We present a versatile perturbative calculation scheme to determine the leading-order correction mobility matrix for particles in low-Reynolds-number fluid with spatially variant viscosity. To this end, we exploit Lorentz reciprocal theorem and reflection method far field approximation. demonstrate how apply framework particular choice of viscosity field, first study finite-size, interface-like...

The paper is concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. In dimension two, we establish both interior and boundary regularity theorem for such a flow under smallness conditions. As a consequence, we establish the existence of global weak solutions that are smooth away from at most finitely many singular times ...

We consider how to design a microfluidic system in which suspended particles spontaneously order into flowing crystals when driven by external pressure. Via theory and numerics, we find that particle-particle hydrodynamic interactions drive self-organization under suitable conditions of particle morphology and geometric confinement. Small clusters of asymmetric "tadpole" particles, strongly con...