Shape transition and migration of 3D vesicles in a confined Poiseuille flow

Vesicles are essential models to understand the behavior of closed soft particle under flow as red blood cells. Their incompressible membranes are made of a fluid lipid bilayer with a resistance to bending. Vesicles are characterized by their deflation that permits to the vesicle shape to exhibit an amazing variety of shape (parachute, bullet, peanut, croissant, and slipper) and different types of dynamical behavior (tank- treading, tumbling, and trembling) in a simple flow. Much has been made of vesicle dynamics in an unbounded Poiseuille flow or 2D confined geometry. Here, we numerically investigate the shape transition and migration of a 3D vesicle in a confined Poiseuille flow by means of boundary element method, in which a wall boundary is additionally implemented. The vesicle motion is determined by three dimensionless parameters: the reduced volume ν, the bending capillary number Ca and the confinement β, namely the ratio of the characteristic size of the vesicle to the radius of the capillary. The intricate interplay among the wall, flow curvature and membrane bending leads to an extension of the set of vesicle morphologies. Particular attention here is paid to determining transition conditions under which a vesicle changes its characteristic shape. Fig. 1a shows a transition example for a slipper-like shape vesicle (featured by an offset of the center of gravity, i.e., Yg≠0) that becomes a bullet-like shape (Yg =0) when the confinement is increased beyond a critical value. The confinement also has a significant effect on the membrane flow structure, as illustrated in Fig. 1b, where one vertex or two ones can take place on the vesicle, depending mainly on the value of β.