Comparing the power law constant (n) for mono- and bi-dispersed filled slurries: using percolation theory concepts

There is an enduring interest in concentrated particulate filled slurries in many industries for a wide variety of products and processes. In previous research, a collection of experimental procedures provided velocity profiles, pressure drops and power law constants for slurries flowing in a tube. A model previously developed for the power law, based on mono-disperse fillers and on percolation theory concepts, is reviewed and extended to bi-modal slurries. The model for the power law constant, n, is shown to be only a function of the volume of non-dissipating clusters in the slurry. Experimental results are used to compare the effects of mono-modal and bi-modal fillers on the viscosity and n in the composite flow of filled Newtonian carrier fluids. The data and analysis demonstrate that n can be related to the ratio of energy dissipated by the slurry divided by the dissipation of a Newtonian fluid flowing under similar conditions. The power law parameters were developed using Bingham model constants employed to approximate dissipation in tube flow. The power law constant was found to be smaller for the bi-modal systems than for mono-modal slurries at the same total filler concentration.