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

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