacers. Spacers carrying the dilute ﬂow in negative polarity carry concentrate in the positive polarity. Automatic inlet and outlet diversion valves direct the dilute and concentrate ﬂows to the correct spacers for each polarity. While the concentrate is being ﬂushed out during reversal, poor quality product is produced. This is diverted to waste by a conductivity-controlled automatic valve. By timing the operation of the automatic diversion valves and the DC polarity reversal of each stack to the ﬂow through the system, high conductivity product is produced for only 36 s. This phased polarity reversal occur every 15 to 30 min. The high conductivity or ‘‘off speciﬁcation’’ product from the ‘‘phased reversal’’ represents 2–4% waste. This waste is high TDS concentrate and cannot be recycled to the feed or concentrate makeup. The highest water recovery EDR plant in operation is the 3.76 million gallons per day (mgd) facility operated by the City of Suffolk, VA (cf. Section 2.8.1). The plant has three stages and achieves 94% water recovery. In Table 2.2, a ﬂow summary is shown for one of the three EDR units (Suffolk) broken down to show where the waste is generated. The units have no continuous chemical feeds. A 14.9 gpm concentrate makeup ﬂow is used to control calcium carbonate scaling potential in the concentrate. If the units did not require this controlled concentrate makeup ﬂow, waste could be reduced to 43.1 gpm giving an ultimate recovery capacity of 95.3%. A 5 mgd EDR plant located on Grand Canary Island operates on a 5000–7000 mg l–1 feed water at 85% water recovery. The unit ﬂow summary is shown also in Table 2.2. The controlled concentrate makeup ﬂow is approximately 1/2 of the total waste. The ultimate water recovery capability based on Table 2.2

EDR unit ﬂow summary

Total EDR feed Total EDR product Total water recovery Waste sources Off-spec product Brine makeup ﬂow Brine makeup (from Electrode ﬂush (sent Brine makeup (from Brine makeup (from Total waste Source: Allison (1993).

electrode ﬂush) to waste) cross leak) water transfer)

Suffolk, VA (gpm)

Grand Canary Island (gpm)

926 870.4 94%

409.1 347.7 85%

17.4 14.9 9.3

7.8 27.8

12.5 1.5 55.6

4.1 11.4 10.3 61.4

Electrodialysis Reversal

391

ﬂows of this plant is only 91.8%. The higher TDS increases water transfer and the additional stages increase cross leakage.

2.4.

PREVENTION OF SCALE FORMATION

The water recovery capability of nearly all EDR plants is limited by the potential for salts of limited solubility to precipitate from the concentrate stream as scale. The polarity reversal of EDR alternately exposed membrane surfaces and the water ﬂow paths to concentrate with a tendency to precipitate scale and desalted water which tends to dissolve scale. This allows the process to operate with supersaturated concentrate streams up to speciﬁc limits without chemical additions to prevent scale formation as follows (Allison, 1993). If chemicals are added to the concentrate, higher levels of super-saturation can be achieved. The design limit for CaCO3 without antiscalants is a Langelier Saturation Index (LSI) of +1.8. Actual scale precipitation starts at an LSI near +2.2. This limit is sufﬁciently high that few EDR units need any chemical additions to prevent CaCO3 scaling from high concentrate LSI. Where chemical addition is used, acid or carbon dioxide addition to the concentrate is employed. The design limit for CaSO4 saturation without antiscalant addition is an ion product of 2.25 Ksp (Ksp is ion product speciﬁc limit). The real limit where precipitation starts is near 4 Ksp. Dell City, Texas has operated a 150,000 gpd EDR system since 1975 with the concentrate CaSO4 ion product at 3.5 Ksp without antiscalant addition. The limit cannot be increased by acid or CO2 addition, as pH adjustment does not increase the solubility of CaSO4. The only way to increase water recovery is to use antiscalants. In 1981 and 1982, the EDR limits of sustained operation at high CaSO4 saturation with sodium hexameta phosphate antiscalant addition were employed under an OWRT contract at Roswell, New Mexico. The ﬁnal test in this program was operation of a 50,000 gpd EDR unit with the concentrate CaSO4 ion product at an average of 12.5 Ksp for over 5000 operating hours. It is now known that the threshold point for BaSO4 is an ion product of 100 Ksp when no antiscalants are used. The limit with antiscalant addition is currently unknown. Several plants are operating at a BaSO4 ion product of 150 Ksp and two plants have reached an ion product of 225 Ksp with a polymer antiscalant dosage of 2–5 mg l–1 to the concentrate. SrSO4 scale has not been detected in any EDR plants. CaF2 precipitation has never occurred in an EDR plant. Plants are operating with ion products 500 Ksp and much higher levels have been encountered in two industrial pilot studies with no precipitation. There are no projected limits for saturation levels. Silica in waters below pH 9.5 is essentially nonionic and is not removed or concentrated by EDR. Tests show silica levels are equal in the feed, product

392

Ion Exchange Membranes: Fundamentals and Applications

and brine of operating EDR plants. High water recoveries can be obtained on high silica waters because silica does not limit EDR recovery. 2.5.

ANTI-ORGANIC FOULING (Allison, 2001)

In late 1979 a small 100,000 gpd industrial EDR system was installed in Texas to desalt municipal water prior to IE demineralization for boiler feed. The municipality uses a surface water source. The original styrene divinyl benzene polymer based anion exchange membranes irreversibly fouled and failed after 14 months of use. New acrylic-based polymer anion exchange membranes had been under ﬁeld testing for several years at this time, and improved organic fouling resistance was becoming evident. This was an opportunity to put the new membrane to a severe test. The failed membranes were replaced with the new membranes and were operated for nine years. The new membranes did experience some organic fouling, but it was found the fouling could be fully controlled by circulating a 5% NaCl salt solution through the stacks at about four month intervals. Analytical results of a new anion exchange membrane (acrylic-based resin membrane) sample taken from an industrial plant in the late 1980s are shown in Table 2.3. Samples from the edge gasket area not exposed to the water being treated and the active ﬂow path area are typically analyzed. In as-received condition, it can be seen that the active ﬂow path area had an electrical resistance 20 times higher than the edge area. The procedures for analysis of membranes involve treating the samples in 2 N HCl and 2 N NaCl solutions as steps in the process to obtain the rest of the results. The treatments put the resin in the chloride form, and the resistance is lower than in the typical sulfate form the Table 2.3 fouling

Analysis of electric resistance of an anion exchange membrane with organic

Property

Received resistance (O cm2) Recovered resistance (O cm2) Ion exchange capacity (meq dry g1) Water content (%) Source: Allison (2001).

Acrylic-Based Membrane

Styrene Divinyl Benzene Membrane

Edge Area

Flow Path Area

Edge Area

Flow Path Area

21.9

43.5

25.1

97.0

12.5

14.1

19.1

72.0

2.29 47.0

2.25 47.3

1.55 44.0

0.75 41.6

Electrodialysis Reversal

393

membrane is in when operating. The recovered edge area electrical resistance is 57.1% of the as-received value. This is due to the sample now being in the chloride form. The ﬂow path resistance is only 3.2% of the as-received value and closed to the edge area value. During the salt treatment of this sample, the NaCl solution color changed from clear to about appearance of a cup of black coffee indicating extraction of organic foulants. The IE capacity and percent water content of both areas are nearly the same. The analysis showed the membranes could be cleaned easily. The same analysis procedure results for pre-1981 styrene divinyl benzene polymer based membrane are also shown in Table 2.3. The ﬂow path as-received electrical resistance is high. After the acid and salt solution treatments, the ﬂow path electrical resistance is also still high and the IE capacity is less than one half the edge values. The IE sites are still present in the membrane, but they are occupied by organic anions that inactivate them. Since the organic material is not removed by the salt solution treatment, the inactivation is permanent. The water content is also lower in the ﬂow path. The fouling organic material occupies space in the resin pores and displaces some of the water volume in the membrane. Since the membranes could not be restored with cleaning in this plant, they had to be replaced. There is a theory that the natural organic molecules that cause the irreversible fouling have a benzene ring and an ionic site in their structure. Bonding between benzene ring structures of the organic material and in the IE resin polymer adds to the ionic bonding to the IE sites in the resin. The combined bonding is strong enough to make removal impossible. The acrylic-based membranes have no benzene ring structures in the polymer to provide this extra bonding and therefore can be cleaned with a salt solution. The acrylic anion exchange membranes do have chlorine tolerance, and it is now common practice to maintain a disinfectant level through ED and EDR systems when they are treating biologically active water. Free residual chlorine in the range of 0.1 mg l1 as well as chloramines to 2 mg l1 and chlorine dioxide at low residuals around 0.1 mg l1 are being used on a continuous residual basis.

2.6. COLLOIDAL DEPOSIT FORMATION ON THE MEMBRANE SURFACE AND ITS REMOVAL (Allison, 2001) The driving force for colloidal deposit formation on an RO membrane is the water ﬂow towards and through the membrane. The water ﬂow carries the colloids to the surface where they are blocked and deposited. In an EDR system, species that carry an electrical charge are carried towards the membranes. Species such as dissolved salts and small organic ions with molecular weights below about 200 pass freely through the membrane to the concentrate. Particles in water nearly always have a negative electrical charge. In an ED or EDR

394

Ion Exchange Membranes: Fundamentals and Applications

Positive Polarity

Negative Polarity (-) Cathode

−

−

−

(+) Anode

−

+

+

+

+

CationExchange Membrane

AnionExchange Membrane

Slow

+

Figure 2.7

+

+

+

CationExchange Membrane

AnionExchange Membrane

Slow

(+) Anode

−

−

−

−

(-) Cathode

Colloid deposition and removal forces in EDR (Allison, 2001).

system the applied DC power is the driving force that moves the particles towards the anion exchange membrane where a deposit can form. Fig. 2.7 shows the deposition force and how in EDR the periodic reversal of the applied DC power reverses the driving force for deposition into a driving force for deposit removal. With over 1500 ED and EDR plants around the world, it is inevitable that a few have been operated with feed turbidities over 0.5 NTU. EDR will survive short-term operation at higher turbidities but will foul if operated for extended time over this limit. As with RO systems, severe deposits are very difﬁcult to remove with a chemical solution cleaning. EDR stacks are made to be disassembled for maintenance if needed. It takes two people about 8 h to disassemble, hand clean the components and reassemble a full size ERD stack (cf. Section 1.5.3). This is a job that can be done by unskilled workers. 2.7.

NITRATE AND NITRITE REMOVAL

Nitrate contamination of drinking water is a widespread problem. It has long been known that levels of nitrates exceeding the 10 mg l1 (as N – nitrogen) limit are associated with certain health problems. Although high nitrogen concentrations in drinking water are found mainly in regions of intensive agricultural use, there are source of nitrate contamination other than agricultural. Nitrates and nitrites are removed efﬁciently and economically using EDR as follows (Prato and Parent, 1993). Fertilizer runoff, farm animal wastes, and septic tank discharge all percolate through the soil into groundwater aquifers and ultimately into water supplies. Agricultural sources of nitrates are by far the most common. Regions of the country where corn is grown experience peak levels of nitrates in groundwater from heavy fertilization. Other sources of nitrate and nitrite contamination are natural and industrial in origin. Standards for maximum levels of nitrates in drinking water have been established by the Federal Government in

395

Electrodialysis Reversal

1975 with passage of the Safe Drinking Water Act (SDWA). As of the May 1990 SDWA regulations, some major allowable inorganic contaminants are as follows:

Contaminant

MCL or SMCL (mg l1)

Chloride Fluoride Nitrate (as N) (as NO3) Nitrite (as N) (as NO2) TDS

250 2 10 45 1 3.3 500

Maximum contaminant level or secondary maximum contaminant level.

Prior to the SDWA, there was no requirement or practical, affordable method to remove nitrates from drinking water. Since that time a number of demineralization technologies have been given a best available technology (BAT) status for nitrate removal. These BAT processes include EDR, RO and IE. Effective removal constitutes reducing the level of nitrates to the maximum contaminant level (MCL). The EDR process can effectively reduce nitrate concentrations to the MCL or lower in public water supplies. The reduction in nitrite concentration is directly related to the design demineralization rate of the EDR system. Operating data illustrate the practicality of the EDR demineralization process for removing nitrates and nitrites as well as TDS. The examples represent a variety of EDR plants and include three public drinking water installations and one industrial application. Table 2.4 presents operating data on all of the various EDR units. All of the waters contain high levels of nitrate, and the industrial feed water contains exceptionally high levels of nitrite.

2.8. 2.8.1

PRACTICE

EDR Operation for Production of Drinking Water The City of Suffolk (population approximately 55,000) is located in Southeast Virginia, USA, and an area that experienced rapid growth over the past two decades. In the late 1980s the City evaluated a number of source alternatives for expanding its water supply to meet the increasing demand for

396

Table 2.4

EDR plant data, Bermuda, Delaware, Industrial, Italian

Plant Speciﬁcations Model

Delaware

Industrial

Italian

2 AquamiteXX

Aquamite X

Aquamite XX

100,000 gpd

300,000 gpd

80 TDS 534 NO3 128 NO3 21 TDS 1753 NO3 655 NO3 64 3 TDS 66 NO3 80.4 NO3 67.2

90 TDS 474 NO3 37

Production

300,000 gpd each 600,000 gpd total

Recovery (%) Product purity (ppm)

90 TDS 278 NO3 8.8

Aquamite XX Aquamite X 300,000 gpd 100,000 gpd 400,000 gpd total 90 TDS 11 NO3 4.5

Raw water (ppm)

TDS 1614 NO3 66

TDS 114 NO3 61

Desalting stages Percent removal (%)

3 TDS 81 NO3 86.7

3 TDS 88 NO3 92.6

TDS 1012 NO3 120 2 TDS 53 NO3 69.2

Water Quality Constituent

Feed (mg l1)

Product (mg l1)

Feed (mg l1)

Product (mg l1)

Feed (mg l1)

Product (mg l1)

Feed (mg l1)

Product (mg l1)

Sodium Calcium Magnesium Potassium Chloride Bicarbonate Sulfate Nitrate Nitrite pH TDS

349 138 40 19 656 259 85 66

72 13 4 2 92 75 10 8.8

12 9 8

1.6 0.5 0.6

24 141 34

14 28 8

15 9

1.2 2.4

61

4.5

7.0 278

6.2 114

5.4 11

11 235 23 128 21 7.0 534

49 63 13 1.7 44 240 25 37

7.9 1614

35 514 113 655 64 7.3 1753

73 127 34 4 120 449 85 120 7.3 1012

7.1 474

Source: Prato and Parent (1993).

Ion Exchange Membranes: Fundamentals and Applications

Bermuda

397

Electrodialysis Reversal

Table 2.5

Feed water quality, Suffolk

Parameter

Concentration (mg l1)

Bicarbonate Calcium Carbonate Chloride Fluoride Magnesium pH Phosphate Potassium Sodium Sulfate TDS

453 2.27 1.2 21.1 4.57 0.931 8.15 2.79 5.05 191 7.04 689

Source: Werner and von Gottberg (1998).

water. The well water has moderate levels (689 mg l1). However, the ﬂuoride level of 4.6 mg l1 is higher than the primary MCL of 4.0 mg l1. Also, the sodium concentration of 191 mg l1 exceeds Suffolk’s water quality guidelines of 50 mg l1 for potable water. Hence, a membrane desalination treatment process was required to raise the well water quality to meet drinking water standard. A typical feed water analysis is shown in Table 2.5. Ionics succeeded in the treatment of this feeding water using EDR as follows (Werner and von Gottberg, 1998). Based on the results of a feasibility study, RO and EDR were identiﬁed as the most appropriate technologies to reduce the levels of ﬂuoride and sodium, and pilot testing was undertaken in 1987 to evaluate the technologies. EDR was eventually selected for full-scale application in Suffolk because it would result in higher water recovery rates and lower operational costs (Thompson et al., 1991). Water recovery was important for Suffolk because concentrate disposal is a major issue. Since EDR could produce 94% water recovery compared to 85% water recovery for RO, the volume of concentrate discharge was lower for EDR. Fig. 2.8 shows a typical ED membrane stack. EDR is an automatic selfcleaning version of ED in which the polarity of the DC voltage is reversed two to four times per hour (Siwak, 1993). A 3.76 mgd EDR facility started operation at Suffolk in August of 1990. Since its commissioning, the plant has produced over ﬁve billion gallons of potable water. The plant has three separate units (Ionics Aquamite 120’s), each of which produces 1.25 mgd. Each unit contains eight parallel lines of membrane stacks, and each line has stages of stacks in series. Operating lines in parallel increases the production capacity of the unit and operating stacks in series increases the salt removal capacity of the plant. Three stages were required to reduce the ﬂuoride level to 1.4 mg l1.

398

Ion Exchange Membranes: Fundamentals and Applications

Feed Inlet Concentrate Inlet Electrode Feed

(-) Cathode

Electrode Waste Top End Plate Cation Transfer Membrane Demineralized Flow Spacer Anion Transfer Membrane Concentrate Flow Spacer

(+) Anode

Electrode Feed

Figure 2.8

Bottom End Plate Electrode Waste Product Outlet Concentrate Outlet

Electrodialysis membrane stack (Werner and von Gottberg, 1998).

Suffolk needed a membrane process that could operate at super-saturated levels of calcium ﬂuoride because high recovery was important to minimize concentrate disposal. Even though the concentration of calcium in the feed is low, the ﬂuoride concentration is quite high, and at 94% water recovery the concentrate stream is super-saturated with calcium ﬂuoride. Reversing the DC polarity switches the dilute and concentrate streams every 30 min. Any calcium ﬂuoride that has started to precipitate in the concentrate stream is dissolved by the dilute stream. Operation in this unsteady state mode can continue up to levels of calcium ﬂuoride saturation of more than 500 Ksp (Allison, 1993). With no change in feed water quality, EDR product water quality has remained constant. Table 2.6 shows typical values for several major chemical parameters. This product water is then blended with the product from the conventional surface water treatment plant prior to its delivery into the City’s distribution system. Fluoride, which is purposely kept at a level exceeding the recommended range of 0.8–1.0 mg l–1 to compensate for the lack of ﬂuoride in surface water supplies, eliminates the need to add more ﬂuoride to the ﬁnal blended product.

399

Electrodialysis Reversal

Table 2.6

EDR product water quality, Suffolk

Parameter

Concentration

Chloride Conductivity Fluoride pH Sodium TDS

7.3 mg l1 280 m mho 1.43 mg l1 7.3 6.1 mg l1 117 mg l1

Source: Werner and von Gottberg (1998). Table 2.7

Operation and maintenance costs, Suffolk

Cost Category

Cost ($/1000 gal)

Fixed Professional services Chemicals Utilities ($0.05/kWh) Maintenance EDR stock replacement Total

0.72 0.06 0.02 0.21 0.17 0.23 1.41

Note: Production in 1997: 827,339,440 gal. Source: Werner and von Gottberg (1998).

Table 2.7 represents recent cost data related to operation of the EDR plant. Fixed costs are associated with such items as wages and salaries, vehicle cost, telephone and other item that apply equally to both treatment plants. Professional services represent cost associated with service obtained from outside the Department such as sludge removal, laboratory testing and other items that apply to each of the plants on an individual basis. EDR stack replacement ﬁgures represent costs associated with replacement of stack membranes, spacers and electrodes. Electrodes are considered a consumable item while the membranes and spacers have a theoretical life expectancy. Costs not represented here are treatment plant replacement costs, and depreciation or debt service on the original plants. 2.8.2

EDR, NF and RO at a Brackish Water Reclamation In Port Hueneme, California, a new state-of-art desalination facility uses three brackish water desalination technologies: RO, nanoﬁltration (NF) and EDR, operated side-by-side to produce over 3 mgd of high-quality drinking water. The Brackish Water Reclamation Demonstration Facility (BWRDF) is the cornerstone of the Port Hueneme Water Agency’s (PHWA) Water Quality Improvement Program. In addition to providing desalted water for local use, the BWRDF also serves as a full-scale research and demonstration facility.

400

Ion Exchange Membranes: Fundamentals and Applications

It is usually a difﬁcult task to compare the long-term performance and operating costs of three technologies due to variables in source water quality, plant capacities, labor, power and chemical costs. Operating three full-scale desalination technologies in parallel at the same site has made direct comparison possible. During the course of the plant’s operation, the PHWA will collect data on long-term cost and performance characteristics of the three-membrane systems. This will provide a realistic comparison of the desalination technologies that can then be utilized by water purveyors across the country to help determine which technology best suits their speciﬁc needs. The PHWA’s Water Quality Improvement Program was implemented over a six-year period starting in 1993. Design of the BWRDF was completed in late 1996 and facility construction was completed in late 1998. During the period of the BWRDF construction, the PHWA also constructed several major pipelines to deliver raw and treated surface water to the facility and to deliver treated and blended water to the customers. The BWRDF has been in continuous operation since January 1999. Because the BWRDF also serves as a full-scale brackish membrane research and demonstration facility, the United States Bureau of Reclamation (USBR) funded approximately 25% of the cost of the facility. The demonstration research was proceeded using the facility as follows (Passanisi and Reynolds, 2000). The three-membrane treatment process, RO, NF and EDR operate sideby-side to produce a total of 3 mgd of treated and blended water, as shown in Table 2.8. The source water for the BWRDF is chlorinated groundwater from inland, upper aquifer well that are under the inﬂuence of surface water and operated by the United Water Conservation District (UWCD). These wells are recharged with surface water from the Santa Clara River through spreading basins. Typical source water characteristics are presented in Table 2.9. The RO system is a two-stage process with 14 ﬁrst stage vessels and seven second stage vessels, each with six elements per vessel. The concentrated reject stream from the ﬁrst stage membranes is the feed water to the second stage membranes. The RO membrane elements are TFC, Filmtec BW40LE-440 elements. The product recovery for the RO system, deﬁned as the product water out of the system divided by the source water entering the system, is Table 2.8

Plant water ﬂow rates

Stream

Flow Rate (mgd)

Raw Reject Bypass Product Total treated

3.843 0.780 0.648 2.415 3.063

Source: Passanisi and Reynolds (2000).

Electrodialysis Reversal

Table 2.9

401

Typical raw water parameters

Parameter Conductivity pH ORP Cl2 residual Ammonia SDI Temperature Turbidity

Measurement 1385 mS cm1 7.4 o 400 mV 1.6 ppm free 0 ppm o 0.5 641F 0.02 NTU

Source: Passanisi and Reynolds (2000).

approximately 75%. The RO pressure required to desalt source water of approximately 1000 mg l1 TDS is about 160 psi. The RO product water has a TDS of about 15 mg l1. The NF system is a two-stage process with 15 ﬁrst stage vessels and seven second stage vessels, each with six elements per vessel. The concentrated reject stream from the ﬁrst stage membranes is the feed water to the second stage membranes. The NF membrane elements are TFC, Filmtec NF90-400 elements. The product recovery for the NF system is approximately 73%. NF pressure required to desalt source water of approximately 1000 mg l1 TDS is about 140 psi. The NF product water has a TDS of about 20 mg l1. The EDR system is an Ionics EDR 2020 with ﬁve parallel lines of three stages of Mark IV membrane stacks (cf. Section 2.2). Each membrane stack contains 600 cell pairs of IE membranes and ﬂow spacers. The product recovery for the EDR system is approximately 85% (some source water is added to the reject water loop to keep the dissolved ion concentrations low enough to prevent mineral scale formation). The EDR system, unlike the RO and NF systems, uses no ﬁltered raw water to blend with the product water. Operating costs characteristics of the three systems were monitored over the ﬁrst year of operation, from February 1999 to January 2000. EDR, RO and NF can be fairly compared using this data as follows (Passanisi and Reynolds, 2000). (a) Water quality and plant ﬂow rates The average TDS of the raw water feed to the plant is 1000 mg l1. The system is designed to produce water of 370 mg l1 TDS and 150 mg l1 of hardness, which matches the water quality of the state water imported from the Calleguas Municipal Water District facility. Table 2.10 gives the average water analysis for the raw water and ﬁnal blended product. It also shows the product and reject quality from the three-membrane system. Representative plant ﬂows are shown in Table 2.11. (b) Labor Total manpower cost was $168,000, which includes two operators for 9 h/ day at productive hourly rate of $32/h. Labor was fairly evenly split between the

402 Table 2.10

Ion Exchange Membranes: Fundamentals and Applications

Membrane system water quality

Ion

Raw Water

Final Blend

Product

Reject

EDR

NF

RO

EDR

NF

RO

Calcium (ppm) Magnesium (ppm) Sodium (ppm) Potassium (ppm) Alkalinity (ppm) Bicarbonate (ppm) Sulfate (ppm) Chloride (ppm) Nitrate (ppm) pH Conductivity (ms cm1) TDS (ppm) Hardness Langelier index Iron (mg l1)

140 52 94 5 220 270 480 56 20 7.2 1390

46 16 53 2 123 150 138 25 8 8.1 595

27 11 67 3 148 178 69 29 8 7.2 533

ND ND 4 ND 8 15 2 2 4 6.0 32

ND ND 3 ND 5 13 2 1 2 5.8 23

951 341 237 19 553 670 3200 239 70 7.2 5725

518 184 310 18 713 868 1725 185 52 7.6 4225

515 193 318 18 740 905 1750 185 56 7.6 4350

1000 560 0.2 ND-300

370 179 0.2 38

320 114 –0.6 ND

20 ND ND ND

15 ND ND ND

o 0.5

NA

NA

NA

NA

3575 2065 1.7 ND263 2.3

3675 2063 1.6 ND-83

SDI

5825 3803 1.3 ND490 NA

2–4.5

Source: Passanisi and Reynolds (2000). Table 2.11

Plant ﬂow rates

Technology

Raw (gpm)

Product (gpm)

Reject (gpm)

Bypass (gpm)

Blended Product (gpm)

EDR NF RO

732 726 683

694 534 506

88 178 167

0 160 188

694 694 694

Source: Passanisi and Reynolds (2000).

technologies, with 16% for EDR, 15% for RO, 16% for NF and 53% for treatment plant operations including general and preventative maintenance, laboratory analyses and reports. Labor related to the EDR system included bi-weekly wash-downs and stack probing. Cleaning in places (CIPs) were performed every 1000 h of runtime. Daily silt density indexes1 (SDIs) on the NF and RO systems, as well as CIPs every 2–3 weeks due to particulate and biofouling, were the major labor requirements for these systems. (c) Chemical consumption The daily cost for EDR chemicals was $30.87, which included hydrochloric acid, antiscalant (Argo AS120) and sodium bisulﬁte. The daily chemical cost for NF was $34.89. This included antiscalant (Argo AS120, Permacare 191

403

Electrodialysis Reversal

Table 2.12

Annual O & M cost comparison ($/kga)

Process

Labor

CIP Chemicals

Pretreatment Chemicals

Power

Total

EDR RO NF Overalla

0.13 0.14 0.14 0.14

0.01 0.01 0.04 0.015

0.03 0.03 0.04 0.035

0.09 0.12 0.1 0.11

0.23 0.27 0.29 0.30a

Source: Passanisi and Reynolds (2000). a Costs based on the actual annual water production ﬁgures.

and Argo AF200) sodium bisulﬁte. Cost for RO was $31.06, including antiscalant (Argo AF200) and sodium bisulﬁte. Cleaning chemical costs were $1302 for EDR, $12,635 for NF and $841 for RO. The NF chemical costs are highest because proprietary cleaners were used for CIPs related to particulate and biofouling, and the cost for NF antiscalant pretreatment is about double per gallon in comparison to RO. (d) Power consumption Power consumption was 1275 kWh/day for EDR, 1460 kWh/day for NF and 1690 kWh/day for RO. Power cost is $0.069/kWh. The variable frequency drive (VFD) pumps2 on the EDR system helped to save on the power consumption. Considerable energy saving can be realized if the NF and RO pressurizing pumps were converted to VFD operation. The current RO and NF systems require an oriﬁce plate and motorized valve to control inlet pressure and ﬂow. If VFDs were used on the NF and RO, the power reduction is estimated to be 40%. (e) Downtime The total downtime for the EDR was 236 h for the year for CIPs, stack probing, stack-wash downs and valve maintenance. The downtime for RO was 600 h and for NF was 530 h. This included moving membrane elements, CIPs and valve repair. Therefore, EDR had the largest production for the year at 342 million gallons (mg), followed by NF with 239 mg and RO with 224 mg. (f) Annual operating costs Table 2.12 summarizes the costs per thousand gallons of water produced ($/kgal) facility. NOTES 1. The values indicating the quantity of substances suspending in a feeding solution. 2. The pump operating with variable frequency.

REFERENCES Allison, R. P., 1993, High water recovery with electrodialysis reversal, Proceedings of 1993 AWWA Membrane Conference, Baltimore, Maryland, USA, August 1–4.

404

Ion Exchange Membranes: Fundamentals and Applications

Allison, R. P., 2001, Electrodialysis treatment of surface and waste water, Ionics Technical Paper, Reprint from Proceedings of 2001 AWWA Annual Conference. Belfort, G., Guter, G. A., 1972, An experimental study of electrodialysis hydrodynamics, Desalination, 10, 221–262. Chiapello, J. M., Bernard, M., 1993, Improved spacer design and cost reduction in an electrodialysis system, J. Membr. Sci., 80, 251–256. Lacy, R. E., Loeb, S., (eds), 1972, Industrial Processing with Membranes, p. 348, WileyInterscience, N.Y. Passanisi, J., Reynolds, T. K., 2000, EDR, NF and RO at a brackish water reclamation facility, Proceedings of 2000 AWWA Annual Conference. Prato, T., Parent, R. G., 1993, Nitrate and nitrite removal from municipal drinking water supplies with electrodialysis reversal, Proceedings of 1993 AWWA Membrane Conference, Baltimore, Maryland, USA, August 1–4. Reahl, E. R., 2004, Half a century of desalination with electrodialysis, Ionics Technical Paper. Siwak, L. R., 1993, Here’s how electrodialysis reverse and why EDR works, International Desalination & Water Reuse Quarterly, Vol. 2/4. Thompson, M. A., Robinson, Jr., M. P., 1991, Suffolk introduce EDR to Virginia, Proceedings, American Water Works Association Membrane Conference, Orlando, FL. von Gottberg, A., 1998, New high-performance spacers in electrodialysis reversal (EDR) systems, Proceedings of 1998 AWWA Annual Conference, Dallas, Texas, USA, June 21–25. Werner, T. E., von Gottberg, A. J. M., 1998, Five billion gallons later–Operating experience at City of Suffolk EDR plant, the American Desalting Association 1998 North American Biennial Conference and Exposition, August 2–6. Zhong, K. W., Zhang, W. R., Hu, Z. Y., Li, H. C., 1983, Effect of characterization of spacer in electrodialysis cells on mass transfer, Desalination, 46, 243–252.

Chapter 3

Bipolar Membrane Electrodialysis 3.1.

OVERVIEW OF TECHNOLOGY

The bipolar membrane is a layered membrane constructed so that one surface is a cation exchange layer, while the opposite surface is an anion exchange layer. The water splitting behavior of the bipolar membrane was studied at ﬁrst by Frilette (1956) using the multichamber cell integrated with Permutit 1373 cation/1374 anion exchange membranes with their bipolar membranes in a NaCl solution (Fig. 3.1). In this experiment, after an electric current was passed, the individual chambers were drained. A series of the experiments with chambers ﬁlled with 0.2 M NaCl at various current densities i is summarized in Table 3.1. At low current densities (Expt. no. 1), the initial low voltage rose rapidly and attained the voltage E within less than half a minute, which is presumably the time required for the membrane to polarize. At higher current densities (Expts. no. 2–4), polarization appeared faster accompanying the increase of coulomb efﬁciency for H+ ion transfer caused by the water splitting in the bipolar membranes. Expt. no. 5 illustrates the apparent loss in coulomb efﬁciency when the conversion of salt to acid is increased threefold due to the loss of H+ ions by competitive electromigration with Na+ ions across the cation exchange membranes during increased operation time. Expt. no. 6 shows the data obtained at Cathode

BP H+

OH−

C

BP

OH−

H+

C

OH−

Na+

HOH

NaOH

BP H+

Na+

HCl

NaOH

C

BP

OH−

H+

Anode

OH−

Na+

HCl

NaOH

Cl2

HCl

HClO + Cl−

1

2

3

4

BP: Bipolar membrane

Figure 3.1

5

6

Multichamber salt-hydrolyzing cell (Frilette, 1956).

