Dynamics and Rheology of Immersed Elastic Capsules in A Simple Shear Flow

Biological fluids like blood serve as nutrient transport and immune response in the human body. These fluids consist of a viscous phase with suspended deformable membranes that enclose an inner fluid, commonly known as capsules. Understanding these fluids provides insights into diseases like aneurysms and aid in developing microfluidic diagnostic devices. The recent development of inertial migration techniques holds promise to facilitate non-invasive blood plasma extraction and improve size-dependent cell segregation. In this work, we investigate the dynamics and rheology behavior of an elastic capsule suspension in a simple inertial shear flow. Governing physical parameters are capsule volume fraction, imposed shear rate, flow inertia and capsule deformability. Computations are performed with our open-source front-tracking solver implemented in Basilisk on octree adaptive grids for local mesh refinement of areas of interest. The capsule stresses are resolved with a linear finite element method and a paraboloid fitting technique to accurately compute the elastic and bending force. While non-inertial capsules have been studied extensively, to our knowledge, this is the first systematic study of the capsule suspensions at finite Re. Our numerical findings highlight the influence of capsule volume fraction on suspension rheology. We analyze quantitatively the deformation and dynamics of the capsule suspensions and their impact on the system.