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The Poisson-Nernst-Planck (PNP) equations are fundamental for modeling ion transport in electrochemical systems, capturing the intricate interplay of concentration gradients, electric fields, and ion fluxes essential for applications such…

Chemical Physics · Physics 2025-01-13 Yitao He , Dan Zhao

In situations involving large potentials or surface charges, the Poisson Boltzman(PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community,…

Chemical Physics · Physics 2007-05-23 Mustafa Sabri Kilic , Martin Z. Bazant , Armand Ajdari

The Poisson-Nernst-Planck (PNP) diffusional model for the immittance or impedance spectroscopy response of an electrolytic cell in a finite-length situation is extended to a general framework. In this new formalism, the bulk behavior of the…

We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system in bounded domains, in two dimensions, with Dirichlet boundary conditions for the Navier-Stokes and Poisson equations, and blocking (vanishing…

Analysis of PDEs · Mathematics 2018-12-26 Peter Constantin , Mihaela Ignatova

The non-linear Poisson-Boltzmann equation for a circular, uniformly charged platelet, confined together with co- and counter-ions to a cylindrical cell, is solved semi-analytically by transforming it into an integral equation and solving…

Soft Condensed Matter · Physics 2009-10-31 R. J. F. Leote de Carvalho , E. Trizac , J. P Hansen

In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity…

Mathematical Physics · Physics 2014-08-01 Chia-Yu Hsieh , YunKyong Hyon , Hijin Lee , Tai-Chia Lin , Chun Liu

We consider the Poisson-Nernst-Planck system which is well-accepted for describing dilute electrolytes as well as transport of charged species in homogeneous environments. Here, we study these equations in porous media whose electric…

Mathematical Physics · Physics 2013-02-26 Markus Schmuck

Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media under periodic fluid flow by an asymptotic multi-scale expansion with drift. The microscopic setting is a two-component…

Mathematical Physics · Physics 2014-07-16 Markus Schmuck , Martin Z. Bazant

A detailed simple model is applied to study a high temperature plasma ball. It is assumed that the ions and delocalized electrons are distributed randomly throughout the charged plasma ball (extra/missing charge is assumed to be found in a…

Plasma Physics · Physics 2007-10-18 Yuri Kornyushin

An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green's 3rd identity…

Numerical Analysis · Mathematics 2023-04-11 Zhen Chao , Weihua Geng , Robert Krasny

We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the…

Analysis of PDEs · Mathematics 2012-06-12 Dieter Bothe , André Fischer , Jürgen Saal

The distribution of voltage in sub-micron cellular domains remains poorly understood. In neurons, the voltage results from the difference in ionic concentrations which are continuously maintained by pumps and exchangers. However, it not…

Soft Condensed Matter · Physics 2020-03-26 Alexis Tricot , Igor M. Sokolov , David Holcman

Static spherically symmetric solutions of the Einstein's field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential-density pairs are investigated. The approach is illustrated with…

General Relativity and Quantum Cosmology · Physics 2020-11-24 Gonzalo García-Reyes

Effects of the adsorption-desorption process on the immittance response of an electrolytic cell are theoretically investigated in the framework of the diffusional Poisson-Nernst-Planck (PNP) continuum model, when the generation and…

This work considers charged systems described by the modified Poisson--Nernst--Planck (PNP) equations, which incorporate ionic steric effects and the Born solvation energy for dielectric inhomogeneity. Solving the steady-state modified PNP…

Numerical Analysis · Mathematics 2025-06-04 Zhonghua Qiao , Zhenli Xu , Qian Yin , Shenggao Zhou

A concentrated suspension of lamellar colloidal particles (e. g. clay) is modelled by considering a single, uniformly charged, finite platelet confined with co- and counterions to a Wigner-Seitz (WS) cell. The system is treated within…

Soft Condensed Matter · Physics 2009-10-30 Emmanuel Trizac , Jean-Pierre Hansen

The Pauli-Poisson equation is a semi-relativistic model for charged spin-1/2-particles in a strong external magnetic field and a self-consistent electric potential computed from the Poisson equation in 3 space dimensions. It is a system of…

Analysis of PDEs · Mathematics 2023-06-12 Jakob Möller

Equilibrium distribution of interacting ionic particles in a charged disordered background is studied using the nonlinear Poisson-Boltzmann equation. For an arbitrarily given realization of the disorder, an exact solution of the equation is…

Disordered Systems and Neural Networks · Physics 2009-11-07 Ramin Golestanian

We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded domains. The assumption on species is either there are two…

Analysis of PDEs · Mathematics 2022-12-27 Dapeng Du , Jingyu Li , Yansheng Ma , Ruyi Pang

The Poisson-Boltzmann (PB) equation provides a mean-field theory of electrolyte solutions at interfaces and in confinement, describing how ions reorganize close to charged surfaces to form the so-called electrical double layer (EDL), with…

Soft Condensed Matter · Physics 2024-09-10 Cecilia Herrero , Laurent Joly