Effective Gravitational Temperature in Sedimentation

Abstract

Particle Image Velocimetry (PIV) is used to study the slow settling motions of spheres in suspensions ranging from dilute to highly concentrated, 0.0001 less than phi less than 0.50. During sedimentation, particle velocity fluctuations are found to be organized into regions of characteristic size xi approx. parallel to (alpha)phi(sup -1/3). A simple model, based upon buoyant mass fluctuations (Delta)m given by random density fluctuations in a region of size xi, accurately predicts the magnitudes of the velocity fluctuations (Delta)V. We also find a new universal relation for particle diffusion during sedimentation. It can be written in a Stokes-Einstein form as D approx. (Delta m g xi)/(6pi eta xi), where the effective temperature Delta m g xi is the gravitational potential energy of density fluctuations. In addition related experiments examining inertial effects and transient states, that are aimed at uncovering the origin of the new length-scale xi, will also be given.