DOI: 10.1016/S0927-5193(07)12017-9

7

C: Cation exchange membrane

8

406

Table 3.1 Expt. No.

E (V)a

9.8 21.6 33.3 55.3 51.6 18.7

Current Density i (A cm2 102)

Operation Time (min)

Approx. Conc.b H+, OH (eq dm3)

3.8 7.5 15.2 30.2 30.2 30.2

10 5 5 2.5 12.5 12.5

0.006 0.008 0.02 0.02 0.06 0.003

Source: Frilette (1956). a Applied e.m.f. in steady state, less 2.7 V for terminal electrodes. b Determined from titration of solutions collected from chambers, 2, 4, 6 and 3, 5, 7. c Electrodes reversed.

Coulomb Efﬁciency for Proton Transfer (%) From OH Chambers 2, 4, 6 34 48 55 63 34 o2

From H+ Chambers 3, 5, 7 31 46 52 60 30 o2

From H+ Chamber 1 50 73 87 80 80 o5

Ion Exchange Membranes: Fundamentals and Applications

1 2 3 4 5 6c

Proton-transport efﬁciency

407

Bipolar Membrane Electrodialysis

electrodes reversed indicating ZH decrease due to the extinction of the water splitting reaction. Electrodialytic water splitting is an energy-efﬁcient means for converting the salts to their acids and bases. The technology uses ion exchange membranes to concentrate the ions in solution and is driven by an electrical potential and in this respect is closely related to electrodialytic concentration. The water splitting reaction is generated in the system in Fig. 3.2, exhibiting three chambers including acid, salt and base bounded by the bipolar, anion and cation exchange membranes. The salt MX, e.g. Na2SO4, is fed to the chamber between the cation and anion exchange membranes. When an electric current is passed across the move across the monopolar electrodes, the cations Na+ and anions SO2 4 membranes and combine with the OH and H+ ions generated at the bipolar membrane to form the base and acid. Fig. 3.3 illustrates the construction and operation of the bipolar membrane working in Fig. 3.2. The membrane is a composite one and consists of three parts, a cation exchange layer, an anion exchange layer and the interface between the two layers. When a direct current is passed across the bipolar membrane toward the cathode, electrical conduction is achieved by the transport of H+ and OH ions, which are obtained from the dissociation of water. To achieve a highly energy-efﬁcient operation, the membrane should have (a) good water permeability to provide water from the external solutions to the interface and (b) a very thin interface between anion Depleted MX soln. HX soln. BP

A

Acid Anode

OH−

MOH soln. C

BP

Salt

Base

H+

OH− X−

H2O

M+

MX soln.

H 2O

BP: Bipolar membrane C: Cation exchange membrane A: Anion exchange membrane

Figure 3.2

Three-compartment cell (Mani, 1991).

H+

Cathode

408

Ion Exchange Membranes: Fundamentals and Applications

A

C

H2O Anode

Cathode H

H+

+

+ OH−

OH−

A: Anion exchange layer C: Cation exchange layer

Figure 3.3

Bipolar membrane construction and operation (Mani, 1991).

and cation exchange layers to allow efﬁcient transport of H+ and OH ions (low electric resistance) (Mani, 1991). The water splitting process is electrodialytic in nature because the process merely involves changing the concentration of ions that are already present in a solution. The theoretical energy for concentrating H+ and OH ions from their concentration in the interface of the bipolar membrane (approximately 107 M at 251C) to the acid and base concentrations at the outer surface of the membrane is expressed by the free energy change DG in going from the interior of the membrane to the outside: DG ¼ nFE ¼ RT ln

aiH aiOH aoH aoOH

(3.1)

where a is the activity of the H+ and OH ions, superscripts i and o refer to the interface and the outer surfaces of the membrane, respectively, F is the Faraday constant, 96,500 C eq1, E is the reversible electromotive force (V), R is the gas constant, n represents the number of eq mole1 of reactant and T is the absolute temperature. For generating 1 N ideal product solution, Eq. (3.1) reduces to (since n ¼ 1) DG ¼ FE ¼ RT lnðaiH aiOH Þ or E ¼

RT ln K W F

(3.2)

where KW is the dissociation constant of water. To overcome this potential, a positive potential E0 ¼ E must be applied across the membrane. Using the data on free energy for dissociation of water DG ¼ 0.0222 kWh ¼ 2.22 3600 V A s (International Critical Tables, 1930), one can calculate the theoretical potential for generating acid and base for an ideal

409

Bipolar Membrane Electrodialysis

1.0

Potential Drop (V)

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

0 0

20

40

1 60

Current Density

Figure 3.4

2 80

3 100

(mA/cm2)

Potential drop across a bipolar membrane (Mani, 1991).

(i.e. perfectly permselective) bipolar membrane as E0 ¼ DG/F ¼ 2.22 3600/ 96,500 ¼ 0.828 V at 251C. Fig. 3.4 shows the actual potential drop behavior of a bipolar membrane in Aquatech Systems commercialized by the Aquatech Systems division of Allied-Signal Inc. In the commercially interesting range of current density, 50–150 mA cm2, the membrane has a potential drop E of 0.9–1.1 V in a 0.5 M Na2SO4 solution being slightly higher than E0 (Mani, 1991). The difference between E and E0 is caused by the electric resistance of the cationic and anionic layers and the resistance of the interface. 3.2.

PREPARATION OF BIPOLAR MEMBRANES

Bipolar membranes must be able to split water into protons and hydroxyl ions at a very fast rate. They are prepared using the following techniques (Wilhelm, 2000).

The lamination by pressure at room temperature or at elevated temperature of solid cation or anion exchange resin sheets, one of which contains the catalytic active component. The lamination by pressure at room temperature or at elevated temperature of solid cation or anion exchange resin sheets with an intermediate layer containing the catalytic active material.

410

Ion Exchange Membranes: Fundamentals and Applications

Casting a ﬁlm from a solution containing an anion exchange resin with the catalytic active component on a solid sheet of the cation exchange resin. Casting a ﬁlm from a solution containing a cation exchange resin with the catalytic active component on a solid sheet of the anion exchange resin. Coextrusion of a cation and anion exchange resin, one of which is containing the catalytically active component.

Today, most bipolar membranes are composed of a three-layered structure, i.e. a cation exchange layer, an anion exchange layer and an intermediate layer containing a weak acid or base catalyst. This intermediate layer is a transition region between the two ion exchange membranes where the water dissociation takes place. To have the required water dissociation capacity it must contain the appropriate concentration of catalytic components. Weakly dissociated ionic groups such as tertiary amines fulﬁll the requirements for catalytic components. Further, certain heavy metal ion complexes such as chromium (III)- or iron (III)-hydroxides having extremely low solubility constant provide the required catalytic water dissociation effect for a long-term period. However, their speciﬁc electrical resistance is relatively high. To minimize the electrical area resistance, the thickness of the interface or transition region between the oppositely charged layers should be as thin as possible. The most commonly used catalytic components in bipolar membranes are listed in Table 3.2 (Strathmann, 2004). Here we will glance over several instances for preparing the bipolar membranes. 3.2.1

Instance 1 Bauer et al. (1988) prepared the monosheet bipolar membrane using the following steps. (a) Preparation of the Cation Selective Layer. A total of 1–1.5 meq g1 cation exchange dry resins consisting of cross-linked sulfonated divinylbenzenestyrene copolymer was dispersed in a 20% (w/w) solution of polyvinylidene Table 3.2 Component used as catalytic material for the preparation of bipolar membranes Material

Form of Application

Cr(OH)3

As salt in the cation exchange layer or the interface As salt in the cation exchange layer or the interface Bond to the matrix of the anion exchange membrane Bond to the matrix of the cation exchange membrane

Fe(OH)3 -NR2 R-PO3H

Source: Strathmann (2004), p.111.

pKa Value

Reference Simons, 1993 Hanada et al., 1991

9

Bauer et al., 1988

7

Shel’deshov et al., 1986

Bipolar Membrane Electrodialysis

411

ﬂuoride in dimethylformamide (DMF). The solution was cast on a glass plate as a 0.4 mm thick ﬁlm and the solvent evaporated at 1251C resulting in a 35 mm thick ﬁlm. (b) Preparation of the Anion Selective Layer. The anion selective layer was prepared by dispersing 21–32% (w/w) chloromethylated polystyrene in a solution of 20% (w/w) of polyvinylidene ﬂuoride in DMF. Amination was performed by adding 1.0–1.5 meq amine in 2 g dimethyl sulfoxide. Here, for the amination, the following rather large numbers of different amines were used, and to obtain cross-linking of the polymer, diamines were used. (1) N,N0 -dimethylpiperazine, (2) bis(dimethylamino)methane, (3) 1,2-bis(dimethylamino)ethane, (4) 1,3-bis (dimethylamino)propane, (5) 1,4-bis(dimethylamino)butane. The solution was cast as a 0.3 mm thick ﬁlm on a glass plate. By evaporating the solvent at 125 1C, a 30mm thick anion exchange layer was obtained. (c) Preparation of the bipolar membrane. The monosheet bipolar membranes were prepared by casting a cation selective layer on top of an anion exchange layer. (d) Performance of the bipolar membrane. Bipolar membranes, prepared by casting a cation selective layer on an anion selective membrane consisting of chloromethylated polystyrene cross-linked with 1,4-bis(dimethylamino)butane, showed good water splitting capabilities at low potential drop and high current efﬁciencies due to their relatively low electrical resistance and high ion selectivity. For the production of concentrated acids and bases, however, the chemical stability, particularly under alkaline conditions, was not yet satisfactory. 3.2.2

Instance 2 Xu et al. (2006) prepared the bipolar membrane from poly(2,6-dimethyl1,4-phenylene dioxide) (PPO) as follows: (a) Preparation of the anion exchange layer. The PPO base membranes were bromomethylated at ﬁrst, then the base membranes were functionalized in a 1 M methyl amine (MA), dimethyl amine (DMA) or trimethyl amine (TMA) solution for 48 h at 251C to obtain the anion exchange layer. The possible reactions and the structure of anion exchange layers are shown in Fig. 3.5. (b) Preparation of the bipolar membrane. The above anion exchange layers were cut into the square of 5 cm 5 cm and washed repetitively with 1.0 M NaOH and 1.0 M HCl solutions for more than two times, and then equilibrated with 1 M NaCl solution to be transformed into Cl form, washed with distilled water and dried in use. Then cation exchange polyelectrolyte solution was prepared by dissolving 1 g commercial sulfonated PPO solution in 4 ml DMF was coated on the anion exchange layers to form bipolar membranes, which were then placed in the air for half an hour, and in the oven for 2 h at 451C. (c) Performance of the bipolar membrane. Fig. 3.6 shows the current– voltage curves across bipolar membranes prepared from anion exchange layers with secondary amine groups, tertiary amine groups and quaternary ammonium

412

Ion Exchange Membranes: Fundamentals and Applications

-C6H2(CH3)2-O- + (1/2)Br2 PPO

-C6H2(CH3)(CH2Br)-OBrominated PPO

+ NH2CH3

-C6H2(CH)3(CH2NHCH3)-OSecondary ammine group

Methyl amine (MA) + NH(CH3)2

-C6H2(CH3)CH2N(CH3)2-OTertiary amine group

Dimethyl amine (DMA) + N(CH3)3

-C6H2(CH3)CH2N+(CH3)3Br−-OQuaternary ammonium group

Trimethyl amine (TMA)

Figure 3.5

Bromination and amination to obtain anion exchange layers (Xu et al., 2006). 12 10

Voltage (V)

8

6 4 2

0 0

25

50

75

100

125

Current Density (mA/cm2) : Secondary amine groups from MA : Tertiary amine groups from DMA : Quaternary ammonium groups from TMA

Figure 3.6

Current-voltage curves across bipolar membranes (Xu et al., 2006).

groups converted from MA, DMA and TMA, respectively, as shown in Fig. 3.5. At a given voltage, the bipolar membrane with quaternary ammonium (trimethyl ammonium) groups shows larger current density as compared to secondary and tertiary amine groups. It is accordingly estimated that stronger

Bipolar Membrane Electrodialysis

413

water dissociation occurs in the quaternary ammonium type membrane than in the secondary and tertiary amine type membranes. It is observed in this study that the quaternary ammonium layer has larger water content and smaller electric resistance. So, in this research the phenomenon is explained as that adequate water is provided to the membrane junction when water dissociation commences. While for the other two membranes, it is explained that the lower water content in the anion exchange layer increases the electric resistance of the layer and limits the inﬂux of water to compensate the dissociated water. However, inspecting the experimental results of the water dissociation at the monopolar anion exchange membranes (cf. Section 8.1, Fig. 8.2; Section 8.8.1, Table 8.3, in Fundamentals), the accelerated water dissociation reaction at the quaternary ammonium type membrane was attributed to the auto-catalytic reaction of the quaternary ammonium group itself. 3.2.3

Instance 3 Hanada et al. (1991, 1993, 1996) (Tokuyama Inc.) prepared the bipolar membranes having cation exchange groups exchanged with heavy metallic ions at the interface between a cation exchange layer and an anion exchange layer. (a) Preparation of the Bipolar Membrane. The surface of a Neocepta CM-1 cation exchange membrane was sandpapered to make the surface uneven, then the membrane was immersed in a 251C aqueous 2 wt. % FeCl2 solution for 1 h, washed with ion exchanged pure water sufﬁciently and dried at room temperature. Iron content of the membrane was measured as 98% of its ion exchange capacity. Polysulfone was chloromethylated, quaternarized with TMA and obtained aminated polysulfonic acid (ion exchange capacity: 0.92 meq g1), which was then dissolved into a methanol–chloroform mixed solution (volume ratio, 1:1, 15 wt. %). Next, the aminated poly sulfonic acid (anion exchange layer) was coated on the sandpapered cation exchange membrane (layer) and dried to prepare the bipolar membrane of 90 mm thickness. (b) Performance of the Bipolar Membrane. Adhesion intensity between the cation exchange layer and the anion exchange layer was 5.1 kg f (25 mm)1. Current efﬁciencies were ZH ¼ 99.2%, ZOH ¼ 99.2%, ZCl ¼ 0.3% and ZNa ¼ 0.5%. Electrolysis voltage was 1.2 V. The performance of the membrane was unchanged and air bubbles and water bubbles were not formed at the interface in the bipolar membrane during the ﬁrst two months. After that, the adhesion intensity was unchanged (5.2 kg f (25 mm)1), but the electron spectroscopy analysis reveals that Fe2+ ions remained at the interface between the cation exchange layer and the anion exchange layer. The experiment described above was repeated without coating of FeCl2. The performance of this bipolar membrane was: adhesion intensity ¼ 5.3 kg f (25 mm)1, current efﬁciency ZH ¼ 99.3%, ZOH ¼ 99.3%, ZCl ¼ 0.3%, ZNa ¼ 0.4% and electrolysis voltage ¼ 3.2 V, which was larger than 1.2 V obtained in the

414

Ion Exchange Membranes: Fundamentals and Applications

previous experiment, demonstrating that the Fe2+ ions decrease the electric potential to generate water splitting reaction. In other words, the Fe2+ ions accelerate the auto-catalytic water dissociation reaction and this phenomenon presumably relates to the phenomena found on the monopolar membranes (cf. Section 8.8.4, Figs. 8.20 and 8.21, in Fundamentals). The experiments in this patent show that heavy metallic ions such as Fe (II, III), Ti (IV), Sn (II, IV), Zr (IV) Pa (II) and Ru (III) accelerate water splitting reaction and maintain the electrolysis voltage less than 2.0 V or 1.8 V. In the fundamental studies for monopolar membranes, Mg (II), Ni (II), Co (II), Mn (II), Cu (II), Fe (III) and Al (III) were found to accelerate the water dissociation reaction (cf. Section 8.8.3, Table 8.7, in Fundamentals). These phenomena are assumed to be related to each other; however the mechanism is not clear.

3.2.4

Instance 4 Umemura et al. (1994, 1995) (Asahi Glass Co.), invented the following perﬂuorinated bipolar membrane. Practicing Instance. A sufﬁciently dried up quaternary ammonium type anion exchange membrane (styrene–divinyl benzene type, reinforced with polypropylene, ion exchange capacity: 3 meq g1 dry resin, 120 mm thick) was ﬁxed on a glass plate. On this membrane, a 10 wt. % ethanol solution of perﬂuorinated sulfonic acid type cation exchange copolymers (ion exchange capacity: 1.1 meq g1 dry resin, consisting from CF2QCF2 and CF2QCFOCF2CFCF3CF2CF2SO3H) were poured. Before the solvent was evaporated sufﬁciently, the copolymer layer (30 mm thick) was pressed down on the anion exchange membrane. The bipolar membrane is obtained by drying the above membrane in an oven at 601C for 30 min. The bipolar membrane was incorporated with an electrodialyzer, a Na2SO4 solution was supplied and electrodialyzed at the current density of 10 A dm2. The water dissociation current efﬁciency and voltage applied to the membrane were 0.95 and 3.4 V, respectively. Comparative Instance. The same anion exchange membrane described in the practicing instance was immersed in a 701C 10 wt. % CrCl2 solution for 10 min, immersed in a 5 wt. % NaOH solution for 10 min, washed sufﬁciently with water and dried. Using the anion exchange membrane described above, the bipolar membrane was prepared in the same way as in the practicing instance. By means of the same electrodialysis (ED) experiment performed in the practicing instance, the water dissociation current efﬁciency was measured as 0.95. The voltage applied to the membrane was 1.3 V, which was less than the 3.4 V obtained in the practicing instance. The experiment seems to show that Cr (II) ions decrease the voltage owing to the water dissociation acceleration. This phenomenon is similar to that observed in Section 3.2.3.

415

Bipolar Membrane Electrodialysis

The water splitting process operates at signiﬁcantly higher temperature because of heat generation in the bipolar membrane. Accordingly, it is expected to develop the technology to prepare the perﬂuorinated bipolar membrane described in this section.

3.3.

PERFORMANCE OF A BIPOLAR MEMBRANE

3.3.1

Electrolyte Concentration in an Intermediate Layer in a Bipolar Membrane The intermediate layer is formed between a cation and an anion exchange layer in the bipolar membrane. Under an applied electric current, electrolyte concentration in the intermediate layer is decreased and a water dissociation (splitting) reaction starts in the water dissociation layer at an over-limiting current circumstance. The thickness of the intermediate layer corresponds to the distance between the cation and the anion exchange layer, which is inﬂuenced by the structural irregularity of a membrane surface. Sata et al. (1995) observed a membrane surface before and after introducing anion exchange groups to a chloromethylstyrene and divinyl benzene copolymer membrane by an atomic force microscope (AFM). Fig. 3.7a–c show AFM images of three different membranes: (a) copolymer membrane (base

200

800 600

100

Nanoscope II Parameters:

400 0 0 nm

200

200

400

600

Z XY Samples

800

a. Base membrane

200 800 100

600 400

0 0 nm

200

200 400

600

800

b. Amination with trimethylamine

Figure 3.7 al., 1995).

84.5 Å/V 267.5 Å/V 400/scan

200

800

100

600 400

0 0 nm

200

200 400

600

800

c. Amination with tributylamine

AFM images of the base membrane and anion exchange membranes (Sata et

416

Ion Exchange Membranes: Fundamentals and Applications

membrane), (b) anion exchange membrane with trimethylbenzylammonium groups and (c) anion exchange membrane with tri-n-butylbenzylammonium groups. Before introducing anion exchange groups, the copolymer membrane has a relatively ﬂat surface. However, after introducing anion exchange groups, the membrane surface is uneven as shown in Fig. 3.7b and c. From the graded scale putting on the perpendicular axis, the dimension of the spaces formed on the membrane is estimated to be in the order of 107 m, which is estimated to be nearly equivalent to the thickness of the intermediate layer. Here, we discuss the electrolyte concentration change in the intermediate layer in the bipolar membrane placed in an electrolyte solution (feeding solution) dissolving cations M+ and anions X and applying current density i being less than the limiting current density ilim on the basis of Fig 3.8. In Fig. 3.8a, J is the ionic ﬂux. Subscripts M+, X and MX refer to M+ ion, X ion and their salt MX. Subscript ‘‘migr’’ and ‘‘diff’’ mean migration and diffusion, respectively. Superscript K and A express cation and anion exchange layer. Fig. 3.8a can also be presented as Fig. 3.8b, and the electrolyte concentration change in the intermediate layer in Fig. 3.8b is expressed by the following equation

J KX-,migr C"

C' J KMX,diff

Cathode

Feeding solution

(a)

J A M+,migr

J KM+,migr

J AX-,migr

C"

J AMX,diff

Intermediate Anion Cation layer exchange exchange layer layer

Feeding solution

(b)

Jmigr C"

C' Jdiff

Figure 3.8

Deionization in an intermediate layer.

Anode

C"

417

Bipolar Membrane Electrodialysis

established using the overall mass transport equation (cf. Chapter 6 in Fundamentals) (Tanaka, 2006). J S ¼ J migr þ J diff ¼ V

dC 0 ¼ li mðC 00 C 0 Þ dt

(3.3)

in which, V is water volume in the intermediate layer (cm3 per cm2), t time (s), i current density (A cm2), C0 and C00 electrolyte concentration in the intermediate layer and the feeding solution, l and m overall transport number and overall solute permeability of ion exchange layer pair (cf. Chapter 6 in Fundamentals). From Eq. (3.3) dC 0 1 ¼ dt li mC 00 þ mC 0 V

(3.4)

Integrating Eq. (3.4) between t ¼ 0 – t and C ¼ C 00 C 0t ; assuming V to be constant Z C 0t Z dC 0 1 t dt (3.5) 00 0 ¼ V 0 C 00 li mC þ mC Solving Eq. (3.5) and rearranging introduce C 0t as follows: m l l 0 00 0 i C þ C 0 10V t þ C 00 i Ct ¼ m m

(3.6)

Putting t-N and C 0t ¼ 0 in Eq. (3.6) l lim C 0t ¼ C 00 ilim ¼ 0 m

t!1

(3.7)

Accordingly, the limiting current density is ilim ¼

m 00 C l

(3.8)

In order to calculate the change of C 0t with time t using Eq. (3.6), the following relationship between the overall membrane pair characteristics are prepared (cf. Section 6.1, Eqs. (6.5) and (6.6) in Fundamentals). l ¼ 9:208 106 þ 1:914 105 r m ¼ 2:005 104 r

(3.9) (3.10)

418

Ion Exchange Membranes: Fundamentals and Applications

Putting overall hydraulic permeability for example r ¼ 1 102 cm4 eq1 s1 in Eqs. (3.9) and (3.10) leads to l ¼ 9:399 106 eq A1 s1 m ¼ 2:005 106 cm s1 Putting the intermediate layer thickness L ¼ 107 m ¼ 105 cm referring to the AFM images in Fig. 3.7, the water volume in the intermediate layer V is evaluated as V ¼ 1 cm 1 cm L ¼ 105 cm3 per cm2 Substituting the above values with, for example, C 00 ¼ C 00 ¼ 0:5 N ¼ 5 104 eq cm3 into Eq. (3.6), C 0t vs. t is calculated as in Fig. 3.9. The limiting current density ilim ¼ 1.067 104 A cm2 is obtained using Eq. (3.8). In this calculation, intermediate thickness (i.e. V) is assumed to be constant, which means that water extracted from the intermediate layer in the ED is supplemented from 0.6

0

0.5

i = 0.002 A /dm2

C'(eq/dm3)

0.4 0.004 0.3 0.006 0.2 0.008 0.1 i lim = 0.01067 0.0

0

2

4

0.010 6

8

10 t (s)

12

14

16

18

20

Figure 3.9 NaCl concentration changes in an intermediate layer formed in a bipolar membrane.

419

Bipolar Membrane Electrodialysis

the feeding solution. The mechanism of water transfer in this process is discussed in Section 3.3.5. If the intermediate thickness is assumed to be less than L ¼ 107 m (i.e. V ¼ 105 cm3 per cm2), the electrolyte concentration in the intermediate layer C0 decreases more rapidly than the changes in Fig. 3.9.

3.3.2

Water Dissociation At over limiting current density i4ilim, water dissociation is generated in the water dissociation layer (cf. Section 8.10 in Fundamentals). When the bipolar membrane is placed for example in a NaCl solution, it is estimated from the ED experiment in Section 8.8 in Fundamentals that water dissociation layer is formed in the anion exchange layer and in the cation exchange layer as shown in Fig. 3.10. In the ﬁgure, the thickness of the water dissociation layer is shown by lA in the anion exchange layer and lK in the cation exchange layer. The water dissociation reaction is not inﬂuenced by the Wien effect (Wien, 1928, 1931) (cf. Section 8.10.8 in Fundamentals), but it is accelerated by the auto-catalytic

lac

K

H+

ac

A

OH-

OH-

H+

Anode

Cathode H+

lK Cation exchange layer

L

Intermediate layer

OH-

lA Anion exchange layer

l : Thickness of the water dissociation layer L : Thickness of the intermediate layer

Figure 3.10

Water dissociation layer formed in a bipolar membrane.

420

Ion Exchange Membranes: Fundamentals and Applications

reaction of quaternary ammonium groups in the anion exchange layer and sulfonic acid groups in the cation exchange layer at the same time. In this situation, the intensity of the water dissociation reaction generated in the anion exchange layer sA is stronger than that generated in the cation exchange layer sK ;sA4sK, so that the water dissociation reaction in the bipolar membrane is governed by the reaction occurring in the anion exchange layer. Electric current efﬁciency Z of the water dissociation reaction in a monopolar membrane is expressed as follows (cf. Section 8.10, Eq. (8.53) in Fundamentals)(Tanaka, 2007): i Z ¼ ka C H 2 O kb C 0H C 0OH l (3.11) F in which, CH2O is the concentration of H2O in the water dissociation layer. C0H and C0OH are the concentration of H+ and OH ions, respectively, at the outsides of the water dissociation layer. ka and kb are the forward and reverse equilibrium reaction constant, respectively. Under an applied electric potential ﬁeld, ka is assumed to increase with the electric ﬁeld due to the auto-catalytic reaction whereas kb remains being constant (cf. Section 8.10.1 in Fundamentals). In the bipolar membrane electrodialysis system, we assume here that the electric current efﬁciency of the cation exchange layer, anion exchange layer and bipolar membrane is given by ZK, ZA and ZB respectively. Current efﬁciency for transporting Na+ and Cl ions across the bipolar membrane is deﬁned by 1ZB and it is expressed by the following equation. 1 ZB ¼ ð1 ZK Þð1 ZA Þ

(3.12)

Rearranging Eq. (3.12) ZB ¼ Z K þ Z A Z K Z A

(3.13)

From the water dissociation experimental results of monopolar membranes (cf. Section 8.8 in Fudamentals), the following relation is assumed to hold. ZA 4ZK

(3.14)

Hanada et al. (1991,1993,1996), introduced inorganic active substances (Fe, Ti, Sn, Zr, Pa, Ru) into the bipolar membrane to enhance the water dissociation (cf. Section 3.2.3 in this chapter). Kang et al. (2004) investigated the optimal contents of inorganic substances such as iron hydroxides and silicon compounds for accelerating the water dissociation reaction and they developed the method to immobilize the inorganic material in the bipolar membrane. In the fundamental studies for monopolar membranes, active components such as

421

Bipolar Membrane Electrodialysis

Mg, Ni, Co, Mn, Cu, Fe, Al were found to accelerate the water dissociation (Tanaka et al., 1982) (cf. Section 8.8.3, Table 8.7, in Fundamentals). In the bipolar membrane the inorganic active components mentioned above must form the active component layer in the intermediate layer as shown in Fig. 3.10, in which the thickness of the active component layer is lac. Further, the electric current efﬁciency for transporting Na+ and Cl ions of the bipolar membrane including the active component layer is given by the following equation assuming the current efﬁciency of the active component layer is Zac. 1 ZB ¼ ð1 ZK Þð1 ZA Þð1 Zac Þ

(3.15)

We arrive at the following equation from Eq. (3.15). ZB ¼ ZK þ ZA þ Zac ZK ZA ZK Zac ZA Zac þ ZK ZA Zac

(3.16)

Zac 4ZA 4ZK

(3.17)

3.3.3

Current Efﬁciency in Bipolar Membrane Electrodialysis Fig. 3.11 illustrates mass transfer in the two compartment splitting system generating H+ ions and OH– ions from salt MX. The ionic ﬂux J transported into the acid chamber due to electromigration is expressed by the following equation.For cations BP A J þ ¼ J BP H þ JM JH

(3.18)

C

BP OH−

M+

Anode

MX

A H+

MOH

X−

MX

HX

Cathode

M+

OH−

H+ X−

Salt

Base

Acid

Salt

BP: Bipolar membrane C: Cation exchange membrane A: Anion exchange membrane

Figure 3.11

Mass transfer in the two compartment splitting systems (Mani, 1991).

422

Ion Exchange Membranes: Fundamentals and Applications

For anions BP J ¼ JA X JX

(3.19)

Here, subscripts H, M and X refer to H+, M+ and X ions, and superscripts BP A and A mean bipolar membrane and anion exchange membrane. J BP M ; J H (Eq. BP (3.18)) and J X (Eq. (3.19)) are caused by the imperfectness of permselectivity of the membranes. The current efﬁciency in the acid chamber Zacid is introduced from Eqs. (3.18) and (3.19) as follows: Zacid ¼

A J BM J A J BP H JH X ¼ X i=F i=F

(3.20)

The ionic transfer and current efﬁciency in the base chamber are introduced in the same way as follows: BP Jþ ¼ JC M JM

(3.21)

BP C J ¼ J BP OH þ J X J OH

(3.22)

Zbase ¼

C J BP J K J BP OH J OH M ¼ M i=F i=F

(3.23)

where subscript OH and superscript C refer to OH ions and the cation exBP C change membrane, respectively. J BP M (Eq. (3.21)) and J X ; J OH (Eq. (3.23)) are due to the imperfectness of permselectivity of the membrane. Oda et al. (1957) and Ishibashi and Hirano (1958) observed that the current efﬁciency is not depending on the current density and temperature, but it is decreased with the increase of the electrolyte concentration. 3.3.4 Energy Consumption and Production Capacity in Bipolar Membrane Electrodialysis Total costs of the water splitting process are broken down into costsrelated membrane area and costs of power consumption (Nagasubramanian et al., 1977). The mass of electrolyte transported across the membrane for unit time J (eq s–1) is: I iS J¼ Z¼ Z (3.24) F F where I (A) is the electric current, i (A m2) is the current density, S (m2) is the membrane area and Z is the current efﬁciency.

