Effects of surfactant transport on the electro-deformation of viscous drops

In this work we report quantification of effects of surfactant transport on a viscous drop under a DC electric field, focusing on characterization through the dimensionless Peclet number. Our findings reveal distinct equilibrium deformations that depend on the type of drops (leaky versus conducting) and the transport regime (convection or diffusion).
The mode of deformation, described by the flow circulation in a leaky dielectric drop, also contributes to the non-trivial deformation. For counter-clockwise circulation, we found leaky dielectric drops consistently yield larger deformation compared to perfectly conducting drops. The deformations result from the non-linear coupling between surfactant concentration and transport: higher surfactant concentrations yield larger (smaller) deformation with strong convective (diffusive) flows. For clockwise circulation, the deformation decreases (increases) with increasing surfactant concentration when convection (diffusion) dominates. We show that in this case conducting drops can yield larger deformations compared to leaky dielectric drops at moderate to high surfactant concentration. Finally, we look at the transient evolution of the drop shape, and discuss novel findings that have yet to be disseminated.