The role of tank-treading motions in the transverse migration of a spheroidal vesicle in a shear flow

Abstract

The behavior of a spheroidal vesicle, in a plane shear flow bounded from one side by a wall, is analysed when the distance from the wall is much larger than the spheroid radius. It is found that tank treading motions produce a transverse drift away from the wall, proportional to the spheroid eccentricity and the inverse square of the distance from the wall. This drift is independent of inertia, and is completely determined by the characteristics of the vesicle membrane. The relative strength of the contribution to drift from tank-treading motions and from the presence of inertial corrections, is discussed. J. Phys. A (Math. Gen.)In press

Vesicles and red blood cells in flow: From individual dynamics to rheology

“…A similar scaling was found by Olla [99][100][101]. The lift force is simply F lift = 6πηR 0 U mig .…”

“…This discrepancy can be attributed to the fact that the vesicle remains rather close to the wall. Indeed, Callens et al [95] performed experiments in microgravity conditions, where only the lift force is present, and found that at distances larger compared to vesicle size, the lift velocity is quantitatively well described by Olla's model [99][100][101], which is also consistent with Eq. (12) cited above.…”

“…A considerable theoretical interest has been devoted to this problem [96][97][98][99][100][101]. The hydrodynamic repulsion between the vesicle and the wall can be analyzed using the method of images [102]: the boundary conditions at the wall can be satisfied by placing a vesicle hydrodynamic image on the opposite side.…”

Motion of red blood cells near microvessel walls: effects of a porous wall layer

“…In the absence of inertial effects, the possible fluid mechanical causes for migration are interactions of the particle with the wall and with the non-uniform shear rate in channel flow (Coupier et al 2008). The presence of a solid wall near the cell introduces an asymmetry in the forces on the cell, which can cause migration of deformable cells, for example as result of tank-treading motion for a spheroidal cell (Olla 1997) or the breaking of fore-aft symmetry in cell shape (Cantat & Misbah 1999; Sukumaran & Seifert 2001). Analyses of vesicles bound to a surface show the generation of lift forces due to asymmetry of vesicle shape or orientation (Seifert 1999; Cantat & Misbah 1999).…”

Red blood cell motions in high-hematocrit blood flowing through a stenosed microchannel

“…Fahraeus and Lindqvist (1931) observed an apparent decrease of blood viscosity when it flowed through capillaries of decreasing diameters due to the radial migration of RBCs. Olla (1997) analyzed the transverse migration of RBCs in a plane shear flow bounded from one side by a wall. He showed that tank-treading motions produced a transverse drift away from the wall, which was independent of inertia, and was completely determined by the characteristics of the RBC membrane.…”