Dynamics of a surfactant-covered drop and the non-Newtonian rheology of emulsions

Complex fluids exhibit rich dynamic macroscopic behavior that stems from the relaxation of material structure. Emulsions, polymer blends and biological fluids are examples of complex fluids with drop-like morphology. Hence, drop dynamics appears as the leitmotiv in the research of these systems. In particular, predicting rheology of emulsions relies on a detailed understanding of the drop-level microhydrodynamics.; The focus of this thesis is on the dynamics of a Newtonian drop suspended in a Newtonian matrix fluid in linear viscous flows. The drop is covered with a dilute monolayer of surfactant which is insoluble in the continuous phases. The problem is challenging because of the nonlinear coupling of drop deformation, surfactant redistribution, and bulk flows. The dynamics depends on the relative strength of various relaxation mechanisms that oppose the distortion of surfactant distribution and drop shape induced by the straining component of the flow. These restoring mechanisms include both Marangoni- and shape-relaxation, and drop rotation by the imposed flow. The evolution of the system is formulated as a nonlinear matrix equation, which is derived by expanding the fluid velocity, surfactant distribution and drop shape in spherical harmonics. Analytical expansions applicable where the surfactant distribution and drop shape are only slightly perturbed from their equilibrium state are developed. Numerical results, including three-dimensional boundary integral simulations are used to determine the range of convergence for the expansions. Calculations of the stress in a dilute emulsion of surfactant-covered drops reveal that the interplay between different microstructural relaxation mechanisms can give rise to a rich rheological behavior.; The developed theory provides a quantitative basis for predicting drop deformation and emulsion rheology and gives useful insights for understanding the behavior of a variety of other complex fluids. Drop deformation serves as a starting point for analyzing certain phenomena in biological systems such as shear induced deformation of biological cells.