Hydrodynamic interaction between two vesicles in a linear shear flow: Asymptotic study

Interactions between two vesicles in an imposed linear shear flow are studied theoretically, in the limit of almost spherical vesicles, with a large intervesicle distance, in a strong flow, with a large inner to outer viscosity ratio. This allows to derive a system of ordinary equations describing the dynamics of the two vesicles. We provide an analytic expression for the interaction law. We find that when the vesicles are in the same shear plane, the hydrodynamic interaction leads to a repulsion. When they are not, the interaction may turn into attraction instead. The interaction law is discussed and analyzed as a function of relevant parameters.