Measurement of Membrane Characteristics Using the Phenomenological Equation and the Overall Mass Transport Equation in Ion-Exchange Membrane Electrodialysis of Saline Water
The overall membrane pair characteristics included in the overall mass transport equation are understandable using the phenomenological equations expressed in the irreversible thermodynamics. In this investigation, the overall membrane pair characteristics (overall transport number , overall solute permeability , overall electro-osmotic permeability and overall hydraulic permeability ) were measured by seawater electrodialysis changing current density, temperature and salt concentration, and it was found that occasionally takes minus value. For understanding the above phenomenon, new concept of the overall concentration reflection coefficient is introduced from the phenomenological equation. This is the aim of this investigation. is defined for describing the permselectivity between solutes and water molecules in the electrodialysis system just after an electric current interruption. is expressed by the function of and . is generally larger than 1 and is positive, but occasionally becomes less than 1 and becomes negative. Negative means that ions are transferred with water molecules (solvent) from desalting cells toward concentrating cells just after an electric current interruption, indicating up-hill transport or coupled transport between water molecules and solutes. 1. Introduction Mass transport across the membrane must be discussed fundamentally on the basis of the thermodynamics because the thermodynamics describes the rule of energy changes inevitably generating in the mass transport. However, the classical thermodynamics discusses only reversible phenomena and it does not treat transport rate. The irreversible thermodynamics came to succeed in discussing the transport rate by introducing the concept of “time” in its system [1–4]. Basic theory of the irreversible thermodynamics is established on the assumption of “microscopic irreversibility” [5–7]. This assumption holds more strictly in the circumstance being more close to equilibrium states. The actual electrodialysis process is not formed in the equilibrium states, so that the irreversible thermodynamics is assumed to exhibit only approximated meaning in the electrodialysis system. However, the irreversible thermodynamics is considered to be applicable in the circumstances being apart to some extent from equilibrium states [8, 9]. The irreversible thermodynamics is the fundamental rule of mass transport and it is expressed by the functions including phenomenological coefficients. On the other hand, the performance of an electrodialyzer is expressed by the functions including parameters such as
References
[1]
I. Progogine, Introduction to Thermodynamics of Irreversible Processes, John Wiley, New York, NY, USA, USA, 2nd edition, 1961.
[2]
P. Glansdorff and I. Prigogine, Thermodynamic Theory Structure, Stability and Fluctuations, Wiley-Interscience, London, UK, 1971.
[3]
S. R. de Groot and P. Mazur, Nonequilibrium Thermodynamics, North-Holland, New York, NY, USA, 1962.
[4]
D. D. Fitts, Nonequilibrium Thermodynamics, Mc-Graw Hill, New York, NY, USA, 1962.
[5]
L. Onsager, “Reciprocal relations in irreversible processes. I.,” Physical Review, vol. 37, no. 4, pp. 405–426, 1931.
[6]
L. Onsager, “Reciprocal relations in irreversible processes. II,” Physical Review, vol. 38, no. 12, pp. 2265–2279, 1931.
[7]
H. B. G. Casimir, “On Onsager's principle of microscopic reversibility,” Reviews of Modern Physics, vol. 17, no. 2-3, pp. 343–350, 1945.
[8]
P. J. Dunlop, “A study of interacting flows in diffusion of the system raffinose-KCl-H2 at ,” Journal of Physical Chemistry, vol. 61, no. 7, pp. 994–1000, 1957.
[9]
P. J. Dunlop and L. J. Gosting, “Use of diffusion and thermodynamic data to test the Onsager reciprocal relation for isothermal diffusion in the system NaCl-KCl-H2O at ,” Journal of Physical Chemistry, vol. 63, no. 1, pp. 86–93, 1959.
[10]
Y. Tanaka, “Irreversible thermodynamics and overall mass transport in ion-exchange membrane electrodialysis,” Journal of Membrane Science, vol. 281, no. 1-2, pp. 517–531, 2006.
[11]
Y. Tanaka, “A computer simulation of continuous ion exchange membrane electrodialysis for desalination of saline water,” Desalination, vol. 249, no. 2, pp. 809–821, 2009.
[12]
Y. Tanaka, “A computer simulation of batch ion exchange membrane electrodialysis for desalination of saline water,” Desalination, vol. 249, no. 3, pp. 1039–1047, 2009.
[13]
Y. Tanaka, “A computer simulation of feed and bleed ion exchange membrane electrodialysis for desalination of saline water,” Desalination, vol. 254, no. 1–3, pp. 99–107, 2010.
[14]
O. Kedem and A. Katchalsky, “Permeability of composite membranes Part 1. Electric current, volume flow and flow of solute through membranes,” Transactions of the Faraday Society, vol. 59, pp. 1918–1930, 1963.
[15]
C. R. House, Water Transport in Cells and Tissues, Edward Arnold, London, UK, 1974.
[16]
S. G. Schultz, Basic Principles of Membrane Transport, Cambridge University Press, Cambridge, UK, 1980.
[17]
R. Z. Schloegel, Fortschritte der physikalischen Chemie. Band 9, 1964.
[18]
A. J. Staverman, “The theory of measurement of osmotic pressure,” Recueil des Travaux Chimiques des Pays-Bas, vol. 70, no. 4, pp. 344–352, 1951.
[19]
O. Kedem and A. Katchalsky, “Thermodynamic analysis of the permeability of biological membranes to non-electrolytes,” Biochimica et Biophysica Acta, vol. 27, no. 2, pp. 229–246, 1958.
[20]
S. Koter, “Transport of electrolytes across cation-exchange membranes. Test of Onsager reciprocity in zero-current processes,” Journal of Membrane Science, vol. 78, no. 1-2, pp. 155–162, 1993.
[21]
A. Yamauchi and Y. Tanaka, “Salt transport phenomena across charged membrane driven by pressure difference,” in Effective Membrane Process—New Prospective, R. Paterson, Ed., pp. 179–185, BHR Group; Information Press, Oxford, UK, 1993.
[22]
Y. Tanaka, “Ion exchange membrane electrodialysis of saline water desalination and its application to seawater concentration,” Industrial & Engineering Chemistry Research, vol. 50, no. 12, pp. 7494–7503, 2011.
