Large deformations of elastic cylindrical capsules in shear flows

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Abstract
The nonlinear problem of the steady-state interaction of a closed fluid-filled cylindrical elastic membrane with a slow viscous shear flow has been solved by a series-expansion technique. The problems of successive orders were both formulated and solved by a symbolic manipulation program, and the calculations were carried to sixth order in a dimensionless parameter related to the applied shear rate. Moderately large deformations (aspect ratios approaching 3) fall within the range of this analysis, which yields the dependences of the following global variables on the system parameters: membrane deformation, orientation, and strain, as well as tank-treading frequency, and mean internal pressure. The solution for the flow field around an isolated capsule is also used to calculate the apparent viscosity of a dilute suspension of flexible cylindrical particles, which yields the paradoxical result that the apparent viscosity decreases as the internal viscosity increases.