Shear Thickening and Scaling of the Elastic Modulus in a Fractal Colloidal System with Attractive Interactions

Dilute oil dispersions of fractal carbon black particles with attractive Van der Waals interactions display continuous shear thickening followed by shear thinning at high shear rates. The shear thickening transition occurs at ${\dot{\gamma }}_c\approx {10}^2-{10}^3{s}^{-1}$ and is driven by hydrodynamic breakup of clusters. Pre-shearing dispersions at shear rates $\dot{\gamma }>{\dot{\gamma }}_c$ produces enhanced-modulus gels where $G’ \sim \sigma_{pre-shear}^{1.5-2}$ and is directly proportional to the residual stress in the gel measured at a fixed sample age. The observed data can be accounted for using a simple scaling model for the breakup of fractal clusters under shear stress.