Tank-treading as a means of propulsion in viscous shear flows

Abstract

The use of tank-treading as a means of propulsion for microswimmers in viscous shear flows is taken into account. We discuss the possibility of a vesicle to control the drift in an external shear flow, by locally varying the bending rigidity of its membrane. By analytical calculation in the quasi-spherical limit, the stationary shape and the orientation of the tank-treading vesicle in the external flow are determined, working to lowest order in the membrane inhomogeneity. The membrane inhomogeneity acts in the shape evolution equation as an additional force term, which can be used to balance the effect of the hydrodynamic stresses, thus allowing the vesicle to assume shapes and orientations that are impossible otherwise. The vesicle shapes and orientations required for migration transverse to the flow, together with the bending rigidity profiles leading to such shapes and orientations, are determined. Considering the variations in the concentration experienced during tank-treading, a simple model is presented, in which a vesicle is able to migrate up or down the gradient of a concentration field by stiffening or softening of its membrane.