Bipolar Membrane Electrodialysis

423

Eq. (3.24) may be written as S¼

JF Zi

(3.25)

The voltage drop across a unit cell of a water splitting stack Ecell (V cell1) is E cell ¼ iRcell þ E bp

(3.26)

Rcell (Om2 cell–1) is the resistance of a unit area of the unit cell and may be obtained from the sum of the individual solution (acid, base and salt chamber) and membrane (anion and cation exchange membrane) resistance (cf. Fig. 3.2): Rcell ¼ Racid þ Rbase þ Rsalt þ Ran:m þ Rcat:m

(3.27)

Rbp (V cell1) is the potential drop across the bipolar membrane and can be written as: E bp ¼ iðRbp;an þ Rbp;cat þ Rbp;int Þ þ E þ E irr

(3.28)

where Rbp,an, Rbp,cat and Rbp,int are the electric resistance of anion, cation and interface layer, respectively, E approaches the thermodynamic water splitting potential E0, and Eirr refers to the potential drop caused by the irreversible characteristics of the membrane. The power consumption for unit cell P (W cell1) is thus given by P¼

JF iRcell þ E bp ¼ i2 SRcell þ iSRbp Z

(3.29)

As it can be seen in Eq. (3.25), the membrane area S is inversely proportional to the current density i for constant product rate J and current efﬁciency Z, so in the process design, the number of membranes integrated in the process is decreased with the increase of the current density. This situation, however, results in the increase of power consumption P as is seen in Eq. (3.25). Thus, the reduction in ﬁxed capital brought about by reducing membrane area by increasing current density must be weighed against the increase in ﬁxed capital brought about by higher power requirements (for rectiﬁers and possibly cooling) and the increased operating cost due to the higher consumption of electricity. 3.3.5

Water Transfer in a Bipolar Membrane In the bipolar membrane system, electrolyte concentration in feeding solutions in acid and base compartments is high, while that in the intermediate layer is nearly zero. Accordingly, an osmotic pressure difference exceeding 100 atmospheres must be generated between the intermediate layer and the feeding solution. In the water dissociation layer, H2O molecules split into H+ and OH ions, so the H2O must be supplied from the feeding solution toward the water

424

Ion Exchange Membranes: Fundamentals and Applications

dissociation layer against the osmotic pressure. The water transfer in the bipolar membrane is important because it inﬂuences the performance of the membrane. However, the mechanism of water transfer is not yet cleared sufﬁciently. Simons (1993) suggests that the Maxwell pressure difference of water DPM between the outside (feeding solution) and the inside (intermediate layer) of the bipolar membrane exceeds the osmotic pressure and supplies the water. Z EI w EdE (3.30) DPM ¼ 0 0

where E is potential, EI potential in the intermediate (depleted) layer, ew dielectric constant of water and e0 dielectric constant in a vacuum. In this theory, however, the thickness of the intermediate layer L is assumed to be zero (cation and anion exchange layers meet each other), and water splitting is assumed to occur at the junction between the cation and anion exchange layer under strong potential difference generated at the junction. Putting EI ¼ 4.6 106 V m1, ew ¼ 60 and e0 ¼ 80 on Eq. (3.30), we obtain DPM>236 atmospheres>100 atmospheres and estimate that water ﬂows from the feeding solutions toward the intermediate layer against osmotic pressure. This problem however might be solved more easily applying the kinetic molecular theory of gases to the behavior of H2O in the bipolar membrane. For instance, the pressure in the water dissociation layer Pwater is presented applying the Gay–Lussac’s Law as 2 1 Pwater ¼ nwater N A ke 3 V water

(3.31)

where nwater is the numbers of H2O molecules in the water dissociation layer, Vwater is the volume of water dissociation layer. NA is the Avogadro’s number, ke is the kinetic energy of a H2O molecule. If nwater is decreased by converting H2O into H+ and OH– in the water dissociation layer, Pwater must be decreased according to Eq. (3.31). Pressure difference between the feeding solution Pfeed and in the water dissociation layer Pwater, i.e. Pfeed – Pwater must increase and create H2O ﬂux J H2 O from the feeding layer toward the water dissociation layer. J H2 O becomes equivalent to the ﬂux of H+ ions JH and OH ions JOH generated by the water splitting reaction as: J H2 O ¼ J H ¼ J OH

(3.32)

As the current density is increased, the rate of water removal from the water dissociation layer is increased. If the water transfer J H2 O is insufﬁcient, the numbers of water molecules in the water dissociation layer nwater reaches zero (nwater ¼ 0) and a part of the bipolar membrane dries and becomes nonconducting resulting in membrane damage (Nagasubramanian et al., 1977).

Bipolar Membrane Electrodialysis

425

Aritomi et al., recognized that water supply from the outside of the bipolar membrane to the interface (water dissociation layer) at high current density becomes the rate limiting step for the water dissociation process (Aritomi et al., 1996). 3.3.6

Heat Generation in a Bipolar Membrane The water splitting process is operated at signiﬁcantly higher current densities and voltage drops. Accordingly, a part of electric current is converted to Joule’s heat, which is related to power consumption. The rest of the electric current works to concentrate H+ and OH ions. As a ﬁrst approximation, the heat generated, Q (kcal h1) is written as: Q ¼ 860 iSðE cell E 0 Þ

(3.33)

3.3.7

Rectiﬁcation Effect of a Bipolar Membrane In a bipolar ED system shown in Fig. 3.8, electrolyte concentration C0 is decreased (Fig. 3.9) and it gives rise to electric resistance increase in the intermediate layer. When the direction of an electric current is reversed in this situation, the electrolyte concentration in the feeding compartment C00 is decreased and that in the intermediate layer C0 is increased, resulting in a decrease in electric resistance. These phenomena give rise to rectiﬁcation effect in the bipolar membrane ED system. The phenomena generated under the reversed electric current can be discussed by altering the minus sign of VdC0 /dt in Eq. (3.3) to plus sign and calculating in the same way as achieved in Section 3.3.1. The basic equation in this situation is introduced as Eq. (3.34), which is the same to Eq. (3.6) excepting the exponent sign. m l l i C 00 þ C 00 10V t þ C 00 i (3.34) C 0t ¼ m m Here the following circumstances are assumed as in the case of forward electric current passing described in Section 3.3.1: l ¼ 9:399 106 eq A1 s1 m ¼ 2:005 106 cm s1 V ¼ 105 cm3 per cm2 ðL ¼ 107 mÞ C 00 ¼ C 00 ¼ 5 104 eq cm3 C 0t vs. t is calculated in Fig. 3.12, showing C 0t to be increased with t. If a 0.5 N NaCl solution is assumed to be fed in this calculation, the solution is saturated at the saturated solubility C 0sat and NaCl crystals are estimated to be precipitated when C 0 4C 0sat ¼ 4.593 eq dm3 (251C) holds in the ﬁgure. If the intermediate thickness is assumed to be less than L ¼ 107 m (i.e. V ¼ 10–5 cm3 per cm2), the

426

Ion Exchange Membranes: Fundamentals and Applications

6

5

0.0

02

04

06 0.0

C' (eq/dm3)

4

0.0

0.0

10

C'sat

3

2

1 i = 0 A/dm2 0

0

1

2

3

4

5 t (s)

6

7

8

9

10

Figure 3.12 NaCl concentration changes in an intermediate layer formed in a bipolar membrane at electric current reversal.

electrolyte concentration in the intermediate layer C 0 increases more rapidly than the changes in Fig. 3.12. The rectiﬁcation effect discussed by Ohki (1965) based on the Donnan equilibrium and the Nernst–Planck equation, indicated that it is strongly affected by the ﬁxed charge densities in the cation and anion exchange layers. When an electric current is not too large in an usual ED system, the Donnan equilibrium theory must be approximately satisﬁed as the irreversible thermodynamics is assumed to be applicable in this circumstance (Dunlop, 1957; Dunlop and Gosting, 1959). However, in the bipolar membrane ED system, the phenomenon includes an extremely dynamic reaction such as water splitting, so that the equilibrium is estimated to not realize in this situation. Accordingly, it might be not reasonable to apply the Donnan equilibrium theory to analyze the rectiﬁcation as in the above investigation. Tanioka et al. (1996) and Tanioka and Shimizu (1997) discussed experimentally the effect of the polymer material and interface structure on the rectiﬁcation phenomena of the bipolar membranes. Fig. 3.13 shows the typical current–voltage curves obtained in this experiment showing that in all sample membranes, an electric current is increased when positive potential (E>0) is supplied, whereas it is suppressed when negative potential (Eo0) is supplied. So, the p–n junction theory applied to a

427

Bipolar Membrane Electrodialysis

2 SAMPLE A SAMPLE C 1

B - 17

I (mA)

SANDWICH

0

-1

-2 -10

Figure 3.13

-8

-6

-4 E(V)

-2

0

2

Current–voltage curves of a bipolar membranes (Tanioka et al., 1996).

semiconductor is also applicable to the behavior of ions in a bipolar membrane. When the voltage is less than 3 V, the reverse electric current ﬂows to some extent. This phenomenon is presumably due to H+ and OH ions produced by water splitting on the feeding side of the anion exchange layer in Fig. 3.8. 3.3.8

(a) (b) (c) (d) (e)

Desirable Properties in the Bipolar Membrane Electrodialysis Process The desirable characteristics of the bipolar membrane ED process are Low power consumption Ability to operate at high current densities High acid and base concentrations High current efﬁciency Low maintenance costs, i.e. use of low cost and long life membrane

A number of these factors are interrelated and an optimization is needed to arrive at a proper balance of the various factors (Nagasubramanian et al., 1977). 3.3.9

Operational Problems in a Bipolar Membrane Electrodialysis Process A major problem in the practical application of bipolar membranes is assumed to be as follows (Strathmann, 2004): (a)

Drastic decrease of the permselectivity of the membrane due to the decreased Donnan exclusion at high product concentrations, which result in a signiﬁcant salt leakage through the membrane into the product.

428

(b)

(c)

3.4.

Ion Exchange Membranes: Fundamentals and Applications

Any di- or multivalent cation precipitate in the alkaline solution and must therefore be removed from the solution. The same is true for organic components, which can precipitate at extreme pH values. At high acid and base concentration, the retention of the anion exchange layer for H+ ions and that of the cation exchange layer for OH– ions is very poor. However, the development of the so-called acid and base blocker membranes have resulted in a substantial improvement of the current utilization in bipolar membrane electrodialysics (Pourcelly et al., 1994).

PRACTICE

Substantial efforts have been made to apply the bipolar membrane technology in the ﬁelds of pollution control, resource recovery and chemical processing as shown in Table 3.3 (Xu, 2005). In this section, we introduce the process ﬂow, pretreatment requirement and process economics presented in the literature. 3.4.1

Recovery of Mixed Acids from Stainless Pickling (Mani et al., 1988) In the production of stainless steel, the surface oxide ﬁlm is removed via a chemical pickling (descaling) step that uses a mixed acid solution comprising 2–5 wt. % HF and 8–15 wt. % HNO3. The spent acid from the pickling step containing metal ﬂuorides and nitrates is conventionally limited, ﬁltered and discharged to landﬁlls and water way. The disposal of these efﬂuents is becoming increasingly difﬁcult and expensive. Aquatech technology, commercialized by the Aquatech Systems division of Allied-Signal Inc., can be used to recover the acids at proper strength and purity for recycling back to the pickling operation. Fig. 3.14 shows a simpliﬁed ﬂow sheet of the process. The process has been fully piloted at the facilities of Washington Steel, a major stainless steel producer in Western Pennsylvania. In the process, spent pickle liquor is neutralized with recycled KOH to precipitate the metal values in the form of hydroxides while the ﬂuorides and nitrates are retained in solution as soluble salts. The neutralized mixture is then ﬁltered and washed with recycled water to recover substantially all of the ﬂuoride and nitrate values. The hydroxide cake from the ﬁltration step, containing 38–45% solids can then be dried and returned to the steel smelter. The KF/KNO solution from the ﬁltration step is then admitted to the salt loop of the three-compartment Aquatech cell. Here, through use of the direct current driving force, KOH is generated in the base loop while an HF/HNO3 mixture is generated in the acid loop. During the water splitting, step concentration decreases from 1.1–1.5 N to 0.3–0.5 N. A portion of the depleted salt solution is used to dilute the base generated while the balance is forwarded to the

Application of the bipolar membrane process

Application Field

Scale

Process Characteristics

Economics Estimation

Recovery of HF and HNO3

Industrial plant Aqualytics system

Recovery of NaOH from a stream containing Na2SO4

Semi-industrial pilot

Total investment: US$ 2,950,000 Operating proﬁts: US$ 1,620,000 Total operating costs: US$ 750,000 Proﬁts per year: US$ 870,000 Energy consumption: 5.0 kWh kg–1 NaOH

Recovery of NH3 and HNO3 from a stream containing NH4NO3

Semi-industrial pilot

Recycling of dimethyl isopropyl amine in the production of aluminum casting molds Flue gas desulphuration

Semi-industrial pilot

Three-compartment cell, Membrane area: 3 105 m2, BPM life time: 2 years, Recovery ratio: 90% for HF, 95% for HNO3, Operating time: 8000 h year1 Membrane area: 0.5 m2, Feed rate: 5 l h–1, Feed conc.: Na: 22 g l1, Current applied: 900 A m–2, Current yield: 82%, Product NaOH conc.: 1 M Membrane area: 120 m2, Feed conc. NH4NO3: 250 g l–1, Current applied: 1000 A m–2, Desalination rate: 97%, Operating time: 8000 h year–1 Membrane area: 0.3 m2, Feed conc. amine sulphate: 1 M, Current applied: 800 A m–2, Current yield: 30–70%, Operating time: 8000 h year1 Three-compartment cell, Membrane area: 560 m2, Cell voltage: 2.0 V at 1000 A m2, Current efﬁciency: 86%, Operating time: 7200 h year1, Two-compartment cell, Membrane area: 5000 m2, Cell voltage: 1.7 V at 1000 A m2, Current efﬁciency: 92%, Operating time: 7200 h year1 Two-compartment cell, Membrane area: 0.19 m2, Elementary cell voltage: 2.2 V at 415 A m2, Conversion ratio: 98.3%, Na faradic yield: 85.4%

Industrial plant SoxalTM process

Pilot scale

Recovery of methanesulphonic acid (MTA) from sodium methanesulphonate (MTS) solutions

Industrial plant (Italy)

Three-compartment cell, Membrane area: 64 m2, Elementary cell voltage: 2.26 V at 800 A m2, Methanesulphonic conversion ratio: 95%, Concentration: MTS 250, MTA 100, NaOH: 80 g l1

Energy consumption: 2.5–5.0 kWh kg–1 amine Three-compartment cell Energy consumption: 1400 kWh ton1 NaOH Two-compartment cell Energy consumption: 1,120 kWh ton1 NaOH For a plant of 10,000 ton year1: total US$ 2.5 M Membrane replacement: US$ 0.03 Kg1 Na-gluconate Recovery chemicals: NaOH US$ 0.5 M Gluconic acid unknown Total investment: US$700,000 Total costs per ton MTA: US$ 354 Market price of MTA: US$ 5500 ton1

429

Recovery of gluconic acid from sodium gluconate

Total cost: US$ 0.34 kg–1 NaNO3

Bipolar Membrane Electrodialysis

Table 3.3

430

Table 3.3. (Continued ) Application Field

Scale

Process Characteristics

Economics Estimation

Recovery of amino acid from a fermentation broth

Industrial plant Aqualytics system

No information available

Production of lactic acid from a fermentation broth

Industrial plant

Three-compartment cell, Membrane area: 3 180 m2, BPM life time: 2 years, Organic acid conc.: 4–6 M, Operating time: 8000 h year1 Two-compartment cell, Membrane area: 280 m2, Current yield: 60%, Conversion ratio: 96%

Regeneration of camphorsulphonic acid

Pilot scale (France)

Production of vitamin C (Ascorbic acid HAsc) from sodium ascorbate (NaAsc) Production of citric acid

Labo scale and semiindustrial pilot Pilot scale (China)

Production of silicic acid

Industrial pilot

Production of salicylic acid

Laboratory pilot

Conversion of sodium acetate to acetic acid

Pilot scale

Energy consumption: 1.4–2.3 kWh kg1 HAsc Energy consumption: 2–5 kWh kg1 citric acid Energy consumption: 0.6 kWh kg1 product (6–10%) Energy consumption: 15–20 kWh kg1 product

Energy consumption: (0.5 M sodium acetate) 1.3–2.0 kWh kg1 product (1.0 M sodium acetate) 1.5–2.5 kWh kg1 product

Ion Exchange Membranes: Fundamentals and Applications

Source: Xu (2005).

Three-compartment cell, BPM area: 0.14 m2, Current density: 500 A m2, Faradic yield: 7%, Salt conversion: 98.5%, Final acid concentration: 0.8 M Two-compartment cell, Current density: 1000 A m2, Current efﬁciency: 75%, Acid concentration: 1 M Two-compartment cell, BPM area: 0.004 m2, Current density: 1000 A m2, Current efﬁciency: 70%, Acid concentration: 30 g l1 Two-compartment cell, Elementary cell voltage 2.5–4 V at 100–200 A m2, Current efﬁciency: 55–75%, Acid concentration: 6–10% Three-compartment cell, Tokuyama BPM, Elementary cell voltage: 30 V at 750 A m2, Current efﬁciency: 80–90% at 401C, Acid concentration: 4.5 (maximum) g l1 Five-compartment cell, BPM area: 0.008 m2, (0.5 M sodium acetate) Current efﬁciency: 99.9% and acid concentration: 1 M, (1.0 M sodium acetate) Current efﬁciency: 96.8% and acid concentration: 1.5 M

Bipolar membrane costs: US$ 0.12 kg1 lactic acid, Energy consumption: 1 kWh kg1 lactic acid Energy consumption: 3,000 kWh ton1 of product

431

Bipolar Membrane Electrodialysis ∼1.5M KOH

ED Dilute ED

Cake Wash Waste Acid

ED Concentrate pH≈9 Neutralization Tank

Feed KF/KNO3

AQUATECH Acid Product

Metal Hydroxide Filter Cake

Figure 3.14 Table 3.4

Aquatech pickle-liquor recovery process (Mani et al., 1988). Hundred-day pilot plant run: overall balance

Stream

Rate l/h

kg/h F

Waste acid Recycle base Acid product Cake Recovery (%)

10 30 18 3.2

15 5 14 1 93

Material handled kg/d NO 3

K+

22 55 21.8 0.2 99

1.8 96

Source: Mani et al. (1988).

water recovery step. The product from the base loop is typically 1.5 N KOH per 0.4 N KF and is forwarded to the waste acid neutralization step. Water (and KF) recovery from the dilute salt solution from the Aquatech unit was achieved using a conventional ED cell containing Allied’s cation membranes and Asahi Glass’s AMV anion membranes. The concentrate from the ED was returned to the Aquatech salt loop while the dilute containing 0.02– 0.04 N salt was used for washing the ﬁlter cake. Table 3.4 shows an overall material balance for the 100 day run. Recoveries of the key materials namely ﬂuorides, nitrates and potassium were found to be quite high. Obviously the neutralization step is effective in breaking the ﬂuoride complexes in the waste pickle liquor. The results of the pilot run are summarized in Table 3.5. All of the membranes had retained their selectivity and mechanical properties and showed no evidence of fouling. The electrical resistance of the monopolar membranes was stable while the bipolar membranes had an acceptably low potential increase ofo0.08 V month1. Table 3.6 shows an

432 Table 3.5 Type

Ion Exchange Membranes: Fundamentals and Applications

Washington Steel Corporation pilot test review: membrane analysis Manufacturer Units

Bipolar Allied Cation Allied Anion RAI 4035

V at 100 mA/cm O cm2 O cm2

Nominal (when new) 100 Days 170 Days 2

1.1 6.0 2.3

1.29 6.9 2.7

1.4 6.8 2.2

Source: Mani et al. (1988). Table 3.6

Aquatech pickle liquor recovery process: capital and operating costs

Basis: 6 106 l/y of spent pickle liquor containing 5 wt% F, 10 wt% 8,000 h/y 1 y life for cell assembly Acids recovered (net): 320 Mt/y of HF and 675 Mt/y of HNO3 Total battery limits capital for plant $1.8 106 (Jan. ‘86 costs; all costs in U.S. Dollars/y) Operating cost summary Raw materials Makeup KOH at $600/ton Filter aid at $400/ton Cell maintenance Electricity at 5 f /kWh Other maintenance Labor and supervision Depreciation at 10% Taxes and insurance at 2% Total operating costs

36,000 18,000 300,000 128,000 78,000 40,000 180,000 36,000 816,000

Product credits HF at $ 1,500/ton HNO3 at $ 225/ton Waste disposal at 8 f /l Metals credit Total credits Savings Returns on investment

480,000 152,000 480,000 150,000 1,262,000 446,000 25%

Source: Mani et al. (1988).

estimated capital and operating cost summary for a plant processing 6 106 l year1 of spent pickle liquor. The battery limits investment covers of the entire plant including ﬁltration, neutralization, tankage, Aquatech system and ED water recovery unit. It should be pointed out that a considerable part of the total investment is for hardware and equipment other than the Aquatech unit itself. 3.4.2 Recovery of Sodium Hydroxide and Sulfuric Acid from Sodium Sulfate (Mani et al., 1988) Sodium sulfate is generated as a waste or by-product in many operations such as waste acid neutralization, ion exchange regeneration, ﬂue gas

433

Bipolar Membrane Electrodialysis

desulfurization, and rayon manufacture. Sulfate concentration in a given stream can be quite low, such as in waste acid neutralization or high, such as in rayon manufacture. Water splitting technology can be applied to many of these sulfate streams, if not directly, then following concentration or puriﬁcation, to upgrade the salt to acid and base thus reducing or eliminating a pollution problem. The applicability of the water splitting technology to sulfate conversion can be illustrated with reference to rayon manufacture. The process ﬂow sheet is shown in Fig. 3.15 and uses a two-compartment cell. In this process, Na2SO4 values from the spin bath are recovered via an evaporative crystallization step. Mother liquor from the evaporation step is returned back to the spin bath. Solid sulfate from the crystallizer, typically Na2SO4, is then dissolved in water and puriﬁed to remove metals such as Ca, Mg and Zn. Puriﬁed sulfate solution is then fed to the acid compartments of a two-compartment Aquatech unit. Here, under a direct current driving force NaOH is generated in the base loop while the sulfate is acidiﬁed in the acid loop. The base is forwarded to the cellulose dissolving step while the acidiﬁed sulfate is returned to the spin bath.

Water

Spin Bath

Spent Bath 28% Na2SO4 7.65% H2SO4

Evaporator 32% Na2SO4 12% H2SO4

Mother Liquor 21.8% Na2SO4 22% H2SO4

Crystallizer

Glauber Salt Water

Water

Purification 31% Na2SO4 Base Acid

20% NaOH SoIn Water Splitter

Figure 3.15

Rayon process ﬂow sheet (Mani et al., 1988).

22% Na2SO4 12.4% H2SO4

434 Table 3.7

Ion Exchange Membranes: Fundamentals and Applications

Sodium sulfate conversion via aquatech: operating cost summary

Basis:

10,000 Mt/y NaOH 12,250 Mt/y H2SO4 8,000 h/y 2y life for cell stacks Battery limits capital:

Items Cell maintenance Electricity at 5 f /kWh Other maintenance Labor and supervision Depreciation at 10% Taxes and insurance at 2 Total operating cost Product credits NaOH at $250/Mt H2SO4 at $80/Mt Total credits Proﬁt Return on investment

$3.7 106 (two-compartment cell) and $5.2 106 (three-compartment cell) (January 1986 costs; all costs in U.S. Dollars) 2-compartment cell

3-compartment cell

360,000 730,000 150,000 140,000 370,000 74,000 1,824,000

612,000 850,000 180,000 160,000 520,000 104,000 2,426,000

2,500,000 980,000 3,480,000 1,656,000 45%

2,500,000 980,000 3,480,000 1,054,000 20%

Source: Mani et al. (1988).

Table 3.7 shows the estimated economics of the Aquatech technology for a generalized sulfate conversion application. The plant has been sized to produce 10,000 MT year1 of NaOH (100% basis) from an aqueous sulfate feed. The total capital equipment for the plant includes the cell stacks, power supply, tanks, plumbing, etc. to convert a ‘‘clean’’ sulfate solution to its aqueous acid/ base constituents. Cell stack life is estimated at two years based on laboratory and pilot studies. The major variable cost items are for electricity and cell maintenance. REFERENCES Aritomi, T., vanden Boomgaard, Th., Strathmann, H., 1996, Current-voltage curve of a bipolar membrane at high current density, Desalination, 104, 13–18. Bauer, B., Gerner, F. J., Strathmann, H., 1988, Development of bipolar membranes, Desalination, 68, 279–292. Dunlop, P. J., 1957, Study of interacting ﬂows in diffusion of the system Rafﬁnose-KClH2O at 251C, J. Phys. Chem., 61, 994–1000. Dunlop, P. J., Gosting, L. J., 1959, Use of diffusion and thermodynamic data to test the Onsager reciprocal relation for isothermal diffusion in the system NaCl-KCl-H2O at 251C, J. Phys. Chem., 63, 86–93.

Bipolar Membrane Electrodialysis

435

Frilette, V. J., 1956, Preparation and characterization of bipolar ion-exchange membranes, J. Phys. Chem., 60, 435–439. Hanada, F., Hirayama, K., Ohmura, N., Tanaka, S., 1991, Bipolar membrane and method for its production, European Patent 0459820. Hanada, F., Hirayama, K., Ohmura, N., Tanaka, S., 1993, Bipolar membrane and method for its production, U.S. Patent 5,221,455. Hanada, F., Hirayama, K., Tanaka, S., Ohmura, N., 1996, Bipolar membrane and method for its production, JP Patent 2524012. International Critical Tables, 1930, Vol. 7, McGraw-Hill, New York. p. 232. Ishibashi, N., Hirano, K., 1958, Production of sodium hydroxide and hydrochloric acid using bipolar membranes, J. Electrochem. Soc. Jpn., 26, 28–32. Kang, M. S., Choi, Y. J., Moon, S. H., 2004, Effects of inorganic substances on water splitting in ion-exchange membranes, II. Optimal contents of inorganic substances in preparing bipolar membranes, J. Colloid Interface Sci., 273, 533–539. Mani, K. N., 1991, Electrodialysis water splitting technology, J. Membr. Sci., 58, 117–138. Mani, K. N., Chlanda, F. P., Byszewski, C. H., 1988, Aquatech membrane technology for recovery of acid/base values from salt streams, Desalination, 68, 149–166. Nagasubramanian, N., Chlanda, F. P., Liu, K. J., 1977, Use of bipolar membranes for generation of acid and base — An engineering and economic analysis, J. Membr. Sci., 2(2), 109–124. Oda, K., Murakoshi, M., Saito, T., 1957, On the properties of double membrane for ion exchange, J. Electrochem. Soc. Jpn., 25, 531–534. Ohki, S., 1965, Rectiﬁcation by a double membrane, J. Phys. Soc. Jpn., 20, 1674–1985. Pourcelly, G., Tugas, I., Gavach, C., 1994, Electrotransport of sulphuric acid in special anion-exchange membranes for the recovery of acids, J. Membr. Sci., 97, 99–107. Sata, T., Yamaguchi, T., Matsusaki, K., 1995, Effect of hydrophobicity of ion exchange groups of anion exchange membranes on permeability between two anions, J. Phys. Chem., 99, 12875–12882. Simons, R., 1993, A mechanism for water ﬂow in bipolar membranes, J. Membr. Sci., 82, 65–73. Strathmann, H., 2004, Ion-Exchange Membrane Separation Process. Membrane Science and Technology Series, 9, Elsevier, Amsterdam pp. 200–205. Tanaka, Y., 2007, Water dissociation reaction generated in a water dissociation layer formed on an ion exchange membrane, J. Membr. Sci., forthcoming. Tanaka, Y., 2006, Irreversible thermodynamics and overall mass transport in ionexchange membrane electrodialysis, J. Membr. Sci., 281, 517–531. Tanaka, Y., Mastuda, S., Sato, Y., Seno, M., 1982, Concentration distribution and dissociation of water in ion exchange membrane electrodialysis III, The effects of electrolytes on the dissociation of water, J. Electrochem. Soc. Jpn., 50(8), 667–672. Tanioka, A., Shimizu, K., 1997, Effect of interface structure and amino groups on water splitting and rectiﬁcation effects in bipolar membranes, Polymer, 38, 5441–5446. Tanioka, A., Shimizu, K., Miyasaka, K., Zimmer, J., Minoura, N., 1996, Effect of polymer materials on membrane potential, rectiﬁcation and water splitting in bipolar membranes, Polymer, 37, 1883–1889. Umemura, K., Naganuma, T., Miyake, H., 1994, Production of a bipolar membrane, JP Patent H6-32918. Umemura, K., Naganuma, T., Miyake, H., 1995, Bipolar membrane, U.S. Patent 5,401,408. Wien, M., 1928, Uber die abweichungen der electrolyte vom Ohmschen gesetz, Phys. Zeits, 29, 751–755.

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Ion Exchange Membranes: Fundamentals and Applications

Wien, M., 1931, Uber leitfahigkeit und dielektrizitatskonstante von elektrolyten bei hochfrequenz, Phys. Zeits, 32, 545. Wilhelm, F.W., 2000, Bipolar membrane preparation, In: Kemperman, A.J.B. (Ed.), Bipolar membrane technology Enschde, Twente University Press, The Netherlands. Xu, T. W., 2005, Ion exchange membranes: State of their development and perspective, J. Membr. Sci., 263, 1–29. Xu, T. W., Fu, R. Q., Yang, W. H., Xue, Y. H., 2006, Fundamental studies on a novel series of bipolar membranes prepared from Poly (2,6-dimethyl-1,4-phenylene oxide) (PPO). II. Effect of functional group type of anion exchange layers on I-V curves of bipolar membranes, J. Membr. Sci., 279, 282–290.

Chapter 4

Electro-deionization 4.1.

OVERVIEW OF TECHNOLOGY

Electro-deionization (EDI) was applied to concentrate radioactive aqueous wastes at ﬁrst by Walters et al. (1955) in 1955. Kollsman, (1957) performed some experimental work for de-ionizing water in 1957. However, the EDI technology was not commercialized until the late 1980s. It is now applied to the supplies of puriﬁed water (PW) in power generation, the electronics, pharmaceutical, food and beverage industries. EDI is essentially a mixed-bed (MB) deionization process built into an electrodialysis (ED) system that continuously regenerates the ion exchange resin using electrical power. The process produces high purity water in the range of 8–17 MO from feed water, which contains 1–100 mg l1 of total dissolved solids (TDS). The electrically generated hydrogen and hydroxyl ions recombine to form water in the concentrate and produce no extra salts. EDI has the advantage of being a continuous process with constant stable product quality, which is able to produce high purity water without the need for acid or caustic regeneration. In a process train in which reverse osmosis (RO) is followed by EDI, water can be produced that is comparable to MB ion exchange treated water. Ganzi et al. (1987) show a schematic of the EDI process as in Fig. 4.1. In this ﬁgure, an applied DC potential is denoted by (+) and (). Here, ion exchange membrane sheets are represented by the vertical lines labeled in terms of their ionic permeability. These membranes, used as barriers to bulk water ﬂow, deﬁne district compartments, through which liquid streams containing ions (Na+ and Cl ions) can ﬂow tangentially. A DC electrical potential, applied by an external power supply, causes the transfer of ions to occur. In the diluting compartment, the space between membranes is ﬁlled with cation and anion exchange resins (or resin ﬁbers). The transfer of ions is represented schematically by arrows. Ions entering the diluting compartment react with the ion exchange resin. Ions then transfer through the resin in the direction of the potential gradient. Ions simultaneously transfer across the membranes, maintaining neutrality in all compartments. Because of the permselective properties of the membranes and the directionality of the electrical potential gradient, ions in the solution become depleted in the diluting compartment and become concentrated in adjacent (concentrating) compartment. The use of ion exchange resins in the diluting compartment is the key to the process. One reason for this is that without the ionic conductivity afforded by the resin, ion transfer does not occur at a practical rate for most fresh-water DOI: 10.1016/S0927-5193(07)12018-0

438

Cation permeable membrane

Ion Exchange Membranes: Fundamentals and Applications

Anion permeable membrane

Feed Cl− Na+

Cl− Anion exchanges

Cation permeable membrane

Na+ Cation exchanges

Anion permeable membrane Enhanced transfer regime

Na+

Na+

Cl−

Cl−

OH− H+

H+

OH−

OH−

Electro regeneration regime

H+ H+ Concentrating Concentrating Diluting compartment compartment compartment Concentrate

Figure 4.1

Product

Concentrate

Schematic of IONPURE process (Ganzi et al., 1987).

source. Without the ion exchange resins, the solution in the diluting compartment is deionized and its electrical resistance increases to such an extent that useful electrical current transfer is outweighed by membrane inefﬁciencies, resulting in back-diffusion of ions from the concentrating to diluting compartments. By ﬁlling the ion exchange resins in the diluting compartment, the conductivity of the compartment is increased and enhanced ionic transport rates are achieved in the enhanced transfer regime depicted in Fig. 4.1. In this regime, the resins remain in the salt forms and the rate limiting step is most often ﬁlm-diffusion of the ions in the bulk solution to the ion exchange resin surfaces. The ﬁlm-diffusion leads to limiting current density under which the electric current is limited by the diffusion of counter-ions to a resin surface and co-ions away from a resin surface. A second reason for the need for resin in the diluting compartment relates to water dissociation reaction generated in the electro-regeneration regime in Fig. 4.1. In this regime, high potential gradients are created at the interface between the cation exchange resins and the anion exchange resins or at the interface between the cation (anion) exchange resins and the anion (cation) exchange membranes. Signiﬁcant amounts of H+ and OH ions are produced due to the water dissociation (water splitting) and the resins become electrochemically regenerated to the H+ and OH forms. The H+ ions and OH ions

Electro-deionization

439

produced in this regime are transported toward the electrodes under the applied potential ﬁeld. They recombine in the desalting or the concentrating compartments and regenerate water. Under these conditions, the resin acts as a continuously regenerated MB ion exchange column, exchanging H+ ions and OH ions in stoichiometric amounts with salts in the solution. EDI devices operating in the electro-regeneration regime can remove weakly-ionized compounds. These phenomena account for the ability of the EDI process to efﬁciently de-ionize water to the 10 to 0.1 microsiemen cm1 region of electrical conductivity (Ganzi et al., 1997). Allison (1996) suggests that the feed water to the EDI process must have very low levels of ﬁne suspending matter because the ion exchange resin essentially acts as a media ﬁlter and there is no developed method to backwash the media. This means extensive pretreatment such as ultra-ﬁltration or RO is needed to assure continuous low levels of the suspending matter. Stack repairs are also more difﬁcult. Stacks are ﬁlled with resin after assembly, but there is no effective means to unload the resin prior to disassembly. Each compartment must be cleaned to remove the resin beads (or resin ﬁbers) prior to re-assembly. There are no real advantages and there are these disadvantages over ED when non-water splitting operation is considered. When EDI is operated in the water splitting mode, the efﬁciency of utilizing power for desalting is low. Typically only 10–20% of the applied DC current transports ionic salts. The rest of the current splits water. With the low power utilization efﬁciency, the process is really practical only on low TDS waters such as RO permeate with a TDS in the range of 100 mg l1 or less. 4.2.

