Effects of Surfactant on the Deformation and Stability of a Drop in a Viscous Fluid in an Electric Field

Abstract

This paper considers the effect of insoluble surfactant on the shape deformation and stability of a droplet immersed in an immiscible viscous fluid under the action of an applied electric field when the convection and surface diffusion of surfactant are balanced at the drop interface. First, we utilize a purely analytical method of domain perturbations to linearize the nonlinear free boundary problem and obtain the steady-state drop shape in the electric field. Then, the linear stability analysis predicts a critical electric Weber number, which is a limit point for the existence of the steady-state shape. When the Weber number exceeds the critical value, the drop experiences time-dependent shape deformation and eventually breaks up. In addition, the morphology evolution of an immiscible blend of polystyrene and poly(vinylidene fluoride) in a DC electric field is investigated experimentally. The effect of a compatibilizer, which acts as a surface-active agent, is also examined by adding the block copolymer of polystyrene and poly(methyl methacrylate). In the limit of a weak electric field, the degree of the shape deformation is in proportion to the Weber number as predicted from the theory. The experimental results are also consistent with the theoretical predictions in that the drop breaks up at a lower value of Weber number in the presence of the compatibilizer than the drop with a clean and completely mobile interface.