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.