Transient three-dimensional drop deformation is studied in dilute emulsions for large capillary numbers, corresponding to strong-flow or low-interfacial-tension conditions. Steady, planar linear flows are considered, described by the dimensionless vorticity orthogonal to the plane of flow. For drop-to-matrix viscosity ratios less than 1, drops widen along the vorticity direction due to the compressional component of the imposed flow. The drops are strongly elongated by the flow, and thus assume flat lamellar configurations, leading to remarkable interfacial area generation. We analyze the limit of capillary number infinite first, and present analytic results demonstrating that in this case drop deformation is described by a universal function of the viscosity ratio, independent of the vorticity. Rigid-body rotation merely affects the time-evolution, i.e., with increasing vorticity, drops are more rotated away from the extensional direction of the flow thereby delaying deformation. We provide an exact solution that describes drop deformation far from the initial conditions. A constant drop width is achieved along the direction of vorticity, leading to the development of a stable lamellar morphology.
Institute for Mathematics and Its Applications>IMA Preprints Series
Cristini, V.; Simeone, M.; Guido, S.; Hooper, R.; Macosko, C.W..
Lamellar microstructure of emulsions.
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