Interactions of two slip spheres moving side by side in a viscous fluid

Abstract

The general motion of two solid spherical particles with different velocities and angular velocities perpendicular to the line joining their centers (non-axisymmetric problem) is investigated. The particles can differ in their sizes, and allowing for the hydrodynamic slip at their surfaces. In order to solve the Stokes equations, general solutions are constructed using two spherical coordinate systems based on the centers of the particles, and the boundary conditions at their surfaces are satisfied by the collocation technique. Numerical results displaying how the resistance coefficients acting on each sphere are obtained with good convergence and represented graphically for various values of slip lengths, size ratio, separation parameter, relative translational and angular velocities of the particles. The normalized force and couple exerted on each particle reach to the single particle limit as the distance between the centers grows large enough and each particle may then be translated and rotated independently of each other. The accuracy of the numerical technique has been tested against the known analytical solution for two spheres with no-slip surfaces.