(715d) [Invited Talk] New Models of Brownian Aggregation and Sedimentation Rates of Colloidal Dispersions
Stabilizing colloidal dispersions against both aggregation and sedimentation is a key challenge in the manufacture of coatings, formulation of food products, drug delivery, membrane fouling, inkjet printing, and flow assurance in oil and gas production. If initially separate particles begin to aggregate at a sufficient rate, ever larger clusters of particles are formed, with the dispersion eventually separating into two distinct layers because of settling (the particles are more dense than their suspending medium) or creaming (the particles are less dense). One of the destabilization mechanisms is perikinetic, or Brownian, aggregation, where particle transport occurs by diffusion. This mechanism was first described by Smoluchowski (S), who considered the steady-state aggregation of initially mono-disperse hard spheres with an initial uniform concentration profile. The S model matches simulation results for aggregation rates only in dilute systems, i.e., for particle volume fractions, Ï?, less than 0.0005. For most practical applications, however, particle volume fractions can be as high as Ï? = 0.4, in which aggregation rates are up to two orders of magnitude faster than the predictions of the S model.
I first discuss recently developed theoretical models that accurately describe Brownian aggregation at moderate to high volume fractions. Transient effects are shown to increase the rates of aggregation, because of the unsteady-state flux that drives aggregation at short times. Entropic packing effects and non-ideal particle diffusion (i.e., mass transfer is driven by the gradient of the particlesâ?? chemical potential and not concentration) are also found to be important, especially at higher volume fractions. One particular model, based on the â??liquid-stateâ? dynamical density-functional theory (DDFT), yields predictions which are in excellent agreement with Brownian Dynamics (BD) simulation results for the time dependence of monomer number density and the half-times of aggregation forÂ Ï? up to 0.35, and with some gelation times (the times for which the effective volume fraction reaches a freezing transition) reported in the literature. I then present the extension of the DDFT-based model to account for interparticle forces between the aggregating particles, which invokes ideas from various perturbation theories of liquids. For dispersions of particles with purely attractive interactions, the classical Fuchs-Smoluchowski (FS) model underpredicts the aggregation rates by up to 1000 fold. In the presence of strong interparticle repulsive forces, the FS model predictions are in fair agreement with the BD simulation results for dilute systems with particle volume fractionsÂ Ï? << 0.1. In contrast, the predictions of the new DDFT-based model compare favorably with the BD simulation results, in both cases, up toÂ Ï? = 0.3. A new quantitative measure for colloidal dispersion stability, different from the classical FS stability ratio, is proposed on the basis of aggregation half-times. Overall, an improved mechanistic understanding of Brownian aggregation is obtained for concentrated particle dispersions.
Finally, I discuss an application of one of the above aggregation models for the prediction of the sedimentation times of colloidal dispersions for which aggregation and sedimentation processes are coupled. Aggregation and net sedimentation times for clusters of certain particle sizes and fractal dimensions are generated and then compared, which provides an upper-bound of the net sedimentation time of the entire dispersion. Moreover, the effective sizes, density differences, and volume fractions of the clusters are obtained. The predicted trend of the net sedimentation time is fairly consistent with the experimental data of the sedimentation times of colloidal silica microspheres of diameters 350, 505 and 750 nm, as measured in water and aqueous NaBr solutions of concentrations ranging from 50 to 1000 mM.