Modeling of unidirectional blood flow in microvessels with effects of shear-induced dispersion and particle migration
G. ROURE, F. R. CUNHA
2022, 43(10):
1585-1600.
doi:10.1007/s10483-022-2908-9
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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.
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