We report on the rheology of dilute suspensions of red blood cells (RBC) and vesicles. The viscosity of RBC suspensions reveals a previously unknown signature: it exhibits a pronounced minimum when the viscosity of the ambient medium is close to the value at which the transition from tank-treading to tumbling occurs. This bifurcation is triggered by varying the viscosity of the ambient fluid. It is found that the intrinsic viscosity of the suspension varies by about a factor of 4 in the explored parameter range. Surprisingly, this significant change of the intrinsic viscosity is revealed even at low hematocrit (5%). We suggest that this finding may be used to detect blood flow disorders linked to pathologies that affect RBC shape and mechanical properties. This opens future perspectives on setting up new diagnostic tools, with great efficiency even at very low hematocrit. Investigations are also performed on giant vesicle suspensions, and compared to RBCs.
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