MASS TRANSFER IN THE EDI SYSTEM

In order to understand the mass transport phenomena arising in the EDI system, Glueckauf (1959) discussed the two-stage ion transport process in the desalting compartment. The ﬁrst concerns the diffusion transfer from the ﬂowing solution into the ion exchange resin particles. The second concerns the transfer of the ions along the ion exchange particle chains from the interior of the compartment to the ion exchange membranes. Matejka (1971) reported the experimental and theoretical work that advanced the theory of ionic transport in the EDI system. On the other hand, Verbeek et al. (1998) proposed the following concept expressing the mass transport in the EDI system as presented in Fig. 4.2. In this system, the anode compartment and cathode compartment are ﬁlled respectively with cation exchange resins and anion exchange resins. Accordingly, the water splitting in this system occurs only at the interface between the electrodes and ion exchange resins. It is therefore possible to describe the physicochemical processes in the cell without terms such as water dissociation described in Section 4.1. Further it is possible to present the ﬂuxes for each ions in the liquid

440

Ion Exchange Membranes: Fundamentals and Applications

AM

CM Cation exchange compartment

O2

Anion exchange compartment OH−

H+ +

Concentrate compartment

−

X− H+ M+

OH− H2

RO: 10 µS/cm Concentrate: 200 µS/cm

Figure 4.2

Deionized water: 55 nS/cm

Mass transport in the EDI system (Verbeek et al., 1998).

(solution) phase and the solid (ion exchange resin) phase in a differential balance element as illustrated in Fig. 4.3, in which both phases are connected through the opening marked with a circle. In Fig. 4.3, ions i (counter-ion denoted by the subscript (i) are assumed to be supplied upward with the feeding solution from the inlet of the element. They ﬂow in the liquid phase and ﬂow out to the outside of the system. The ionic concentration change in the element is expressed by the following partial differential equation expressed on the z-axis of the space coordinate in the direction of ﬂuid ﬂow. @C i @C i 1 ¼ v aS Ji (4.1) @t @z Here, Ci is the counter-ion concentration (mol l1) in the liquid phase, t time, aS (m2 per m3) the speciﬁc surface of the ion exchange resin, e the porosity of ion exchanger bed, and Ji (mol m2s1) the ﬂux of ion i passing through the opening. We deﬁne the counter-ionic ﬂux in the solid phase J¯ i from the left hand side in the element, passing through the solid phase, taking in Ji from the opening, and ﬂowing out at the right hand side of the system. These phenomena are expressed by the following partial differential equation expressed on the

441

Electro-deionization

Ci +

∂Ci dZ ∂Z

liquid phase

Solid phase

Ji

dz

dx

Ji

Ji +

∂Ji dx ∂x

z Ci

Figure 4.3

x

Material balance in a liquid and a solid phase (Verbeek et al., 1998).

x-axis of the space coordinate in the direction of external electrical ﬁeld, taking ¯ i as the counter-ionic concentration in the solid phase. C ¯i @C @J¯ i ¼ aS J i (4.2) @t @x The counter-ions i are assumed to be supplied from the liquid phase to the opening along the z-axis perpendicular to the surface of the solid phase (ion exchange resins ﬁlled in the compartment). So, we have the following Nernst– Planck equation established on the z-axis drawn in the liquid ﬁlm formed on the surface of the ion exchange resins for counter-ions i and co-ions j as follows: J i=j ¼ Di=j

@C i=j @c zi=j C i=j ui=j @z @z

(4.3)

in which, Di/j, zi/j and ui/j are respectively the diffusion constant, charge number and mobility of the ions i or j in the solution ﬁlm. For neutral species k, the ﬂux is expressed by the following diffusion equation. J k ¼ Dk

@C k @z

(4.4)

Next, the following ions are considered to be important in ultrapure water 2+ (UPW) production: H+, Na+, K+, NH+ , Mg2+, OH, Cl, NO 4 , Ca 3,

442

Ion Exchange Membranes: Fundamentals and Applications

3 2 SO2 4 , HCO , CO3 , Si(OH)O , and in addition, dissolved neutral CO2, Si(OH)4. Some of these components are coupled by the following chemical reactions with the corresponding reaction constants:

Water dissociation H2 O2Hþ þ OH

K W ¼ 1014

Carbonate system þ CO2 þ H2 O2HCO 3 þH 2 þ HCO 3 2CO3 þ H

(4.5)

K C;1 ¼ 106:43

K C;2 ¼ 1010:33

(4.6) (4.7)

Silicate system SiðOHÞ4 2Hþ þ SiOðOHÞ 3

K S ¼ 109:8

(4.8)

The co-ions j are not absorbed by the ion exchanger and they do not participate in a chemical reaction, so their net ﬂuxes Jj become zero: Jj ¼ 0

(4.9)

There is no net current in the liquid ﬁlm formed on the surface of ion exchange resins: m X

ðzi J i Þ þ

i¼1

n X ðzj J j Þ ¼ 0

(4.10)

j¼1

In addition, the rule of electro-neutrality applies at every position of the solution: m X i¼1

ðzi C i Þ þ

n X ðzj C j Þ ¼ 0

(4.11)

j¼1

Finally, the main driving force for ion transport in the solid phase is the external electric ﬁeld. Diffusion can be neglected as the resulting ﬂuxes are much smaller than the ﬂux caused by migration. In this situation, the counter-ion ﬂux in the solid phase J¯ i is expressed by ¯ i @c J¯ i ¼ zi u¯ i C (4.12) @x The total electric current I and external ﬁeld gradient @c/@x are given by Ohm’s law as follows: @c ¼ Rl @x F ð1 Þb=d

I Rd

n 2 C ¯ i ¯ i Þdxdz z¼0 x¼0 ðSi¼1 zi u

(4.13)

443

Electro-deionization

Here, b, d and l are respectively the width, the thickness and the length of the compartment. The EDI process expressed by the equations described above was calculated using the computer program. The results are exempliﬁed as follows: Fig. 4.4 shows the dynamic Na+ ion concentration changes in the course of time in the cation exchange compartment ﬁlled with totally regenerated cation exchange resins (H+ type). Part (a) is calculated without continuous electrochemical regeneration, indicating H+ ions to be replaced by Na+ ions. Part (b) is calculated with continuous electrochemical regeneration due to water splitting, indicating the decreasing of Na+ ion concentrations. 10

CNa (10−5M)

8 6 4 2 0

0

0.1

0.2

0.3

z (m) (a) without electrochemical regeneration 10

CNa (10−5M)

8 6 4 2 0 0

0.1

0.2

0.3

z (m) (b) with electrochemical regeneration

Figure 4.4 Na+ ion concentration changes in a cation exchange compartment (Verbeek et al., 1998).

444

Ion Exchange Membranes: Fundamentals and Applications

5 4 C i (10−5 M)

I

II

III

3 2

(a) in a liquid phase

1 0 0

0.05

0.10 z (m)

0.15

0.20

3.0 2.5

C i (M)

2.0 I

II

III

1.5 (b) in a solid phase 1.0 0.5 0 0

0.05 = Na+

0.10 z (m) = Ca2+

0.15

0.20

= H+

Figure 4.5 Ionic concentration proﬁles in a cation exchange compartment (Verbeek et al., 1998).

Fig. 4.5 shows the ionic concentration proﬁles in a cation exchange compartment in a steady state in case of abnormally increased calcium concentration in a feeding solution (e.g. due to failure in the softening stage). In the ﬁrst part of the compartment, part I, the cation exchange resins are selectively loaded with Ca2+ ions because of high selectivity for Ca2+ ions of the cation exchanger as shown in (b). Accordingly Ca2+ ion concentration in the solution is gradually decreased, however, Na+ ion concentration is unchanged (a). In the next part, part II, Na+ ions in the solution are gradually loaded to the cation exchange resins, so Na+ ion concentration is decreased in the solution (a) and increased in the resins (b). However, Na+ ion concentration in the resins begins to decrease via the peak due to the Na+ ion concentration decrease in the solution (b). In the ﬁnal part, part III, the concentrations of both Na+ ions and Ca2+ ions are

445

Electro-deionization

decreased and instead of them the concentration of H+ ions is increased (due to water splitting) in the solution and in the resins (a, b). The reasonability of the changes in Fig. 4.5 is conﬁrmed experimentally (Neumeister et al., 2000). 4.3.

STRUCTURE OF THE EDI UNIT AND ENERGY CONSUMPTION

The structure of the EDI unit is illustrated in Fig. 4.6 (Deguchi and Karibe, 1998). Based on the principle of ED, cation exchange membranes and anion exchange membranes are arranged alternately. Desalting cells and concentrating cells incorporated with spacers are arranged between the membranes. Cation exchange resins (or resin ﬁbers) and/or anion exchange resins (or resin ﬁbers) are ﬁlled in the desalting cells. A cathode chamber and an anode chamber are placed at both outsides of the cell arrangement and a direct current is passed. The electric current is expressed as: I¼

QF ðN t N p Þ nZ

(4.14)

where I is the direct current (A), Q the feeding solution ﬂow rate (ml s1), Nt the ion concentration in the feeding solution (eq l1), Np the ion concentration in the product solution (eq l1), n the constant, F Faraday constant and Z the current efﬁciency. Energy consumption is P ¼ I 2 Rm

(4.15)

where P is the direct current electric power (W), Rm the electric resistance of the system (O). Ebara Corporation developed an EDI (GDI) apparatus with ion exchange nonwoven fabric (IEN) and ion conducting spacer (ICS) (Akahori Feeding solution A C A C A C A

+

C A C A C A

C A C A C A C A C A

D CD C D CD CD C D C D C D CD C DC D C D

Anode

C

− Cathode

Desalted solution Concentrated solution A = Anion exchange membrane D = Desalting cell

Figure 4.6

c = Cation exchange membrane C = Concentrating cell

EDI cell arrangement (Deguchi and Karibe, 1998).

446 20

100

18

90

16

80

14

70

12

60

10

50

8

40

6

30

4

20

2

10

0

0

SiO2 remaining ratio (%)

Specific resistance (MΩ cm)

Ion Exchange Membranes: Fundamentals and Applications

0 100 200 300 400 500 600 Electric power consumption (Wh/m3)

Figure 4.7 Energy consumption vs. electric resistance and silica removal in the GDI process (Akahori and Konishi, 1999).

and Konishi, 1999). IEN and ICS are prepared by radiation graft polymerization and placed between ion exchange membranes. They reduce cell pair resistance and promote water dissociation. Fig. 4.7 gives electric resistance and silica removal plotted against energy consumption in the GDI process, showing that UPW (over 17.5 MO cm) is produced at energy consumption of 250 Wh m3. 4.4.

WATER DISSOCIATION IN AN EDI PROCESS

Fig. 4.8 is a schematic, sectional view through an EDI apparatus, illustrated ion ﬂow direction through an ion-depleting and ion-concentrating compartment. DiMascio and Ganzi (1999) suggest that the surfaces of ion exchange resins and ion exchange membranes are in contact with each other, and form the resin/membrane interfaces and resin/resin interfaces at which water splitting reactions arise at over limiting current density. They discussed the auto-catalytic inﬂuence of functional groups (quaternary ammonium groups and tertiary alkyl amine groups) in an anion exchange membrane and anion exchange resin to the intensities of the water dissociation reaction. The feature of the water dissociation generated in the EDI system considerably resembles to that in the bipolar

447

Electro-deionization

AM

CR

AR σH

JOH

CR

CM

AM σH

2O

2O

JOH

JH

JH

JH

JOH

−

+

a Anode

c

b

Ion depleting compartment

c Ion concentrating Cathode compartment

CM: Cation exchange membrane AM: Anion exchange membrane CR: Cation exchange resin AR: Anion exchange resin JH: H+ ion flux JOH: OH− ion flux σ H O: H2O regeneration rate 2 a: Water dissociation generation at a resin/membrane interface b: Water dissociation generation at a resin/resin interface c: H2O regeneration

Figure 4.8

Water dissociation reaction in an EDI system.

membrane ED system described in Chapter 3. Here, we discuss the mechanism of the water dissociation reaction in the EDI system. Water dissociation reaction is presented by the following equation and it is generated in the water dissociation layer formed at the resin/membrane interface ‘‘a’’ and the resin/resin interface ‘‘b’’ in Fig. 4.8 as suggested by DiMascio and Ganzi (1999). ka

H2 O 3 Hþ þ OH kb

(4.16)

ka and kb are respectively forward and reverse equilibrium reaction rate constant. The water dissociation reaction produces the H+ ion ﬂux JH and OH ﬂux JOH in the water dissociation layer formed at the resin/resin interface and membrane/resin interface. The H+ ions and OH ions are recombined at ‘‘c’’ at the outside of the water dissociation layer to regenerate H2O. The H2O regeneration rate sH2 O is equivalent to JH and JOH. J H ¼ J OH ¼ sH2 O

(4.17)

Applying the discussions on the water dissociation reaction in the bipolar membrane ED, the mechanism of the water dissociation in the EDI system is understood with the illustration in Fig. 4.9 (cf. Fig. 3.10 in Section 3.3.2), showing the intermediate layer to be formed between the resin and membrane.

448

Ion Exchange Membranes: Fundamentals and Applications

Water dissociation layer A

k

H+

lK

Cathode

Cation exchange membrane

OH-

H+

OH-

L

lA

Intermediate layer

Anion exchange resin

Anode

l : Thickness of the water dissociation layer L: Thickness of the intermediate layer

Figure 4.9

Water dissociation layer formed in an EDI system.

The similar illustration is conceivable between the resin and resin. The thickness of the intermediate layer L is estimated to be L ^ 107 m according to the atomic force microscope (AFM) images observed by Sata et al. (1995) (cf. Section 3.3.1, Fig. 3.7). Water dissociation reaction is generated in the water dissociation layer formed in the intermediate layer. Electric current efﬁciency Z of the water dissociation reaction is expressed as follows (cf. Section 8.10, Eq. (8.53) in Fundamentals) (Tanaka, 2007). i Z ¼ ðka C H2 O kb C 0H C 0OH Þl (4.18) F Electric current efﬁciency in the electro-deionization process ZE is expressed by Eq. (4.19), which is introduced in the bipolar ED process (cf. Section 3.3.2, Eq. (3.13)). Z E ¼ ZK þ ZA ZK ZA

4.5.

(4.19)

REMOVAL OF WEAKLY-IONIZED SPECIES IN AN EDI PROCESS

Weakly-ionized species such as silica, carbon dioxide, boron and ammonia are difﬁcult to remove through the membrane process such as RO, electrodialysis reversal (EDR) etc. However, EDI removes these species effectively. Hernon et al. (1999) discussed how the EDI process successfully removes various weaklyionized species as follows.

449

Electro-deionization

-

Ca++

CO2 SiO2 Na+ HCO3−

Figure 4.10

Cathode (-) Mg++

Na+

-

-

H+

Cation-Exchange membrane Ca++ High-Purity product water

Cl− SO4=

Anion-Exchange membrane SO4=

Cl−

+

+

HCO3− HSiO3− CO3= Anode (+)

+

OH− +

Basic ﬂow scheme of the EDI process (Hernon et al., 1999).

4.5.1

Effect of Water Dissociation in an EDI Process Fig. 4.10 illustrates the basic ﬂow scheme of EDI process. In EDI, the ion exchange resins facilitate mass transfer of weakly-ionized species mainly due to water splitting. Namely, in the diluting cell, the DC electrical ﬁeld splits water at the surface of the ion exchange resin beads, producing hydrogen and hydroxyl ions which act as continuous regenerants of the ion exchange resin. This allows a portion of the resins in the EDI to always be in the fully generated state. In turn, the fully generated resins are able to ionize weakly-ionized species. Once ionized, these species are quickly removed under the inﬂuence of the DC electrical ﬁeld. Fig. 4.10 roughly depicts how different ions are removed as water travels through the EDI diluting cell, strongly-ionized ions being removed ﬁrst in the ﬂow-path and weakly-ionized species removed as the water moves down the ﬂow-path. EDI’s performance in removing these weakly-ionized species will thus assuredly leads to greater use of EDI in the production of UPW.

4.5.2

Silica Removal in an EDI Process To further explore the performance limits of EDI on weak ion removal, Hernon et al. (1999) conducted the following laboratory study, focusing on the effect of ﬂow rate and amperage on silica removal in a full-scale, 50 gpm unit. EDI feed water for this test contained 20 ms cm1 of NaCl and 0.5 ppm of CO2 when the feed water was treated with RO. As shown in Fig. 4.11, silica removal decreases with increasing ﬂow rate for constant amperage. Increasing ﬂow rate results in lower residence time, more utilization of available current for strong ion transfer, and less water splitting available for weak ion removal. However, even at velocities that exceed nominal velocities by 50%, silica removal remained above 95%. Fig. 4.12 shows the effect of amperage on silica removal for a constant ﬂow. Initially, silica removal increases with increasing amperage due to higher extent of resin/membrane regeneration; however, it levels off at a certain

450

Ion Exchange Membranes: Fundamentals and Applications

100

Silica removal (%)

98

96

Feed conductivity: 20 micros/cm, CO2=6 ppm

94

92

90 40

Figure 4.11

50

60 Flow rate (gpm)

70

80

EDI performance at varying ﬂow rate (Hernon et al., 1999).

100

Silica removal (%)

98

96

Feed conductivity=20 micros/cm, CO2=6 ppm

94

92

90 0.6

0.8

1.0 I /I0

Figure 4.12

EDI performance at varying current density (Hernon et al., 1999).

1.2

Electro-deionization

451

current I0 which is a function of ﬂow rate and feed composition. Operation at current densities higher than I0 does not impact silica removal any further as the limiting factor at this point for silica removal is the residence time. The above studies conﬁrm that the degree of weak ion removal in an EDI unit is tied to the degree of water splitting occurring within it. The above studies also provide a basis for calculating design conditions for the removal of weakly-ionized species. 4.5.3

Carbon Dioxide Removal in an EDI Process Carbon dioxide removal by EDI is an important facet of its performance. When carbon dioxide is present in an ion exchange feed stream, the carbon dioxide competes with silica for ion exchange sites on an anion resin. Carbon dioxide often represents the largest anion load on an ion exchange system, especially when the ion exchange unit is preceded by an RO unit. The presence of excess amounts of carbon dioxide both limits the capacity of ion exchange resin to remove silica and limits the efﬁciency of silica removal by the ion exchange bed. As will discuss in Section 4.6.1 silica removal is critical in both power generation and in semiconductor production. The presence of an excess amount of carbon dioxide in effect exposes a plant to potentially serious silica problem. Carbon dioxide cannot normally be removed via other membrane demineralization process such as RO and EDR unless chemical adjustments are made to change alkalinity levels. EDI on the other hand, is a membrane demineralization process routinely reduces CO2 levels by over 99% in most applications (cf. Table 4.4). 4.5.4

Boron Removal in an EDI Process Boron is often present in water and is problematic as it can cause defects in semiconductor chip manufacturing. Boron is not well removed by the ion exchange resin process due to its poor ionization and low selectivity (Yagi et al., 1994). Table 4.1 shows removal of boron by both RO and EDI at four plants. The RO units typically remove only a small portion of the boron from the feed water. However, the EDI units consistently remove over 96% of the boron in the feed water. 4.5.5

Ammonia Removal in an EDI Process The ammonia study was part of a largest project addressing the development of total water-recycle systems for Space Station. In a self-contained life support system, such as the future-planned Space Station, the ability to efﬁciently recycle water is key to long-term mission success. It is projected that a four-person team will use a supply of 225 lbs of water for general use during a space mission to Mars and back. All water used will need to be recycled through an intricate recovery system and treated through a sequence of processes to produce drinking water. Ammonium ions are generated as a decomposition product of urea and

452

Ion Exchange Membranes: Fundamentals and Applications

Table 4.1

Boron levels and removals at various sites

RO feed boron (ppb) RO product boron (ppb) EDI feed boron (ppb) EDI product boron (ppb) RO boron removal (%) EDI boron removal (%) RO feed pH EDI feed pH

Power Plant #2

Semiconductor Semiconductor Semiconductor Plant #2 Plant #3 Plant #4

22 14 14 0.45 36.3 96.8 6.5 5.7

280 170 71 2.75 39.3 96.1 7.7 6.5

110 83.5 83.5 2.8 24.1 96.6 7.8 6.4

85 64.5 64.4 0.74 24.1 98.9 7.9 6.4

Source: Hernon et al. (1999).

over time will build up in concentration, thus rendering the water unsuitable for human consumption. EDI, being one of the puriﬁcation steps, is required to reduce the level of ammonia from 200 ppm down to the range of 0.5–1 ppm. Fig. 4.13 shows the percent ammonia removal by EDI. EDI operation was optimized in terms of ﬂow rate and current. The system was operated in a semi-continuous mode with a continuous 200 ppm ammonia feed at 160 ml min1. The concentrate stream in turn was continuously recycled from a separate waste tank. The waste tank volume was kept constant by periodically removing a small amount of water that would make up for any water transfer from the dilute to the concentrate through the membranes. The amount of periodic waste blowdown corresponds to a water recovery value of 99.9%. Due to such continuous recycle, the waste concentration increased over time as pictured in Fig. 4.13. Such high concentration resulted in turn to a slight decrease in ammonia removal due to back-diffusion. 4.6.

PRACTICE

4.6.1 Ultrapure Water Production in Electric Power Generation and Semiconductor Manufacturing Processes In the nuclear power plants, UPW is used for makeup to high-pressure stream boiler. In the semiconductor plants, the UPW is used for rinsing semiconductor wafers after various processing steps. Ionic Inc. applied the EDI process operating in the following locations (Hernon et al., 1995). (a) (b) (c) (d) (e) (f)

Grand Gulf Nuclear Station (GGNS) Arkansas Nuclear ONE (ANO) Seabrook Nuclear Station (SNS) A New England semiconductor manufacturing plant (Semi 1) A Midwest semiconductor manufacturing plant (Semi 2) An Arizona semiconductor manufacturing plant (Semi 3)

453

Electro-deionization

35000

100 99

NH4+ removal (%)

25000

97 96

20000

95 15000

NH4+ removal (%) ppm NH4+ in concentrate

94 93

10000

ppm NH4+ in concentrate

30000

98

92 5000

91

0

90 168

672 840 Operating hours pH = 10.3, 99.9% water recovery

Figure 4.13

336

504

1008

1176

1344

NH+ 4 removal by EDI (Hernon et al., 1999).

In all these installations, EDI is one building block of a multi-step treatment process. The use of various treatment steps in the treatment process depends largely on differences in feed water characteristics such as TDS, pH, organic load, dissolved gases, temperature and the presence of various undesirable constituents, such as trihalomethanes. Table 4.2 summarizes some of the feed water variables to each of these units as well as the unit processes that are used in each installation. Fig. 4.14 shows conductivity reductions which is directly related to TDS removed across the EDI unit at GGNS. In the ﬁgure, 100% reduction corresponds to the minimum conductivity achievable due to water dissociation. During all of the operating terms, the overall conductivity reduction averages over 99.5%. The values in the other stations and plants have been steady in the range of 99% to 99.5+%. EDI feed water and product water samples were analyzed for sodium, calcium, magnesium, chloride and sulfate. Rates of removal range from one to three orders of magnitude depending on the speciﬁc ion and its feeding water concentration. EDI product water quality approaches MB ion exchange quality. Table 4.3 summarizes the results of these analyses. In power plants high silica levels in the UPW supply to steam generators can lead to silica deposition on the electrical generator turbine blades. CO2 competes with silica ions for exchange sites, so the amount of CO2 in a feed stream affects both bed life and silica removal efﬁciency in the ion exchange bed. Table 4.4

454

Ion Exchange Membranes: Fundamentals and Applications

Table 4.2

EDI installations, raw feed water sources and pretreatment steps

Location

Feed Source

Feed TDS (ppm)

Temp. (1C)

Flowrate (gpm)

GGNS ANO SNS Semi 1 Semi 2 Semi 3

Surface Surface Well Surface Well Surface

400 100 475 230 900 700

17–25 10–30 25 20 15–25 20–25

50 200 150 65 100 200

Stream Flowsheet MMF–ACF–UF–EDR–RO–EDI MMF–ACF–UF–EDR–RO–EDI UF–RO–EDI CF–UF–RO–EDI MMF–DEGAS–UF–RO–EDI UF–RO–EDI

Source: Hernon et al. (1995).

Conductivity reduction (%)

100

99

98

97

96

95

Figure 4.14

3000

4000 5000 Operating time (h)

6000

EDI conductivity reduction, GGNS (Hernon et al., 1995).

presents summary of silica and carbon dioxide feed levels and the corresponding percent removals achieved with EDI at the six sites mentioned above. 4.6.2

Ultrapure Water Production in Pharmaceuticals Various grades of water are used by the pharmaceutical industry for a number of applications. Deﬁnitions of each water type and quality are provided in the United States Pharmacopoeia (USP). Of this water, water for injection (WFI) and PW are of primary interest to water treatment engineers and equipment suppliers. Table 4.5 provides a summary of the numerical interpretation of the Pharmacopoeia chemistry limits for this water. A leading manufacturer of ophthalmic products (eye drops, contact lens cleaner etc.) planned to increase its capacity by establishing a new production facility in the continental United States. As water is the main ingredient in ophthalmic solutions, the choice of a design for the new plant’s central water

455

Electro-deionization

Table 4.3

EDI feed and product ion levels

Ion GGNS

Feed Prod Feed Prod Feed Prod Feed Prod Feed Prod Feed Prod

ANO SNS Semi 1 Semi 2 Semi 3

Na+ (ppb)

Ca2+ (ppb)

Mg2+ (ppb)

Cl (ppb)

SO2 4 (ppb)

1560 2 871 3 1210 2.4 289 o2 1710 o2 437 4

10 o0.5 42 0.7 165 2.5 158 o0.5 320 o0.5 35 o3

4 o0.5 7 o0.5 nd nd nd nd 160 o5 25 o5

58 o2 594 o2 528 o2 140 o2 2200 o2 78 o2

70 o4 88 o4 157 o2 245 o4 1110 o4 31 o4

Source: Hernon et al. (1995).

Table 4.4

Sillica and CO2 levels and removal Silica

GGNS ANO SNS Semi 1 Semi 2 Semi 3

CO2

Feed SiO2 (ppb)

Product SiO2 (ppb)

Rejection (%)

Feed Total CO2 (ppb)

Product Total CO2 (ppb)

Rejection (%)

640 3830 170 208 86 165

3 138 8 o2 o2 o2

>99.5 96.4 95.2 >99.0 >97.7 >98.8

2920 4780 5910 2800 3260 5340

17 8 o10 o10 o10 o10

99.4 99.8 >99.8 >99.6 >99.7 >99.8

Source: Hernon et al. (1995).

puriﬁcation system was a primary concern. The operational and performance requirements for the water puriﬁcation system were as follows (Parise et al., 1990): (a) (b) (c) (d) (e)

Product quality equal to or better than that speciﬁed for USP PW. Product quantity of 16 gpm, to be available on a continuous basis, 24 h per day, 6 days per week. Minimize the use of hazardous chemicals and chemical waste discharge. Minimize the opportunity for bacterial growth in the system. Achieve consistent product quality and minimize equipment downtime.

After evaluation of the available water puriﬁcation technologies, the following RO/Continuous Deionization (CDI) system developed by Ionpure

456 Table 4.5

Ion Exchange Membranes: Fundamentals and Applications

Water quality standard (Numerical interpretation of USPC standard)

Constituent pH Chloride (mg l1) Sulfate (mg l1) Ammonia (mg l1) Calcium (mg l1) Carbon dioxide (mg l1) Heavy metal Oxidizable substancesb Total solids (mg l1) Total bacterial count Pyrogen

Puriﬁed Water

Water for Injection

5.0–7.0 %0.5 %1.0 %0.1 %1.0 %5.0 %0.1 mg l1 as Cua Passes USP permanganate test %10 %50 CFU ml1 Non speciﬁed

5.0–7.0 %0.5 %1.0 %0.1 %1.0 %5.0 %0.1 mg l1 as Cua Passes USP permanganate test %10 %10 CFU/100 ml %0.25 EU ml1

Source: Parise et al. (1990). a Limits for other heavy metals may be determined. b Limits for speciﬁc oxidizable substances may be determined. Table 4.6

Puriﬁed water system feed quality (Raw water analysis)

Cations

ppm

Anions

ppm

Ca Mg Na K Fe Cu Ba Sr Al

119.1 20.4 31.1 4.9 0.1 0.1 0.0 0.3 0.4

OH CO3 HCO3 SO4 Cl NO3 F

0.0 0.0 92.0 35.1 37.1 2.2 2.4

Note: Other dissolved SiO2 ¼ 4.5 ppm; pH ¼ 8.2. Source: Parise et al. (1990).

Technologies Corporation was selected (Parise et al., 1990). The CDI module is the EDI system developed by Millipore Corporation. The analysis of the municipal feed water in Table 4.6 indicated that a single pass RO system, followed by a single pass CDI unit would meet the client’s ﬁnal product quality speciﬁcation. The system design is shown in block format as Fig. 4.15. Raw municipal water entered the system at 60 psig. And was pumped through dual on-line multimedia ﬁlters to remove medium- and large-sized particles down to a 10 mm level. The next process in the system was ﬁltration by activated carbon to remove organic contaminants and chlorine. Following the carbon beds were dual on-line cation exchange softeners to reduce the incoming total hardness to

457

Electro-deionization

Dual multimedia filters

Dual carbon filters

Dual softeners

Raw municipal

5 Micron prefilters

RO system

CDI

Feed water Recirculation pump Product 20 gpm to points of use 0.2 Micron post filter

Booster pump 254 nm UV unit

Storage tank sterile vent filter

Figure 4.15 EDI system to produce puriﬁed water meeting the United States Pharmacopoeia (Parise et al., 1990).

less than 1 ppm. The last step in the pretreatment train was ﬁltration to a nominal 1 mm level with polyethylene cartridge ﬁlters. The pretreatment train had one more design feature to minimize bacterial growth. Whenever the RO system was idle, a pump was activated to recycle water around the pretreatment train, from just before the RO inlet, to the carbon ﬁlter. This eliminated the stagnant condition that would otherwise occur when the RO was inoperative. The RO system currently utilizes 1500 square feet of Hi-Flux CP polysulfone membrane to remove suspended and dissolved contaminants, and is operated at 400 psig to produce 20 to 32 gpm of product water. The RO is currently operating at 50% recovery, but is capable of operating at up to 70% recovery. The 20 gpm RO product is next fed to a CDI installation consisting of twocell-pair CDI modules. The CDI modules remove dissolved ionic contaminants to polish the RO product water up to the required ﬁnal production resistivity 0.50 MO cm. The CDI system is producing 16 gpm of ﬁnal product water. The 60-cell-pair stacks are running at 220 V and 1.1 A each. The ﬁnal product quality from the CDI system varies with the RO product conductivity. With an RO product TDS of 17.7 ppm, the CDI product resistivity is 1 MO cm. With an RO product TDS of 10.6 ppm, the CDI product resistivity stays between 3 and 4 MO cm. The CDI modules operate at a recovery of 80%. The CDI product water is fed to a storage tank, from which water is re-circulated at 20 gpm through a 254 nm ultraviolet (UV) unit and ﬁnal 0.2 mm ﬁnal ﬁlters, before being sent to the distribution loop.

