Rheological estimation of aggregate size for a colloidal suspension of carbon black particles

Abstract

Colloidal aggregation is quantitatively characterized by a rheological analysis of the colloidal suspension at various particle concentrations. The rheological analysis is combined with fractal concept to estimate the compactness, size, and size variation with shear stress on colloidal aggregates. The rheological measurement is carried out for a colloidal suspension of 24 nm carbon black particles suspended in ethylene glycol. The particle concentration ranges from 6.0 to 8.5 percent in volume, which is non-dilute regime where colloidal gelation occurs. Elastic modulus behavior with the particle concentration provides fractal dimension of aggregates. With the fractal dimension, concentration-dependent shear stress behavior is used to estimate aggregate size and its variation with shear stress through a rheological modeling. The estimated fractal dimension of aggregate is 2.020 and the average aggregate size exponentially decreases with the shear rate in the range 1152.24 nm at 1 s−1 to 150.00 nm at 1000 s−1. These estimations are compared with those from optical measurement using static small-angle X-ray scattering (SAXS) technique. The SAXS analysis gives the fractal dimension of 2.495 and the average aggregate size is 320.56 nm. It is found that the optical measurement gives slightly higher fractal dimension and the aggregate size is numerically close to that predicted one around the shear rate 68.7 s−1 where steep size reduction turns into being slow.