A simplified lattice Boltzmann model for two-phase electro-hydrodynamics flows and its application to simulations of droplet deformation in electric field

Abstract

This paper proposes a numerical scheme within the lattice Boltzmann framework for effective simulations of two-phase electro-hydrodynamic (EHD) flows, in which the simplified multiphase lattice Boltzmann method serves as the flow solver and a leaky dielectric model is utilized to recover electric potential equation. The resultant formulations present direct evolution of macroscopic variables, due to which the present method outperforms the conventional lattice Boltzmann method in terms of memory cost and boundary treatment. Numerical validations are first carried out under the same parametric conditions as the benchmarking experimental studies with the conductivity ratio ranging from 0.03 to 1000, demonstrating that the present method is a practical and accurate tool to study large-conductivity-ratio two-phase EHD flows in scientific applications. Through the comparison with previous theoretical and numerical studies, the performance of the present method is further evaluated by varying physical parameters such as electric capillary number, electric field strength, interfacial tension, and electrical properties of liquids. The good agreements with the reference data confirm the accuracy and robustness of the proposed method. Additional studies of the dynamics of a deformed droplet in uniform electric field are carried out using the validated method. Specifically, we conduct a close numerical examination on the effect of the electrical conductivity ratio and permittivity ratio on the electric forces, and highlight the role of the dielectric electrophoretic force and the Coulomb force on the electric forces the deformation of a leaky dielectric droplet in the electrical conductivity ratio and the permittivity ratio phase diagram.