AN ENERGETIC VARIATIONAL APPROACH FOR ION TRANSPORT

被引：47

作者：

Xu, Shixin ^{[1
]}

Sheng, Ping ^{[2
]}

Liu, Chun ^{[3
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

[2] Hong Kong Univ Sci & Technol Clear Water Bay, Dept Phys, Kowloon, Hong Kong, Peoples R China

[3] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2014年 / 12卷 / 04期

基金：

美国国家科学基金会;

关键词：

Energetic Variational Approach; Poisson-Nernst-Planck (PNP) system; (Least) Action Principle; (Maximum) Dissipation Principle; Onsager's relation; IRREVERSIBLE-PROCESSES; RECIPROCAL RELATIONS;

D O I：

10.4310/CMS.2014.v12.n4.a9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The transport and distribution of charged particles are crucial in the study of many physical and biological problems. In this paper, we employ an Energy Variational Approach to derive the coupled Poisson-Nernst-Planck-Navier-Stokes system. All of the physics is included in the choices of corresponding energy law and kinematic transport of particles. The variational derivations give the coupled force balance equations in a unique and deterministic fashion. We also discuss the situations with different types of boundary conditions. Finally, we show that the Onsager's relation holds for the electrokinetics, near the initial time of a step function applied field.

引用

页码：779 / 789

页数：11

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