Electrohydrodynamic viscous fingering of leaky dielectric fluids in a channel

Viscous fingering is a commonly observed interfacial instability during fluid displacement, where a fingerlike shape is formed at the fluid interface when a more viscous fluid is displaced by a less viscous fluid. In this study, a hybrid numerical model based on the lattice Boltzmann method and finite difference method is developed for investigating the control of viscous fingering of leaky dielectric fluids confined in a channel using electrohydrodynamics. Extensive simulations are carried out for studying the effects of the strength and direction of the electric field as well as the fluid properties, including the permittivity ratio and conductivity ratio, on viscous fingering. It is shown that a horizontal electric field, i.e., when the direction of the electrical field is perpendicular to the direction of fluid motion, can either promote or suppress the viscous fingering, depending on the permittivity ratio and conductivity ratio. For a vertical electric field, the extent of promotion of viscous fingering first decreases and then increases with the increase in conductivity ratio at a constant permittivity ratio. Also, various interfacial morphologies, such as broad fingers and thin jets, are observed under different fluid properties. A phase diagram for both the horizontal and vertical electric field is established based on the simulations with different permittivity and conductivity ratios to characterize the interfacial morphologies. This study offers insight into the electrohydrodynamic effects on the viscous fingering of leaky dielectric fluids, which could facilitate the control of multiphase flow in various applications, such as enhanced oil recovery and coupled chromatographic systems for separation.