Diffusiophoresis of interacting particles in nonelectrolyte gradients

The diffusiophoretic motion of an arbitrary, finite cluster of colloidal spheres is considered. The spheres are allowed to differ in radius and in surface properties, and they may move independently or be linked by any infinitesimally thin rods to form a rigid aggregate. The range of the interaction between the solute and the particle surfaces is assumed to be small compared to the radius of each particle and to the gap thickness between any two neighboring particles, but the polarization effect of the diffuse solute in the thin particle–solute interaction layer caused by the strong adsorption of the solute is incorporated. A slip velocity of the fluid and a normal flux of the solute at the outer edge of the diffuse layer are used as the boundary conditions for the fluid domain outside the thin diffuse layers. Using a collocation technique along with these boundary conditions, the transport equations governing the problem are solved at the quasisteady state and the particle interaction effects are computed for various cases. For two-sphere systems, the translational and angular velocities of the particles at all orientations and separation distances agree well with the asymptotic solution obtained by using a method of reflections. The particle interactions in linear chains of three spheres show that the existence of the third sphere can significantly affect the mobilities of the other two spheres. For the cases of a rigid dumbbell composed of two spheres, the numerical solutions for the particle velocities compare favorably with the formulas derived analytically. Finally, our numerical results for the interaction between two spheres are used to find the effect of volume fraction of particles on the mean diffusiophoretic velocity in a bounded suspension.