Particle interactions in osmophoresis

Abstract

An exact analytical study is presented for the osmophoretic motion of two spherical vesicles in a constant solute concentration gradient arbitrarily oriented with respect to the line of vesicle centers. The vesicles may be formed from different semipermeable membranes, contain arbitrary solutes and have unequal radii. The appropriate equations of conservation of solute species and fluid momentum are solved in the quasisteady limit using spherical bipolar coordinates and the translational and angular velocities of the vesicles are calculated for various cases. The interaction between vesicles can be strong and peculiar when the surface-to-surface spacing gets close to zero. The influence of the interaction, in general, is stronger on the smaller vesicle than on the larger one. For the osmophoresis of two identical vesicles along their line of centers, both migrate slower than the velocity they would possess if isolated. On the contrary, for the case of two identical vesicles undergoing osmophoresis normal to their line of centers, they migrate faster than their undisturbed velocity except when the two vesicles are very close together. A comparison between our exact results for osmophoretic velocities and those evaluated from asymptotic formulas obtained using a method of reflections is made for a case of two identical vesicles. The asymptotic formulas for the vesicle velocities up to O(r 12 −6) , where r 12 is the center-to-center distance between the vesicles, are found to underestimate (for the axisymmetric osmophoresis) or to overestimate (for the transverse motion) the effect of particle interactions; the error can be significant when the vesicle surfaces are less than half the vesicle radius apart. Our numerical results for the interaction between two vesicles are also used to find the effect of the volume fraction of vesicles on the average osmophoretic velocity in a bounded dispersion.