| Summary: | In this study, a free energy model of the Lattice Boltzmann Method (LBM) is performed to simulate the motion, deformation, and decomposition of a droplet in the presence of electrohydrodynamic flow in porous media. To simulate the multi-phase flow in the presence of dielectric current by using the LBM, three distribution functions are used. To implement the free energy mode of HCZ, two equilibrium distribution functions are considered, one for solving the Navier-Stokes equation and the other for solving the Cahn-Hillard equation. Initially, the ability of the code to apply surface tension is tested by using the Laplace law and the droplet release test. Results show that there is a linear relation is between surface tension and κ which is a parameter in the HCZ model. The results show that the present numerical program is capable of modeling the regulated surface tension force as well. Then, the Rayleigh–Taylor instability simulation is used to evaluate the code's ability to apply volume forces. Also, the obtained results of the written numerical program are in good agreement with the numerical results of other valid references. Obtained results show that the difference between droplet deformation measured by numerical method and Taylor function is less than 2%. After modeling the droplet motions to investigate the droplet deformation, two electric fields are inserted into the droplet with reverse directions of each other. Then, by various tests, it is shown that at a given potential difference the droplet breaks down after much deformation and is divided into smaller droplets. The decomposition of droplets in a pre-mixed emulsion is a common technique to produce the monodisperse droplets. The presence of monodisperse droplets in an emulsion improves the physical properties of polymer from the science expert's perspective. The results of this study are used to improve the quality of polymer components.
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