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We simulate the cross-flow migration of rigid particles such as platelets in a red blood cell (RBC) suspension using the Stokes flow boundary integral equation method. Two types of flow environments are investigated: a suspension undergoing a bulk shear motion and a suspension flowing in a microchannel or duct. In a cellular suspension undergoing bulk shear deformation, the cross-flow migration of particles is diffusional. The velocity fluctuations in the suspension, which are the root cause of particle migration, are analyzed in detail, including their magnitude, the autocorrelation of Lagrangian tracer points and particles, and the associated integral time scales. The orientation and morphology of red blood cells vary with the shear rate, and these in turn cause the dimensionless particle diffusivity to vary non-monotonically with the flow capillary number. By simulating RBCs and platelets flowing in a microchannel of 34 μm height, we demonstrate that the velocity fluctuations in the core cellular flow region cause the platelets to migrate diffusively in the wall normal direction. A mean lateral velocity of particles, which is most significant near the edge of the cell-free layer, further expels them toward the wall, leading to their excess concentration in the cell-free layer. The calculated shear-induced particle diffusivity in the cell-laden region is in qualitative agreement with the experimental measurements of micron-sized beads in a cylindrical tube of a comparable diameter. In a smaller duct of 10 × 15 μm cross section, the volume exclusion becomes the dominant mechanism for particle margination, which occurs at a much shorter time scale than the migration in the bigger channel.
Zhao et al. (Sun,) studied this question.