Modeling of unidirectional blood flow in microvessels with effects of shear-induced dispersion and particle migration

A cell-free layer,adjacent to microvessel walls,is present in the blood flow in the microcirculation regime.This layer is of vital importance for the transport of oxygen-saturated red cells to unsaturated tissues.In this work,we first discuss the physics of formation of this cell-free layer in terms of a balance between the shear-induced dispersion and particle migration.To this end,we use high-viscosity drops as prototypes for cells,and discuss our results in terms of physical parameters such as the viscosity ratio and the capillary number.We also provide a short-time analysis of the transient drift-dispersion equation,which helps us better explain the formation process of the cell-free layer.Moreover,we present models for investigating the blood flow in two different scales of microcirculation.For investigating the blood flow in venules and arterioles,we consider a continuous core-flow model,where the core-flow solution is considered to be a Casson fluid,surrounded by a small annular gap of Newtonian plasma,corresponding to the cell-free layer.We also propose a simple model for smaller vessels,such as capillaries,whose diameters are of a few micrometers.In this lower-bound limit,we consider a periodic configuration of aligned,rigid,and axi-symmetric cells,moving in a Newtonian fluid.In this regime,we approximate the fluid flow using the lubrication theory.The intrinsic viscosity of the blood is theoretically predicted,for both the lower and upper-bound regimes,as a function of the non-dimensional vessel diameter,in good agreement with the previous experimental works.We compare our theoretical predictions with the experimental data,and obtain qualitatively good agreement with the well-known Fåhræus-Lindqvist effect.A possible application of this work could be in illness diagnosis by evaluating changes in the intrinsic viscosity due to blood abnormalities.