Surfactant and dilatational viscosity effects on the deformation of liquid droplets in an electric field

Abstract

HypothesisA conducting droplet suspended in an insulating continuous phase, e.g. an aqueous electrolyte in an oil, is deformed by an applied electric field to nonspherical equilibrium shapes, and can even break-up under strong fields. Many technologies use electro-deformation to manipulate fluid dispersions, with surfactants present on the droplet interfaces forming stabilizing monolayers. While surfactants lower the interface tension which facilitates electro-deformation, the monolayer elasticity resists deformation. High molecular weight surfactants, with large dilatational viscosities, can potentially retard the deformation dynamics. NumericsA boundary integral method simulates the dynamic interfacial deformation of a perfectly conducting droplet in a dielectric in a uniform field. The interface contains an insoluble monolayer which is a Newtonian fluid with constant dilatational viscosity obeying a Langmuir state equation. A range of initial surfactant surface concentrations are studied, with elasticity proportional to concentration. FindingsEquilibrium drop deformations, unaffected by surface viscosity, are strongly resisted by elasticity at high surface concentrations, and field strengths necessary for break-up increase with elasticity. Dilatational viscosity scales with the ratio, κ∗, the surface viscosity (divided by the droplet radius) to the bulk viscosity, and can extend the deformation time. Extended times are described by a time rescaling proportional to κ∗.