“Concentrated capacity” model of ion-exchange funneling in a modified (thin film coated) heterogeneous electrodialysis membrane
Authors:
Stanislav Antontsev, Anvarbek M. Meirmanov, Isaak Rubinstein and Boris Zaltzman
Journal:
Quart. Appl. Math. 62 (2004), 77-95
MSC:
Primary 35J55; Secondary 35J60, 92E20
DOI:
https://doi.org/10.1090/qam/2032573
MathSciNet review:
MR2032573
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Abstract: Inexpensive highly permselective heterogeneous ion exchange membranes are prohibitively polarizable by a direct electric current for use in electrodialysis. According to recent experiments, polarizability of these membranes may be considerably reduced by casting on their surface a thin layer of cross-linked polyelectrolyte, weakly charged with the same sign as the membrane’s charge. The present paper is concerned with this effect. In order to explain this feature, a simple limiting ion-exchange ’funnel’ model of a modified membrane is derived from the original two-layer model. In this model, asymptotically valid for a thin coating, solution of the ionic transport equations in it is replaced, via a suitable averaging procedure, by a single nonlinear boundary condition for the membrane/solution interface, which itself has the same order as the bulk equation. Rigorous analysis of the ’funnel’ model shows that the value of the limiting current through a modified membrane, which is the main quantitative characteristic of its polarizability, is equal to that through a homogeneous membrane for any positive value of the funneling parameter. The limiting problem for a vanishing funneling parameter is analyzed.
I. Rubinstein and B. Zaltzman, Electro-osmotically induced convection at a permselective membrane, Physical Review E, 62, pp. 2238–2251, 2000.
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I. Rubinstein, B. Zaltzman, J. Pretz, and C. Linder, Experimental verification of the electroosmotic mechanism of overlimiting conductance through a cation exchange electrodialysis membrane, Russian Electrochemistry 38, pp. 853–864, 2002.
I. Rubinstein, B. Zaltzman and T. Pundik, Ion-Exchange Funneling in Thin Film Coating Modification of Heterogeneous Electrodialysis Membrane, Phys. Rev. E, 65, art. number 041507, 2002.
C. Linder, G. Saveliev, Y. Mirsky, and O. Kedem, in ICOM2000, Kibbutz Ma’ale Hachamisha, Hills of Jerusalem, Israel, September 24–27, 2000, Abstracts, pp. 104–105.
- Isaak Rubinstein, Electro-diffusion of ions, SIAM Studies in Applied Mathematics, vol. 11, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990. MR 1075016
- David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin, 2001. Reprint of the 1998 edition. MR 1814364
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I. Rubinstein and B. Zaltzman, Electro-osmotically induced convection at a permselective membrane, Physical Review E, 62, pp. 2238–2251, 2000.
I. Rubinstein and B. Zaltzman, Electroosmotic slip of the second kind and instability in concentration polarization, Mathematical Models and Methods in Applied Sciences, 11 (2), pp. 263–300, 2001.
I. Rubinstein, B. Zaltzman, J. Pretz, and C. Linder, Experimental verification of the electroosmotic mechanism of overlimiting conductance through a cation exchange electrodialysis membrane, Russian Electrochemistry 38, pp. 853–864, 2002.
I. Rubinstein, B. Zaltzman and T. Pundik, Ion-Exchange Funneling in Thin Film Coating Modification of Heterogeneous Electrodialysis Membrane, Phys. Rev. E, 65, art. number 041507, 2002.
C. Linder, G. Saveliev, Y. Mirsky, and O. Kedem, in ICOM2000, Kibbutz Ma’ale Hachamisha, Hills of Jerusalem, Israel, September 24–27, 2000, Abstracts, pp. 104–105.
I. Rubinstein, Electrodiffusion of Ions, SIAM, Philadelphia, p. 149, p. 109, p. 170, 1990.
D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order. Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, p. 517, 2001.
O. A. Ladyzhenskaya and N. N. Uraĺtseva, Linear and quasilinear elliptic equations. (Translated from the Russian) Academic Press, New York-London, p. 495, 1968.
S. M. Nikoĺskij, Approximation of functions of several variables and imbedding theorems. (Translated from the Russian) Springer-Verlag, New York-Heidelberg, p. 418, 1975.
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© Copyright 2004
American Mathematical Society
