First error bounds for the porous media approximation of the Poisson-Nernst-Planck equations

DOI10.1002/zamm.201100003zbMath1332.76060OpenAlexW2020888676MaRDI QIDQ2883223

Markus Schmuck

Publication date: 11 May 2012

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.201100003

zbMATH Keywords

homogenizationporous mediaPoisson-Nernst-Planck equationstwo-scale convergencesupercapacitorsscanning electron microscopy (SEM)

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Magnetohydrodynamics and electrohydrodynamics (76W05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (11)

Upscaling the Flow and Transport in an Evolving Porous Medium with General Interaction Potentials ⋮ Rate of Convergence of General Phase Field Equations in Strongly Heterogeneous Media Toward Their Homogenized Limit ⋮ Homogenization of the linearized ionic transport equations in random porous media ⋮ Computational investigation of porous media phase field formulations: microscopic, effective macroscopic, and Langevin equations ⋮ New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials ⋮ Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems ⋮ Basic and extendable framework for effective charge transport in electrochemical systems ⋮ Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients ⋮ On a pore-scale stationary diffusion equation: scaling effects and correctors for the homogenization limit ⋮ Homogenization of the Poisson--Nernst--Planck equations for Ion Transport in Charged Porous Media ⋮ Effective macroscopic interfacial transport equations in strongly heterogeneous environments for general homogeneous free energies

Uses Software

• ALBERTA

Cites Work

• Modeling and deriving porous media Stokes-Poisson-Nernst-Planck equations by a multi-scale approach
• Dispersion, convection, and reaction in porous media
• An extension theorem from connected sets, and homogenization in general periodic domains
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• Electrodiffusion Model of Rectangular Current Pulses in Ionic Channels of Cellular Membranes
• Homogenization of the linearized ionic transport equations in rigid periodic porous media
• ANALYSIS OF THE NAVIER–STOKES–NERNST–PLANCK–POISSON SYSTEM
• Homogenization of a Nonlinear Convection-Diffusion Equation with Rapidly Oscillating Coefficients and Strong Convection

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