458

Ion Exchange Membranes: Fundamentals and Applications

The multimedia ﬁlters are back-washed twice per week. The carbon ﬁlters are steam sterilized and back-washed every two weeks. The softeners are regenerated automatically based on total ﬂow. The RO system is sanitized monthly with 100 ppm of sodium hypo-chlorite, and cleaned as needed to maintain ﬂux, the frequency of which depends on the SDI of the incoming raw water. No periodic maintenance is performed on the CDI modules. 4.6.3

Economic Comparison Between EDI and Mixed-Bed Ion Exchange EDI is an effective technology alternative to MB ion exchange polishing following RO. Edmonds and Salem (1998) provided the following economic comparison of EDI and MB for new plant installation. In this study, a comparison of three product ﬂow cases (50, 200 and 600 gpm, see Table 4.7) and three feed water TDS cases (low, medium and high) were considered. The deionized water quality required was normally deﬁned as greater than or equal to 17 MO cm and silica reduction to less than 20 ppb. Capital costs for the EDI and the MB equipment were obtained and given in Table 4.8. Installation costs were estimated to be percentage of the total capital cost. A factor of 0.2 was used for the EDI systems and a factor of 0.4 was used for the MB systems. The major operating costs considered for each process were as follows: Both systems had labor and water use/wastewater costs. Electricity and replacement EDI stacks were other operation costs for the EDI. MB system costs also included chemicals and replacement resins. The following cost factors were used: operating labor, $40/h; electricity, $0.07/kWh; water, $1/kgal; wastewater, $2/kgal; sulfuric acid, $0.05/lb of 100%; sodium hydroxide, $0.15/lb of 100%; cation resin, $55/ft3; anion resin, $150/ft3 and stack replacement cost, $6300/12.5 gpm product. A summary of the annualized costs for each case is given also in Table 4.8. The total system annualized costs were developed from the capital equipment costs, the operating cost items and installation factors as described above. As the RO product water TDS increases, EDI becomes increasingly cost effective. At the high ﬂow, low TDS case (600 gpm, 4.16 ppm), EDI is slightly (10%) more Table 4.7

EDI/MB feed water quality (ppm)

Constituent

Low TDS

Medium TDS

High TDS

Na+ HCO 3 Cl CO2 SiO TDS

1.2 2.68 0.28 0.9 0.5 4.16

5.27 3.15 6.32 1.0 0.5 14.74

9.25 3.78 11.9 1.2 0.5 24.9

Note: pH ¼ 6.7. Source: Edmonds and Salem (1998).

459

Electro-deionization

Table 4.8

Capital equipment cost and system annualized cost

Flow

High TDS Medium TDS Low TDS

gpm

EDI MB EDI/MB EDI MB EDI/MB EDI MB EDI/MB

Capital Equipment Cost (1000 $)

System Annualized Cost (1000 $)

50

200

600

50

200

600

60 152 0.39 60 152 0.39 60 151 0.40

150 216 0.69 150 216 0.69 150 216 0.69

385 397 0.97 385 354 1.09 385 352 1.09

30.8 73.8 0.42 28.7 60.2 0.48 27.6 49.6 0.56

83.6 120.9 0.69 75.6 94.2 0.80 71.1 72.6 0.98

177.8 240.2 0.74 153.5 176.7 0.87 140.3 126.2 1.11

Source: Edmonds and Salem (1998).

expensive than MB system. This is primarily the result of the replacement frequency of the ED stacks. EDI demonstrates a clear capital cost advantage in the 50 to 200 gpm range over MB polishing for new plants. MB polishers require considerable ancillary equipment (chemical storage and delivery systems, waste neutralization system) that negatively impacts their cost effectiveness in lowto-moderate ﬂow range. The 600 gpm case shows that the capital cost of EDI and MB systems are approximately equal. It was found that EDI, in low-to-moderate ﬂow rate system cases, is signiﬁcantly less expensive, on an annualized cost basis, than MB. In addition, EDI offers other cost beneﬁts over MB that was not quantiﬁed in this study. These include minimization of wastewater monitoring and discharge activity, signiﬁcantly reduced space requirements, reduction in spill protection plan designs and tasks, and less chemical handling for plant-operators. EDI also has the ability to respond to feed water TDS changes without compromising deionized water production and quality, with minimal impact on operation costs. REFERENCES Akahori, M., Konishi, S., 1999, Development of electrodeionization apparatus containing novel ion-exchange materials, J. Ion Exch, 10, 60–69. Allison, R. P., 1996, The continuous electro-deionization process, American Desalting Association 1996 Biennial Conference & Exposition, Monterey, CA, USA August 4–8. Deguchi, T., Karibe, T., 1998, Electro deionization, In: Water Treatment Handbook, Maruzen Publishing Co., Tokyo, pp. 220–225. DiMascio, F., Ganzi, G. C., 1999, Electrodeionization apparatus and method, U. S. Patent 5,858,191. Edmonds, C., Salem, E., 1998, An economic comparison between EDI and mixed-bed ion exchange, Ultrapure Water, November 1998.

460

Ion Exchange Membranes: Fundamentals and Applications

Ganzi, G. C., Egozy, Y., Giuffrida, A. J., Jha, A. D., 1987, High purity water by electrodeionization performance of the ionpure continuous deionization system, Ultrapure Water, 4(3), 43–50. Ganzi, G. C., Jha, A. D., DiMascio, F., Wood, J. H., 1997, Electrodeionization, theory and practice of continuous electrodeionization, Ultrapure Water, 14(6), 64–71. Glueckauf, E., 1959, Electro-deionization through a packed bed, Brit. Chem. Eng., 4, 646–651. Hernon, B., Zanapalidou, H., Prato, T., Zhang, L., 1999, Removal of weakly ionized species by EDI, Ultrapure Water, 16(10), 45–49. Hernon, B. P., Zhang, L., Siwak, L. R., Schoepke, E. J., 1995, Process report, Application of electrodeionization in ultrapure water production, 1995, 56th Annual Meeting International Water Conference, Pittsburg, PA, October 29–November 2. Kollsman, P., 1957, Method and application for treating ionic ﬂuids by dialysis, US Patent No. 2,815,320. Matejka, Z., 1971, Continuous production of high-purity water by electrodeionization, J. Appl. Chem. Biotech., 21, 117–120. Neumeister, H., Flucht, R., Furst, L., Nguyen, V. D., Verbeek, H. M., 2000, Theory and experiments involving an electrodeionization process for high-purity water production, Ultrapure Water, 17(4), 22–30. Parise, P. L., Parekh, B. S., Waddington, G., 1990, The use of ionpure continuous deionization for the production of pharmaceutical and semiconductor grades of water, Ultrapure Water, 7(8), 14–27. Sata, T., Yamaguchi, T., Matsusaki, K., 1995, Effect of hydrophobicity of ion exchange groups of anion exchange membranes on permeability between two anions, J. Phys. Chem., 99, 12875–12882. Tanaka, Y., 2007, Water dissociation reaction generated in a water dissociation layer formed on an ion exchange membrane, J. Membr. Sci., the article in submitting. Verbeek, H. M., Furst, L., Neumeister, H., 1998, Digital simulation of an electrodeionization process, Computers Chem. Eng., 22(Suppl.), S913–S916. Walters, W. R., Weiser, D. W., Marek, L. J., 1955, Concentration of radioactive aqueous wastes, Ind. Eng. Chem., 47(1), 61–67. Yagi, Y., Hayashi, F., Uchitomi, Y., 1994, Evaluation of boron behavior in ultrapure water manufacturing system, Proceedings of the Semiconductor Pure Water and Chemical Conference, San Jose, CA, pp. 54–62, March 8–10.

Chapter 5

Electrolysis 5.1.

OVERVIEW OF TECHNOLOGY

The feature of sodium chloride electrolysis industry is to produce chlorine and caustic soda, i.e. chlor-alkali, at the same time. Because of this reason, serious problems come out when the production–consumption difference of chlorine is not consistent with that of caustic soda. Actually, the situations of the chlor-alkali production have been inﬂuenced by the chlor-alkali consumption difference changing between too much and too little (Takarada, 2004). In the ﬁrst half of the twentieth century, the caustic soda consumption was increased for the production of rayon, pulp, glass etc.; however, the consumption of chlorine was limited to the ﬁelds such as disinfections, bleaching etc., so that the chlor-alkali process was restricted and if anything, alkali production by means of an ammonia soda process was developed. In and after the middle of the twentieth century, the chlor-alkali industry was expanded due to chlorine consumption increase in synthetic chemical industry, petrochemical industry, synthetic ﬁber industry etc. However, in the next stage, chlorine consumption was decreased largely owing to the environmental protection and the chlor-alkali process came to be restricted again. The chlor-alkali process is classiﬁed into the process using mercury, asbestos diaphragms and ion exchange membranes. Here we have to pay attention to the mercury-poisoning problem caused by the mercury process and the process conversion policy proceeded by the Japanese government. Fig. 5.1 gives the production capacity change of the chlor-alkali process in Japan, showing that the mercury method had fallen into disuse by 1986, and the processes were uniﬁed to the ion exchange membrane method until 1999 (Furuya, 2000). We have also to pay attention to the fact that this conversion was carried out to realize lower energy consumption and lower capital cost in ion exchange membrane process compared to the other ones as indicated in Figs. 5.2 and 5.3 (Asawa, 1991). Fig. 5.4 illustrates the principle of the ion exchange membrane electrolysis system, in which a saturated NaCl solution and pure water are supplied to an anode cell and a cathode cell, respectively. When an electric current is passed, the following reactions occur. At an anode 2Cl ! Cl2 þ 2e DOI: 10.1016/S0927-5193(07)12019-2

E0 ¼ 1:36 V

(5.1)

462

Ion Exchange Membranes: Fundamentals and Applications

Figure 5.1 2000).

Production capacity change of chlor-alkali processes in Japan (Furuya,

Figure 5.2

Energy consumption in chlor-alkali processes (Asawa, 1991).

At a cathode 2H2 O þ 2e ! H2 þ 2OH

E0 ¼ 0:828 V

(5.2)

Total reaction 2NaCl þ 2H2 O ! 2NaOH þ H2 þ Cl2

E0 ¼ 2:2 V

(5.3)

463

Electrolysis

Figure 5.3

Construction cost of chlor-alkali processes (Asawa, 1991).

Here, Cl2 gas is generated at the anode, Na+ ions transferred from the anode cell to the cathode cell through the cation exchange membrane and combine with OH ions generated at the cathode to produce NaOH. The cation exchange membrane indicated in the ﬁgure is a double layer membrane consisting of a perﬂuorocarboxylic acid layer and a perﬂuorosulfonic acid layer. 5.2. 5.2.1

ION EXCHANGE MEMBRANE

Perﬂuorosulfonic Acid Membrane In the electrolysis system, cation exchange membranes have to exhibit both high chlorine resistance and high current efﬁciency in highly concentrated caustic soda. In the system in Fig. 5.4, the perﬂuorosulfonic acid membrane presented in Fig. 5.5 was used at the ﬁrst developing stage because of chemical and thermal stability. This membrane is based on perﬂuorosulfonyl ﬂuoride monomer copolymerized with tetraﬂuoroethylene and was developed by

464

Ion Exchange Membranes: Fundamentals and Applications

Perfluorosulfonic layer Anode

Perfluorocarboxylic layer

Anode cell

Cathode cell

Cathode

1/2H2 Na+

1/2Cl2

H2O OH−

Cl−

OH−

OH−

H2O

HCl Sat. NaCl sol.

Figure 5.4

Cation exchange membrane

Water

Principle of ion exchange membrane electrolysis of sodium chloride. [(CF2 CF2)x (CF2 CF)]y O (CF2 CFCF3 O)m (CF2)n SO3− Nafion Dow membrane Aciflex Flemion

Figure 5.5

: m ≥ 1; n = 2, x =5-13.5; y = 1000 : m = 0; n = 2 : m = 0, 3; n = 2-5; x = 1.5-14 : m = 0, 1; n = 1-5

Structural formula of a perﬂuorosulfonic acid membrane (Sudoh, 2004).

du Pont (Putnam, 1967; Connally, 1966). Ion exchange capacity can be adjusted by changing x, y, m and n for the commercially available membrane shown in the ﬁgure. The Naﬁon perﬂuorosulfonic acid membrane is usually reinforced with a support cloth made of Teﬂon and is useful as a separator in a wide range of applications (DuPont, 2002). Gierke (1977) investigated micro structure of a Naﬁon membrane by means of X-ray diffractometry and suggested the ion-cluster channel model as illustrated in Fig. 5.6, which shows that the distribution of ﬁxed ions is not uniform, the clusters are connected through narrow channels and the distance between the clusters is nearly 50 A˚. An electron microscopic observation revealed the shape of the cluster diameter to be 40 A˚. Diameter of the channel

465

Electrolysis

Figure 5.6

Ion-cluster channel model (Gierke, 1977).

between the clusters was estimated to be nearly 10 A˚ from water-passing velocity measurements through the membrane. Sudoh (2004) measured the cluster diameter of Naﬁon membranes combined with long-chain counter ions by means of the water-passing experiment and obtained the following values. Counter ions

Cluster Diameter (A˚)

H+ (CH3)4N+ (C4H9)4N+ (C8H17)4N+

38 30.93 15.09 17.32

5.2.2

Sulfonic Acid/Carboxylic Acid Double Layer Membrane The electric conductivity of the perﬂuorosulfonic acid membrane is high enough, however, it cannot perfectly prevent back migration of OH ions generated at a cathode toward an anode cell. It was found that a perﬂuorocarboxylic acid membrane effectively prevents the back migration of OH ions. At present, a double layer membrane consisting of sulfonic acid and carboxylic acid layers is generally used (Grot et al., 1972). Table 5.1 shows the performance of sulfonic acid type Rf-SO2 3 ; carboxylic =Rf-COO Þ membranes. The acid type Rf-COO and double layer type ðRf-SO2 3 sulfonic acid type membrane has lower electric resistance and lower ohmic loss in the electrolysis process; however, it has larger hydrophilicity and larger OH ion penetrability, so that it cannot realize higher current efﬁciency. On the contrary, the carboxylic acid membrane shows lower hydrophilicity and higher current

466 Table 5.1

Ion Exchange Membranes: Fundamentals and Applications

Comparison of ion exchange groups and membrane characteristics

Ion Exchange Group

Rf-SO2 3

Rf-COO

Rf-COO/Rf-SO2 3

pKa Hydrophilicity Current efﬁciency Electric resistance Chemical stability pH range HCl neutralization O2/Cl2 Current density

o1 high o80% low high 41 possible o0.5% high

2–3 low 493% high high 43 impossible 42% low

2–3/o1 low/high 493% low high 41 possible o0.5% high

Source: Ohmura, 1984.

efﬁciency, but it has defects such as higher electric resistance and larger ohmic loss. Further, even though it is carboxylic acid membrane, it cannot perfectly prevent the back migration of OH ions from the cathode cell to the anode cell. The OH ions in this situation discharge at the anode, generate O2, ClO 3 ions etc., decrease the Cl2 generation efﬁciency, lower the product Cl2 purity and shorten the anode life. For preventing OH ion discharge at the anode, the OH ions are usually neutralized by injecting HCl into the anode cell. However, the HCl injection converts Rf-COO groups to Rf-COOH groups, which increase the electric resistance of the carboxylic acid membrane (Ohmura, 1984). In order to prevent the problems mentioned above, a double layer membrane consisting of a perﬂuorocarboxylic acid layer and a perﬂuorosulfonic acid layer was investigated. Aciﬂex membrane developed by Asahi Chemical Co. was prepared by either coating perﬂuorocarboxylic acid polymer on perﬂuorosulfonic acid membrane or lamination of two different polymer ﬁlms containing carboxylic and sulfonic acid, or by chemical conversion of perﬂuorosulfonic acid to perﬂuorocarboxylic acid. A comparison of these membranes is shown in Table 5.2. Chemical treatment was considered to be the best method for preparation of membrane for chlor-alkali process. With this method, the thickness of the carboxylic acid layer which forms on the surface of perﬂuorosulfonic acid membrane can be easily reduced to less than 10 mm, resulting in a corresponding reduction in the electric resistance of the membrane. When the carboxylic acid and sulfonic acid layers face each other, respectively, on the cathode and anode sides as shown in Fig. 5.4, it becomes possible to inject HCl into the anode cell (Seko et al., 1982). The current efﬁciency and the electric resistance are shown in Fig. 5.7 for the double layer membrane prepared by chemical treatment. As shown in this ﬁgure, the electric resistance increases linearly with the thickness of carboxylic acid layer. The current efﬁciency increases greatly until the thickness of the carboxylic acid layer reaches 7 mm, where saturation tends to occur. From the point of view of power consumption, the optimum thickness of the carboxylic acid layer is in the range of 2–10 mm. Thus, chemical treatment was assumed to

467

Electrolysis

Table 5.2

Comparison of monolayer and doublelayer perﬂuoro-ionomer membranes

Type of Membrane

Monolayer Perﬂuorocarboxylic Acid Membrane COOH

Doublelayer Membrane of Perﬂuorocarboxylic and Sulfonic Acid by Lamination or Coating COOH/SO3H

Doublelayer Membrane of Perﬂuorocarboxylic and Sulfonic Acid by Chemical Treatment COOH/SO3H

Thickness of COOH layer (mm) Current efﬁciency (percent) 8N NaOH Electric resistance Necessary number of functional monomers Membrane fabrication

4125

20–50

o10

96

96

96

High

Medium

Low

1

2

1

Extrusion

Extrusion and lamination or coating

Extrusion and chemical treatment

Source: Seko et al., 1982.

be the most appropriate method for preparation of carboxylic acid layer in the Aciﬂex membrane because the highest current efﬁciency was realized with a minimum increase in electric resistance. Fig. 5.8 shows the relationship between the current efﬁciency, caustic soda concentration and ion exchange capacity of double layer Aciﬂex membrane, prepared by chemical treatment of perﬂuorosulfonic acid membrane. Each membrane shows maximum current efﬁciency at a certain caustic soda concentration. This is because with increasing concentration of the external caustic solution up to a certain value, the membrane tends to shrink and the COO ﬁxed ion concentration in the membrane tends to increase. However, if the concentration of the caustic soda increases beyond this value, hydroxide ion diffusion tends to increase due to increased electrolyte sorption, thus tending to decrease current efﬁciency. Increasing the ion exchange capacity of the membrane results in the occurrence of the maximum current efﬁciency at higher caustic soda concentration. Therefore, in order to obtain high concentration of catholyte, the membrane should have carboxylic acid groups of higher exchange capacity. Flemion developed by Asahi Glass Co. is a double layer membrane and is produced by the lamination of two different polymer ﬁlms containing carboxylic and sulfonic acids as follows (Umemura and Shimodaira, 2004).

468

Ion Exchange Membranes: Fundamentals and Applications

Electric resistance

Current efficiency (%)

100 90 80 70 60

2

4 6 8 10 12 14 Thickness of COOH (micron)

Figure 5.7 Thickness of COOH layer, current efﬁciency, and electric resistance of a multilayer perﬂuorocarboxylic and sulfonic acid membrane prepared by chemical treatment (Seko et al., 1982).

Step 1 Resin A is synthesized by copolymerization of CF2¼CF2 and CF2¼CFO(CF2)3CO2CH3. Resin B is synthesized by copolymerization of CF2¼CF2 and CF2¼CFOCF2CF(CF3)OCF2CF2SO2F. Two-layered Film X is produced by afﬁxing Resin A layer (25 mm thick) on Resin B layer (65 mm). Film Y (20 mm) is produced from Resin B. Step 2 A textile is woven with a polytetraﬂuoroethylene monoﬁlament and a polyethylene terephthalate multiﬁlament. A reinforcing material (100 mm) is formed by ﬂattening the textile using a roll press. Step 3 Film Y, reinforcing material, Film X and a polyethylene terephthalate ﬁlm (tearing material) are piled up in this order, and pressed using a roller. A multilayered membrane is obtained by stripping the tearing material. Step 4 A paste is prepared by mixing zirconium oxide (29.0 wt.%), methyl cellulose (1.3 wt.%), cyclohexanol (4.6 wt.%), cyclohexane (1.5 wt.%) and water (63.6 wt.%). A gas-removing layer is formed on the surface of Film Y of the multilayered membrane by transcribing the paste using a roll press. Step 5 –CO2CH3 groups and –SO2F groups in the multilayered membrane are hydrolyzed to ion exchange groups by immersing the membrane in a solution dissolving 30 wt.% of dimethyl sulfoxide and 15 wt.% of potassium hydroxide.

469

Electrolysis

Current efficiency (%)

100

IEC = 0.69

IEC = 0.74

IEC = 0.80

90 IEC: Ion exchange capacity (meq/gram dry resin)

80 40 A/dm2 90°C 70

6

8 10 12 Concentration of NaOH (M)

14

Figure 5.8 Current efﬁciency, ion exchange capacity and concentration of NaOH, for double-layer perﬂuorocarboxylic and sulfonic acid membranes prepared by chemical treatment (Ohmura, 1984).

5.3. MATERIAL FLOW AND ELECTRODE REACTION IN AN ELECTROLYSIS SYSTEM 5.3.1

Material Flow in an Electrolysis System We discuss here the material ﬂow in an electrolysis system illustrated in Fig. 5.9 according to the explanation by Yawataya (1986). A salt solution ðC 0NaCl ðmol dm3 Þ; V 0A ðdm3 h1 ÞÞ; is assumed to be supplied to an anode cell at a ﬂux J 0NaCl ¼ C 0NaCl V 0A (mol h1). Impurities in the salt solution are assumed to be strictly removed through pretreatment. C 0HCl is HCl concentration in the feeding salt solution due to a small amount of hydrochloric acid addition for neutralizing OH ions transferred from the cathode. C 00i s are the concentrations of components at the exit of the anode cell involving NaCl and every kind of byproduct, and V 00A is the amount of this solution. Cl2 and O2 are generated at the anode and create the ﬂux J 0Cl2 and J 0O2 ; respectively. J Cl2 is the amount of product Cl2 and J O2 is the amount of O2 mixing with the product Cl2. A part of the Cl2 is dissolved into the anode solution and carried to the outside of the system. However, the Cl2 is recovered in the succeeding process. J 0H2 and J 0OH are, respectively, the ﬂux of H2 and OH generated by the reaction at the cathode. V 0C is the amount of water supplied to the cathode cell for maintaining the NaOH concentration C 00NaOH of the product extracted from the system to be constant. V 00C and J 00NaOH are, respectively, the amount (dm3 h1) and the ﬂux (mol h1) of NaOH produced in this system; J 00NaOH ¼ C 00NaOH V 00C :

470

Ion Exchange Membranes: Fundamentals and Applications

Anode

Cathode

J′ V A′

V ′c JCl2

′ CNaCl ′ C HCl

JH

JO2

2

J Na J ′Cl2

J H2O J O′′

2

J ′H 2

J OH

J ′O2

J NaCl

J ′OH

′′ J NaOH

J ′′ V A′′

V c′′ C NaCl ′′ CCl ′′

Anode cell

Cathode cell

′′ C NaOH

2

C HClO ′′ C NaClO ′′ C NaClO ′′

3

Figure 5.9

Material ﬂow in an electrolysis system (Yawataya, 1986).

JNa is the ﬂux of Na+ transported from the anode cell to the cathode cell across the cation exchange membrane. J H2 O (mol h1) is the ﬂux of H2O accompanying the Na+. With a little amount of OH, JOH is transferred from the cathode cell to the anode cell across the membrane. JNaCl is the ﬂux of NaCl across the membrane due to the diffusion. The diffusion of NaOH is included into JNa and JOH in this calculation, so it must decrease the transport number of Na+ and increase that of OH. 5.3.2

Reaction at a Cathode in an Electrolysis System OH ions are generated by the following reactions at the cathode. Primary reaction; the same as (5.2) 2H2 O þ 2e ! H2 þ 2OH

(5.4)

Secondary reaction 1 O2 þ H2 O þ 2e ! 2OH 2

(5.5)

ClO þ H2 O þ 2e ! Cl þ 2OH

(5.6)

471

Electrolysis

Current efﬁciency for OH generation eOH totaled by the above reactions becomes 1, so that OH ﬂux at the cathode J 0OH is expressed by the following equation: I I ¼ (5.7) J 0OH ¼ OH F F in which, I is an electric current and F the Faraday constant. The ﬂux of NaOH in the product taken out from the cathode cell J 00NaOH is given by the following equation: I J OH (5.8) J 00NaOH ¼ J 0OH J OH ¼ F Accordingly, current efﬁciency for NaOH in the product ZOH is ZOH ¼

J 00NaOH J OH J Na ¼1 ¼ ðI=F Þ ðI=F Þ ðI=F Þ

(5.9)

Equation (5.9) shows that NaOH current efﬁciency depends on Na+ ion transport number of the cation exchange membrane. Water molecules are converted to J 0OH (mol h1) by the following electrolysis reaction at the cathode. 1 1 NaCl þ H2 O ! NaOH þ H2 þ O2 2 2

(5.10)

The ﬂux of water transferred from the anode cell into the cathode cell is J H2 O ðmol h1 Þ ¼ 18 103 J H2 O ðdm3 h1 Þ: The amount of water supplied to the cathode is V 0C ðdm3 h1 Þ: Accordingly, NaOH concentration extracted from the cathode cell C 00NaOH (mol dm3) is introduced as follows: C 00NaOH ¼

J 00NaOH J 0OH J OH ¼ 0 00 VC V C þ 18ðJ H2 O J 0OH Þ 103 ðI=F ÞZOH ¼ 0 V C þ 18ðJ H2 O J 0OH Þ 103

ð5:11Þ

5.3.3

Reaction at an Anode in an Electrolysis System The primary and the secondary reactions at the anode involving, respectively, the generation of Cl2, J 0Cl2 and O2, J 0O2 are as follows: I 0 (5.12) J Cl2 ¼ A 2F An electric current generated at the anode is expressed by the following equation: I ¼ 2FJ 0Cl2 þ 4FJ 0O2

(5.13)

472

Ion Exchange Membranes: Fundamentals and Applications

From Eqs. (5.12 ) and (5.13), Eq. (5.14) is introduced. I 0 J O2 ¼ ð1 A Þ 4F

(5.14)

O2 is assumed to be generated by another chemical reaction with rate J 00O2 ; except for the above reactions, so that the ﬂux of total O2, J O2 is given by the following equation: J O2 ¼ J 0O2 þ J 00O2

(5.15)

Now, Cl2 generated at the anode undergoes changes as follows. (a)

Dissolving into the anode solution. Cl2 ðgÞ ! Cl2 ðaqÞ

(b)

Decomposition to form HClO Cl2 þ NaOH ! NaCl þ HClO

(c)

(5.17)

The rate of this reaction is V 00A C 00HClO (mol h1). Equation (5.17) shows that the reaction consumes 1 mol NaOH and 1 mol Cl2 to generate 1 mol HClO. Decomposition to form NaClO Cl2 þ 2NaOH ! NaCl þ NaClO þ H2 O

(d)

(5.16)

(5.18)

Equation (5.18) shows that the reaction consumes 2 mol NaOH and 1 mol Cl2 to generate 1 mol NaClO. Decomposition to form NaClO3 þ 2HClO þ ClO ! ClO 3 þ 2Cl þ 2H

(5.19)

Taking account of Cl2 consumption generating HClO and ClO, Eq. (5.19) changes to 3Cl2 þ 6NaOH ! NaClO3 þ 5NaCl þ 3H2 O

(e)

(5.20)

Equation (5.20) shows that the reaction consumes 6 mol NaOH and 3 mol Cl2 to generate 1 mol NaClO3. Oxygen generation caused by HClO decomposition A part of HClO formed in the solution generates O2 ðJ 00O2 Þ according to the following reaction. 2HClO þ 2NaOH ! 2NaCl þ 2H2 O þ O2

(5.21)

473

Electrolysis

Based on the reactions described above, the destination of OH ions transferred from the cathode to the anode across the membrane is introduced as shown in the following equation. J OH ¼ V 0A C 0HCl þ 4J 0O2 þ V 00A C 00HClO þ 2V 00A C 00NaClO þ 6V 00A C 00NaClO3 þ 4J 00O2

ð5:22Þ

The ﬁrst term in Eq. (5.22) shows OH ﬂux for neutralizing HCl added to the feeding salt solution. The second term corresponds to OH ﬂux to generate O2 by the following equation. (5.23) 4OH ! O2 þ 2H2 O þ 4e Finally, the current efﬁciency for product Cl2, ZCl2 is introduced as the following equation. J Cl2 ðI=2F Þ J 0Cl2 2J 00O2 ðJ 00HClO þ J 00NaClO þ 3J 00NaClO3 Þ ¼ ðI=2F Þ 2F ð2J 0O2 þ 2J 00O2 Þ ¼1 I 2F 00 ðJ Cl2 þ J 00HClO þ J 00NaClO þ 3J 00NaClO3 Þ ð5:24Þ I Here, J 00Cl2 is the Cl2 ﬂux discharged from the anode cell dissolving into the anode solution. This ﬂux is recovered in the succeeding process. J 0O2 is the electric current loss due to the O2 generation at the anode (cf. Eq. (5.13)). J 00O2 is another chemical reaction rate generating O2. J 00HClO þ J 00NaClO þ 3J 00NaClO3 shows the electric current loss due to the consumption of Cl2. When HCl is added to the salt solution supplied to the anode, ZCl2 is increased because every side reaction is suppressed. However, in this situation, if a part of product Cl2 is consumed to obtain HCl, ZCl2 is substantially decreased and is comprehensively consistent with ZOH (Eq. (5.9)). ZCl2 ¼

5.4.

ELECTROLYZER AND IT’S PERFORMANCE

5.4.1

Monopolar and Bipolar Systems The electrolyzer is classiﬁed into the monopolar and bipolar systems. The structure of both systems is illustrated in Fig. 5.10. The electrical connections between the electrolyzers are shown in Fig. 5.11. In the monopolar electrolyzer: (1) (2)

Unit cells are arranged in parallel. An electric current is supplied to each unit cell from monopolar electrodes.

474

Ion Exchange Membranes: Fundamentals and Applications

I

C

CC

AC

AC

CC

CC

AC

G

G

G

G

G

G

C

A

M

G

A

G

G

C C

M

G

G

A

M

A

G

I (a) Monopolar system

I

C

AC

CC

AC

CC

AC

CC

G

G

G

G

G

G

A

C

M

G

A

G

G

C

M

G

A

C

M

G

A

I

G

(b) Bipolar system A: Anode, C: Cathode, AC: Anode cell, CC: Cathode cell M: Cation exchange membrane, G : Gasket, I: Electric current

Figure 5.10

(3) (4) (5)

Structure of mono and bipolar electrolyzers.

Total electric current supplied to an electrolyzer corresponds to the current supplied to a unit cell multiplied by the number of unit cells. Total voltage applied to the electrolyzer is equivalent to the voltage applied to the unit cell. A high electric current low voltage rectiﬁer supplies an electric current to many small-scale electrolyzers. In the bipolar electrolyzer:

(1) (2) (3)

Unit cells are arranged in series. An electric current is supplied to each unit cell from bipolar electrodes. An electric current passing through the electrolyzer is equivalent to the current ﬂowing through the unit cell.

