Stability of the tank treading modes of erythrocytes and its dependence on cytoskeleton reference states

We studied the tank treading motion of an erythrocyte (red blood cell, or RBC) in linear shear flows by using a boundary-element fluid-dynamics model coupled with a multiscale structural model of the cell. The purpose was to investigate the correlation between the reference (stress-free) state of the cytoskeleton and the cell dynamics in shear flows with relatively high capillary numbers. We discovered that there exist two distinctive modes of tank treading, mode 1 and mode 2. In mode 1 the membrane elements originating from the dimple areas keep close to the central plane, whereas in mode 2 these elements remain near the farthermost locations from the central plane. Mode 1 is also characterized by significantly higher breathing and swinging oscillations. During tank treading one mode may become unstable and switch to the other. Their stability depends on the viscosity ratio and the capillary number. At a fixed viscosity ratio, when the capillary number is increased the cell experiences sequentially a region dominated by mode 2, a mode 1/mode 2 bistable region and a region dominated by mode 1. More profoundly, these regions are highly sensitive to the reference state of the cytoskeleton. For example, compared with a cell with a biconcave reference state, a cell with a spheroidal reference state features a much smaller region dominated by mode 2. This finding may guide experiments to identify the actual reference state of these cells.