(665d) The Importance of Non-Ideal Diffusion and Entropic Packing Effects in Brownian Aggregation of Hard Spheres

Colloidal dispersions are ubiquitous. Hence, understanding their stability is an important scientific endeavor. Stability of colloidal dispersions is a key challenge in the manufacture of coatings, environmental pollution, formulation of food products, drug delivery, membrane fouling, inkjet printing, and flow assurance in oil and gas production. One of the destabilization mechanisms is perikinetic aggregation, where particle transport occurs by diffusion. This was first described by Smoluchowski who considered the steady-state aggregation of initially mono-disperse hard spheres with an initial uniform concentration profile. This model matches simulation results for aggregation rates only in dilute systems, i.e., for particle volume fractions, φ, less than 0.0005 [1]. However, for most practical applications, particle volume fractions can be as high as φ = 0.4. A limited number of theoretical [2] and semiempirical approaches [3] have been developed for perikinetic aggregation in concentrated systems. These models predict aggregation rates that are higher than the predictions of the Smoluchowski model by an order of magnitude. Nonetheless, understanding of the mechanism that leads to the enhancement of aggregation kinetics is still limited. Transient effects have been shown to increase the rates of perikinetic aggregation, because of the unsteady-state flux that drives aggregation at short times [1]. The aggregation rates predicted by this model, however, only match Brownian Dynamics Simulations (BDS) results for φ up to about 0.1. In addition to these effects, non-ideal particle diffusion and entropic packing effects are found to be important, especially at higher concentrations. The Smoluchowski model assumes that particle diffusion is driven by a concentration gradient. This is strictly valid only in the infinite dilution limit. The more general approach is to consider the non-ideal diffusion of particles driven by a chemical potential gradient. Additionally, the initial uniform concentration profile used in the Smoluchowski model becomes unrealistic at high volume fractions. Entropic packing effects lead to a local ‘liquid-like’ structure in the concentrated dispersions. We have developed a new model based on the `liquid-state’ dynamical density-functional theory that accounts for transient, non-ideal particle diffusion, and packing effects in perikinetic aggregation. The predictions of the new model for hard-sphere dispersions are in excellent agreement with BDS results for the time dependence of monomer number density and the half-times of aggregation for φ up to 0.35, and with gelation times (at which the volume fraction reaches the limit of a freezing transition) reported by Lattuada [2]. Thus, transient, non-ideal particle diffusion, and packing effects result in enhancement of aggregation kinetics of hard spheres. The model is then extended to account for thermodynamic and hydrodynamic interactions whose effects are re-evaluated for concentrated dispersions. Predictions of the model with interactions also agree with BDS results. Additionally, the transition between perikinetic and shear-induced or orthokinetic aggregation is re-examined and found to depend not only on the Peclet number as thought earlier, but also on time and particle volume fraction.

[1] A. V. Kelkar, J. Dong, E.  I. Franses, and D. S. Corti, J. Colloid Interface Sci., 389, 188, (2013)

[2] M. Lattuada, J. Phys. Chem. B, 116, 120, (2012)

[3] M. Heine and S. E. Pratsinis, Langmuir, 23, 9882, (2007)