LOW-REYNOLDS-NUMBER HYDRODYNAMIC INTERACTIONS IN A SUSPENSION OF SPHERICAL-PARTICLES WITH SLIP SURFACES

The motion of two rigid spherical particles in an arbitrary configurat ion in an infinite viscous fluid at low Reynolds numbers is considered . The fluid is allowed to slip at the surfaces of the spheres and the particles may differ in radius. The resistance and mobility functions that completely characterize the linear relations between the forces a nd torques and the translational and rotational velocities of the part icles are analytically calculated in the quasi-steady limit using a me thod of twin multipole expansions. For each function, an expression of power series in r(-1) is obtained, where r is the distance between th e particle centers. The agreement between these expressions and the re levant results in the literature is quite good. Based on a microscopic model, the analytical results for two-sphere hydrodynamic interaction s are used to find the effect of the volume fraction of particles of e ach type on the average settling velocities in a bounded suspension of slip spheres. Our results, presented in simple closed forms, agree ve ry well with the existing solutions for the limiting cases of no slip and perfect slip at the particles surfaces. In general, the particle-i nteraction effects are found to be more significant when the slip coef ficients at the particle surfaces become smaller. Also, the influence of the interactions on the smaller particles is stronger than on the l arger ones. (C) 1997 Elsevier Science Ltd.