An energetic variational approach for ION transport

Shixin Xu, Ping Sheng, Chun Liu

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)779-789
Number of pages11
JournalCommunications in Mathematical Sciences
Issue number4
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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