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

Hypothesis: A 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. Numerics: A 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. Findings: Equilibrium 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, kappa*, 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 kappa*. (C) 2021 Elsevier Inc. All rights reserved.