Qualitative properties of steady-state Poisson-Nernst-Planck systems: Perturbation and simulation study

V. Barcilon*, D. P. Chen, R. S. Eisenberg, J. W. Jerome

*Corresponding author for this work

Research output: Contribution to journalArticle

91 Scopus citations

Abstract

Poisson-Nernst-Planck (PNP) systems are considered in the case of vanishing permanent charge. A detailed case study, based on natural categories described by system boundary conditions and flux, is carried out via simulation and singular perturbation analysis. Our results confirm the rich structure inherent in these systems. A natural quantity, the quotient of the Debye and characteristic length scales, serves as the singular perturbation parameter. The regions of validity are carefully analyzed by critical comparisons and contrasts between the simulation and the perturbation solution, which can be represented in closed form.

Original languageEnglish (US)
Pages (from-to)631-648
Number of pages18
JournalSIAM Journal on Applied Mathematics
Volume57
Issue number3
StatePublished - Jun 1 1997

Keywords

  • Boundary layer solution
  • Categories of boundary conditions
  • Interior solution
  • Poisson-Nernst-Planck systems
  • Simulation
  • Singular perturbation solution

ASJC Scopus subject areas

  • Applied Mathematics

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