Theory to predict particle migration and margination in the pressure-driven channel flow of blood

The inhomogeneous concentration distribution of erythrocytes and platelets in microchannel flows particularly in directions normal to the mean flow plays a significant role in hemostasis, drug delivery, and microfluidic applications. In this paper, we develop a coarse-grained theory to predict these distributions in pressure-driven channel flow at zero Reynolds number and compare them to experiments and simulations. We demonstrate that the balance between the deformability-induced lift force and the shear-induced diffusion created by hydrodynamic interactions in the suspension results in both a peak concentration of red blood cells at the channel center and a cell-free or Fahraeus-Lindqvist layer near the walls. On the other hand, the absence of a lift force and the strong red blood cell-platelet interactions result in an excess concentration of platelets in the cell-free layer. We demonstrate a strong role of hematocrit (i.e., erythrocyte volume fraction) in determining the cell-free layer thickness and the degree of platelet margination. We also demonstrate that the capillary number of the erythrocytes, based on the membrane shear modulus, plays a relatively insignificant role in the regimes that we have studied. Our theory serves as a good and simple alternative to large-scale computer simulations of the cross-stream transport processes in these mixtures.