On a phase-field model for electrowetting and other electrokinetic phenomena

Abstract

In three space dimensions, we present existence results for weak solutions to a novel two-phase model for various electrokinetic phenomena, including in particular dynamic electrowetting with electrolytes. The model is thermodynamically consistent. It combines Navier-Stokes- and Cahn-Hilliard-type phase-field equations with Nernst-Planck equations for ion density-evolution and with an elliptic transmission problem for the electrostatic potential. As physical energy estimates guarantee only boundedness of ion densities in the Llog L-Orlicz class uniformly with respect to time, an iteration method is proposed to establish higher regularity and integrability results of these quantities. In an appendix, the derivation of the model is sketched