Correlations and Gravitational Temperature in Settling Suspensions

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 equal to 11 a phi(exp -1/3) and buoyant mass DELTA m given by the rms density fluctuations in a region of size L(exp 3) assuming random statistics. A simple model incorporating the suspension viscosity and excluded volume effects accurately predicts the magnitudes of the observed velocity fluctuations DELTA V. These lead to a universal relation for particle diffusion that can be written in a Stokes-Einstein type form as D approximately equal to (DELTA m gL)/(6 pi (eta)L).