Communications in Mathematical Sciences
Volume 12 (2014)
An energetic variational approach for ion transport
Pages: 779 – 789
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.
energetic variational approach, Poisson-Nernst-Planck (PNP) system, (least) action principle, (maximum) dissipation principle, Onsager’s relation
2010 Mathematics Subject Classification
35Q35, 35Q92, 76W05, 92B05