272426 On the Brownian Coagulation of Colloidal Dispersions
The classical theories of “perikinetic” or Brownian coagulation of colloidal systems proposed by Smoluchowski and Fuchs are applicable to the early stages of aggregation of hard or interacting spheres in dilute dispersions. The analysis can be extended to the full aggregation process by using population balance equations. Herein, it is often assumed that the rate constant of aggregation for dissimilar associations is independent of particle size. These classical analyses also assume that aggregation occurs due to the transport of particles towards each other via a steady-state flux.
A critical evaluation of the assumptions inherent to the classical approaches is carried out. The coagulation dynamics are reassessed using a non-steady-state flux. Brownian Dynamics Simulation (BDS), which is a stochastic-dynamics approach, is employed to provide an accurate description of the phenomenon. BDS results are used as benchmarks for comparisons of the predictions of the non-steady-state flux approach to the classical approach. These comparisons highlight the importance of accounting for the initial transient dynamics, particularly for large particle sizes. Population balance schemes utilizing both the Brownian kernel and a size-independent kernel are employed to study the full aggregation dynamics. BDS results are used to test the differences in the predictions of these two approaches. The size-independent kernel was found to work reasonably well for most cases. The BDS results also establish the concentration range over which the classical theories apply (particle volume fractions ≤ 0.05).
A new model has also been developed that utilizes a chemical potential gradient as the driving force for coagulation. In addition, the diffusion coefficient is chosen to be a function of the particle volume fraction in the dispersion. This accounts for both ‘thermodynamic’ and ‘hydrodynamic’ concentration effects. Thus, this analysis is not restricted to dilute colloidal systems (i.e., systems with particle volume fraction less than 0.05). By directly including non-steady-state dynamics and hydrodynamic interactions, this new approach provides an accurate description of Brownian coagulation for particle volume fractions up to at least 0.40.