Effective Gravitational Temperature in Sedimentation
Particle Image Velocimetry (PIV) is used to study the slow settling motions of spheres in suspensions ranging from dilute to highly concentrated, 0.05 less than phi less than 0.50. During sedimentation, velocity fluctuations are found to be organized into regions of characteristic size L approximately 11 a phi(exp-1/3) and buoyant mass DELTA m given by the rms density fluctuations in a region of size L(sup 3) assuming random statistics with excluded volume effects. A simple model accurately predicts the magnitudes of the velocity fluctuations DELTA V. Finally, we find a new universal relation for particle diffusion during sedimentation that can be written in a Stokes-Einstein type form as D approximately (DELTA mg L)/(6 pi eta L), where the effective temperature DELTA mg L is the gravitational potential energy of density fluctuations.