Abstract
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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>Data Availability The data that support the findings of this study are available from the corresponding author upon reasonable request (frcunha@unb.br).
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Acknowledgements
The authors would like to acknowledge the CAPES Foundation of the Ministry of Science and Technology of Brazil, the CNPq Council of the Ministry of Science and Technology of Brazil (Nos. 421177/2018-7, 310399/2020-3, and 312951/2018-3) and the University of Brasília for the financial support of this work. The authors would also like to acknowledge Dr. S. J. COWLEY for his helpful discussion concerning the asymptotic analysis of the concentration boundary layer. A preliminary version of part of these results has been presented in the proceedings of the Ibero-Latin American Congress on Computational Methods in Engineering in 2016.
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Roure, G., Cunha, F.R. Modeling of unidirectional blood flow in microvessels with effects of shear-induced dispersion and particle migration. Appl. Math. Mech.-Engl. Ed. 43, 1585–1600 (2022). https://doi.org/10.1007/s10483-022-2908-9
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DOI: https://doi.org/10.1007/s10483-022-2908-9