A theoretical investigation of the frisbee motion of red blood cells in shear flow

The dynamics of a single red blood cell in shear flow is a fluid-structure interaction problem that yields a tremendous richness of behaviors, as a function of the parameters of the problem. A low shear rates, the deformations of the red blood cell remain small and low-order models have been developed, predicting the orientation of the cell and the membrane circulation along time. They reproduce the dynamics observed in experiments and in simulations, but they do not simplify the problem enough to enable simple interpretations of the phenomena. In a process of exploring the red blood cell dynamics at low shear rates, an existing model constituted of 5 nonlinear ordinary differential equations is rewritten using quaternions to parametrize the rotations of the red blood cell. Techniques from algebraic geometry are then used to determine the steady-state solutions of the problems. These solutions are relevant to a particular regime where the red blood cell reaches a constant inclination angle, with its membrane rotating around it, and referred to as frisbee motion. Comparing the numerical solutions of the model to the steady-state solutions allows a better understanding of the transition between the most emblematic motions of red blood cells, flipping and tank-treading.

Automated summary

At low shear rates, studying the dynamics of a single red blood cell in shear flow involves complex behaviors that require mathematical models and techniques from algebraic geometry. By rewriting existing models and determining steady-state solutions, a better understanding of the transition between different motions of red blood cells can be achieved.