Coarse-grained theory to predict the concentration distribution of red blood cells in wall-bounded Couette flow at zero Reynolds number

We develop a coarse-grained theory to predict the concentration distribution of a suspension of vesicles or red blood cells in a wall-bound Couette flow. This model balances the wall-induced hydrodynamic lift on deformable particles with the flux due to binary collisions, which we represent via a second-order kinetic master equation. Our theory predicts a depletion of particles near the channel wall (i.e., the Fahraeus-Lindqvist effect), followed by a near-wall formation of particle layers. We quantify the effect of channel height, viscosity ratio, and shear-rate on the cell-free layer thickness (i.e., the Fahraeus-Lindqvist effect). The results agree with in vitro experiments as well as boundary integral simulations of suspension flows. Lastly, we examine a new type of collective particle motion for red blood cells induced by hydrodynamic interactions near the wall. These swapping trajectories, coined by Zurita-Gotor et al. [J. Fluid Mech. 592, 447-469 (2007)], could explain the origin of particle layering near the wall. The theory we describe represents a significant improvement in terms of time savings and predictive power over current large-scale numerical simulations of suspension flows. (C) 2013 AIP Publishing LLC.