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Blood flow in a microchannel with complex geometries has been investigated to develop biomedical microdevices (e.g. Faivre et al., 2006) or to understand pathology in small vessels, such as lacunar infarcts. In a small channel, say 100 μm in diameter, the blood is no longer assumed to be a homogeneous fluid because the size of the red blood cells (RBCs) cannot be neglected compared to the generated flow field (...