Effect of surfactant on drop dynamics in linear flows

The effective stress of an emulsion of surfactant on drop dynamics in linear flows was analyzed. A compact perturbation solution for the deformation of a surfactant-covered drop, suspended in a fluid of the same viscosity, subjected to an arbitrary linear flow was developed. A third order perturbation solution for small deviations from sphericity was explicitly derived. Predictions of the small deformation theory for drop shape, surfactant distribution and emulsion rheology were in quantitative agreement with the numerical simulations, and in qualitative agreement with experimental data.