An efficient scheme is presented for the numerical calculation of hydrodynamic interactions of many spheres in Stokes flow. The spheres may have various sizes, and are freely moving or arranged in rigid arrays. Both the friction and mobility matrix are found from the solution of a set of coupled equations. The Stokesian dynamics of many spheres and the friction and mobility tensors of polymers and proteins may be calculated accurately at a modest expense of computer memory and time. The transport coefficients of suspensions can be evaluated by use of periodic boundary conditions.

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A calculation is presented for the effect of the hydrodynamic interaction on the diffusion-controlled rate coefficient for particles that coalesce by diffusion under the influence of an interaction potential. The hydrodynamic effect is found to make a substantial reduction in the rate compared to the Debye m~el which includes only the effects of diffusion and the forces between the reacting particles. For the case where the particles are hard spheres the reduction is 46%. For ionic species the reduction varies between 25% and 60% depending on the extent of attraction or repulsion.

Animalcules can swim in a viscous fluid at low Reynolds number and low Stokes number by moving their body parts in a periodic coherent fashion. The swimming motion is analyzed in a simple model of beads subject to periodic one-body forces. In the model the animalcule is held together by reactive two-body forces. The nonlinear equations of Stokesian dynamics are formulated on the basis of the Oseen tensor. Under suitable conditions the solution of the equations of motion has a limit cycle character. The limit cycle is analyzed for small amplitude motion in the framework of a bilinear theory. The linearized equations of motion are solved analytically for longitudinal and transverse modes of motion for a linear trimer, and expressions are derived for the swimming velocity and the mean dissipation to second order in the force amplitude. The results of the bilinear theory are compared to numerical solution of the nonlinear equations of motion. A similar comparison is made for chains of twelve beads.

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A theory for the concentration dependence of the rate of diffusion-controlled reactions is formulated. One of the reacting partners is taken to be a collection of static sinks. The steady state situation for a random distribution of these sinks is studied. The rate coefficient is predicted to increase with concentration of sinks and the dependence on concentration is shown to be nonanalytic.

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