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Journal Articles Journal of Fluid Mechanics Year : 2013

Off-plane motion of a prolate capsule in shear flow

Abstract

The objective of this study is to investigate the motion of an ellipsoidal capsule in a simple shear flow when its revolution axis is initially placed off the shear plane. We consider prolate capsules with an aspect ratio of two or three enclosed by a membrane, which is either strain-hardening or strain-softening. We seek the equilibrium motion of the capsule as we increase the capillary number $\mathit{Ca}$ , which measures the ratio between the viscous and elastic forces. The three-dimensional fluid–structure interaction problem is solved numerically by coupling a boundary integral method (for the internal and external flows) with a finite element method (for the wall deformation). For any initial inclination with the flow vorticity axis, a given capsule converges towards a unique equilibrium configuration which depends on $\mathit{Ca}$ . At low capillary number, the stable equilibrium motion is the rolling regime: the capsule aligns its long axis with the vorticity axis, while the membrane tank-treads. As $\mathit{Ca}$ increases, the capsule takes a complex wobbling motion at equilibrium, precessing around the vorticity axis. As $\mathit{Ca}$ is further increased, the capsule long axis oscillates about the shear plane, while the membrane rotates around a capsule cross-section that also oscillates over time (oscillating–swinging regime). The amplitude of the oscillations about the shear plane decreases as $\mathit{Ca}$ increases and the capsule finally takes a swinging motion in the shear plane. It is found that the transitions from rolling to wobbling and from wobbling to oscillating–swinging depend on the mean energy stored in the membrane.
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Dates and versions

hal-02019733 , version 1 (14-02-2019)

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C. Dupont, Anne-Virginie Salsac, D. Barthès-Biesel. Off-plane motion of a prolate capsule in shear flow. Journal of Fluid Mechanics, 2013, 721, pp.180-198. ⟨10.1017/jfm.2013.62⟩. ⟨hal-02019733⟩
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