Boundary effects on osmophoresis: motion of a spherical vesicle parallel to two plane walls

Abstract

A theoretical study is presented for the quasisteady osmophoretic motion of a spherical vesicle in a solution located between two infinite parallel plane walls in the limit of negligible Reynolds and Peclet numbers. The applied solute concentration gradient is uniform and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The presence of the neighboring 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 fundamental solutions in both the rectangular and the spherical coordinate systems. The boundary conditions are enforced first at the plane walls by the Fourier transforms 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 as well as the relative separation distances between the vesicle and the two plates. For the special case of osmophoretic motions of a spherical vesicle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the vesicle velocity, depending upon the relevant properties of the vesicle, the relative vesicle-wall separation distances, and the solutal boundary condition at the walls. In general, the boundary effect on osmophoresis is quite complicated in comparison with that on sedimentation.