475

Electrolysis

Monopolar system

Bipolar system

21,000 kW D. C. 60 KA 350 V

Rectifier

21,000 kW D. C. 60 KA 350 V

Rectifier

350V

350V

Electrolyzer Electrolyzer

Figure 5.11

(4) (5)

5.4.2

Electrical connections between the electrolyzers (Ohmura, 1984).

Voltage applied to the electrolyzer is equal to the voltage applied to the unit cell multiplied by the number of the unit cells. A low electric current high voltage rectiﬁer supplies an electric current to few large-scale electrolyzers.

Energy Consumption Decrease in an Electrolyzer Table 5.3 shows the speciﬁcations of commercially available bipolar electrolyzers. Fig. 5.12 shows the capacity changes of the monopolar and bipolar systems in the world. The increase of the monopolar system during 1990–1995 is due to increase of the process conversion from the mercury to ion exchange membrane process because rectiﬁers in the mercury process were applicable to the ion exchange membrane process. The increase of the bipolar system after 1995 is due to the increase of current density because ohmic loss of the bipolar system is less than that of monopolar system.

476

Table 5.3

Speciﬁcations of commercially available bipolar electrolyzers

Denomination

Main materials Anode Anode cell Cathode Cathode cell Source: Takarada, 2004.

kA m kA m2 m2 V % kWh t1 NaOH

Toso–Chlorine Engineers

Asahi Glass

Krupp Uhde

DeNora

ML32NCH

BiTAC873

AZEC-B1

HU

DN350

6 8 2.70 100 3.18 96 2220

5 6 3.28 73 3.08–3.15 96–96.5 2150–2187

5 6 2.88 80 3.08 96 2150

5 6 2.72 160 3.12 96 2178

5 8 3.50 90 3.15 96.5 2188

DSA Ti Oxidated Ni Ni

DSA Ti Ni system Ni

DSA Ti Raney Ni Ni

Metallic Ti RuO2 Ni

DSA Ti RuO2 Ni

Ion Exchange Membranes: Fundamentals and Applications

Rating current density Maximum current density Effective membrane area Unit cell number Voltage (at rating) Current efﬁciency Energy consumption

2

Asahi Chemical

477 Production capacity (106 ton/year)

Electrolysis

12 10 8 6 4

M

o

p no

ar r

ola

Bip

2 0 1970

ol

1975

1980

1985 year

1990

1995

2000

Figure 5.12 Production capacity changes of the mono and bipolar systems (Takarada, 2004).

Further decrease in the unit cell voltage is estimated to be realized by the following technical development. (1) (2) (3) (4)

Cut down air bubble electric resistance. Make zero gap space between the ion exchange membrane and the electrodes. Decrease in over voltage of the electrodes. Decrease in electric resistance of ion exchange membrane.

Air bubbles increase the unit cell voltage so that it is strongly expected to prevent the bubble attachment to the membrane surface. Asahi Chemical Co. prevents the bubble attachment by making the Aciﬂex membrane surface structure coarse (Ohmura, 1984). Asahi Glass Co. coated a porous layer consisting of non-conductive inorganic materials on the Flemion membrane (Suzuki and Sirogami, 1984). In order to realize zero gap space between the membrane and electrode, the structure and materials of the electrodes and electrode chambers must be developed. Further, we must develop the technology to avoid damage of the membrane structure. Bipolar electrode chambers developed by Asahi Chemical Co. are manufactured by joining Ti (anode cell) and Ni (cathode cell) between which a Ti/Fe plate is placed. Fig. 5.13 shows the electrode conﬁguration developed by Chlorine Engineers and Toso Corp. (Chlorine Engineers Corp., 2006). Electric current ﬂows from the cathode to anode through the diaphragm between the electrodes. For the bipolar electrolyzer, an anode chamber made of Ti has six times larger resistance than a cathode chamber made of Ni. In this electrode chamber, the electric current route through Ti is shortened by making

478

Ion Exchange Membranes: Fundamentals and Applications

Figure 5.13 Electrode conﬁguration of a bipolar electrolyzer (Chlorine Engineers Corp., 2006).

the diaphragm a wave shape and keeping enough capacity to exhaust Cl2 gas. The grooves and projections of the wave-shaped diaphragm are arranged alternately (Fig. 5.14). An electrolyte solution supplied from the bottom of the electrolyzer is repeatedly mixed and separated at the edge of the grooves and projects. It is evenly distributed on the electrolysis surface. The following is typical unit cell voltage (Takarada, 2004): Theoretical electrolysis voltage Anode over voltage Cathode over voltage Membrane electric resistance Electric resistance due to air/solution bubbles and unit structure Total

2.21 V 0.05 V 0.12 V 0.33 V 0.21 V 2.92 V

Here the following situations are assumed: current density, 4 kA m2; NaOH concentration in the product, 32%; Concentration of feeding salt solution, 205 g l1; Temperature, 901C. Extremely low anode over voltage 0.05 V is owing to a metallic DSA electrode. Cathode over voltage 0.12 V was achieved by catalytically active electrodes. 5.4.3

Electrolysis Process Fig. 5.15 shows the chlor-alkali process. At ﬁrst, saturated salt water obtained by dissolving raw salt into water is supplied to the primary reﬁning process, in which Ca2+ and Mg2+ ions are removed by Na2CO3 and NaOH adding and settling. Further, SO2 4 ions are removed by adding BaCl2 or BaCO3. In the secondary reﬁning process, the remaining little amounts of Mg2+ and Ca2+ ions are removed using chelate resins to be of ppb order concentration.

479

Electrolysis

Figure 5.14

Bipolar element assembly (Chlorine Engineers Corp., 2006).

The reﬁned salt water is supplied to the anode cells and electrolyzed. The salt water discharged from the anode cells is fed to chlorate (NaClO3) decomposition process after product Cl2 gas is separated and returned to a raw salt dissolving tank. The cathode solution discharged from the cathode cells is separated from H2 gas and circulated. In this process, a part of the solution is fed to the chlorate decomposition tank and water is added to keep deﬁnite NaOH concentration. A high concentration of NaOH solution or solid NaOH is obtained by evaporating the overﬂow from the cathode solution circulating tank. 5.5. PURIFICATION OF SALT WATER IN AN ELECTROLYSIS PROCESS 5.5.1

Primary Puriﬁcation in an Electrolysis Process Chemical reactions that occurred in the primary reﬁning process are Ca2þ þ Na2 CO3 ! CaCO3 þ 2Naþ

(5.25)

Mg2þ þ NaOH ! MgðOHÞ2 þ 2Naþ

(5.26)

2 SO2 4 þ BaCl2 ðor BaCO3 Þ ! BaSO4 þ 2Cl ðor CO3 Þ

(5.27)

CaCO3, Mg(OH)2 and BaSO4 are separated using a sedimentation separator (thickener or circulator) and by ﬁltration (sand ﬁlter, ceramic ﬁlter or leaf ﬁlter).

480

Ion Exchange Membranes: Fundamentals and Applications

Anolyte dechlorin.

Salt Water

Na2CO3 NaOH

Salt water saturaion

Salt water prim. Pur.

Salt water sec, pur.

HCl BaCl2 Cl2

Chlorate decom.

50% NaOH

H2 Anolyte NaCl 200g/l

Anode

Catholyte 33 % NaOH

Cathode

Catholyte evapration Catholyte circulation tank 33% NaOH

Figure 5.15

Salt water

Diluted catholyte

NaCl 300 g/l

30% NaOH

Water

Chlor-alkali process (Bergner, 1982).

Ca2+, Mg2+ and SO2 4 concentrations in puriﬁed salt water are controlled as (Aikawa, 1994) Ca2+ ions Mg2+ ions SO2 4 ions

5.5.2

1–3 ppm o1 ppm o4 g l1

Secondary Puriﬁcation in an Electrolysis Process Two or three columns ﬁlled with imino-2-acetic acid (-CH2-N(CH2COOH)2) or aminophosphoric acid (-CH2-NH-PO(OH)2) chelate resins are operated as a merry-go-round, to which primarily puriﬁed salt water is supplied. Table 5.4 shows the salt–water quality after the secondary puriﬁcation (Chlorine Engineers Corp., 1987).

481

Electrolysis

Table 5.4

NaCl Na2SO4 NaClO Ca+Mg Sr Ba Hg Al SiO2 Fe Ni TOC I

Salt water quality after secondary puriﬁcation

1

gl g l1 g l1 ppb ppm ppm ppm ppm ppm ppm ppm ppm ppm

Standard

Measured Values

300–305 o5 o20 o20 as Ca o0.06 o0.5 o15 o0.1 o5 o0.2 o0.01 o10 o0.2

305 4 9 Cao10, Mgo10 0.01 0.13 o0.01 o0.05 o1.0 o0.03 o0.01 8.5 o0.2

Source: Chlorine Engineers Corp., 1987.

5.5.3

Inﬂuence of Impurities in Salt Water on the Performance of an Electrolyzer An atmosphere in the membrane is alkaline because OH ions back migrate through the membrane. pH values in the membrane become higher near the cathode side because a NaOH solution ﬂows in the cathode cell. Cationic impurities supplied to the anode cell transfer across the membrane toward the cathode cell under an electromotive force. Under the circumstance mentioned above, the cationic impurities combine with OH ions and precipitate as hydroxides in the membrane. The precipitating points depend on the solubility of the hydroxide, and it is observed that Mg(OH)2 precipitates near the anode side and Ca(OH)2, Sr(OH)2 and Ba(OH)2 precipitate near the cathode side in the membrane. These events increase the voltage and decrease the current efﬁciency in the electrolysis. Table 5.5 shows the effects of impurities on the performance of electrolysis (Aikawa, 1994). Fig. 5.16 shows the inﬂuence of Ca2+ and Mg2+ ions added to the salt water on cell voltage and current efﬁciency, respectively, in the laboratory cells integrated with a Naﬁon 90209 membrane (Momose et al., 1991). The cell potential increases in both the Mg2+ and Ca2+ ions addition tests, with Mg2+ ion addition apparently showing a larger increase. On the other hand, the current efﬁciency decreases after the Ca2+ ion addition, while addition of Mg2+ ion has no such effect. In order to clarify the variation in cell performance described above, the location of impurity accumulation in the degraded membrane was investigated by electron probe X-ray microanalysis (EPMA). Naﬁon 90209 includes a carboxylate layer acting as high-selectivity layer. The ﬁgure indicates that the Ca2+ ion penetrated the membrane from the anolyte and precipitated in carboxylate layer, which is the cathode side of the membrane (see Photo 5.1a). It precipitated in the form of a particle close to the cathode side

482

Table 5.5

Effects of impurities on the performance of electrolysis Inﬂuence to Membrane Z

Anion SiO2 F I SO4 ClO3 Composite compound Ca+SiO2 Al+SiO2 Ca+Mg+SiO2 Ba-I Organic compound

Ano

Cath

J

D

J

J J J J

J J J J

J

J J

J

J J J

Remark

J

Ca(OH)2 deposit in the membrane Mg(OH)2 deposit in the membrane Sr(OH)2, Sr+SiO2 deposit in the membrane I+Ba deposit in the membrane, adhere to the anode deposit in the membrane indistinct composite compound deposit in the membrane inﬂuence to anode Ba+I deposit in the membrane Na2SO4 deposit in the membrane NaCl solubility decrease deposit deposit deposit deposit

in in in in

the the the the

membrane membrane, adhere to the anode membrane membrane

adhere to the anode

Source: Aikawa, 1994. Note: Z: Current efﬁciency, V: Voltage, Ano: Anode, Cath: Cathode, J: Inﬂuence, D: Inﬂuence slightly.

Ion Exchange Membranes: Fundamentals and Applications

Cation Ca Mg Sr Ba Ni Fe

V

Inﬂuence to Electrodes

483

Electrolysis

Cell voltage (V)

3.5 C.D. : 3KA/m2 NaOH : 32wt% Temp. : 90°C

3.4

Mg addition (0.6ppm) addition Ca addition (1ppm)

3.3

3.2

Current efficiency (%)

100 Mg 95 addition 90 Ca 85

0

10

20

30

Days on line (day)

Figure 5.16 Changes of cell voltage and current efﬁciency by adding Ca2+ and Mg2+ ions in feeding salt water (Momose et al., 1991).

membrane surface (see Photo 5.1b). The ﬁgure also shows that the Mg2+ ion precipitated in the sulfonate layer, which is on the anode side of the membrane (see Photo 5.1c) and it precipitated in the form of a layer near the anode side membrane surface (see Photo 5.1d). The difference in location of calcium and magnesium accumulation in the degraded membrane can be understood by considering the difference in their hydroxide solubility. That is, the solubility products of Mg(OH)2 and Ca(OH)2 are 4.11 1012 and 9.33 107 at 901C, respectively, which show that the solubility product of Mg(OH)2 is much lower than that of Ca(OH)2. Further, it should be noticed that pH distribution in the Naﬁon membrane is 9.1–10.5 near the anode side surface (sulfonate layer) and sufﬁciently high (414) near the cathode side layer (carboxylate layer). In this situation, the Mg2+ ion entering the membrane from the anolyte immediately begins to precipitate as the hydroxide since the pH is adequately high to cause the cell potential increase. On the other hand, the Ca2+ ion penetrates further until reaching the carboxylate layer where the pH is sufﬁciently high to cause the precipitation and selectivity decrease (cf. Fig. 5.16).

484

Ion Exchange Membranes: Fundamentals and Applications

Photo 5.1 Distribution of precipitate in the membrane analyzed by EPMA. (a) Calcium line proﬁle; (b) Calcium line proﬁle near the cathode side surface; (c) Mg line proﬁle; (d) Mg line proﬁle near the anode side surface (Momose et al., 1991).

REFERENCES Aikawa, H., 1994, Brine puriﬁcation for ion exchange membrane chlor-alkali process, Bull. Soc. Sea Water Sci. Jpn., 48(6), 439–450. Asawa, T., 1991, Sodium chloride electrolysis, Asahi Glass process, In: Nakagaki, S., Shimizu, H. (Eds.), Membrane Treatment Technology System, Fuji Techno System, Tokyo, Japan, vol. 1, pp. 510–515. Bergner, D., 1982, Alkalichlorid-Elektrolyse nach dem Membranverfahren, Chem. Eng. Techn., 54, 562–570. Chlorine Engineers Corp., 1987, Technical report, Tokyo, Japan. Chlorine Engineers Corp., 2006, Product Bulletin, Tokyo, Japan. Connally, D. J., 1966, (to E. I. du Pont de Nemours and Co.) U.S. Patent 3 282 875 (Nov. 1, 1966). DuPont, 2002, Naﬁon perﬂuorinated membranes, Product information in the catalog (18th March). Furuya, T., 2000, Sodium chloride electrolysis, In: Electrochemical Society of Japan (Ed.), Electrochemistry Handbook, vol. 5, pp. 380–386 Tokyo, Japan. Gierke, T. D., 1977, American Electrochemical Society Meeting, Atlanta, October.

Electrolysis

485

Grot, W. G. F., Munn, G. E., Walmsley, P. N., 1972, Perﬂuorinated ion exchange membranes, Paper presented at 141st National Meeting of Electrochemical Society, Houston Texas, May 7–11. Momose, T., Higuchi, N., Arimoto, O., Yamaguchi, K., Walton, C. W., 1991, Effects of low concentration levels of calcium and magnesium in the feed brine on the performance of a membrane chlor-alkali cell, J. Electrochem. Soc., 138(3), 735–741. Ohmura, J., 1984, Sodium chloride electrolysis using ion exchange membranes – Asahi Chemical process, In: Shimizu, H., Nishimura, M. (Eds.), Advanced Membrane Treatment Technology and its Applications, Fuji Techno System, Tokyo, Japan, pp. 645–649. Putnam, P. E., 1967, (to E. I. du Pont de Nemours and Co.) U.S. Patent 3 301 893 (Jan. 31, 1967). Seko, M., Miyauchi, H., Ohmura, J., Kimoto, K., 1982, Ion-exchange membrane for the chlor-alkali process, J. Electrochem. Soc. Jpn., 50(6), 470–476. Sudoh, M., 2004, Perﬂuorocarbon ion exchange membrane, membrane structure and characteristics, In: Seno, M., Tanioka, A., Itoi, S., Yamauchi, A., Yoshida, S. (Eds.), Functions and Applications of Ion Exchange Membranes, Industrial Publishing & Consulting Inc., Tokyo, Japan, pp. 106–117. Suzuki, Y., Sirogami, Y., 1984, Sodium chloride electrolysis using ion exchange membranes – Asahi Glass Flemion process, In: Shimizu, H., Nishimura, M. (Eds.), Advanced Membrane Treatment Technology and its Applications, Fuji Techno System, Tokyo, Japan, pp. 656–660. Takarada, H., 2004, Perﬂuorocarbon ion exchange membrane, Production of sodium hydroxide using ion exchange membranes, In: Seno, M., Tanioka, A., Itoi, S., Yamauchi, A., Yoshida, S. (Eds.), Functions and Applications of Ion Exchange Membranes, Industrial Publishing & Consulting Inc., Tokyo, Japan, pp. 106–117. Umemura, K., Shimodaira, T., 2004, Perﬂuorinated cation-exchange membrane and electrolysis of sodium chloride, JP Patent, 2004-188375. Yawataya, T., 1986, Ion Exchange Membrane for Engineers, 2nd ed., Kyoritsu Shuppan Co., Tokyo, Japan, pp. 149–157.

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Chapter 6

Diffusion Dialysis 6.1.

OVERVIEW OF TECHNOLOGY

Diffusion dialysis is a separation process using the ionic diffusion caused by the concentration difference across a membrane. The phenomenon is governed by the Fick’s law and the diffusion velocity is generally low, so that in order to promote the process efﬁciency it becomes necessary to decrease membrane thickness and increase the membrane area. The feature of diffusion dialysis process using ion exchange membranes, however, is to utilize high mobility of H+ ions across an anion exchange membrane, and it is applied to recover acid from an electrolyte solution in the following instances (Itoi and Mochida, 1985):

Treatment of waste solutions from an aluminum foil etching process. Composition control in an aluminum anodizing bath. Acid separation in a metallic rust removing process. Acid separation in a chemical reaction process. Acid concentration control in a metal surface treatment process. Puriﬁcation of crude acid. Treatment of waste acid in a stainless steel washing process.

6.2.

TRANSPORT PHENOMENA IN DIFFUSION DIALYSIS

In the process illustrated in Fig. 6.1, a high concentration salt solution including acid (feed) is supplied to the bottom of the feeding cell that ﬂows upward in the cell and ﬂows out at the top of the cell (deacid). A low concentration solution (water) is supplied to the top of the recovering cell that ﬂows down in the cell and ﬂows out at the bottom of the cell (recovery). In this system, the acid transfers across the anion exchange membrane because of its high mobility in the membrane. However, the salt transfer is restricted because of Donnan exclusion due to the interaction between the salt cations and the functional groups (quaternary ammonium groups) in the membrane. At the steady state the ﬂux of acid or salt J (mol h1) is deﬁned by the following Fick’s law: J ¼ US DC av 2

where S (m ) is membrane area. DOI: 10.1016/S0927-5193(07)12020-9

(6.1)

488

Ion Exchange Membranes: Fundamentals and Applications

Deacid

C′out

C ′′in = 0

Q′out

Q′′in

Water

M+

H+ Feeding cell

Recovering cell

A Feed

C′in

C ′′out Recovery

Q ′′out Q′in A: Anion exchange membrane

Figure 6.1

Mass transport in diffusion dialysis.

U (mol (h m2)1 (mol l1)1) in Eq. (6.1) is the overall dialysis coefﬁcient of solutes (acid or salt) deﬁned by 1 1 1 1 ¼ þ þ U K k0 k00

(6.2)

where K is the diffusion coefﬁcient for the anion exchange membrane. k0 and k00 are the diffusion coefﬁcients for the boundary layer formed, respectively, on the feeding and recovering surfaces of the membrane. Table 6.1 shows the overall diffusion coefﬁcient U measured for Neocepta AFN (Noma, 1991). U is inﬂuenced by temperature and solute concentration in a feeding solution. Membranes having larger Uacid and smaller Usalt show excellent performance in diffusion dialysis. The effects of acids on the degrees of acid permeabilities are arranged as HCldHNO3>H2SO4>HF>H3PO4. Usalt for larger charge number is increased. Usalt for HNO3–Cu(NO3)2 and HNO3–Zn(NO3)2 systems takes larger values because they form anionic complex salt. DCav (mol l1) in Eq. (6.1) is the average concentration difference of solutes between the feeding and the recovering cells. DC av ¼

ðC 0in C 00out Þ C 0out lnððC 0in C 00out Þ=C 0out Þ

(6.3)

489

Diffusion Dialysis

Table 6.1

Overall diffusion coefﬁcient of Neocepta AFN at 251C

Aciddsalt mixture

Acid concentration (N)

Salt concentration (N)

Uacid (mol/ hm2)/(mol/l)

Usalt (mol/ hm2)/(mol/l)

Usalt/Uacid

HCldNaCl HCldFeCl2 HCldFeCl3 H2SO4dNa2SO4 H2SO4dFeSO4 H2SO4dZnSO4 H2SO4dAl2(SO4)3 HNO3dAl(NO2)3 HNO3dZn(NO3)2 HNO3dCu(NO3)2 H3PO4dMgHPO4

2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.5 1.5 1.5 3.0

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.5 1.5 1.6 0.2

8.6 8.6 8.5 3.5 3.6 3.6 3.6 9.3 9.8 9.6 0.85

0.47 0.17 0.055 0.14 0.037 0.053 0.004 0.048 0.14 0.17 0.018

5.5 102 2.0 102 6.5 103 4.0 102 1.03 103 1.5 102 1.1 103 5.2 103 1.4 102 1.8 102 2.1 102

Source: Noma (1991).

The solute concentrations in the recovered solution C 00out and in the deacid solution C 0out are expressed by the following equations: Q00in USðð1=Q0in Þ ð1=Q00in ÞÞ 1 0 C 0in C out ¼ 1 0 00 Qin ðQin =Q0in Þ exp USðð1=Q0in Þ ð1=Q00in ÞÞ 1 (6.4) C 00out ¼

exp USðð1=Q0in Þ ð1=Q00in ÞÞ 1 C 0in ðQ00in =Q0in Þ exp USðð1=Q0in Þ ð1=Q00in ÞÞ 1

(6.5)

Membrane area S is obtained by the following equation introduced from Eq. (6.5): S¼

1

1Y

ln Uðð1=Q0in Þ ð1=Q00in ÞÞ 1 ðQ00in =Q0in ÞY ¼ C 00out =C 0in (acid recovering ratio).

(6.6)

where Y The performance of diffusion dialysis is given by the following equations: Acid recovering ratio or salt moving ratio ¼

C 00out Q00out C 0in Q0in

Acid remaining ratio or salt remaining ratio ¼

6.3.

C 0out Q0out C 0in Q0in

(6.7)

(6.8)

DIFFUSION DIALYZER AND ITS OPERATION

A practical scale diffusion dialyzer consists of gaskets (feeding and recovering cells) and anion exchange membranes (10–1000 sheets) as shown in Fig. 6.2. Fig. 6.3 gives the process ﬂow which consists of mainly a diffusion dialyzer itself

490

Ion Exchange Membranes: Fundamentals and Applications

Deacid

Water

Recovery

Feed Feeding cell

Figure 6.2

Membrane Recovering cell

Membrane

Feeding cell

Cell arrangement in a diffusion dialyzer (Kawahara, 1984a).

Head tank

Head tank

Deacid

Feed Filter P Feed tank

Figure 6.3

Water

Dialyzer Recovery

P Recovery tank

P

Heater Water tank

Diffusion dialysis process ﬂow (Kawahara, 1984a).

and a ﬁlter to remove sludge or oil slicks in the feeding solution (Kawahara, 1984a). The velocities of the feeding solution and water are controlled using control valves and head tanks adjusting the level to 2.5 m. Flow resistance in the dialyzer is low because linear velocity is in the range of 50–300 cm h1. In winter season water is heated to prevent lowering of operating performance. When substances in the feeding solution are precipitated on the membrane surface, the stack is disassembled and the membranes are washed about one to two times in a year. The dialyzer is operated continuously and stably. Energy consumption is very low since electric energy consumption is only for pumping the solutions through the stack. Operating process is quite simple and operating costs are low. The main cost factor is charges related to the capital investment which are considerably high because the diffusion of the acids is slow and a large membrane area is required. The useful membrane life under operating condition in an environment of strong

491

Diffusion Dialysis

acids is relatively short. The process costs are, therefore, determined by costs and life of the membrane. 6.4.

PRACTICE

6.4.1

Composition Control in an Anodized Aluminum Processing Bath Fig. 6.4 gives an aluminum sash manufacturing process consisting of the aluminum surface treatment by alkali etching and anodic oxidation. The solution in the aluminum anodizing bath is taken out and treated in a diffusion dialyzer to separate Al and H2SO4. Fig. 6.5 shows the material balance in the diffusion dialysis process operating in the aluminum sash manufacturing plant. In this process, a part of an anodic solution in the bath is fed continuously to the diffusion dialyzer. 75–85% of H2SO4 in the feeding solution is altogether recovered from the solution in the dialyzer, which is returned to the anodizing bath with newly supplied H2SO4 to maintain constant acid concentration in the bath. The above mentioned process is developed by Asahi Glass Co., and it not only improves the product quality but also decreases the quantities of new H2SO4 addition and alkali supplement for neutralization of discharged acid (Kawahara, 1984b).

Greese removing

Alkali etching

Alkali recovery

Anodic oxidation

H2SO4 recovery

Coloring

Electrodeposition painting

Figure 6.4

Aluminum sash manufacturing process (Kawahara, 1984b).

492

Ion Exchange Membranes: Fundamentals and Applications

Al 4720 g/h 275.5 l/h

H2SO4 150 g/l Al 18 g/l

275.5 l/h

Aluminum anodizing bath

32.3 l/h

243.2 l/h H2SO4 127.4 g/l Al 1.0 g/l 98 % H2SO4 H2SO4

257 l/h 289.3 l/h

Diffusion dialyzer

Water Deacid

H2SO4 35.7 g/l Al 16.3 g/l

Figure 6.5 Material balance in a H2SO4 recovering process by diffusion dialysis in a 1000 t month1 aluminum sash manufacturing factory (Kawahara, 1984b).

Running costs of the process are: a. b. c.

Ion exchange renewal: 880,000 yen year1. Electric power: 104,000 yen year1. Others: 72,000 yen year1. Total: 1,056,000 yen year1. Cost saving merits in chemical reagent consumption are:

a. b.

98% H2SO4 160 l year1: 2,400,000 yen year1. 48% NaOH 265 l year1: 8,500,000 yen year1. Total: 10,900,000 yen year1.

6.4.2

Recovery of Nitric Acid in an Acid Washing Process Pretreatment in a plating process, surface treatment of stainless steel or etching treatment of electronic parts includes an acid washing process using acid such as H2SO4, HCl, HNO3, HF, etc., or their mixed acid. In these processes, metal is dissolved into the acid solution and its washing performance is gradually lowered. In order to prevent such a problem, Tokuyama Inc. developed diffusion dialysis technology for recovering HNO3 from the acid washing solution as shown in Fig. 6.6. The speciﬁcations and performance of the process are enumerated as follows (Motomura, 1986):

493

Diffusion Dialysis

Flocculant precipitation tank

Head tank

Air Steam Water

Back flow pump

Flocculant tank

Water tank

Dialyzer From acid washing tank

Cooler To acid washing tank

Mud pump Filter

Feed tank

Filtrate tank

Figure 6.6

To drainage

Recovery tank

Waste tank

Diffusion dialysis process for recovering HNO3 (Motomura, 1986).

100

HNO3 Recovery (%)

90 80 70 5 4 3 2 1 0

Al Leak (%)

1 1983

Figure 6.7

(1)

2

3

4

5

6

7 month

8

9

10

11

12

13 1984

Performance of HNO3 diffusion dialysis (Motomura, 1986).

Diffusion dialysis a. Feeding solution 6.8 m3 day1, HNO3 100 g l1, Al(NO3)3 100 g l1, SS 200–500 ppm. b. Diffusion dialyzer Neocepta TSD-50-400. c. Process performance See Fig. 6.7.

494

(2)

(3)

Ion Exchange Membranes: Fundamentals and Applications

Running cost and merits a. Running cost Ion exchange membrane renewal ¼ 75,000 yen month1. Filter ¼ 33,000 yen month1. Electric power ¼ 20,000 yen month1. Water supply ¼ 12,000 yen month1. Flocculant ¼ 4,000 yen month1. Total ¼ 144,000 yen month1. b. Merits HNO3 consumption per 1 t of steel material: Before diffusion dialysis adoption ¼ 365 kg t1. After diffusion dialysis adoption ¼ 213 kg t1. Steel material treated ¼ 100 t month1. HNO3 unit cost (as 65% HNO3) ¼ 55 yen kg1. Gain for recovering HNO3 ¼ (365 213) kg t1 100 t month1 55 yen kg1 ¼ 836,000 yen month1+58,000 yen month1 (cost saving for neutralization agent Ca(OH)2) ¼ 894,000 yen month1. Accordingly, cost merit ¼ (894,000 144,000) yen month1 12 month year1 ¼ 9,000,000 yen month1. Maintenance a. Renewal of ﬁlter materials: one time during four to ﬁve months (acid washing solution feeding side) and one time in a month (water supplying side). b. Heat exchanger washing: one time during ﬁve to six months. c. Diffusion dialyzer: no disassembly and no washing during two years.

REFERENCES Itoi, S., Mochida, M., 1985, Present status of the dialysis technique, Ionics, Ionics Co., Tokyo, No. 120, pp. 171–176. Kawahara, T., 1984a, Industrial diffusion dialyzer, In: Shimizu H., Nishimura, M. (Eds.), The Latest Membrane Treatment Technology and its Applications, Fuji Techno System Co., Tokyo, pp. 248–252. Kawahara, T., 1984b, Recovery of waste acid by diffusion dialysis, In: Shimizu, H., Nishimura, M. (Eds.), The Latest Membrane Treatment Technology and its Applications, Fuji Techno System Co., Tokyo, pp. 455–463. Motomura, H., 1986, Recovery of nitric acid and ﬂuoric nitric acid by diffusion dialysis, In: Industrial Application of Ion Exchange Membranes, Vol. 1, Research Group of Electrodialysis and Membrane Separation Technology, Soc. Sea Water Sci., Jpn., 223–233. Noma, Y., 1991, Diffusion dialysis membrane, In: Nakagaki, M., Shimizu, H. (Eds.), Membrane Treatment Technology, Part I, Fundamentals, Fuji Techno System Co., Tokyo, pp. 174–179.

Chapter 7

Donnan Dialysis 7.1.

OVERVIEW OF TECHNOLOGY

Fig. 7.1 illustrates the principle of Donnan dialysis incorporated with a cation exchange membrane. Strip and feed dissolving, respectively, electrolytes AX and BX are assumed to be supplied into, respectively, the extracting and feeding cells. Here, electrolyte concentrations at the entrance of the extracting and feeding cell are, respectively, C 00in;A ; C 00in;B ¼ 0; and C 00in;A ¼ 0; C 00in;B : In this system, cations A (designated as driving ion) in the extracting cell transfer into the feeding cell by diffusion due to the concentration difference ðC 00A 4C 00in;A ¼ 0Þ: When the permselectivity of the cation exchange membrane is perfect, the anions X do not permeate the membrane. Accordingly, the solution phase in the feeding cell is charged positively (potential c0 ), while that in the extracting cell is charged negatively (c00 oc0 ) and the electroneutrality is disturbed. In order to maintain the electroneutrality in the system, cation B in the feeding cell is transferred with H2O across the cation exchange membrane under the potential gradient dc/dx and extracted into the extracting cell. In a steady state, B ion concentration increases to C 00B in the extracting cell. In this circumstance, the movement of B ions is against the concentration difference ðC 0B oC 00B Þ and exhibits the uphill transport. The movement of the cations A and B is induced by the diffusion of driving ion A and potential difference to maintain the electroneutrality. This phenomenon leads to the exchange of cation A and cation B between the two cells through the membrane. The principle of the Donnan dialysis mentioned above is also realized in a system incorporated with an anion exchange membrane. The process is applicable to concentrate or desalinate B ions dissolving in feed and was called Donnan dialysis by Wallace (1967). The Donnan dialysis process does not use an electric current, so it is energy saving compared to electrodialysis. Compared to an ion exchange process, Donnan dialysis has advantages that it does not need regeneration and is operated continuously. However, the system is not economical because the effect of the driving force (concentration difference C 00A C 0A and resultant potential difference c0 c00 ) is weak and it becomes necessary to use larger membrane area (capital cost) to maintain the output of a process. The system was investigated in laboratories as in the following instances. However, the industrial scale application of the process has not been seen up to now. (a) (b)

Recovery of Cr3+ or CN ions in a metal surface treatment process. Recovery of Cu+ ions in mining waste.

