Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion

Measurements of the dimensions and membrane rotational frequency of individual erythrocytes steadily tank-treading in a rheoscope are used to deduce the surface shear viscosity of the membrane. The method is based on an integral energy principle which says that the power supplied to the tank-treading cell by the suspending fluid is equal to the rate at which energy is dissipated by viscous action in the membrane and cytoplasm. The integrals involved are formulated with the aid of an idealized mathematical model of the tank-treading red blood cell (RBC) (Keller and Skalak, 1982, J. Fluid Mech., 120:24-27) and evaluated numerically. The outcome is a surface-averaged value of membrane viscosity which is representative of a finite interval of membrane shear rate. The numerical values computed show a clear shear-thinning characteristic as well as a significant augmentation of viscosity with cell age and tend toward agreement with those determined for the rapid phase of shape recovery in micropipettes (Chien, S., K.-L. P. Sung, R. Skalak, S. Usami, and A. Tozeren, 1978, Biophys. J., 24:463-487). The computations also indicate that the rate of energy dissipation in the membrane is always substantially greater than that in the cytoplasm.