Electrodiffusional free boundary problem, in a bipolar membrane (semiconductor diode), at a reverse bias for constant current

Primicerio, M.; Rubinstein, I.; Zaltzman, B.

doi:10.1090/qam/1724297

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.

I. Rubinstein and B. Zaltzman, Electrodiffusional free boundary problem in concentration polarization in electrodialysis, Math. Models Methods Appl. Sci. 6 (1996), no. 5, 623–648. MR 1403724, DOI https://doi.org/10.1142/S0218202596000250
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

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, 149–166 (1988)

P. Ramirez, H. J. Rapp, S. Reichle, H. Strathmann, and S. Mafe, Current-voltage curves of bipolar membranes, J. Appl. Phys. 72, 259–263 (1992)

Franco Brezzi and Lucia Gastaldi, Mathematical properties of one-dimensional semiconductors, Mat. Apl. Comput. 5 (1986), no. 2, 123–137 (English, with Portuguese summary). MR 884997

F. Brezzi, A. C. Capelo, and L. Gastaldi, A singular perturbation analysis of reverse-biased semi-conductor diodes, SIAM J. Math. Anal. 20, 372–387 (1989)

Luis A. Caffarelli and Avner Friedman, A singular perturbation problem for semiconductors, Boll. Un. Mat. Ital. B (7) 1 (1987), no. 2, 409–421 (English, with Italian summary). MR 896332
Christian Schmeiser, A singular perturbation analysis of reverse biased $pn$-junctions, SIAM J. Math. Anal. 21 (1990), no. 2, 313–326. MR 1038894, DOI https://doi.org/10.1137/0521017

S. L. Kamenomostskaya, On the Stefan problem, Math. Sb. (N.S.) 53, 489–514 (1961) (in Russian)

O. A. Oleĭnik, A method of solution of the general Stefan problem, Soviet Math. Dokl. 1 (1960), 1350–1354. MR 0125341