Numerical simulation of the motion of red blood cells and vesicles in microfluidic flows

Abstract

We study the mathematical modeling and numerical simulation of the motion of red blood cells (RBC) and vesicles subject to an external incompressible flow in a microchannel. RBC and vesicles are viscoelastic bodies consisting of a deformable elastic membrane enclosing an incompressible fluid. We provide an extension of the finite element immersed boundary method by Boffi and Gastaldi (Comput Struct 81:491–501, 2003), Boffi et al. (Math Mod Meth Appl Sci 17:1479–1505, 2007), Boffi et al. (Comput Struct 85:775–783, 2007) based on a model for the membrane that additionally accounts for bending energy and also consider inflow/outflow conditions for the external fluid flow. The stability analysis requires both the approximation of the membrane by cubic splines (instead of linear splines without bending energy) and an upper bound on the inflow velocity. In the fully discrete case, the resulting CFL-type condition on the time step size is also more restrictive. We perform numerical simulations for various scenarios including the tank treading motion of vesicles in microchannels, the behavior of ‘healthy’ and ‘sick’ RBC which differ by their stiffness, and the motion of RBC through thin capillaries. The simulation results are in very good agreement with experimentally available data.