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

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

doi:10.1137/s0036139995312149

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

Mathematics

Research output: Contribution to journal › Article › peer-review

121 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 language	English (US)
Pages (from-to)	631-648
Number of pages	18
Journal	SIAM Journal on Applied Mathematics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1137/s0036139995312149
State	Published - Jun 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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10.1137/s0036139995312149

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title = "Qualitative properties of steady-state Poisson-Nernst-Planck systems: Perturbation and simulation study",

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.",

keywords = "Boundary layer solution, Categories of boundary conditions, Interior solution, Poisson-Nernst-Planck systems, Simulation, Singular perturbation solution",

author = "V. Barcilon and Chen, {D. P.} and Eisenberg, {R. S.} and Jerome, {J. W.}",

year = "1997",

month = jun,

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pages = "631--648",

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T1 - Qualitative properties of steady-state Poisson-Nernst-Planck systems

T2 - Perturbation and simulation study

AU - Barcilon, V.

AU - Chen, D. P.

AU - Eisenberg, R. S.

AU - Jerome, J. W.

PY - 1997/6

Y1 - 1997/6

N2 - 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.

AB - 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.

KW - Boundary layer solution

KW - Categories of boundary conditions

KW - Interior solution

KW - Poisson-Nernst-Planck systems

KW - Simulation

KW - Singular perturbation solution

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DO - 10.1137/s0036139995312149

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JF - SIAM Journal on Applied Mathematics

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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