Three particle hydrodynamic interactions in suspensions

We present an outline of a method to determine the components of the grand mobility matrix of a system of three hydrodynamically interacting spherical particles with arbitrary particle configuration. We present the results of a study of some components of the grand mobility matrix in the case of two special configurations. The results derived for one configuration, with the three particles on a line, are compared with some results from the literature. In the other configuration, we have put the particles on the corners of an equilateral triangle. Besides the study of the mobility matrix, we have derived virial expansions for the translational and rotational self-diffusion coefficients up to quadratic order in φ, the volume fraction. Three particle contributions are incorporated in these expressions. We also present virial expansions, where three particle hydrodynamic interactions are included, for the translational and rotational sedimentation velocities. There are some results available in the literature in the case of the translational self-diffusion coefficient and the translational sedimentation velocity, which are different from our results. We discuss these differences. As far as we know, the results of the three particle contribution to the virial expansions of the rotational self-diffusion coefficient and the rotational sedimentation velocity are new. All the virial expansions mentioned above are compared with experimental results and simulation data from the literature.