Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Mathematical models for the deformation of electrolyte droplets

Pages: 649 - 661, Volume 8, Issue 3, October 2007      doi:10.3934/dcdsb.2007.8.649

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Rolf Ryham - Department of Mathematics, Rice university, MS-136, Houston, TX 77005, United States (email)
Chun Liu - Department of Mathematics and Center for Materials Physics, Penn State University, University Park, PA 16802, United States (email)
Ludmil Zikatanov - Department of Mathematics, Penn State University, University Park, PA 16802, United States (email)

Abstract: Using phase field methods, we introduce a penalty formulation for restricting the support of solutions of the hydrodynamic Poisson-Nernst-Plank equations to evolving subregions of the domain. The formulation is derived through variational principles from a free energy involving the phase field and electrostatic energy. We validate the model by energetic arguments and several dynamic, finite element simulations of the (linear) Navier-Stokes, Poisson-Nernst-Plank and Allen-Cahn system.

Keywords:  Poisson-Nernst-Plank, phase-field, energetic variational method.
Mathematics Subject Classification:  Primary: 35Q35, 35Q39; Secondary: 35J60.

Received: August 2006;      Revised: March 2007;      Available Online: July 2007.