Brownian dynamics simulations of shear-induced aggregation of charged colloidal particles in the presence of hydrodynamic interactions

HYPOTHESIS

In spite of the abundant literature on Brownian simulations of the aggregation behavior of colloidal suspensions both under quiescent conditions and in the presence of shear, few works performed simulations including the effect of hydrodynamic interactions. Even fewer works have investigated the effects of shear on the aggregation of electrostatically-stabilized colloidal suspensions.

SIMULATIONS

In this work, we employed Brownian dynamics simulations implementing the Rotne-Prager-Yamakawa approximation to account for hydrodynamic interactions and investigated the aggregation kinetics of electrostatically-stabilized colloidal suspensions exposed to simple shear, for various Péclet number values, particle volume fractions and surface potential values.

RESULTS

The increase in Péclet number (i.e., in the shear rate), leads to an overall increase in the aggregation rate and the formation of large aggregates that, for sufficiently high volume fractions, rapidly grow, leading to either breakup and restructuring phenomena or percolation of the system. In some cases, a bimodal distribution of the cluster population was observed. Our simulations further indicate that at the highest Péclet, the aggregation dynamics is independent of the energy barrier and entirely controlled by shear. A comparison with a simple BD method reveals that neglecting long-range hydrodynamic interactions leads to a substantial underestimation of the aggregation rate.

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

The aggregation kinetics of sedimenting colloidal particles under fully destabilized conditions has been investigated over a wide range of particle volume fractions (Φ) and Péclet numbers (Pe) using the recent PSE algorithm implementing the Rotne-Prager-Yamakawa (RPY) approximation for long-range Hydrodynamic Interactions (HI). Fast Lubrication Dynamics (FLD) and simple Brownian Dynamics (BD) methods have also been employed to assess the importance of long range hydrodynamic interactions on the resulting dynamics. It has been observed that long-range hydrodynamic interactions are essential to capture the fast aggregation rates induced by the increase in sedimentation rate of clusters with increasing mass, which manifests with an explosive-like cluster growth after a given induction time. On the contrary, simulations employing only short-range hydrodynamic interactions (such as FLD) and BD (which neglects completely hydrodynamic interactions) are incapable of predicting this very rapid kinetics, because sedimentation simply leads to all particles and clusters moving vertically with identical velocity. It has been observed that at high volume fractions and low Pe values, a gel point can be formed and a phase diagram predicting when gelation is reached has been obtained. It was also observed that, as Pe increases, the anisotropy of the resulting clusters decreases, suggesting that denser clusters with spherical-like morphology are formed due to cluster breakage and restructuring. We can conclude that long-range hydrodynamic effects are of crucial importance in understanding the aggregation dynamics of settling clusters, revealing important features of the complex interplay between sedimentation, and colloidal interactions.

Numerical investigation of the respective roles of cohesive and hydrodynamic forces in aggregate restructuring under shear flow

HYPOTHESIS

Aggregate structure is conditioned by a balance of cohesive forces between primary particles and hydrodynamic forces induced by the surrounding flow. Numerical simulations for different ratios between radial and tangential components of cohesive forces to hydrodynamic forces should highlight the role of the each force in aggregate restructuring under shear flow.

EXPERIMENTS

Aggregates sharing similar morphological characteristics were algorithmically created. The forces between primary particles were accounted for using models taken from the literature. Aggregates with different cohesive forces were then submitted to shear by imposing a shear stress in the liquid phase. Hydrodynamic forces were calculated following two approaches: first, with a free draining approximation to extract general trends, then with immersed boundaries in a lattice Boltzmann flow solver to fully resolve the flow and particle dynamics.

FINDINGS

Aggregate structural changes were tracked over time and their stable final size, or eventual breakage, was recorded. Their final structure was found to depend little on normal cohesive forces but is strongly impacted by tangential forces. Normal forces, however, strongly affect breakage probability. Furthermore, resistance to deformation at the aggregate scale induces a flow disturbance that reduces drag forces compared to the free-draining approximation, significantly impacting aggregate restructuring.

