Red Blood Cell membrane in low Reynolds flow and a vorticity-based characterization of shapes*

While some existing numerical methods have successfully simulated the coupling between the fluid and the red blood cell they usually are highly complex to implement. We introduce an alternative phase-field model formulation of two-dimensional cells that solves the vorticity and the stream function that simplifies the numerical implementation [1]. We integrate the 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. We can also use the influence of the cell on the vorticity to characterise the stability or meta-stability of a given shape.

[1] Soft Matter, 2021, DOI: 10.1039/D1SM00559F