The self-assembly of colloidal particles has been widely addressed in the literature due to its relevance in various systems such as paints, ceramics, waste water, food products or pharmaceuticals. The Smoluchowski’s equation has provided a basis for the description of the kinetics of aggregation of colloidal particles under diffusing limited conditions. Nevertheless, its application is restricted to dilute conditions, where several key assumptions are justified. Among others, the viscosity of the dispersion is assumed to be close to the solvent viscosity. However, the viscosity significantly rises upon an increase in particle concentration and upon aggregate formation, which then tends to decrease the aggregation rate.
In this work, we propose a correction to the conventional diffusion-limited aggregation kernel which accounts for the viscosity effects arising in concentrated colloidal systems. First, by means of computer simulations and theoretical arguments, we derive an expression for the diffusion coefficient of a tracer particle immersed in a concentrated dispersion of hard sphere particles. We investigate how the diffusion coefficient of the tracer particle depends on the host volume fraction and on the size ratio of tracer and host particles. The results are then interpreted in terms of an effective size-dependent viscosity which is experienced by the tracer particle: while sufficiently large tracer particles experience the macroscopic viscosity of the colloidal dispersion, small tracer particles rather experience the solvent viscosity. Finally, we introduce this size-dependent viscosity in the aggregation kernel and perform Population Balance Equations simulations to quantify the impact of a viscosity increase on the kinetics of aggregation and on the particle size distribution.
lucrece.nicoud@chem.ethz.ch
