(450a) Rheology of Dilute Suspensions of Fractal Clusters with Arbitrary Structure
The viscosity of dispersions containing particulate solid has been studied in the past, however, specifically only for well-defined geometries of the particles. The well studied geometrical shapes predominantly encompass spheres, and prolate or oblate spheroids. In practice the processing of solid suspensions, and in particular coagulation of dispersions of colloidal particles, leads to the formation of clusters with a great diversity of shapes and sizes. Several works in the literature pointed out that the viscosity of suspension strongly depends on the geometry of the contained clusters, their concentration in the suspension, their orientation with respect to the flow, and the magnitude of the applied shear. Little literature has been published since Einstein's pioneering work on the dependence of viscosity of suspensions on clusters with arbitrarily shape and structure.
In the present work, we have developed a generalized framework to account for the contribution to the viscosity of suspensions of clusters, made of identical spherical particles, with arbitrary shape and structure. A wide database of clusters has been created, which have been generated through a combination of different Monte-Carlo methods, and covers a broad range of fractal dimension values, from 1.8 to 3, as well as aspect ratios, and number of particles. In order to determine their hydrodynamic properties, Stokesian Dynamics was implemented and used to estimate the grand resistance matrix of these clusters, treated as rigid bodies. The grand resistance matrices of several clusters with the same mass and fractal dimension have been averaged, in order to account for the variability in the structure of clusters, and to create an average representative cluster with given properties. These average matrices have been used to compute the clusters' first order contribution to the orientation averaged bulk stress tensor, which was obtained by performing Brownian dynamic simulations on individual clusters, including coupling between their rotational and translational motion. The viscosity of dilute suspension was obtained from the average bulk stress tensor for different flow field configurations, and shear rate values.
Suspension, Stokesian dynamics, rigid body