Asymptotic Analysis on Dielectric Boundary Effects of Modified Poisson--Nernst--Planck Equations

DOI10.1137/18M1167218zbMath1453.82049OpenAlexW2808961516WikidataQ129580017 ScholiaQ129580017MaRDI QIDQ4577218

Pei Liu, Shenggao Zhou, Lijie Ji, Zhenli Xu

Publication date: 17 July 2018

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1167218

zbMATH Keywords

boundary layersmatched asymptotic expansionPoisson-Nernst-Planck equationsdielectric interfaces

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21) Transport processes in time-dependent statistical mechanics (82C70) Statistical mechanics of liquids (82D15) Motion of charged particles (78A35) Boltzmann equations (35Q20) Electrochemistry (78A57) PDEs in connection with statistical mechanics (35Q82)

Related Items (7)

Structure-preserving and efficient numerical methods for ion transport ⋮ Linear-scaling selected inversion based on hierarchical interpolative factorization for self Green's function for modified Poisson-Boltzmann equation in two dimensions ⋮ The time decay rates of the classical solution to the Poisson-Nernst-Planck-Fourier equations in \(\mathbb{R}^3\) ⋮ Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations ⋮ Global existence of the non-isothermal Poisson-Nernst-Planck-Fourier system ⋮ Optimal decay rates of the solution for generalized Poisson-Nernst-Planck-Navier-Stokes equations in \(\mathbb{R}^3\) ⋮ Modified Poisson--Nernst--Planck Model with Coulomb and Hard-sphere Correlations

Cites Work

• Mean-field theory and computation of electrostatics with ionic concentration dependent dielectrics
• Ionic size effects: generalized Boltzmann distributions, counterion stratification and modified Debye length
• Modified Poisson--Nernst--Planck Model with Accurate Coulomb Correlation in Variable Media
• Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels
• Asymptotic Expansions of I-V Relations via a Poisson–Nernst–Planck System
• Ion Flow through Narrow Membrane Channels: Part II
• Qualitative Properties of Steady-State Poisson--Nernst--Planck Systems: Perturbation and Simulation Study
• On the structure of generalized Poisson–Boltzmann equations
• The Surface Tension of Debye-Hückel Electrolytes
• Geometric Singular Perturbation Approach to Steady-State Poisson--Nernst--Planck Systems
• Current-Voltage Relations for Electrochemical Thin Films
• Electrochemical Thin Films at and above the Classical Limiting Current
• The influence of dielectric decrement on electrokinetics
• Poisson–Nernst–Planck Systems for Ion Channels with Permanent Charges

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