Osmophoresis of a spherical vesicle in a circular cylindrical pore

Abstract

AbstractThe problem of the osmophoretic motion of a spherical vesicle along the centerline of a circular cylindrical pore is studied theoretically in the quasi‐steady limit of negligible Reynolds and Peclet numbers. The imposed solute concentration gradient is uniform and parallel to the pore wall, which may be either impermeable to the solute molecules or prescribed with the far‐field concentration distribution. The presence of the pore wall causes two basic effects on the vesicle velocity: (1) the local concentration gradients on the vesicle surface are altered by the wall, thereby speeding up or slowing down the vesicle; (2) the wall enhances 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 cylindrical and spherical coordinates. The boundary conditions are enforced first at the pore wall 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 distance between the vesicle and the pore wall. The collocation results agree well with the approximate analytical solution obtained by using a method of reflections. The presence of the wall will enhance the vesicle velocity, although its dependency on the ratio of vesicle‐to‐pore radii is not necessarily to be monotonic. In general, the boundary effect on osmophoresis is quite significant. © 2005 American Institute of Chemical Engineers AIChE J, 2005