Boundary effects on osmophoresis: Motion of a spherical vesicle perpendicular to two plane walls

Abstract

The problem of the osmophoretic motion of a spherical vesicle situated at an arbitrary position between two infinite parallel plane walls is studied theoretically in the quasisteady limit of negligible Peclet and Reynolds numbers. The imposed solute concentration gradient is uniform and perpendicular to the plane walls. The presence of the confining walls causes two basic effects on the vesicle velocity: first, the local concentrations on both sides of the vesicle surface are altered by the walls, thereby speeding up or slowing down the vesicle; secondly, the walls enhance the viscous interaction effect on the moving vesicle. To solve the equations of conservation of mass and momentum, the general solutions are constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the plane walls by the Hankel transform and then on the vesicle surface by a collocation technique. Numerical results for the osmophoretic velocity of the vesicle relative to that under identical conditions in an unbounded solution are presented for various values of the relevant properties of the vesicle–solution system as well as the relative separation distances between the vesicle and the plane walls. The collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the neighboring walls will enhance the vesicle velocity, but its dependence on the relative vesicle–wall separation distances is not necessarily monotonic. The boundary effect on osmophoresis of a vesicle normal to two plane walls is found to be significant and stronger than that parallel to the confining walls.