Exact periodic solutions are found for the relative motion of three spheres sedimenting in a Stokes fluid. Nearby solutions are found to be nearly periodic for a long time. Existence of the exact periodic solutions is proved using the point-particle approximation and symmetry properties of Stokes equations. Numerical simulations for finite-sized particles are performed using a method of multipole expansions.
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Caflisch et al. (1988) studied this question.
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