Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] 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, https://doi.org/10.1142/S0218202596000250
  • [2] 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
  • [3] R. Simons, Strong electric field effects on proton transfer between membrane-bound amins and water, Nature 280, 824 (1979)
  • [4] 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)
  • [5] 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)
  • [6] 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
  • [7] 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)
  • [8] 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
  • [9] Christian Schmeiser, A singular perturbation analysis of reverse biased 𝑝𝑛-junctions, SIAM J. Math. Anal. 21 (1990), no. 2, 313–326. MR 1038894, https://doi.org/10.1137/0521017
  • [10] S. L. Kamenomostskaya, On the Stefan problem, Math. Sb. (N.S.) 53, 489-514 (1961) (in Russian)
  • [11] O. A. Oleĭnik, A method of solution of the general Stefan problem, Soviet Math. Dokl. 1 (1960), 1350–1354. MR 0125341

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35R35, 35Q60, 78A35, 82D37

Retrieve articles in all journals with MSC: 35R35, 35Q60, 78A35, 82D37

Additional Information

DOI: https://doi.org/10.1090/qam/1724297
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society