Many-sphere Hydrodynamic Interactions Iii. the Influence of a Plane Wall

The hydrodynamic interactions between spherical particles in a viscous fluid play an essential role in the theory of suspensions’). Characteristic of these interactions via the fluid is their very long range. As a consequence, the influence of boundary walls on properties of suspensions can be of importance even in cases where the vessel containing the suspension is very large. The velocity of sedimentation, for example, becomes infinite in an unbounded suspension a paradoxical situation (noticed by Smoluchowski*)) which can be resolved%) by accounting for the presence of the wall supporting the fluid. The effect of boundary walls on Brownian motion has been studied experimentally by means of light-scattering in a thin film cel13). Such wall effects may also play an important role in recent experiments on two-dimensional ordering of colloidal suspensions in this geometry4). A second consequence of the long range of hydrodynamic interactions is the importance of non-additivity: that two-sphere hydrodynamic interactions do not suffice to describe diffusion in a suspension which is not dilute has been demonstrated both theoretically5) and experimentally6). Recently a scheme has been developed to WSZWI the hydrodynamic interactions of clusters of 2, 3, 4, 5 ) . . . spheres, and applied to a calculation of diffusion coefficient7) and effective viscosity’), valid up to high concentrations. The application of resummation techniques in calculating transport properties of concentrated suspensions has been made possible by the use of general