Stable equilibrium configurations of an oblate capsule in simple shear flow
نویسنده
چکیده
The objective of the paper is to determine the stable mechanical equilibrium states of an oblate capsule subjected to a simple shear flow, by positioning its revolution axis initially off the shear plane. We consider an oblate capsule with a strain-hardening membrane and investigate the influence of the initial orientation, capsule aspect ratio a/b, viscosity ratio λ between the internal and external fluids, and capillary number Ca which compares the viscous to the elastic forces. A numerical model coupling the finite element and boundary integral methods is used to solve the three-dimensional fluid-structure interaction problem. For any initial orientation, the capsule converges towards the same mechanical equilibrium state, which is only a function of the capillary number and viscosity ratio. For a/b = 0.5, only four regimes are stable when λ = 1: tumbling and swinging in the low and medium Ca range (Ca . 1), regimes for which the capsule revolution axis is contained within the shear plane; then wobbling during which the capsule experiences precession around the vorticity axis; and finally rolling along the vorticity axis at high capillary numbers. When λ is increased, the tumbling-to-swinging transition occurs for higher Ca; the wobbling regime takes place at lower Ca values and within a narrower Ca range. For λ > 4, the swinging regime completely disappears, which indicates that the stable equilibrium states are mainly the tumbling and rolling regimes when λ > 1. We finally show that the Ca-λ phase diagram is qualitatively similar for higher aspect ratio. Only the Ca-range over which wobbling is stable increases with a/b, restricting the stability ranges of inand out-of-plane motions, but this phenomenon is mainly visible for viscosity ratios quite larger than 1.
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تاریخ انتشار 2015