Hydrodynamics of creeping flow of power law liquids through particle assemblages

Abstract

The equations of motion describing the creeping flow of power law liquids past particle assemblages have been solved numerically using the finite element method. The free surface cell model has been employed to analyse the hydrodynamic interactions between the particles. Detailed flow field features such as stress profiles on the particles and macroscopic quantities such as drag coefficient have been predicted for a wide range of fluid behaviour (1 ≥ n ≥ 0.2) and bed voidage, (0.3 ≤ ε ≤ 0.9999) thereby covering the complete spectrum of conditions encountered during the fluid flow through fixed, fluidized and distended beds. The observed dependences of the stress profiles and the drag coefficients on the power law index and bed voidage have been explained qualitatively with the aid of physical reasoning and order of magnitude considerations. Finally, the numerical results reported herein are compared with the appropriate experimental results available in the literature.