The role of hydrodynamic interactions on the aggregation kinetics of sedimenting colloidal particles

Prediction of the aggregation rate of nanoparticles in porous media in the diffusion-controlled regime

The fate and aggregation of nanoparticles (NPs) in the subsurface are important due to potentially harmful impacts on the environment and human health. This study aims to investigate the effects of flow velocity, particle size, and particle concentration on the aggregation rate of NPs in a diffusion-limited regime and build an equation to predict the aggregation rate when NPs move in the pore space between randomly packed spheres (including mono-disperse, bi-disperse, and tri-disperse spheres). The flow of 0.2 M potassium chloride (KCl) through the random sphere packings was simulated by the lattice Boltzmann method (LBM). The movement and aggregation of cerium oxide (CeO2) particles were then examined by using a Lagrangian particle tracking method based on a force balance approach. This method relied on Newton's second law of motion and took the interaction forces among particles into account. The aggregation rate of NPs was found to depend linearly on time, and the slope of the line was a power function of the particle concentration, the Reynolds (Re) and Schmidt (Sc) numbers. The exponent for the Sc number was triple that of the Re number, which was evidence that the random movement of NPs has a much stronger effect on the rate of diffusion-controlled aggregation than the convection.

Aggregation of nanoparticles and morphology of aggregates in porous media with computations

HYPOTHESIS

The main hypothesis is that the aggregation process for nanoparticles (NPs) propagating in porous media is affected by the structure of the flow field as well as by the properties of the primary NPs. If this were true, then the aggregation could be predicted and controlled. However, to obtain reliable results from computations, one needs to account for the interactions between the NPs as well as the details of the fluid velocity, thus making advances over prior efforts that either ignored the aggregation of NPs, or used probabilistic methods to model aggregation.

EXPERIMENTS

Computational experiments were conducted using the lattice Boltzmann method in conjunction with Lagrangian particle tracking (LPT). The LPT accounted for the physicochemical interaction forces among NPs. Computationally obtained aggregation kinetics and fractal dimensions of Cerium oxide (CeO2) particles, suspended in potassium chloride (KCl) solutions with different concentration, were verified against experimental results. The model was then employed to investigate the effects of ionic strength, fluid velocity, and particle size on the aggregation kinetics and the aggregate morphology, as NPs propagated in the pore space between randomly packed spheres.

FINDINGS

The aim of this study was to develop a computational model to simulate the aggregation of NPs and obtain the morphology of aggregates in confined geometries, based on the physics of NP interactions and the flow field. The most important factor that impacted both the aggregation process and the aggregate structure was found to be the concentration of the electrolyte. The pore velocity influenced the aggregation kinetics and the NP fractal dimension, especially in diffusion-limited aggregation. The primary particle size affected the diffusion-limited aggregation kinetics and the fractal dimension of reaction-limited aggregates noticeably.

Hydrodynamic lubrication in colloidal gels

Colloidal gels are elasto-plastic materials composed of an out-of-equilibrium, self-assembled network of micron-sized (solid) particles suspended in a fluid. Recent work has shown that far-field hydrodynamic interactions do not change gel structure, only the rate at which the network forms and ages. However, during gel formation, the interplay between short-ranged attractions leading to gelation and equally short-ranged hydrodynamic lubrication interactions remains poorly understood. Here, we therefore study gelation using a range of hydrodynamic descriptions: from single-body (Brownian Dynamics), to pairwise (Rotne-Prager-Yamakawa), to (non-)lubrication-corrected many-body (Stokesian Dynamics). We confirm the current understanding informed by simulations accurate in the far-field. Yet, we find that accounting for lubrication can strongly impact structure at low colloid volume fraction. Counterintuitively, strongly dissipative lubrication interactions also accelerate the aging of a gel, irrespective of colloid volume fraction. Both elements can be explained by lubrication forces facilitating collective dynamics and therefore phase-separation. Our findings indicate that despite the computational cost, lubricated hydrodynamic modeling with many-body far-field interactions is needed to accurately capture the evolution of the gel structure.

Hydrodynamic stability criterion for colloidal gelation under gravity

Attractive colloids diffuse and aggregate to form gels, solidlike particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever-decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels.