An effective gravitational temperature for sedimentation

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Abstract
The slow sedimentation of suspensions of solid particles in a fluid results in complex phenomena that are poorly understood. For a low volume fraction (phi) of particles, long-range hydrodynamic interactions result in surprising spatial correlations in the velocity fluctuations; these are reminiscent of turbulence, even though the Reynolds number is very low. At higher values of phi, the behaviour of sedimentation remains unclear; the upward back-flow of fluid becomes increasingly important, while collisions and crowding further complicate inter-particle interactions. Concepts from equilibrium statistical mechanics could in principle be used to describe the fluctuations and thereby provide a unified picture of sedimentation, but one essential ingredient--an effective temperature that provides a mechanism for thermalization--is missing. Here we show that the gravitational energy of fluctuations in particle number can act as an effective temperature. Moreover, we demonstrate that the high-phi behaviour is in fact identical to that at low phi, provided that the suspension viscosity and sedimentation velocity are scaled appropriately, and that the effects of particle packing are included.