Electrodiffusional free boundary problem, in a bipolar membrane (semiconductor diode), at a reverse bias for constant current
Authors:
M. Primicerio, I. Rubinstein and B. Zaltzman
Journal:
Quart. Appl. Math. 57 (1999), 637-659
MSC:
Primary 35R35; Secondary 35Q60, 78A35, 82D37
DOI:
https://doi.org/10.1090/qam/1724297
MathSciNet review:
MR1724297
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Abstract: A singular perturbation problem, modeling one-dimensional time-dependent electrodiffusion of ions (holes and electrons) in a bipolar membrane (semi-conductor diode) at a reverse bias is analyzed for galvanostatic (fixed electric current) conditions. It is shown that, as the perturbation parameter tends to zero, the solution of the perturbed problem tends to the solution of a limiting problem which is, depending on the input data, either a conventional bipolar electrodiffusion problem or a particular electrodiffusional time-dependent free boundary problem. In both cases, the properties of the limiting solution are analyzed, along with those of the respective boundary and transition layer solutions.
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R. Simons, Strong electric field effects on proton transfer between membrane-bound amins and water, Nature 280, 824 (1979)
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F. Brezzi, A. C. Capelo, and L. Gastaldi, A singular perturbation analysis of reverse-biased semi-conductor diodes, SIAM J. Math. Anal. 20, 372β387 (1989)
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I. Rubinstein and B. Zaltzman, Electrodiffusional free boundary problem in concentration polarization in electrodialysis, Math. Models Methods Appl. Sci. 6, 623β648 (1996)
I. Rubinstein, Electrodiffusion of Ions, SIAM Studies in Applied Mathematics 11, SIAM, Philadelphia, PA, 1990
R. Simons, Strong electric field effects on proton transfer between membrane-bound amins and water, Nature 280, 824 (1979)
K. N. Mani, F. P. Chlanda, and C. H. Byszewski, Aquatech Membrane Technology for Recovery of Acid/Base Values from Salt Streams, Desalination 68, 149β166 (1988)
P. Ramirez, H. J. Rapp, S. Reichle, H. Strathmann, and S. Mafe, Current-voltage curves of bipolar membranes, J. Appl. Phys. 72, 259β263 (1992)
F. Brezzi and L. Gastaldi, Mathematical properties of one-dimensional semi-conductors, Math. Appl. Comp. 5, 123β137 (1986)
F. Brezzi, A. C. Capelo, and L. Gastaldi, A singular perturbation analysis of reverse-biased semi-conductor diodes, SIAM J. Math. Anal. 20, 372β387 (1989)
L. A. Caffarelli and A. Friedman, A singular perturbation problem for semi-conductors, Bolletino Un. Mat. Ital. B (7) 1, 409β421 (1987)
C. Schmeiser, A singular perturbation analysis of reverse based pn-junctions, SIAM J. Math. Anal. 21, 313β326 (1990)
S. L. Kamenomostskaya, On the Stefan problem, Math. Sb. (N.S.) 53, 489β514 (1961) (in Russian)
O. A. Oleinik, A method of solutions of the general Stefan problem, Soviet Math. Dokl. 1, 1350β1354 (1960)
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© Copyright 1999
American Mathematical Society