Effects of surfactant solubility on the hydrodynamics of a viscous drop in a dc electric field

Surfactants (amphiphilic surface active agents) are often used to control the dynamics of viscous drops and bubbles in microfluidics applications. Surfactant sorption kinetics has been shown to play a critical role in the deformation of drops in extensional and shear flows, yet to the best of our knowledge these kinetics effects on a viscous drop in an electric field have not been accounted for. In this paper we numerically investigate the effects of sorption kinetics on a surfactant-covered viscous drop in an electric field. Over a range of electric conductivity and permittivity ratios between the interior and exterior fluids, we focus on the dependence of deformation and flow on the transfer parameter J, and Biot number Bi that characterize the extent of surfactant exchange between the drop surface and the bulk. Our findings suggest solubility affects the electrohydrodynamics of a viscous drop in distinct ways as we identify parameter regions where (1) surfactant solubility alters both the drop deformation and circulation of fluid around a drop and (2) surfactant solubility affects mainly the flow and not the deformation.