Experimental observations of non-continuum effects in suspensions: Falling-ball versus towed-ball rheometry

Abstract

Viscosity is an intrinsic material property of Newtonian liquids, independent of the fluid’s strain rate and state of stress. Experiments performed on a test sphere traversing a homogeneous Newtonian fluid should establish the same viscosity whether by measuring the force on a test sphere moving at a constant velocity or by measuring the velocity of a test sphere animated by a constant force. Here we report on the results of experiments designed to compare constant force and constant velocity experiments for test spheres translating through suspensions of non-colloidal, neutrally buoyant spheres dispersed in viscous Newtonian fluids. Measurements were made of the apparent viscosity of a suspension relative to that of the pure fluid using either a settling ball animated by a constant gravitational force (ηrF) or a towed ball translating with a constant velocity (ηrV). The primary experimental parameters were the solids fraction (ϕ) in the suspension, and the ratio of the radius of the suspended spheres, as, to the radius of the test sphere, ab(λ=as∕ab). As expected, the constant velocity and constant force experiments produced indistinguishable ηr’s for the homogeneous Newtonian fluids. However, over the range of suspension concentrations examined, ηrV was found to be significantly larger than ηrF. In all of the dilute and moderately concentrated suspensions, and in concentrated suspensions with very narrow size distributions, both ηrV and ηrF were found to be independent of the radius and the velocity of the test sphere. In concentrated suspensions possessing broad particle size distributions, both ηrV and ηrF were found to be shear thinning. However, the ratio ηrV∕ηrF was observed to be independent of the shear rate. Even the most dilute suspensions examined proved to be non-Newtonian in the sense that ηrV∕ηrF>1, with ηrV∕ηrF observed to increase linearly with ϕ as the latter increased from 0.1 to 0.5. Over the range of our data, ηrV∕ηrF decreases and approaches 1 as λ decreases for all ϕ.