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We build a new mathematical model of shape optimization for maximizing ionic concentration governed by the multi-physical coupling steady-state Poisson-Nernst-Planck system. Shape sensitivity analysis is performed to obtain the Eulerian…

Optimization and Control · Mathematics 2025-05-13 Jiajie Li , Shenggao Zhou , Shengfeng Zhu

The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description…

Chemical Physics · Physics 2012-03-28 Sandip Ghosal , Zhen Chen

Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…

Soft Condensed Matter · Physics 2021-03-03 Michiel Sprik

Ion partitioning between different compartments (\emph{e.g.} a porous material and a bulk solution reservoir), known as Donnan equilibrium, plays a fundamental role in various contexts such as energy, environment, or water treatment. The…

Chemical Physics · Physics 2026-02-10 Jeongmin Kim , Benjamin Rotenberg

The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…

Numerical Analysis · Mathematics 2022-02-23 Jie Ding , Cheng Wang , Shenggao Zhou

Although electrostatics can be incorporated into machine-learned interatomic potentials, existing approaches are computationally very demanding, limiting large-scale, long-time simulations of electrostatics-driven phenomena such as…

In this article we address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the…

Numerical Analysis · Mathematics 2015-04-24 Riccardo Sacco , Fabio Manganini , Joseph W. Jerome

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves…

Materials Science · Physics 2015-05-13 D. V. Posvyanskii , A. Ya. Shul'man

In this paper, we propose a Poisson-Nernst-Planck-Navier-Stokes-Cahn-Hillard (PNP-NS-CH)model for an electrically charged droplet suspended in a viscous fluid subjected to an external electric field. Our model incorporates spatial…

Fluid Dynamics · Physics 2023-05-18 Yuzhe Qin , Huaxiong Huang , Zilong Song , Shixin Xu

Finite element modeling of charged species transport has enabled analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck equations…

Computational Engineering, Finance, and Science · Computer Science 2022-05-13 Sungu Kim , Makrand A. Khanwale , Robbyn K. Anand , Baskar Ganapathysubramanian

At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. P\'eraud et al., Phys. Rev. F, 1(7):074103, 2016]. However, at length and time scales larger than the Debye…

Computational Physics · Physics 2019-04-10 Aleksandar Donev , Andrew J. Nonaka , Changho Kim , Alejandro L. Garcia , John B. Bell

This work is concerned with the stationary Poisson--Nernst--Planck equation with a large parameter which describes a huge number of ions occupying an electrolytic region. Firstly, we focus on the model with a single specie of positive…

Analysis of PDEs · Mathematics 2023-11-20 Jhih-Hong Lyu , Chiun-Chang Lee , Tai-Chia Lin

We present a finite volume scheme for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with size exclusion yielding cross-diffusion. Our method…

Numerical Analysis · Mathematics 2026-03-04 Clément Cancès , Maxime Herda , Annamaria Massimini

Electrochemical cells serve as a building block for producing and storing electrical energy from chemical reactions. The analysis of ion transport in these systems forms the foundation for understanding more complex electrochemical systems…

Chemical Physics · Physics 2026-02-05 Grace Origer , Ritu R. Raj , Nathan Jarvey , P. N. Romero Zavala , Wilson A. Smith , Ankur Gupta

The paper presents a mean field theory of electrolyte solutions, extending the classical Debye-H\"{u}ckel-Onsager theory to provide a detailed description of the electrical conductivity in strong electrolyte solutions. The theory…

Soft Condensed Matter · Physics 2024-09-27 N. N. Kalikin , Yu. A. Budkov

In this paper, we construct a semi-implicit finite difference method for the time dependent Poisson-Nernst-Planck system. Although the Poisson-Nernst-Planck system is a nonlinear system, the numerical method presented in this paper only…

Numerical Analysis · Mathematics 2019-01-17 Dongdong He , Kejia Pan

Based on a discontinuous Galerkin method in the spatial directions and an improved implicit-explicit pressure-correction scheme in the temporal direction, this paper discusses a fully discrete scheme for the…

Numerical Analysis · Mathematics 2026-05-01 Bikram Bir , Amiya K. Pani

Species transport models typically combine partial differential equations (PDEs) with relations from hindered transport theory to quantify electromigrative, convective, and diffusive transport through complex nanoporous systems; however,…

Machine Learning · Computer Science 2023-12-06 Danyal Rehman , John H. Lienhard

Maxwell-Amp\`{e}re-Nernst-Planck (MANP) equations were recently proposed to model the dynamics of charged particles. In this study, we enhance a numerical algorithm of this system with deep learning tools. The proposed hybrid algorithm…

Numerical Analysis · Mathematics 2023-12-12 Cheng Chang , Zhouping Xin , Tieyong Zeng

One important development in interaction potential models, or atomistic force fields, for molecular simulation is the inclusion of explicit polarisation, which represents the induction effects of charged or polar molecules on polarisable…

Soft Condensed Matter · Physics 2017-05-25 Agílio A. H. Pádua