Abstract
We show that the motion of individual red blood cells in an oscillating moderate shear flow is described by a nonlinear system of three coupled oscillators. Our experiments reveal that the cell tank treads and tumbles either in a stable way with synchronized cell inclination, membrane rotation and hydrodynamic oscillations, or in an irregular way, very sensitively to initial conditions. By adapting our model described previously, we determine the theoretical diagram for the red cell motion in a sinusoidal flow close to physiological shear stresses and flow variation frequencies and reveal large domains of chaotic motions. Finally, fitting our observations allows a characterization of cell viscosity and membrane elasticity.