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The evolution of macroscopic living beings on Earth required the establishment of vascular systems to transport nutrients and eliminate waste. For example, oxygen transport from the respiratory organs to tissues occurs via a high volume fraction of red blood cells (RBCs) that circulate through the vascular system. If blood was analogous to a concentrated suspension of solid particles or a suspension of droplets of similar dimensions, it would display a viscosity several orders of magnitude larger than its actual value, which would compromise the transport pathway. The amazing fluidity of blood originates from the deformability of RBCs and the microstructures they form in flow. Consequently, blood is shear-thinning. The deformability of RBCs is postulated to be a major determinant of impaired perfusion, increased blood viscosity and occlusion in microvessels. Despite advances in understanding the molecular organization of RBCs, the relationships between the rheology of each element of the cell’s composite structure, the global deformability of the cells and the behavior of the cells in microflows are not understood. In this chapter, we describe recent advances in the description of the flow of RBCs. We focus on flows for which experimental, analytical and numerical advances have been made and discuss the physics underlying hemorheological phenomena where cell deformability is important.

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