Multi-component electro-hydro-thermodynamic model with phase-field method. I. Dielectric

We derive a multi-component electro-hydro-thermodynamic (EHTD) model for both leaky and
perfect dielectric materials via the principle of energy dissipation. Differing from previous
electro-hydrodynamic (EHD) models focusing on fluid mechanics, the electrochemical potential
expression is revised and the electric field related term is added to the mass and momentum
conservation equations. Resulting from this new correction, we obtain a generalized electro-
hydro-thermodynamic stress tensor including the effect of Kortweg and Maxwell stresses. We
observe the magnificent impact of the electric field on the thermodynamic equilibrium of the
system in two aspects: (i) phase diagram modified by the electric field; (ii) electric field induced
surface tension decrease/increase. In addition, the proposed model is validated and shows well
conformity with previous analytical solutions in literature. As exemplary applications, we perform
phase-field simulations to study the ternary droplet coalescence and spinodal decomposition
and observe several typical morphological transformations, such as satellite drop formation and
Quincke rotation.