On Modeling and Simulation of Electrokinetic Phenomena in Two-Phase Flow with General Mass Densities

We formulate phase-field models for electrowetting with electrolyte solutions for general mass densities taking, in particular, mass density contrast into account. Based on Onsager's variational principle and volume averaging for gross velocities, we obtain a nonlinear coupling of hydrodynamic equations with the Nernst--Planck equations of ion transport, the Cahn--Hilliard equation for the phase-field, and an elliptic transmission problem for the electrostatic potential. Nonstandard boundary conditions for the Cahn--Hilliard equation allow for contact angle hysteresis. We comment on sharp interface limits and present energy estimates in the diffuse- and in the sharp interface settings. Finally, two- and three-dimensional numerical simulations underline the capability of diffuse interface approaches to model droplet transport, coalescence, and splitting.