Dynamic modes of microcapsules in steady shear flow: effects of bending and shear elasticities

The dynamics of microcapsules in steady shear flow were studied using a theoretical approach based on three variables: the Taylor deformation parameter αD , 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 at low viscosity ηin of internal fluid (αD and θ relaxes to constant values), (ii) tumbling (TB) at high ηin (θ rotates), and (iii) swinging (SW) at middle ηin and high shear rates γ (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.