Flow of non-Newtonian power law liquids through packed and fluidized beds

Abstract

The creeping flow of power law liquids through assemblages of spherical particles has been studied theoretically. The inter-particle interactions are modelled via the zero vorticity cell model. The governing equations have been solved numerically to obtain the theoretical estimates of the drag force experienced by an assemblage placed in a streaming power law fluid. The results reported herein encompass wide ranges of fluid behaviour (values of power law index) and bed voidage thereby covering packed and fluidized bed conditions. Detailed comparisons with experimental data suggest that this theory can be used to predict pressure drop for power law fluid flow in packed beds as well as velocity-bed expansion characteristics for a fluidized bed. By analogy with the Newtonian case, intuitively, one would expect these results to be applicable to hindered settling in power law fluids, and indeed this is borne out by the limited amount of data covering the range 1≥n≥0.8 available in the literature.