Effect of uniform electric field on the droplet deformation in uniform flow field

In this article, we theoretically investigate the transient electric field-driven deformation of a droplet. Notably, the droplet is subjected to both a uniform flow and an electric field simultaneously. We explore two cases: one with a perpendicular arrangement of uniform flow and electric field, where the electric field is not stronger than the uniform flow, and another with an aligned arrangement of both. The leaky dielectric model is used and the droplet shape is assumed to remain prolate spheroidal at all times. The droplet behavior was modeled and the corresponding program was written in MATLAB software. According to the selected equations, the outputs of the program are logical and consistent with the available data and experiments. Among the advantages of the theoretical solution, one can mention the possibly tracing the origin of desired events and system reaction and the lower computational cost. The solution method can be extended to investigate similar problems.