October  2007, 8(3): 649-661. doi: 10.3934/dcdsb.2007.8.649

Mathematical models for the deformation of electrolyte droplets

1. 

Department of Mathematics, Rice university, MS-136, Houston, TX 77005, United States

2. 

Department of Mathematics and Center for Materials Physics, Penn State University, University Park, PA 16802

3. 

Department of Mathematics, Penn State University, University Park, PA 16802, United States

Received  August 2006 Revised  March 2007 Published  July 2007

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.
Citation: Rolf Ryham, Chun Liu, Ludmil Zikatanov. Mathematical models for the deformation of electrolyte droplets. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 649-661. doi: 10.3934/dcdsb.2007.8.649
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