Dynamic Modes of Microcapsules in Steady Shear Flow: Effects of Bending and Shear Elasticities

Abstract

The dynamics of microcapsules in steady shear flow was studied using a theoretical approach based on three variables: The Taylor deformation parameter ${\alpha }_{\mathrm{D}}$, the inclination angle $\theta$, and the phase angle $\varphi$ of the membrane rotation. It is found that the dynamic phase diagram shows a remarkable change with an increase in the ratio of the membrane shear and bending elasticities. A fluid vesicle (no shear elasticity) exhibits three dynamic modes: (i) Tank-treading (TT) at low viscosity ${\eta }_{\mathrm{in}}$ of internal fluid (${\alpha }_{\mathrm{D}}$ and $\theta$ relaxes to constant values), (ii) Tumbling (TB) at high ${\eta }_{\mathrm{in}}$ ($\theta$ rotates), and (iii) Swinging (SW) at middle ${\eta }_{\mathrm{in}}$ and high shear rate $\dot{\gamma }$ ($\theta$ oscillates). All of three modes are accompanied by a membrane ($\varphi$) rotation. For microcapsules with low shear elasticity, the TB phase with no $\varphi$ rotation and the coexistence phase of SW and TB motions are induced by the energy barrier of $\varphi$ rotation. Synchronization of $\varphi$ rotation with TB rotation or SW oscillation occurs with integer ratios of rotational frequencies. At high shear elasticity, where a saddle point in the energy potential disappears, intermediate phases vanish, and either $\varphi$ or $\theta$ rotation occurs. This phase behavior agrees with recent simulation results of microcapsules with low bending elasticity.

11 pages, 14 figures

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Cited by in corpus (2)

• Micro-Capsules in Shear Flow
• Dynamic Modes of Red Blood Cells in Oscillatory Shear Flow