Osmophoresis of a spherical vesicle in a spherical cavity

A semianalytical study is presented for the osmophoretic motion of a spherical vesicle with a semipermeable membrane located at an arbitrary position within a spherical cavity filled with a fluid solution, where a constant solute concentration gradient is imposed in an arbitrary direction with respect to the line connecting the vesicle and cavity centers. The general solutions of conservation equations for the solute species and fluid momentum are established from the superposition of basic solutions in the two spherical coordinate systems about the vesicle and cavity, and the boundary conditions are satisfied by a collocation method. The translational and rotational velocities of the osmophoretic vesicle are calculated for various cases. In the particular case of a vesicle in a concentric cavity, these results agree excellently with the available exact solution. The effects of the cavity wall on osmophoresis are significant and interesting. In general, the normalized translational and rotational velocities of the vesicle increase with increases in the vesicle-to-cavity radius ratio and its relative distance from the cavity center, and the translational velocity deflects little from the imposed solute concentration gradient. The direction of rotation of a confined vesicle undergoing osmophoresis is opposite to that of a corresponding settling particle.