DOI: 10.1016/S0927-5193(07)12021-0

496

Ion Exchange Membranes: Fundamentals and Applications

Discharge (Raffinate)

C′out

Strip C′′in,A Q′′in C′′in,B =0

Q′out

C′′A CA C′A C′′B CB C′B H2O ′ ′ – ′

′ Don diff

Q′in

=0 C′in,B

Caton exchange membrane

Feed

Figure 7.1

(c) (d) (e) (f) (g)

7.2.

" Don

Extracting cell

Feeding cell C′in,A

′′

C''out

Q''out

Extract (Product)

Principle of Donnan dialysis.

Exchange of Na+ and Ca2+ ions in a water softening process. ions in a UO2(NO3)2 solution. Extraction of UO2+ 2 Conversion of sodium lactate into lactic acid. Removal of ammonium ion from waste water. Removal of F ion from drinking water etc.

MASS TRANSPORT IN DONNAN DIALYSIS

In Fig. 7.1, ﬂux of counter-ion i in an ion exchange membrane is expressed by the following extended Nernst–Planck equation including the diffusion,

497

Donnan Dialysis

migration and convection (cf. Eq. (7.32) in Fudamentals): dC i FDi zi C i dc þ Civ (7.1) dx RT dx where Ci is the ionic concentration, c the electric potential, Di the diffusion constant, zi the ionic charge number, F the Faraday constant, R the gas constant and T the absolute temperature. In a strictly permselective ion exchange membrane, counter-ions i do not carry an electric current. X i¼F zi J i ¼ 0 (7.2) J i ¼ Di

i

Electroneutrality in the membrane is indicated by the following equation: X zi C i þ zm Q ¼ 0 (7.3) i

zm is the ionic charge number of ﬁxed ionic groups in the membrane and Q the concentration of the ﬁxed ionic groups. Sudoh et al. (1987) discussed the transport phenomena in the Donnan dialysis system based on the Nernst–Planck equation with the mass transport coefﬁcient in the boundary layer. Cwirko and Carbonell (1990) discussed Donnan dialysis phenomena across charged porous membranes, and determined the effect of membrane properties (average pore radius and surface charged density) and solution concentration on ﬂuxes of ions and a solution in a steady state. Higa et al. (1988) presented the uphill transport theory across ion exchange membranes in multicomponent ionic systems. The theory is formulated on the basis of both the Donnan equilibrium and the Nernst–Planck equation, and it enables to simulate uphill transport of ions in a nonstationary dialysis by numerical computation. Miyoshi (1998) suggested that it is better to use monovalent driving ions to obtain a larger ﬂux because they can move more easily inside the membrane than bivalent ones, which interact more strongly with the ionized site of the membrane. Potential difference in Fig. 7.1 is written as follows (cf. Fig. 4.1 in Fundamentals): Dc0Don þ Dcdiff ¼ Dc00Don þ ðc0 c00 Þ Dc0Don

(7.4)

Dc00Don

and are the Donnan potentials (cf. Eq. (3.7) in Fundamentals). Dcdiff is the diffusion potential (cf. Eq. (7.58) in Fundamentals). Potential difference c0 c00 causing the driving force in the Donnan dialysis process is obtained from Eq. (7.4) as follows: c0 c00 ¼ Dc0Don Dc00Don þ Dcdiff

(7.5) 0

In equilibrium state the electrochemical potentials in both solutions Z and Z00 in Fig. 7.1 become equal: Z0 ¼ RT ln a0i þ zi F c0 ¼ Z00 ¼ RT ln a00i þ zi F c00

(7.6)

498

Ion Exchange Membranes: Fundamentals and Applications

where ai is the activity of i ions. The potential difference generating the driving force in the Donnan dialysis process, c0 c00 is introduced from Eq. (7.6). 00 1=zi RT a 0 00 ln i0 (7.7) c c ¼ ai F Equation (7.7) is also expressed as follows (Donnan, 1924): 00 1=zi ai ¼ constant a0i

7.3.

(7.8)

PRACTICE

Extraction of UO2+ Ions in a UO2(NO3)2 Solution by Donnan Dialysis 2 Wallace (1967) concentrated uranyl ions from dilute solutions of uranyl nitrate by applying Donnan dialysis as below. Fig. 7.2 represents experimental unit consisting of two end plates, shown as shaded areas, and a series of membrane spacers (feeding cell and extracting cell), each separated from an adjacent one by a membrane. Fig. 7.3 is a schematic of a membrane spacer. Each spacer was 3 3 inch2 with a 2 2 inch area in the middle comprising the ﬂow compartment. The membranes were AMFion C-103C cation exchange membrane (American Machine & Foundry Co.). The membranes between the spacers are punched with two holes on opposite sides of the same edge to accommodate the ﬂow between the spacers. After these preparations, a 0.01 M UO2(NO3)2 and a 2.0 M HNO3 solution were supplied to

7.3.1

Feed Strip

Extract Discharge

Figure 7.2

Donnan dialysis experimental unit (Wallace, 1967).

499

Donnan Dialysis

Figure 7.3

Membrane separator (Feeding cell and extracting cell) (Wallace, 1967).

feeding and extracting cells, respectively, and Donnan dialysis performance was evaluated. Here UO2(NO3)2 and HNO3 correspond to, respectively, B and A in Fig. 7.1. In this investigation, the cation concentration at the outlet of extracting cell C 00out is expressed by the following equation: C 00out ¼

Q0in ðC 0in C 0out Þ Q00out

(7.9)

where C is the concentration of the cation, Q the volumetric ﬂow and subscripts in and out refer to, respectively, the inlet and outlet of feeding cell and extracting cell (cf. Fig. 7.1). If the feed stream ﬂows too rapidly or the strip stream too slowly, not enough anions are introduced into the strip to satisfy the valence of the cations from the feed. When this happens, the product becomes saturated with the cation and some loss to the discharge must occur. Therefore, for complete recovery of the cation, the charge balance across the membrane requires z C 00in Q00in ^zþ C 0in Q0in

(7.10)

in which z+ and z are, respectively, the charge number of cations (UO2)2+ and anions (NO3). In cation concentration studies, it is convenient to deﬁne an operating parameter a a

z C 00in Q00in zþ C 0in Q0in

(7.11)

500

Ion Exchange Membranes: Fundamentals and Applications

Equation (7.10) is satisﬁed for all values of a^1. When a ¼ 1, conditions for complete recovery are just met and considerable losses to the discharge are expected. However, these loses should decrease as a increases, since the excess of anion in the strip, occurring with larger values of a, will provide a larger driving force for the transfer of the cation into the strip stream. As the strip stream progresses through the cell, water is transferred by osmosis from feed stream into the strip stream, thereby decreasing the concentration in the strip and increasing its ﬂow. Although the rate of osmosis is slow, the strip stream ﬂow is also slow, so that considerable dilution can occur. Osmosis, therefore, limits the concentration of cation in the product. The investigation done by Wallace is presented in Table 7.1. In this exions were concentrated from a 0.01 M UO2(NO3)2 feed with a periment, UO2+ 2 2 M HNO3 strip. The feed ﬂow was kept constant within separate groups of the test but a was varied. Each test was run for seven hours. Steady state was attained in all tests, except the ﬁrst two at feed ﬂow of 5 ml min1. and a at 0.8 and 1.0; Uranium losses to the discharge decreased with increasing values of a at constant feed ﬂow; the uranium concentration in the product C 00out;UO2 remained fairly constant up to a ¼ 1.5, then decreased with increasing a. Uranium loses C 0out;UO2 =C 0in;UO2 decreased with decreasing feed ﬂow Q0in at constant a. The concentration of free acid C 00out;H in the extract increased with increasing a, and approximated the value predicted from the excess acid added in the strip. The residual free acid in the discharge C 0out;H was in all tests slightly higher than that predicted for a simple exchange of H+ for UO2+ 2 . This indicates that a small amount of HNO3 diffuses through the membrane. This diffusion is also indicated by the small increase in C 0out;H as a is increased and feed ﬂow Q0in is decreased.

7.3.2

Ammonium Ion Removal from Waste Water by Donnan Dialysis Electrodialysis process of waste water for removing ammonium ions gives rise to organic fouling of ion exchange membranes (cf. Section 14.3 in Fundamentals). In order to prevent such a trouble, Ajinomoto Co. developed Donnan dialysis process as follows (Takeuchi et al., 1987). Fig. 7.4 illustrates Donnan dialysis unit (Effective membrane area: 0.5 dm2) incorporated with a Selemion CMV cation exchange membrane (Asahi Glass Co.). 400 ml of waste water preceding an activated sludge treatment process dissolving soluble organic materials and organic solid matter, was fed into the feeding cell. A 2 N HCl, 2 N NaCl or 2 N KCl solution (Strip) was supplied into the extracting cell. The solutions in both cells were stirred (300 rpm) using stirrers at room temperature. Ammonium state nitrogen concentration in the feeding cell was decreased with time as shown in Fig. 7.5 indicating the HCl strip to be most effective.

Donnan Dialysis

Table 7.1

Concentration of uranyl nitrate with nitric acid Flow

Feed Q0in ml min1 5.0

4.0 3.0

a

Strip Q00in ml min1

Extract Q00out ml min1

0.040 0.050 0.060 0.075 0.100 0.200 0.060 0.080 0.160 0.036 0.045 0.060 0.160

0.0995 0.112 0.142 0.176 0.230 0.339 0.158 0.207 0.314 0.111 0.141 0.181 0.344

0.80a 1.0a 1.2 1.5 2.0 4.0 1.5 2.0 4.0 1.2 1.5 2.0 5.3

UO2+ Concentration 2

H+ Concentration

Extract C 00out;UO2 M

C 0out;UO2 =C 0in;UO2 %

Extract C 00out;H M

Discharge C 0out;H M

0.282 0.274 0.273 0.268 0.210 0.148 0.220 0.189 0.124 0.189 0.185 0.155 0.084

24.6 17.8 7.46 3.34 1.33 0.67 1.41 0.56 0.18 1.76 0.15 0.09 o0.05

0.0126 0.0297 0.0466 0.109 0.269 0.551 0.0941 0.218 0.534 0.0207 0.0726 0.188 0.596

0.0292 0.0231 0.0244 0.0270 0.0292 0.0315 0.0274 0.0293 0.3420 0.0266 0.0285 0.0308 0.0401

Source: Wallace, 1967. Note: Feed C 0in ¼ 0.01 M UO2(NO3)2 (no HNO3); Strip C 00in ¼ 2.0 M HNO3. a Not at a steady state.

501

502

Ion Exchange Membranes: Fundamentals and Applications

Cation exchange membrane

Feeding cell

Figure 7.4

Extracting cell

Donnan dialysis experimental unit (Takeuchi et al., 1987).

0.8 0.7 : 2N HCl : 2N NaCl : 2N KCl

CAmmonium N (g/dl)

0.6 0.5 0.4 0.3 0.2 0.1 0.0

0

1

2

3

4

5

6 7 t (hr)

8

9

10 11 12

Figure 7.5 Changes of ammonium state nitrogen concentration in the feeding cell with time (Takeuchi et al., 1987).

Donnan Dialysis

503

REFERENCES Cwirko, E. H., Carbonell, R. G., 1990, A theoretical analysis of Donnan dialysis across charged porous membranes, J. Membr. Sci., 48, 155–179. Donnan, F. G., 1924, The theory of membrane equilibria, Chem. Rev., 1, 73–90. Higa, M., Tanioka, A., Miyasaka, K., 1988, Simulation of the transport of ions against their concentration gradient across charged membranes, J. Membr. Sci., 37, 251–266. Miyoshi, H., 1998, Diffusion coefﬁcients of ions through ion exchange membrane in Donnan dialysis using ions of different valence, J. Membr. Sci., 141, 101–110. Sudoh, M., Kamei, H., Nakamura, S., 1987, Donnan dialysis concentration of cupric ions, J. Chem. Eng. Jpn., 20, 34–40. Takeuchi, H., Nagai, K., Ioh, H., Ozawa, M., 1987, Treatment of waste water dissolving ammonium ions, JP Patent, S62-160189. Wallace, R. M., 1967, Concentration and separation of ions by Donnan membrane equilibrium, Ind. Eng. Chem. Proc. Des. Dev., 6, 423–431.

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Chapter 8

Energy Conversion 8.1.

DIALYSIS BATTERY

8.1.1

Overview of Technology Dialysis battery is a technology to generate electricity using salt concentration (chemical potential) difference across an ion exchange membrane placed in salt solutions. It is also termed ‘reverse electrodialysis’ and is applicable at the place where diluted and concentrated salt solutions such as seawater, river water or spring brine are supplied simultaneously. It is a primary battery and generates a constant direct current continually. In spite of the following assessment research, the process has not been practiced till now (Itoi, 1986).

Concentrated Solution

Diluted Solution

Location

Dead Sea Solar Pond Sea

Mediterranean Sea River

Israel Mexico, Taiwan USA, Japan etc.

Fundamental study started in 1952 by Manecke (1952). Pattele (1954) generated electric power of 0.015 W. Weinstein and Leitz (1976) generated 0.33 W (m2 pair)1 using an electrodialyzer (232 cm2, 30 pairs). Ohya et al. (1990) supplied concentrated seawater to a battery (200 cm2, 40 pairs) and generated maximum 0.5 W of electric power.

8.1.2

Principle of a Dialysis Battery System Fig. 8.1 shows operating circumstances in a unit cell in a dialysis battery. Here a and C are, respectively, activity coefﬁcient and concentration of electrolytes dissolving in solutions. L is molar conductivity of a solution. a is distance between ion exchange membranes. t and r are, respectively, apparent transport number and electric resistance of the membrane. E is electric potential generated between the solutions in contact with both membrane surfaces. Subscripts 1 and 2 refer to, respectively, diluted and concentrated sides. Subscripts K and A refer to, respectively, the cation and anion exchange membranes.

DOI: 10.1016/S0927-5193(07)12022-2

506

Ion Exchange Membranes: Fundamentals and Applications

a1

a2

a1

C1

C2

C1

1

2

1

d1

Diluting compartment

d2

Cation exchange membrane

Concentrating compartment

d1

Anion exchange membrane

Diluting compartment

a : electrolyte activity C : electrolyte concentration : molar conductivity of a solution d : distance between membranes

Figure 8.1

Operating circumstances in a dialysis battery.

E is expressed by the following equation (cf. Eq. (2.6) in Fundamentals). RT a2 ln E K ¼ ðtK 1Þ a1 F (8.1) RT a2 ln E A ¼ ðtA 1Þ a1 F in which R, T and F are, respectively, the gas constant, absolute temperature and the Faraday constant. The dialysis battery is assumed to be formed as an electric circuit as shown in Fig. 8.2, by arranging N unit cells described in Fig. 8.1 and connecting an external load rext. rint is internal electric resistance of the battery and I is an electric current generated by the battery. Voltage produced by the battery V is expressed by the following equation using Eq. (8.1). RT a2 (8.2) ln V ¼ NðE K þ E A Þ ¼ 2NðtK þ tA 1Þ a1 F Relationship between NaCl concentration C (mol dm3) and NaCl activity a is approximated by the following empirical equations at 251C (Tanaka, 1986). ! a2 9:532 103 þ 0:6477C 2 1:329 102 C 22 þ 1:154 102 C 32 ¼ a1 9:532 103 þ 0:6477C 1 1:329 102 C 21 þ 1:154 102 C 31 (8.3)

507

Energy Conversion

rext

I

rint V

Figure 8.2

Electric circuit in a dialysis battery.

Internal electric resistance rint is N 1000d 1 1000d 2 rK þ rA þ þ rint ¼ S L1 C 1 L2 C 2

(8.4)

S is effective membrane area. Relationship between L [(S/cm)/(mol/cm3)] and C (mol dm3) of a NaCl solution is approximated by the following empirical equation at 251C (Tanaka, 1986). L ¼ 126:18 83:98C 0:5 þ 82:19C 47:40C 1:5 þ 9:202C 2

(8.5)

Electric current I and electric power W in Fig. 8.2 are I¼

V rint þ rext

W ¼ I 2 rext ¼

(8.6) V 2 rext ðrint þ rext Þ2

(8.7)

W in Eq. (8.7) becomes maximum at rext ¼ rint

(8.8)

Substituting Eq. (8.8) into Eqs. (8.6) and (8.7) leads to the following maximum values I max ¼

V 2rint

W max ¼ 8.1.3

V2 4rint

(8.9)

(8.10)

Performance of a Dialysis Battery (Computation) In this section, we compute electric power generated from a dialysis battery using the equations described in Section 8.1.2 based on the following assumptions.

508

Ion Exchange Membranes: Fundamentals and Applications

Distance between the membranes d1 ¼ d2 ¼ 0.05 cm Electric resistance of ion exchange membrane rK ¼ rA ¼ 2 O cm2 Transport number of an ion exchange membrane tK ¼ tA ¼ 0.95 Effective membrane area S ¼ 200 dm2 Numbers of membrane pairs integrated in the battery N ¼ 3000 pairs Electrolyte concentration in a diluted side C1 and concentrated side C2 For a River/Sea system: C1 ¼ 0.05 M, C2 ¼ 0.5 M For a Sea/Brine system: C1 ¼ 0.5 M, C2 ¼ 3.4 M Fig. 8.3 gives electric power W plotted against external resistance rext. If we assume equipment cost of the dialysis battery described here to be 100,000,000 yen per unit, the system cost for unit electric power becomes For a River/Sea system: 100,000,000/9,752 ¼ 10,250,000 yen per kW For a Sea/Brine system: 100,000,000/32,881 ¼ 3,040,000 yen per kW These values are extremely high compared to the system cost for water power generation 100,000 yen per kW and for pump up generation 250,000 yen per kW. 8.2.

REDOX FLOW BATTERY

8.2.1

Overview of Technology The term ‘‘redox’’ means reduction and oxidation and it means an oxidation–reduction reaction between two chemical species occurring on inactive electrode surfaces in the battery. It is also termed ‘‘redox ﬂow battery’’ because chemical species stored outside the battery are supplied by pumps to the battery. The redox ﬂow battery is a secondary battery and its performance is characterized as follows. (a) (b) (c) (d) (e) (f)

Operating at room temperature Long life No explosion and no ignition Easy to scale up Easy automatic operation Easy to recycle

The basic principle of the technology was established by NASA in 1974 (Thaller, 1974) and the iron/chromium (Fe/Cr) system was initially selected (Hagedorn and Thaller, 1980). At nearly the same time, Electrochemical Laboratory, the Ministry of International Trade and Industry, Japan initiated the development research in the Moon Light project for the Fe/Cr system battery (Nozaki et al., 1984). However, the system did not lead to practical application because of the following problems in an electrolysis solution and a battery stack. (1) Occurrence of cross contamination of Fe and Cr ions across the ion exchange membrane. (2) Breaking of charge balance between the

509

Energy Conversion

35

30 Sea/Brine 25

W (kW)

Wmax = 32.88 kw 20

15

Wmax = 9.75 kw River/Sea

10

5

0

0

1

2

3

4

5

rext (Ω)

Figure 8.3

Generating power of a dialysis battery.

electrodes due to side reactions. (3) Low electromotive force (1 V) and low output density. After that, the direction of the development research was converted to a vanadium (V2+/V3+ for an anode and V5+/V4+ for a cathode) system. The advantages of this system are (1) high electromotive force (1.3 V), (2) high output density (several times as much as that for a Fe/Cr system) and (3) no performance deterioration due to contamination of ions across the membranes. The fundamental research on vanadium system battery was carried out in Australia (Rychcik and Skyllas-Kazcos, 1988). This system was not investigated in Japan because of lack of resources; however, the problem was solved by developing the technology to recover vanadium from soot and smoke discharged from a thermal power plant (Sato et al., 1998). The following are early achievements in a vanadium system in Japan. 1990 1991 1996 1997

1 kW plant, Electrochemical Laboratory, Ebara Corp. 10 kW plant, Mitsui Shipbuilding Co. 450 kW plant, Sumitomo Electric Industry Co., Kansai Electric Power Co. 200 kW plant, Mitsubishi Chemical Co., Kashima North Electric Power Corp.

510

8.2.2

Ion Exchange Membranes: Fundamentals and Applications

Principle of a Redox Flow Battery System Electrochemical reaction in the iron/chromium battery is presented as follows. At a cathode :

Fe3þ þ e

At an anode :

Cr2þ

discharge

! Fe2þ

(8.11)

! Cr3þ þ e

(8.12)

charge

discharge charge

Standard electrode potential difference E0 is +0.77 V for Fe3+/Fe2+ and 0.42 V for Cr3+/Cr2+, so that the theoretical electromotive force E0 for Eqs. (3.11) and (3.12) is computed as E 0 ¼ 0:77 ð0:42Þ ¼ 1:19V

(8.13)

Electrochemical reaction in the vanadium battery is At a cathode :

V5þ þ e

At an anode :

V2þ

discharge

! V4þ

(8.14)

! V3þ þ e

(8.15)

charge

discharge charge

From standard electrode potential difference E0 ¼ +1.14 V for V5+/V4+ and E0 ¼ 0.26 V for V2+/V3+, the theoretical electromotive force E0 is computed as E 0 ¼ 1:14 ð0:26Þ ¼ 1:4 V

(8.16)

Structure of a redox ﬂow battery is an array of a unit battery cell consisting of cathodes, anodes and cation exchange membranes with bipolar plates and terminal electrodes as illustrated in Fig. 8.4 for a vanadium battery in discharging operation. Electrolysis solutions dissolving active vanadium ions into sulfuric acid solutions are placed in a cathode solution tank and an anode solution tank, and are supplied, respectively, to cathode cells and anode cells. A direct current is generated through the electrochemical reactions in Eqs. (8.14) and (8.15). In this process, cation exchange membranes pass only H+ ions and do not pass vanadium ions, so that vanadium ions dissolving in each solution do not mix with each other. Direct electric current output is converted to an alternating current through an inverter and supplied to loads. In charging operation, an electric current generated by a power plant is supplied to the battery through the inverter, and stored in the battery due to the reverse electrochemical reactions. 8.2.3 Practice 8.2.3.1 Parts of the Redox Flow Battery System The battery system is composed of the following parts (Shigematsu, 2002). (a) Battery Cell The battery cell illustrated in Fig. 8.4 must be designed to make the oxidation–reduction reaction efﬁciency as high as possible and internal electric

511

Energy Conversion

Load −

+ A/D Inverter

K

BP

K

BP

K

BP

K

V2+ V5+ H+

V2+/V3+ A Tank

V5+/V4+ C Tank

V3+ V4+

TA

C A

C: Cathode A: Anode K: Cation exchange membrane T: Terminal electrode

C A

C A

CT

BP: Bipolar plate C Tank: Cathode solution tank A Tank: Anode solution tank

Figure 8.4 Discharging process in a vanadium redox ﬂow battery. Reverse reaction occurs in a charging process.

resistance as low as possible. The surface of the material in contact with the feeding electrolysis solutions must be anti-acidic because the solutions include sulfuric acid. Electrodes are prepared using woven or non-woven carbon ﬁbers. The electrodes only offer the place at which the oxidation–reduction reactions occur and they do not react with themselves. Accordingly, it is necessary to offer largest area and solution penetrability. The ﬁber material should have afﬁnity with the solution. Further, it is necessary to have largest hydrogen over potential and oxygen over potential for preventing side reactions due to water splitting. (b) Ion Exchange Membrane Cation exchange membranes are incorporated with the vanadium redox ﬂow battery. The function of the cation exchange membranes in this situation is to accelerate H+ ion transport and reject vanadium ion transport across the membranes for preventing vanadium ion mixing between cathode cells and anode cells. At the same time, electric resistance of the membrane is desired to be as low as possible. The above requirements are in the trade-off relationship with each other, so it is necessary to design to minimize total energy loss.

512

Ion Exchange Membranes: Fundamentals and Applications

(c) Bipolar Plate Many battery cells are arranged in series through bipolar plates as seen in an electrolyzer. The function of the bipolar plate is ﬁrst to connect a cathode with an anode and second to prevent the mixing of each solution. The bipolar plate is prepared with carbon resins (plastic carbon). (d) Flame The above-mentioned parts are arranged in the ﬂame, which is prepared from polyvinyl chloride, polyethylene etc. 8.2.3.2 Plant Operation of a Redox Flow Plant Fig. 8.5 exempliﬁes the performance of a charge/discharge cycle operation carried out by Kashima North Electric Power Corp. using a 10 kW battery. The speciﬁcations of a 200 kW battery are as follows (Sato et al., 1998). Basic speciﬁcations: Output: 200 kW, 4 h Current density: 80–100 mA cm2 Electric power efﬁciency: 80%

Figure 8.5 Charge/discharge operation of a 10 kW redox ﬂow battery. Current density, 80 mA/cm2; charge/discharge time, each 2.5 h (Sato et al., 1998).

513

Energy Conversion

Battery module: Module: 8 stacks Stack: 3 substacks Substack: 21 cells Electrode area: 4000 cm2 Stack output: 25 kW Electrolyte solution: Volume: 22 m3 Concentration: 1.8 M. System cost for a 50 MW plant (eight hours output) is estimated to be less than 200,000 yen per kW as follows, which is less than that of a newly established thermal power plant (200,000–250,000 yen per kW) (Sato et al., 1998). Ion exchange membrane Carbon resin electrode Stack material Electrolysis solution Pipe, rack, tank Meter, electrical system Total

26,000 19,000 12,000 36,000 37,000 9,000 139,000 yen per kW

8.2.3.3 Application of Redox Flow Batteries Redox ﬂow batteries are now operating in the following instances. (a)

(b)

(c)

(d)

(e)

Effective electric power utilization: In factories or buildings, batteries are charged in night time and discharged in day time, thus electricity charges are reduced by availing night charges. Measures against an interruption or an instantaneous lowering of power supply: It is available to avoid inferior semi-ﬁnished good production. Combination with natural energy utilization: Output of natural energy utilization unit such as solar generators, wind-driven generators is not stable. The output becomes stable with the aid of the redox ﬂow battery operation. Electric load leveling: It is available in adjustment of electric supply and demand in an electricity undertaking. Emergency uninterruptible power supply: Emergency lightning, hospital equipment, etc.

514

8.3.

Ion Exchange Membranes: Fundamentals and Applications

FUEL CELL

8.3.1

Overview of Technology The fuel cell is a primary battery and was invented by Lord Glove in England in 1839. However, it was not popular until General Electric Co. started its investigation in the later half of 1950s and a 1 kW battery was loaded in Gemini No. 5 in 1965. During the day time, a space station generates electric power from solar energy and electrolyzes water using the electricity to obtain hydrogen and oxygen. During the night time, the station creates water from hydrogen and oxygen using the fuel cell. Such a generation system came to be widely applied in NASA space development projects because it does not discharge wastes, is light weight and its generation efﬁciency is high. Ion exchange membranes incorporated in the fuel cell at ﬁrst were inferior in chemical durability because they were based on polystyrene. However, perﬂuorinated Naﬁon membranes developed by Du Pont Co. exhibited excellent durability and were applied for the fuel cell in Biosatellite in 1969. On the other hand, ion exchange membrane technology in Japan was developed with seawater concentration for sodium chloride production and sodium chloride electrolysis for chlor-alkali production. In the course of development research, Asahi Glass Co. and Asahi Chemical Co. produced, respectively, perﬂuorinated Flemion membranes and Aciplex membranes having excellent endurance in alkaline atmosphere. Fuel cell technology investigation in Japan was started in 1981 in Moon Light project carried out by Agency of International Science and Technology, Ministry of International Trade and Industry, Japan. The development research was advanced extensively in cooperation with many research organizations. In the middle of the 21st century, the fuel cells are estimated to be widely applied to electric traction for industrial tracks, delivery vehicles and passenger cars; to cogeneration systems for households and buildings and to portable telephone power sources, etc. 8.3.2

Principle of a Fuel Cell System The fuel cells are classiﬁed into phosphoric acid fuel cell (PAFC), molten carbonate fuel cell (MCFC), solid oxide fuel cell (SOFC) and polymer electrolyte fuel cell (PEFC). We discuss only the PEFC in this section because only PEFC includes an ion exchange membrane (polymer electrolyte). The greatest merit of the PEFC is that it can be operated at less than 1001C. It consists of a fuel electrode, an air electrode and an ion exchange membrane as illustrated in Fig. 8.6. In this system, water molecules are obtained from hydrogen gas and oxygen gas by the following chemical reaction. H2 þ O2 ! H2 O

(8.17)

515

Energy Conversion

H2 e−

Fuel electrode (Anode) Ion exchange membrane

I

H+

Air electrode (Cathode) O2 (Air)

Figure 8.6

H2 → 2H+ + 2e−

2H+ + 2e− + 1/2O2 → H2O

Polymer electrode fuel cell.

The relationship between the enthalpy change DH and Gibbs’ free energy change DG in the reaction (8.17) is DG ¼ DH TDS

(8.18)

in which T is the absolute temperature and DS entropy change. DH and DG are evaluated as DH ¼ 285.83 kJ mol1 and DG ¼ 237.13 kJ mol1. Accordingly, the theoretical maximum efﬁciency of the PEFC Z is calculated as Z¼

DG 237:13 100 ¼ 100 ¼ 82:9% DH 285:83

(8.19)

The efﬁciency calculated above far exceeds the theoretical efﬁciency of a heat engine given by the Carnot’s cycle. Electrochemical reactions on the electrodes in Fig. 8.6 are Anode ðFuel electrodeÞ : H2 ! 2Hþ þ 2e

(8.20)

Cathode ðAir electrodeÞ : 12O2 þ 2Hþ ! H2 O ðLiquidÞ

(8.21)

Gibb’s free energy change in the above reactions is DG ¼ nF E 0

(8.22) 1

in which F is the Faraday constant (96,485 C mol ). Theoretical electromotive force of the PEFC E0 is E0 ¼

DG 237:13 1000 ¼ ¼ 1:229 V nF 2 96; 485

(8.23)

Under an applied electric current, unit cell voltage in the PEFC is decreased as shown in Fig. 8.7 because of energy loss generated in the cell. This

516

E = 1.481 V T ∆S = 48.7 kJ/mol

A

Theoretical voltage

E0 =1.229V

Diffusion polarization

Voltage

- ∆G = 237.13 kJ/mol

B

Activation polarization

V I − V curve C

Electric current

I

A: Energy which can not be converted into electric power (Heat generation) B: Energy loss due to internal cell resistance (Heat generation) C: Electric energy which can be taken out to the external circuit

Figure 8.7

Performance and energy consumption in a fuel cell (New Sunshine Program, 1999, p. 14).

Ion Exchange Membranes: Fundamentals and Applications

−∆ ∆ H = 285.53 kJ/mol

Resistance polarization

Energy Conversion

517

phenomenon is caused by the following (New Sunshine Program Promotion Center, 1999). (1)

(2)

(3)

Diffusion polarization: Electrochemical reaction in Eqs. (8.20) and (8.21) brings about diffusion due to the occurrence of concentration difference (concentration polarization) of each component. A part of electromotive force of the PEFC is consumed by the concentration polarization. Resistance polarization: Electric resistance of the ion exchange membrane, electrode, separator and the interface between the membrane and electrode consumes the electromotive force (IR loss). Activation polarization: Oxidation–reduction reaction in Eqs. (8.20) and (8.21) proceeds via the peak of activation energy. The reaction is accelerated by the potential shift (over voltage) established in the reaction system. A part of electromotive force in the PEFC is consumed to generate the over voltage.

