Dielectrophoresis of a surfactant-laden viscous drop

Abstract

The dielectrophoresis of a surfactant-laden viscous drop in the presence of non-uniform DC electric field is investigated analytically and numerically. Considering the presence of bulk-insoluble surfactants at the drop interface, we first perform asymptotic solution for both low and high surface Péclet numbers, where the surface Péclet number signifies the strength of surface convection of surfactants as compared to the diffusion at the drop interface. Neglecting fluid inertia and interfacial charge convection effects, we obtain explicit expression for dielectrophoretic drop velocity for low and high Péclet numbers by assuming small deviation of drop shape from sphericity and small deviation of surfactant concentration from the equilibrium uniform distribution. We then depict a numerical solution, assuming spherical drop, for arbitrary values of Péclet number. Our analyses demonstrate that the asymptotic solution shows excellent agreement with the numerical solution in the limiting conditions of low and high Péclet numbers. The present analysis shows that the flow-induced redistribution of the surfactants at the drop interface generates Marangoni stress, owing to the influence of the surfactant distribution on the local interfacial tension, at the drop interface and significantly alters the drop velocity at steady state. For a perfectly conducting/dielectric drop suspended in perfectly dielectric medium, Marangoni stress always retards the dielectrophoretic velocity of the drop as compared with a surfactant-free drop. For a leaky dielectric drop suspended in another leaky dielectric medium, in the low Péclet number limit, depending on the electrical conductivity and permittivity of both the liquids, the Marangoni stress may aid or retard the dielectrophoretic velocity of the drop. The Marangoni stress also has the ability to move the drop in the opposite direction as compared with a surfactant-free drop. This non-intuitive reverse motion of the drop is observed for drops with less viscosity and for particular values of electrical conductivity and permittivity ratios. In the high Péclet number limit, the surfactants completely immobilize the fluid velocity at the drop interface. As a result, the drop behaves like a solid sphere. Further, it is also demonstrated that the flow-induced non-uniform distribution of surfactants always increases the deformation of the drop as compared with a uniformly coated drop which is due to the decreased (or increased) interfacial tension near the poles of the drop for prolate (or oblate) type deformation.