(470b) A Nonlocal Theory to Predict the Concentration Distribution of Red Blood Cells Flowing in a Microchannel

When red blood cells move throughout our microcirculation, they do not flow with a uniform distribution across the blood vessel, but instead leave a significant layer of clarified fluid near the vessel wall, a phenomenon famously coined the “Fahraeus-Lindqvist effect.”  The size and shape of this clarified layer plays an important role in reducing the blood’s effective viscosity in the microcirculation, reducing bleeding times by concentrating platelets near vessel walls, and controlling adsorption of nanoparticles in the blood stream. We develop a kinetic model to predict the concentration distribution of deformable particles, and hence the Fahraeus-Lindqvist layer, in two different wall-bounded flows: Couette flow, and Poiseuelle flow.  This theory balances the hydrodynamic lift on deformable particles (in this case, blood cells or vesicles) with the flux due to particle collisions, which we represent non-locally using a Boltzmann-type approximation.  We determine the scaling of the Fahraeus-Lindqvist layer with wall shear rate, channel height, and volume fraction (aka, Hematocrit).  We also predict a significant layering of particles near the channel wall, consistent with many recent simulations of suspensions of deformable particles.  Our theory is not self-sufficient, as it requires data (simulation or experimental) on the details of a binary collision process and the hydrodynamic lift of a single particle in a wall-bounded shear flow.  Nevertheless, it represents a significant improvement in terms of time savings and predictive power over current large-scale numerical simulations of suspension flows.  Our theory agrees reasonably well with recent boundary integral simulations of suspensions of deformable particles (red blood cells and vesicles).