Viscosity of Dispersed and Aggregated Suspensions of Spheres

Abstract
Viscosities of suspensions of dispersed spheres and permanent aggregates ranging from doublets and triplets to clusters composed of a very large average number of spheres are reported. In all cases, glass spheres of a very narrow distribution of particle diameter were used and the suspending fluid was a chlorinated biphenyl (Aroclor). Results were obtained using a Couette type viscometer as a function of volume fraction of the dispersed phase. In addition, measurements on the aggregated systems were made as a function of the number of spheres per aggregate with the average aggregate size controlled over a relatively narrow range. Aggregates were obtained by a sintering and sieving technique. For the larger aggregates the shape was generally elliptical. This is the first time rheological data has been reported for suspensions with a dispersed phase composed entirely of permanent aggregates of controlled size, size distribution, and shape. The results for the dispersed and aggregated systems, with concentrations as high as Φ=0.5 volume fraction solids, are shown to fit the Mooney equation over the entire concentration range, if the Einstein coefficient is increased for the aggregated systems to a limiting maximum values as suggested by Gillespie and if experimental values of the maximum volumetric packing fraction of solids are used. The value of the Einstein coefficient is shown to be a function of the hydrodynamic volume of the aggregates and reach a maximum value for the larger aggregates.