8.3.3 Practice 8.3.3.1 Parts of PEFC (Poly Electrolyte Fuel Cell) (a)

Membrane electrode assembly (MEA) and cell stack: MEA is composed of an ion exchange membrane, a cathode catalyst layer, anode catalyst layer and gas diffusion layers placed between an anode separator and a cathode separator as illustrated in Fig. 8.8. Passways are provided in the anode and cathode separator for feeding, respectively, fuel gas and air into the electrodes. Passway in the water separator is provided for cooling the assembly. The cell stack is an array of MEA between terminal electrodes (current collectors) placed on both outsides of the array as shown in Fig. 8.9. The cell stack is uniﬁed by fastening plates attached on both outsides of the terminal electrodes. (b) Ion exchange membrane: Perﬂuorinated ion exchange membranes, such as Naﬁon membrane (Du Pont Co.), Flemion membrane (Asahi Glass Co.), Aciplex membrane (Asahi Chemical Co.) or Dow membrane (Dow Chemical Co.), are applied to the PEFC system (Yoshitake, 1999). The membrane characteristics are generally, the thickness: 30–175 mm and ion exchange capacity: 0.91–1.1 meq g1. The functions of the ion exchange membrane are (1) to carry H+ ions generated at the fuel electrode toward the air electrode, (2) to prevent the direct contact between H2 and O2 and (3) to prevent the formation of a short circuit between both electrodes (Fuel Cell Generation System Technology Investigative Committee, 2002).

518

Ion Exchange Membranes: Fundamentals and Applications

Figure 8.8 Unit cell arrangement in a PEFC. MEA, Membrane electrode assembly; IEM, ion exchange membrane; GDL, gas diffusion layer AC: anode catalyst layer; CC, cathode catalyst layer; AS, anode separator; CS, cathode separator; WS, water separator (Fuel Cell Generation System Technology Investigative Committee, 2002, p. 57).

Figure 8.9 Cell stack arrangement in a PEFC. MEA, Membrane electrode assembly; AS, anode separator; CS, cathode separator; WS, water separator; Se, seal; TE, terminal electrode; FP, fastening plate (Fuel Cell Generation System Technology Investigative Committee, 2002, p. 58).

Ion conductivity of the membrane is enhanced by water in the membrane, so it is necessary to increase water content of the membrane by injecting moisture into the feeding fuel and air. In order to keep the water content to suitable values, it is important to control the following

Energy Conversion

(c)

519

water transport in the assembly. Namely, moisture is injected into the fuel gas transporting from the anode toward the cathode across the membrane with H+ ions generated by Eq. (8.20) (electro-osmosis). The H+ ions are converted to H2O by Eq. (8.21) at the cathode, and the H2O generated at the cathode diffuses from the cathode toward the anode (back diffusion) (Yasuda, 2000). If the feeding water or generated water in the assembly ﬁlls the ﬁne pores in the electrodes, energy and voltage is decreased by the increase of cell resistance. Accordingly, it becomes necessary to control water supply to the system. Catalyst: Catalysts reduce the energy consumption of the cell by decreasing the activation energy peak of the electrode reactions (Eqs. (8.20) and (8.21)). Platinum/ruthenium catalyst is used for the fuel electrode to avoid the performance deterioration caused by carbon monoxide. Platinum catalyst is used for the air electrode. The catalyst layers are formed on the electrodes as follows (NEDO Research and Development Report, 1999). (1) The catalyst is applied to a base plate (carbon plate) of both electrodes. Then they are pasted with the membrane (Fig. 8.10(a)). (2) Catalyst layers are formed on both surfaces of the membrane. Then the membrane is pasted with the carbon plates (Fig. 8.10(b)).

8.3.3.2 Performance of a Fuel Cell System Cell voltage change of a unit cell PEFC system (membrane area: 225 cm2) being supplied by pure hydrogen is exempliﬁed in Fig. 8.11 (Mitsuta et al., 1997). Current density and operating pressure in this operation are, respectively, 250 mA cm2 and 1 ata. Decreasing rate of cell voltage was 4 mV per 1000 h.

Figure 8.10 Formation of catalyst layers in a membrane electrode cell assembly (NEDO Research and Development Report, 1999).

520

Ion Exchange Membranes: Fundamentals and Applications

Figure 8.11 Cell voltage change of a unit cell PEFC system with time (Mitsuta et al., 1997).

Fig. 8.12 gives the performance of a 20-cell unit operated at 367 mA cm2 and 6 ata (Washington, 2000). Cell voltage decreasing rate in this unit was 2.2 mV per 1000 h. Cell voltage decrease during the operation is caused by (1) decrease of effective reaction area of the catalyst due to the increase of catalysis particle diameter or the increase of moisture in the catalysis layer, (2) fouling of the membrane and (3) an excessive or an insufﬁcient moisture injection to the electrodes (Fuel Cell Generation System Technology Investigative Committee, 2002). 8.3.3.3 (a)

Application of Fuel Cells Electrically powered car: Fig. 8.13 exempliﬁes an electrically powered car system in which hydrogen and air are supplied to the PEFC and a motor is derived from electric power generation. Ultra-capacitor is applied for recovering braking energy and increasing driving force. In 1993, Ballad Power Systems Inc. in Canada developed an electrically powered car (electric output; 120 kW, motor output; 80 kW, mileage; 160 km) by supplying compressed hydrogen and air to the PEFC. In 1997, DaimlerChrysler developed the NECAR 3 passenger car (electric output; 50 kW, mileage; 400 km) refueling methanol. In 1998, fuel cell bus service seated 62 passengers stated between Vancouver and Chicago refueling compressed hydrogen. A fuel cell car developed by Adam Opel Gmbh in Germany supplying liquid hydrogen was applied for leading marathon runners in Sydney Olympic in 2000. Highway test driving was started in California

521

Energy Conversion

Figure 8.12

Performance of a 20-cell PEFC unit (Washington, 2000).

Air feeder

Moisture injector

Driving motor

Cell stack

Moisture injector

Compressed hydrogen tank

Ultra capacitor or Secondary battery

Cooling system

Figure 8.13 Polymer fuel cell system in an electrically powered car (Fuel Cell Generation System Technology Investigative Committee, 2002, p. 78).

522

Ion Exchange Membranes: Fundamentals and Applications

Figure 8.14 Household cogeneration system (Fuel Cell Generation System Technology Investigative Committee, 2002, p. 85).

(b)

participated by NECAR 4a (DaimlerChrysler, compressed tank), Focus (Ford, compressed hydrogen), FCX-3 V (Honda, compressed tank) etc. in November 2000. Upper cost limit of an electrically powered fuel car is assumed to be 5–15% more than traditional cars, and the system cost is estimated to be 5,000–10,000 yen per kW. Household cogeneration: Fig. 8.14 shows a household cogeneration system, which consists of (1) fuel treating unit, (2) blower, (3) PEFC cell stack, (4) heat recovering unit and (5) inverter. In the fuel treating unit, town gas is converted to hydrogen including carbon dioxide and a very small quantity of carbon monoxide. In the PEFC cell stack CS, a direct current and heat are generated from H2 and O2 being supplied, respectively, from the fuel treating unit FTU and the blower Blw. In the inverter Inv, the direct current is converted to an alternating current, which is consumed in the household for lighting, heating etc. In the heat recovering unit HRU, heat discharged from PEFC cell stack and fuel treating unit is converted to warm water of temperature higher than 601C, which is also consumed in the household. The household cogeneration apparatuses are developed and commercialized by many electrical product ﬁrms and gas companies.

REFERENCES Fuel Cell Generation System Technology Investigative Committee, 2002, Society of Electricity, Japan, 2002, Fuel cell technology, Ohm Co., Tokyo, pp. 55–98. Hagedorn, N. H., Thaller, L. H., 1980, Redox storage systems for solar application, NASA TM-81464, NASA, U.S. Department of Energy.

Energy Conversion

523

Itoi, S., 1986, Dialysis battery technology development project. Paper presented at the meeting of Research group of dialysis battery, March 1986, Tokyo. Manecke, G., 1952, Membranak kumulator, Z. Phys. Chem., 201, 1–15. Mitsuta, K. et al., 1997, Development of an exterior manifold type PEFC module, The 4th FCDIC symposium, pp. 265–268. NEDO Research and Development Report, 1999, Development of polymer electrolyte fuel cell – Development of a high current density 10kW mobile power source system. New Sunshine Program Promotion Center, Agency of Industrial Science and Technology, 1999, Ministry of International Trade and Industry, Japan, Polymer Electrolyte Fuel Cell, pp. 13–14. Nozaki, K., Kaneko, H., Negishi, A., Ozawa, T., 1984, Proceedings of the Symposium on Advances in Battery Materials Vol. 84-4, Electrochemical Society, Inc., Princeton, NJ, p. 143. Ohya, H., Watanabe, S., Hiroishi, K., Negishi, Y., 1990, Scale-up of multi-compartment dialytic battery with ion-exchange membranes, Bull. Soc. Sea Water Sci. Jpn., 44, 361–364. Pattele, R. E., 1954, Production of electric power by mixing fresh and salt water in the hydro-electric pile, Nature, 174, 660. Rychcik, M., Skyllas-Kazcos, M., 1988, Characteristics of a new all-vanadium redox ﬂow battery, J. Power Sources, 22, 59–67. Sato, K., Sawahama, M., Miyahayashi, M., Kageyama, Y., Nakajima, M., 1998, Development of new fuel and electric power storage battery, Soda Chlorine, 49(4), 149–158. Shigematsu, T., 2002, Redox ﬂow battery for electric power storage in practically available stage, Material Stage, 1(10), 40–43. Tanaka, Y., 1986, Performance of a dialysis battery. Paper presented at the meeting of research group of dialysis battery, September 1986, Tokyo. Thaller, L. H., 1974, Proceedings of the 9th Inter-Society Energy Conversion Engineering Conference, American Society of Mechanical Engineering, p. 924. Washington, K., 2000, Development of a 250kW class polymer electrolyte fuel cell. Paper presented at the Stack, Fuel Cell Seminar, pp. 468–472. Weinstein, J. N., Leitz, F. B., 1976, Electric power from differences in salinity: The dialytic battery, Science, 191, 557–559. Yasuda, K., 2000, Development and application of polymer electrolyte fuel cells, Lecture 2, Material development in PEFC, NTS Co., Tokyo. Yoshitake, Y., 1999, Development of ion exchange membranes for PEFC, Text book in FCDIC lecture meeting, pp. 22–33.

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INDEX Acid dosage 341 Acrylic acid 12 Acrylic-based polymer anion exchange membranes 392 Activation polarization 517 Active component layer 421 Actual transport number 22 Adhesion of bacteria on the membrane surface and generation of the water dissociation 167 Air bubble cleaning 228 Air bubble attachment to the membrane surface in an electrolyzer 477 Alternating current electric resistance 18 Aluminum chloride catalyst 9 Amino acid permeability 522 Ammonia removal in an EDI process 451 Ammonium ion removal from waste water by donnan dialysis 500 Amphoteric electrolyte 361 Anion exchange layer 407, 410 Anti-alkaline circumstance 370 Anti-fouling anion exchange membranes 344 Anti-organic fouling 369, 392 Anti-organic fouling membranes 312 Antiscalants 391 Apparent transport number 21 Application of fuel cells 520 Application of redox ﬂow batteries 513 Ascending ﬂow velocity 107 Assumption of partial equilibrium 67 Atomic force microscope (AFM) 415 Auto-catalytic reaction 153, 163, 173, 184, 420 Auto-catalytic water dissociation 157 Auto-catalytic water dissociation reaction 151 Bacteria cells 378 Batch process 331 Battery cell 510 Benzene 13 Benzoyl peroxide 7, 9–11, 14 Bernoulli theorem 238 Bipolar electrode chambers in the electrolyzer 477 Bipolar membrane electrodialysis 405 Bipolar plate in a redox ﬂow plant 512 Bis (4-tertiary-butyl-cyclohexyl)peroxyl dicarbonate 4 Block polymerization 7 Boltzmann distribution law 50 Boron removal in an EDI process 451 Boundary layer 116, 133 Boundary layer thickness 97 Bridging agent 5 Bubble agitation 229 Bursting strength 28

Calcium and magnesium accumulation in the degraded membrane 483 Calcium ﬂuoride saturation 398 Carbon dioxide removal in an EDI process 451 Carnot–Clausius equation 69 Catalyst 5, 7, 14 Catalyst in a fuel cell 519 Catalytic hydrolysis 150 Catalytic water dissociation effect 410 Catalytic water dissociation reaction 148 Cation exchange layer 407, 410 Cell voltage applied to a membrane pair 287 Cell voltage change of a unit cell PEFC 519 Cheese production process 364 Chemical additions to prevent scale formation 391 Chemical potential change 46 Chemical potential difference 68, 75 Chilton–Coburn transfer factor 251 Chlor-alkali consumption difference 461 Chlor-alkali industry 461 Chlor-alkali process 461 Chloromethyl ether 5, 9 Chloromethyl styrene 11, 13 Chronopotentiometry 101 Cluster diameter 464 Co–ion leakage 112 Co-ions 63 Colloidal deposit formation on the membrane surface and its removal 393 Comparison of the desalination technologies 400 Composition control in an anodized aluminum processing bath 491 Composition of milk and whey 364 Computation of current density distribution 192 Computation of electric resistance and H+, OH– ion concentration in the water dissociation layer 179 Computation of energy consumption in electrodialysis 288 Computation of leakage current ratio 276 Computation of the limiting current density of an electrodialyzer 268 Concentrating cells 321 Concentration diffusion 47 Concentration distribution in a boundary layer 104 Concentration distribution of H+ and OH– ions in the water dissociation layer 176 Concentration ﬂuctuation 105, 131 Concentration noise 131 Concentration polarization 97 Concentration polarization on a concentrating surface of an ion exchange membrane 134 Concentration polarization potential 100 Concentration potential 99 Concentration process 336 Concentration reﬂection coefﬁcient 89, 92 Concentration–osmosis 81, 84, 128, 246

526 Conductivity 44 Convection 120, 123, 245 Convection current 126 Convection velocity 43, 128 Counter-ions 63 Cowan plot 99 Current density distribution 187 Current density distribution around an insulator 192 Current density distribution equation 187 Current density distribution in an electrodialyzer 187 Current density in a boundary layer 126 Current density vs. voltage drop in a boundary layer 135 Current efﬁciency in bipolar membrane electrodialysis 421 Current efﬁciency of H+ and OH– ions generated in the water dissociation layer 180 Current interruption 101 Current leakage equation 271 Current–pH relationship 139, 149 Current–Voltage relationship 97 Darcy’s law 206 DC polarity reversal 390 Dead space 222 Debye radius 114 Dependence of limiting current density on electrolyte concentration and solution velocity of a solution 248 Depleted layer 114 Desalination of amino acid and amino acidic seasonings 361 Desalination of extracted meat essences, ﬁsh essences and fruit ﬂesh essences 363 Desalination of natural essences 363 Desalination of sugar liquor 372 Desalting cells 321 Desirable properties in the bipolar membrane electrodialysis process 427 Developed region 205 Developing region 205 Dialysis battery 505 Dibenzoyl peroxide 4 Diffusion 120, 123, 245 Diffusion coefﬁcient 62, 488 Diffusion constant 62 Diffusion current 126 Diffusion dialysis 487 Diffusion dialyzer and its operation 489 Diffusion layer and boundary layer 245 Diffusion polarization 517 Diffusion potential 59, 72, 132, 497 Diffusional model 141 Dilauroyl peroxide 4 Dimethyl phthalate 7 Dioctyl phthalate 9–10 Direct current electric resistance 18

Index Disassembling and assembling works 342 Dissipation function 69, 75, 77 Dissociation rate constant 146 Distance between the membranes 327 Distribution coefﬁcient of solution ﬂowing into each desalting cell 234 Divinylbenzene 3, 7, 9–10, 14 Divinylbenzene co-polymerization 10 Dixylyl ethane 3 Donnan dialysis 495 Donnan equilibrium equation 38 Donnan equilibrium state 37 Donnan equilibrium theory 37, 59, 497 Donnan exclusion 48, 63, 487 Donnan potential 48, 59, 497 Double layer membrane 416 Drinking water standard 397 Economic comparison between EDI and mixed-bed ion exchange 458 EDR operation for production of drinking water 395 EDR, NF and RO at a brackish water reclamation 399 Effect of a spacer on solution ﬂow (experimental) 215 Effect of a spacer on solution ﬂow (theoretical) 205 Effect of solution ﬂow on limiting current density and static head loss in a channel 227 Effect of water dissociation in an EDI process 449 Effective osmotic pressure 74 Electric conductance 77 Electric conductivity 43, 64 Electric conductivity (permeability) 70 Electric conductivity and thickness of the water dissociation layer and potential gradient in the water dissociation layer 181 Electric current density 44 Electric current efﬁciency of the cation exchange layer, anion exchange layer and bipolar membrane 420 Electric current interruption 92, 100 Electric current leakage 271, 327 Electric current shadowing 202 Electric current switching off concept 89 Electric neutrality 44, 59, 75, 495 Electric potential difference 46 Electric power generated from a dialysis battery 507 Electric resistance 18, 296 Electric resistance of the water dissociation layer 178 Electric transport number 71 Electrically powered car 520 Electro–osmotic convection 112 Electro-deionization 437 Electro-gravitational movement 135 Electro-migration 81, 84, 89, 123 Electro-osmosis 81, 84, 89, 128, 246 Electrochemical potential difference 68 Electrode and electrode chamber 325

527

Index Electrode conﬁguration in the electrolyzer 477 Electrode potential 99 Electrodialysis 33, 321 Electrodialysis desalination system powered by photo-voltaic power generation 344 Electrodialysis of milk and whey 364 Electrodialysis phenomena 74, 79 Electrodialysis process 327 Electrodialysis program 285 Electrodialysis reversal 103, 383 Electrodialysis system for the demineralization of milk or whey 371 Electrodialytic disinfection 378 Electrodialytic recovery of acid 355 Electrodialytic recovery of wastewater from a metal surface treatment process 347 Electrodialytic reuse of wastewater in a plating process 353 Electrodialyzer 33, 321 Electrokinetic phenomena 71 Electrolysis 461 Electrolysis process 478 Electrolyte concentration in an interface layer in a bipolar membrane 415 Electrolyzer and it’s performance 473 Electromotive force 75 Electroosmosis 71 Electroosmotic coefﬁcient 25 Electroosmotic permeability 77–78 Electroosmotic pressure 72 Energy consumption 285 Energy consumption and optimum current density 340 Energy consumption and production capacity in bipolar membrane electrodialysis 422 Energy consumption decrease in an electrolyzer 475 Energy consumption in a desalinating process and in a concentrating process 287 Energy consumption in a stack 285 Energy conversion 505 Energy requirements in an electrodialysis system 285 Enriched layer 115 Entropy change 69 Entropy production 68 Equation of concentration gradient 122 Equation of continuity 117 Equation of material balance 117, 120 Equation of motion 118 Equation of potential gradient 122 Equipotential line 192 Equivalent network circuit 196, 273 Etching process of aluminum products 355 Exchange ﬂow 91 Exchange ﬂow parameter 91 Expansive agent 5 Experimental research on the water dissociation 150

Extended nernst–Planck equation 42, 116–117, 246 Extraction of UO2+ ions in a UO2(NO3)2 solution by 2 donnan dialysis 498 Fastening frame 323 Feeding cell and extracting cell in a Donnan dialyzer 495 Feeding cell and recovering cell in an diffusion dialyzer 487 Fick’s diffusion equation 48 Film thickness 303 Filtration of a feeding solution 340 Flame in a redox ﬂow plant 512 Flow distribution equation 209 Flow lines in the gasket 217 Flow pattern image 220 Fluctuation 109 Fluctuation phenomena in a boundary layer 130 Food hygiene standard 363 Formaldehyde 3 Formation of ﬁlms on the membrane surface 305 Formation of thin cation exchange layer on the anion exchange membrane 314 Forward and reverse equilibrium reaction constant 173, 420 Forward equilibrium constant 146 Fouling parameter 304 Frank–Kamenetskii equation 253 Free energy change 46 Friction factor of a spacer and solution distribution to each desalting cell 230 Fuel cell 514 Fuel cell in biosatellite 514 Gasket 323 Gay–Lussac’s law 424 Generation and transport of H+ and OH– ions in the water dissociation layer 174 Grotthuss protonic conduction 148 H+ ion permselective cation exchange membrane 355 Heat generation in a bipolar membrane 425 Henderson equation 133 Heterogeneous membrane 14 Homopolymerization 12 Household cogeneration 522 Hydraulic (mechanical) permeability 70 Hydraulic conductivity 77–78, 87, 91 Hydrodynamic convection 114 Hydrodynamic convection current 114 Hydrodynamic instability 110 Hydrodynamics 205 Hydrolysis of magnesium ions 149 Inﬂuence of impurities in salt water on the performance of an electrolyzer 481

528 Inﬂuence of ionic electrolytes in a solution on the water dissociation reaction 155 Inﬂuence of low electrolyte concentration and high electric potential ﬁeld on the water dissociation reaction 158 Inlet current density nonuniformity coefﬁcient 192 Inorganic active components 421 Intermediate layer 410, 447 Invention of an ion exchange membrane 3 Ion exchange capacity 19, 296 Ion exchange membrane for the demineralization of mlik or whey 369 Ion exchange membrane in a fuel cell 517 Ion exchange membrance in a redox ﬂow battery 511 Ion product speciﬁc limit 391 Ion-cluster channel model 464 Ionic ﬂux in a boundary layer 123 Iron/chromium battery 510 Irradiation graft polymerization 11 Irreversible thermodynamic membrane pair characteristics 93 Irreversible thermodynamics 67 Isoelectric point of amino acid 362

Kirchhoff equation 197, 273 Laminar ﬂow 228 Langelier saturation index 391 Laser interferometry method 105 Latex method 5 Leakage 271 Light scattering spectra 110 Limiting current density 97, 99, 222, 245, 349, 378, 385 Limiting current density analysis based on the mass transport in a desalting cell 250 Limiting current density equation 247, 263 Limiting current density equation introduced from the Nernst–Planck equation 247 Limiting current density in electrodialysis of milk and whey 366 Limiting current density of an electrodialyzer 263 Local electro-neutrality 114 Local ﬂow distribution in a ﬂow channel 223 Logarithmic mean concentration 77–78

2-methyl vinylpyridine 11 Macroreticular anion exchange membrane 312 Manifold 321 Mass transfer in the EDI system 439 Mass transport effect 217 Mass transport in a boundary layer 116 Mass transport in donnan dialysis 496 Material ﬂow and electrode reaction in an electrolysis system 469

Index Maxwell pressure difference 424 Measurement of solution leakage 279 Mechanical (hydraulic) transport number 71 Mechanical strength 28 Mechanism of surface fouling 300 Mechanism of water dissociation 173 Mechanism to decrease divalent ion permeability 48 Membrane characteristic stability against various agents 293 Membrane characteristics 37 Membrane deterioration 293 Membrane electrode assembly (MEA) 517 Membrane pair electric resistance 83 Membrane pair reﬂection coefﬁcient 87 Membrane pair water content 83 Membrane potential 44, 59 Membrane property change with elapsed time 293 Membrane property measurements 17 Membrane surface potential 143 Mercury-poisoning problem 461 Mesh step model 213 Microorganisms 306 Migration 120, 245 Migration current 126 Mixing efﬁciency of the spacer 213 Monopolar and bipolar systems 473 Monovalent ion permselectivity 357 Moon light project 508, 514 NASA space development projects 514 Natural convection 106, 117, 246 Navier–Stokes equation 209 Nernst diffusion layer 114 Nernst diffusion model 301 Nernst equation 46, 61 Nernst–Einstein equation 47 Nernst–Planck equation 47, 59, 67, 175, 247, 497 Nernst–Planck model 97 Nernst–Planck–Poisson equation 113 Nickel plating process 347 Nitrate and nitrite removal 394 Nitrate contamination of drinking water 394 Nitrogen concentrations in drinking water 394 No benzene ring structures 393

Ohmic potential 132 Ohmic voltage 99 One-Pass ﬂow process 327 Onsager reciprocal relation 91–92 Onsager’s reciprocal theorem 67, 76 Operational problems in a bipolar membrane electrodialysis process 427 Optical noise 110, 130 Organic fouling 308, 344, 349, 374 Osmotic pressure 74, 77 Osmotic volume ﬂow coefﬁcient 91

Index Outlet current density nonuniformity coefﬁcient 190 Overall dialysis coefﬁcient of solutes 488 Overall electro-osmotic permeability 81 Overall hydraulic conductivity 81 Overall mass transport 81 Overall mass transport equation 85, 278 Overall mass transport equation and solution leakage 278 Overall membrane pair characteristics and mass transport across a membrane pair 81 Overall solute permeability 81 Overall transport number 81 Overﬂow extracting system 321 Overlimiting current 105, 111 Oxidation-reduction reaction in a redox ﬂow battery 508, 511 Partial molar volume 38 Partially circulation (Feed and bleed) process 332 Parts of an electrodialyzer 323 Parts of PEFC (Poly electrolyte fuel cell) 517 Parts of the redox ﬂow battery system 510 Paste method 10 Perﬂuorocarboxylic acid layer 463, 466 Perﬂuorosulfonic acid layer 463, 466 Perﬂuorosulfonic acid membrane 463 Perﬂuorosulfonyl ﬂuoride 463 Performance change of ion exchange membranes in long-term seawater electrodialysis 299 Performance of a bipolar membrane 415 Performance of a dialysis battery 507 Performance of a fuel cell system 519 Performance of diffusion dialysis 489 Periodic reversal of the applied DC power 394 Permeability 70 Permeability to larger organic ions of an anion exchange membrane 370 Permselectivity 296 Permselectivity between ions and water molecules 92 Permselectivity between ions having different charged sign 37 Permselectivity between ions having the same charged sign 42 Permselectivity coefﬁcient 43, 51–52 Phenol sulfonic acid 3 Phenomenological equation 85 Phenomenological equation and phenomenological coefﬁcient 67 Photographic image of a ﬂow pattern 220 Plant operation of a redox ﬂow plant 512 Plasticizer 7, 9 Poisson’s equation 143 Polyethylene ﬁlm 11–12 Polymer electrolyte fuel cell (PEFC) 514 Polymerization initiators 4 Polypropylene net 9 Polyvinyl chloride net 10–11

529 Polyvinyl chloride powder 10 Potable water production from brackish water 343–344 Potable water standard 344 Potential difference in Donnan dialysis 497 Potential drop across the membrane 97 Potential gradient in a boundary layer 132 Precipitation controlling agent dosage 342 Precipitation of insoluble metallic hydroxides on the membrane surface and generation of the water dissociation 164 Preparation of bipolar membranes 409 Preparation of ion exchange membranes 3 Press 326 Pressure distribution in a duct in an electrodialyzer 236 Pressure reﬂection coefﬁcient 89, 91 Prevention of scale formation 391 Primary puriﬁcation in a electrolysis process 479 Principle of a dialysis battery system 505 Principle of a fuel cell system 514 Principle of a redox ﬂow battery system 510 Principle of separation of salt and water 78 Principle of the donnan dialysis 495 Procedure for calculating the limiting current density of an electrodialyzer 265 Protonation and deprotonation reactions 147 Puriﬁcation of salt water in electrolysis process 479 Reaction at a cathode in an electrolysis system 470 Reaction at an anode in a electrolysis system 471 Reaction initiator 9 Recovery of mixed acids from stainless pickling 428 Recovery of nitric acid in an acid washing process 492 Recovery of sodium hydroxide and sulfuric acid from sodium sulfate 432 Rectiﬁcation effect of a bipolar membrane 425 Redox ﬂow battery 508 Reduced diffusion coefﬁcient 117, 123 Reduced transport-diffusion coefﬁcient 123 Reﬂection coefﬁcient 73, 77–78, 87, 91 Refractive index 103 Reinforcement 9–10 Removal of ﬁlms on the membrane surface 307 Removal of weakly-ionized species in an EDI process 448 Repulsion zone 142 Requirements for improving the performance of an electrodialyzer 326 Resin/membrane interfaces 446 Resin/resin interfaces 446 Resistance polarization 517 Reuse of wastewater by electrodialytic treatment 351

530 Reverse electrodialysis 505 Reynolds number, schmidt number and shape factor 257 Safe drinking water act 395 Salt diffusion coefﬁcient in the ﬁlm 303 Salt production using brine discharged from a reverse osmosis seawater desalination plant 358 Sampling and pretreatmemt of membranes 17 Sandwich method 3 Scale trouble prevention 341 Schlieren-diagonal method 104, 135 Seafood essences 363 Seawater concentration for salt production 355 Second wien effect 184 Secondary puriﬁcation in an electrolysis process 480 Semi-conducting material manufacturing process 353 Separation of salt and water by electrodialysis 77 Separation process 337 Sherwood number 256 Silica removal in an EDI process 449 Simplicity of structure of an electrodialyzer 327 Simultaneous treatment of wastewater by electrodialysis and reverse osmosis 353 Slot 324 Solar batteries 344 Solute diffusion 81, 84, 91 Solute permeability 78, 87 Solute permeability coefﬁcient 23 Solution concentration–osmosis 91 Solution disturbing effect of a spacer 220 Solution feeding frame 323 Solution ﬂow and I–V curves 205 Solution leakage in an electrodialyzer 326 Solution velocity distribution between desalting cells 326 Solution velocity in a boundary layer 128 Space charge 112 Spacer 325, 327, 385 Spacer exerted force 205 Speciﬁc electric conductivity 44 Stack pressure drop 385 Stacks 321 Standard deviation of solution velocity ratio 262 Stanton number, peclet number and potential difference number 253 Streaming current 72 Streaming potential 71 Structure of an electrodialyzer 321 Structure of the EDI unit and energy consumption 445 Styrene 7, 9–11, 13–14 Styrene–butadiene membrane 5 Styrene–butadiene rubber latex 5 Styrene–divinylbenzene copolymer 7 Sugar manufacturing process 375 Sugar recovering ratio 374

Index Sulfonic acid/Carboxylic acid double layer membrane 465 Super-saturation 391 Surface fouling 300 Surrounding technology of an electrodialysis system 340 Suspension polymerization 14 Swelling ratio 28 Swelling solution 13 Tensile strength 28 Tetrachloroethane 5 Tetraﬂuoroethylene 463 Theoretical electromotive force of the PEFC 515 Theoretical energy for concentrating H+ and OH ions from their concentration in the interface of the bipolar membrane 408 Theoretical maximum efﬁciency of PEFC 515 Theoretical potential for generating acid and base for an ideal ion exchange membrane 408 Theory of teorell, meyer and sievers (TMS theory) 59 Titanium tetrachloride 5 Tortuous path spacer 385 Transport depletion method 375 Transport number 20, 43, 65, 76–78 Transport number in the ﬁlm 303 Transport phenomena 37 Transport phenomena in diffusion dialysis 487 Transport-diffusion coefﬁcient 117 Trimethylamine 5 Trunk polymer 11 Turbulence promotion 385 Turbulent convection 114 Turbulent convection current 109 Turbulent ﬂow 228 U-shaped ﬂow path 387 Ultraﬁltration coefﬁcient 91 Ultrapure water production in electric power generation and semiconductor manufacturing processes 452 Ultrapure water production in pharmaceuticals 454 Unit cell voltage in the electrolyzer 478 Uphill transport in Donnan dialysis 489 Van’t Hoff equation 74 Vanadium battery 510 Vertical sheet-ﬂow 321 Vinyl toluene 3 Vinylpyridine-didinylbenzene copolymer 11 Voltage ﬂuctuation 110, 131 Volume ﬂow 76, 91 Washing with a chemical reagent 307 Waste molasses 374 Wastewater treatment 351

531

Index Water content 19 Water dissociation 99, 139, 374, 379 Water dissociation arising in seawater electrodialysis 169 Water dissociation in an EDI process 446 Water dissociation in bipolar membrane electrodialysis 419 Water dissociation reaction generated in the water dissociation layer 183

Water permeation coefﬁcient 26 Water recovery in the EDR process 389 Water transfer in the EDR process 389 Water transfer in a bipolar membrane 423 Wien effect 143–144, 162, 173, 419 Zero current density 89 Zero gap space between the ion exchange membrane and the electrode 477