In-plane elasticity controls the full dynamics of red blood cells in shear flow

The problem of understanding the movement of red blood cells (RBCs) is at the heart of hemorheology. It has thus motivated an extensive body of experimental and numerical works, which showed that RBCs display a rich dynamical behavior in pure shear flow. However, a clear physical understanding of the coupling between cell orientation, membrane deformations, and membrane circulation is still not emerging, notably due to the lack of a comprehensive and tractable model to serve as the theoretical foundation for data analysis. Here, we propose a low-order model which, combined with detailed simulations and existing experimental data, demonstrates how membrane in-plane deformations and elasticity are the essential ingredients responsible for RBC dynamics at low shear stresses. Our approach demonstrates that out-of-plane deformations and fluid inertia are not necessary to explain the RBC dynamics and underlines the importance of the membrane stress-free shape. By reproducing all the details of known RBC dynamics in shear flow, our low-order model provides a single framework to understand the full dynamics of RBCs at low shear stresses.