On the hydrodynamic interaction of two coaxial spheres oscillating in a viscous fluid with a slip regime

The purpose of this study is to examine the impact of slip length on the movement of two oscillating rigid spheres swimming through Stokes flow. Moreover, the two rigid spheres oscillate about the axis of symmetry through the line connecting their poles. The global solution of the Stokes equations is composed of the superposition of the fundamental solutions in the two spherical coordinate systems established at the origin of each sphere and obtained by a collocation technique. Besides, the force coefficients in-phase (IP) and out-of-phase (OOP) upon each sphere are calculated and presented for one sphere for distinct parameters of the radii ratio, separation distance, velocity ratio, and slip length graphically and tabularly. Streamline patterns are shown for different parameters. Furthermore, we found from our analysis that the impress of slip-length and frequency is more effective on both the IP and OOP where at the low frequency they retarded with the increase of slip-length and raised at the high frequency. Eventually, the precision of the numerical procedure has been examined versus distinguished solutions for two spheres with no-slip surfaces.