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

TL;DR

This paper theoretically investigates how microcapsules behave in steady shear flow, revealing that their dynamic modes depend on membrane elasticities, with distinct behaviors like tank-treading, tumbling, and swinging, influenced by shear and bending elasticities.

Contribution

It introduces a theoretical model that captures the effects of shear and bending elasticities on microcapsule dynamics, explaining phase transitions and synchronization phenomena.

Findings

Microcapsules exhibit three main dynamic modes: tank-treading, tumbling, and swinging.

Increasing shear elasticity suppresses intermediate phases and alters rotation behaviors.

Synchronization of membrane rotation with shape modes occurs at specific frequency ratios.

Abstract

The dynamics of microcapsules in steady shear flow was studied using a theoretical approach based on three variables: The Taylor deformation parameter $\alpha_{\rm D}$, the inclination angle $\theta$, and the phase angle $\phi$ 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 $\eta_{\rm {in}}$ of internal fluid ($\alpha_{\rm D}$ and $\theta$ relaxes to constant values), (ii) Tumbling (TB) at high $\eta_{\rm {in}}$ ($\theta$ rotates), and (iii) Swinging (SW) at middle $\eta_{\rm {in}}$ and high shear rate $\dot\gamma$ ($\theta$ oscillates). All of three modes are accompanied by a membrane ($\phi$) rotation. For microcapsules with low shear elasticity, the TB phase with no $\phi$ rotation and the coexistence phase of SW and TB motions are induced by the energy barrier of $\phi$ rotation. Synchronization of $\phi$ 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 $\phi$ or $\theta$ rotation occurs. This phase behavior agrees with recent simulation results of microcapsules with low bending elasticity.