An advanced boundary element integral method is proposed to investigated rheology of deformable liquid drops and elastic capsules in homogeneous and bounded flows at very low Reynolds numbers (Stokes flows). Development and implementation of numerical methods for accurate tracking of two- and three-dimensional interfaces are proposed. Several case studies are considered including suspension flow of liquid drops in channels, of liquid drops in homogeneous shear flow in the presence of surfactants, and of elastic capsules in homogeneous shear flow and channels. If successful, the results will contribute to the advancement of basic understanding and prediction of suspension flows with deformable dispersed phases, with potential relevance to industrial, natural and physiological processes.
