Red blood cells in low Reynolds number flow: A vorticity-based characterization of shapes in two dimensions

Studies on the mechanical properties of red blood cells improve the diagnosis of some blood-related diseases. Some existing numerical methods have successfully simulated the coupling between a fluid and red blood cells. This paper introduces an alternative phase-field model formulation of two-dimensional cells that solves the vorticity and stream function that simplifies the numerical implementation. We integrate red blood cell dynamics immersed in a Poiseuille flow and reproduce previously reported morphologies (slippers or parachutes). In the case of flow in a very wide channel, we discover a new metastable shape referred to as ' anti -parachute' that evolves into a horizontal slipper centered on the channel. This sort of metastable morphology may contribute to the dynamical response of the blood. A novel model membrane modelling can be used to study red blood cells by solving the vorticity and stream function, simplifying the numerical implementation, and produce a new metastable shape for lower confinement.