Dynamics and rheology of a single two-dimensional multilobe vesicle in a confined geometry
Résumé
A vesicle is a common model used to represent red blood cell (RBC) in silico and in vitro. We investigate here the dynamics and the rheology of a vesicle under shear flow confined between two parallel walls in wide ranges of applied shear rate and the viscosity contrast (viscosity ratio between the internal and external fluids of the vesicle). The Helfrich model is used to describe the vesicle membrane energy and the spectral boundary integral method to compute the velocity of the vesicle membrane. Multilobe shapes are observed in a wide range of shear rates and viscosity contrasts. A phase diagram is determined in this parameter space. The cytoskeleton of a RBC is not necessary for the multilobe manifestation, in contrast with recent claims. Here we show that these shapes are due to membrane tension only. This highlights the fact that the two-dimensional (2D) vesicle model used here, besides its relevant predictions in previous studies (such as slipper and parachute shapes), can capture several other shapes and dynamics observed for RBCs. The 2D vesicle can thus be used as a reliable model, at least as an exploration basis, to investigate blood flow where the three-dimensional model may prove to be computationally demanding, especially for dense suspensions. We investigate the rheology of the multilobe shapes in the dilute regime and find that the effective viscosity exhibits a significant jump associated with a transition to multilobe dynamics. We provide simple interpretations to these findings. We discuss the stability of the centered solutions and the emergence of the off-centered ones.