Many - Sphere Hydrodynamic Interactions 1 I . Mobilities at Finite Frequencies

A well-known problem in low Reynolds number hydrodynamics 1) is to calculate the hydrodynamic interactions between spherical particles moving in a fluid, as its solution is necessary for understanding the properties of suspensions. While the first treatment of such hydrodynamic interactions dates from 1911 when Smoluchowski 2) analysed the hydrodynamic friction between two spherical particles, there has recently been a revival of interest in this problem3-1°)t. This renewed interest is greatly motivated by recent advances in experimental lightscattering techniques in which multiple scattering is reduced, either by using scattering cells of different sizes"'12), or by using a solvent and solute which have refractive indices that are not too different~3), or still by using a two-beam, two-detector light scattering spectrometerl4). These techniques enable one to single out the effects due to hydrodynamic interactions in suspensions, so that a comparison between theory and experiment can be made. As an example, we note that the experiments by Knops-Werkhoven and Fijnaut ~3) on the mutual diffusion coefficient of dilute silica dispersions were in good agreement with the values obtained theoretically by Batchelor 5) and FelderhoPS). In general, correction terms to e.g. the diffusion constant can, for dilute suspensions, be obtained by taking only hydrodynamic pair interactions into account. Since it was doubtful that this is a reasonable approximation for suspensions which are not dilute, we recently developed a systematic expansion to treat the full many sphere problem~°). This work extended the original analysis