Viscosity contribution of an arbitrary shape rigid aggregate to a dilute suspension

The study of rheological response of solid suspensions is essential in understanding the relationships governing their kinematics and dynamics. However the study is complicated mainly by the complex interplay between suspension rheology and hydrodynamic behavior of the suspended solids, which for most of the practically occurring situations have complex and arbitrary shapes, and exact equations accounting for their hydrodynamic contribution are not available. For this reason, using a recently developed methodology capable of computing the average rigid body resistance matrix of arbitrary shaped clusters made of uniform sized spheres, Brownian dynamic simulations under shear conditions are performed for clusters with different geometries with the objective of estimating their intrinsic viscosity. The population of clusters chosen encompassed a broad range of morphologies, such as fractals with a wide range of masses and fractal dimension values, dense clusters with spherical and spheroidal aspect ratios, similar to those produced during coagulation experiments of colloidal suspensions. It was found that fractal clusters with low fractal dimensions and spheroidal clusters have sufficient structural anisotropies to show deviations from Einstein's relationship, and display a moderate shear thinning behavior, as well as a non-negligible linear viscoelasticity. On the other hand, clusters with high fractal dimensions tend to behave progressively more like spheres as their fractal dimension increases. We also found that the intrinsic viscosity of all clusters, independent of their morphology, can be quantitatively predicted by means of an equivalent ellipsoid model, in which clusters are modeled as ellipsoids with the same principal moments of inertia.