Particles in Thickening: Mathematical Model

Abstract

A mathematical model to describe the changes in the particle size distribution immediately below the solid/liquid interface in gravity thickening was formulated and tested against experimental results. The distribution is predicted to change by coagulation and differential sedimentation. Modifications to the collision efficiency functions for Brownian motion, fluid shear, and differential sedimentation were necessary to account for the high concentrations in thickening. The model correctly predicted the observed trends for both the coagulation and differential sedimentation aspects of the experimental results for changes with time, solids concentration, particle stability, and the subsidence velocity of the interface. The model is limited by the fact that the subsidence velocity cannot be predicted and by the simplified approach to the hydrodynamics of differential sedimentation which is incorporated. The substantial agreement between the model and experimental results indicates that the conceptual approach of the model is well‐founded. The lack of agreement in some cases also has led to further insight into the mechanisms of particle transport in a concentrated heterodisperse suspension.