The application of dynamic clustering data to the sedimentation rates of concentrated suspensions

A modified Stokes equation is proposed for the settling of concentrated suspensions of spherical particles in Newtonian fluids. The proposed hindered settling model was derived semi-analytically incorporating data obtained on dynamic particle clustering in concentrated suspensions by Graham and Bird. The approach differs from previous models which either neglected the influence of one particle on another or treated these interactions in an empirical manner with minimal physical or mechanistic basis for their design. The phenomenon of dynamic clustering which has recently been observed experimentally and shown to occur in flowing suspensions and sedimentation provides the basis for this study. Cluster size distributions are estimated based on suspension properties and a summation of Stokes terms provides a settling velocity prediction of concentrated systems. The validity of the model is supported by comparing calculated sedimentation rates with measured values for a number of data sets obtained from a variety of different authors.