A Numerical Analysis of Rheology of Capsule Suspensions Using a GPU-Accelerated Boundary Element Method

Understanding the behavior of capsules in flow and the rheology of capsule suspensions is of fundamental importance for diverse problems in nature and engineering. The particle Reynolds number of capsules is often small, and the flow field is given by the boundary integral formulation of the Stokes equations. The boundary element method (BEM) based on the boundary integral formulation is thus one of the most accurate methods for simulating capsules under Stokes flow regime. A high computational cost of BEM, however, has limited its application to relatively small scale problems. We have developed a graphics process unit (GPU) computing of BEM for capsules and biological cells in Stokes flow. We have investigated rheological properties of capsules, and those of capsule suspensions using the GPU-accelerated BEM. Here, we provide an overview of our recent studies, particularly focusing on the shear viscosity of dense suspensions of capsules in simple shear flow; an overshoot phenomenon of the capsule deformation in oscillating shear flow; and the sedimentation of red blood cells.