Rheological analysis of particle aggregation in a colloidal suspension of carbon black particles

We examine scaling theories to estimate microstructural parameters of fractal aggregates in a colloidal suspension. The scaling theories are based on fractal theories and rheological properties of the colloidal suspension. Rheological measurement in oscillatory and steady shear modes is performed for colloidal suspensions of 56 nm carbon black particles in Newtonian ethylene glycol at the particle volume fractions φ ranging from 0.005 to 0.05. Elastic modulus G’ of the colloidal suspension at φ = 0.02-0.05 in the state of colloidal gel is used to estimate fractal dimension df of the aggregates. Steady-shear measurement gives yield stress τy as a function of φ. Shear dependence of the aggregate radius R is given by a power-law scaling, i.e., R∝S−m, where S is the shear rate. The power-law exponent m is estimated from df and a scaling relation between τy and φ. The estimation gives df = 2.14 and m = 0.33. The parameters df and m which can be determined by either direct measurement or theoretical calculation are used to establish a microrheological model for predicting shear viscosity of aggregated suspension as a function of φ and S. Both the concentration dependence and the shear dependence of aggregates are combined to obtain an expression for the shear viscosity. Hydrodynamic interaction effect among the aggregates is roughly considered in calculating average shear stress on the aggregate. It is found that this consideration critically contributes to behavior similarity with experimental result. It is shown that the predictions by the model reasonably agree with the experimental result.