Dynamics and rheology of a suspension of vesicles and red blood cells

The dynamics and the rheology of a suspension of vesicles (a model for red blood cells) in the limit of small Reynolds number are studied by means of two-dimensional numerical simulations, based on the boundary integral and phase field methods. The focus is on the link between the microscopic dynamics of the particles and the overall behavior of the suspension (i.e. rheology). A dilute suspension of vesicles in a linear shear flow is analyzed in detail and the influence of the three parameters governing the dynamics of a single vesicle (reduced volume; viscosity contrast; capillary number) is extensively described. The nontrivial behavior of the rheological quantities (effective viscosity and normal stress difference) is explained and the role of the membrane of the vesicle detailed. The influence of the curvature of the flow lines on the dynamics of the vesicles is investigated for the first time, and consistent inward migration is reported. The suggested interpretation remains valid for the flow of the majority of complex fluids, like emulsions and polymer suspensions, and is thus expected to have an impact in other fields. Moreover, the behavior of a suspension of vesicles in a microscopic Taylor-Couette cell is investigated, and a transition to ordered states is reported at very low volume fraction. The behavior of sets of vesicles in a parabolic flow, a setup that mimics red blood cells in the microvasculature, is presented. Vesicles submitted to s