Oscillatory tank-treading motion of erythrocytes in shear flows

In this paper, we investigate the oscillatory dynamics of the tank-treading motion of healthy human erythrocytes in shear flows with capillary number Ca = O(1) and small to moderate viscosity ratios 0.01 ≤ λ ≤ 1.5. These conditions correspond to a wide range of surrounding medium viscosities (4-600 m Pa s) and shear flow rates (2-560 s(-1)), and match those used in ektacytometry systems. For a given viscosity ratio, as the flow rate increases, the steady-state erythrocyte length L (in the shear plane) increases logarithmically while its depth W (normal to the shear plane) decreases logarithmically. In addition, the flow rate increase dampens the oscillatory erythrocyte inclination but not its length oscillations (which show relative variations of about 5-8%). For a given flow rate, as the viscosity ratio increases, the erythrocyte length L contracts while its depth W increases (i.e., the cell becomes less deformed) with a small decrease in the length variations. The average orientation angle of the erythrocyte shows a significant decrease with the viscosity ratio as does the angle oscillation while the oscillation period increases. These trends continue in higher viscosity ratios resulting eventually in the transition from a (weakly oscillatory) tank-treading motion to a tumbling motion. Our computations show that the erythrocyte width S, which exists in the shear plane, is practically invariant in time, capillary number, and viscosity ratio, and corresponds to a real cell thickness of about 2.5 μm. Comparison of our computational results with the predictions of (low degree-of-freedom) theoretical models and experimental findings, suggests that the energy dissipation due to the shape-memory effects is more significant than the energy dissipation due to the membrane viscosity. Our work shows that the oscillatory tank-treading motion can account for more than 50% of the variations found in ektacytometry systems; thus, researchers who wish to study inherent differences between erythrocytes within a population must devise a way of monitoring individual cells over time so that they can remove the oscillation effects.