Viscosity scaling in concentrated dispersions and its impact on colloidal aggregation

Gaining fundamental knowledge about diffusion in crowded environments is of great relevance in a variety of research fields, including reaction engineering, biology, pharmacy and colloid science. In this work, we determine the effective viscosity experienced by a spherical tracer particle immersed in a concentrated colloidal dispersion by means of Brownian dynamics simulations. We characterize how the effective viscosity increases from the solvent viscosity for small tracer particles to the macroscopic viscosity of the dispersion when large tracer particles are employed. Our results show that the crossover between these two regimes occurs at a tracer particle size comparable to the host particle size. In addition, it is found that data points obtained in various host dispersions collapse on one master curve when the normalized effective viscosity is plotted as a function of the ratio between the tracer particle size and the mean host particle size. In particular, this master curve was obtained by varying the volume fraction, the average size and the polydispersity of the host particle distribution. Finally, we extend these results to determine the size dependent effective viscosity experienced by a fractal cluster in a concentrated colloidal system undergoing aggregation. We include this scaling of the effective viscosity in classical aggregation kernels, and we quantify its impact on the kinetics of aggregate growth as well as on the shape of the aggregate distribution by means of population balance equation calculations.