Mathematical models for the deformation of electrolyte droplets
Rolf Ryham - Department of Mathematics, Rice university, MS-136, Houston, TX 77005, 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.
Received: August 2006; Revised: March 2007; Available Online: July 2007.
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