Shear-Induced Heteroaggregation of Oppositely Charged Colloidal Particles

This paper investigates numerically the shear-induced aggregation of mixed populations of colloidal particles leading to the formation of clusters. Suspensions with different amounts of positively and negatively charged colloidal particles are simulated. To resolve the aggregation kinetics and structural properties of the formed clusters, we resort to a mixed deterministic-stochastic simulation method. The method is built on a combination of a Monte Carlo algorithm to sample a statistically expected sequence of encounter events between the suspended particles and a discrete element method built in the framework of Stokesian dynamics to simulate the encounters in a fully predictive manner. Results reveal a strong influence of the composition of the population on both the aggregation kinetics and the aggregate structure. In particular, we observe a size-stabilization phenomenon taking place in the suspension when the relative concentration of the majority particles lies in the range 80-85%; i.e., starting from primary particles, after a short growth period, we observed a cessation of aggregation. Inspection of the aggregate morphology shows that the formed clusters are composed of few minority particles placed in the inner region, while the aggregate surface is covered by majority particles, acting to provide a shielding effect against further growth.

Multiscale Simulation of Non-Metallic Inclusion Aggregation in a Fully Resolved Bubble Swarm in Liquid Steel

Removing inclusions from the melt is an important task in metallurgy with critical impact on the quality of the final alloy. Processes employed with this purpose, such as flotation, crucially depend on the particle size. For small inclusions, the aggregation kinetics constitute the bottleneck and, hence, determine the efficiency of the entire process. If particles smaller than all flow scales are considered, the flow can locally be replaced by a plane shear flow. In this contribution, particle interactions in plane shear flow are investigated, computing the fully resolved hydrodynamics at finite Reynolds numbers, using a lattice Boltzmann method with an immersed boundary method. Investigations with various initial conditions, several shear values and several inclusion sizes are conducted to determine collision efficiencies. It is observed that although finite Reynolds hydrodynamics play a significant role in particle collision, statistical collision efficiency barely depends on the Reynolds number. Indeed, the particle size ratio is found to be the prevalent parameter. In a second step, modeled collision dynamics are applied to particles tracked in a fully resolved bubbly flow, and collision frequencies at larger flow scale are derived.

Numerical Study of Soft Colloidal Nanoparticles Interaction in Shear Flow

The mechanical behavior of nanoparticle assemblies depends on complex particle interactions that are difficult to study experimentally. Depending on the nanoparticle morphology, these interactions could lead to adhesive and elastic-plastic behavior during contact deformation. The aim of this research is to study the effect of contact interactions between polymer nanoparticles and their impact on the macroscopic properties of formed aggregates. For this purpose, the discrete element method (DEM) was used to develop an interaction model combining elastic-plastic deformation and adhesion to study the behavior of spherical polymeric nanoparticles. Initially, a pair of particles interacting in the normal direction was simulated to evaluate the effect of adhesion and plastic deformation in the pull-off force of the contact. Based on these results, the simulations were extended to a dispersed system of nanoparticles, in which multibody interactions become dominant. Considering the aggregation between the nanoparticles induced by a shear flow, we performed an analysis of the number of aggregates and aggregates size in time to characterize the strength of clusters formed during the process. The simulation results showed that the interaction strength upon breakage of the clusters, correlating with the aggregates size, depends on the nanoparticle's softness. In this way, we verified that the type of contact interaction directly influences the macroscopic mechanical response of nanoparticle assemblies. Therefore, our model represents a new way of predicting the mechanical behavior of polymer nanoparticle systems and of optimizing it by adjusting primary particle properties.

Toward Better Control of Inclusion Cleanliness in a Gas Stirred Ladle Using Multiscale Numerical Modeling

The industrial objective of lowering the mass of mechanical structures requires continuous improvement in controlling the mechanical properties of metallic materials. Steel cleanliness and especially control of inclusion size distribution have, therefore, become major challenges. Inclusions have a detrimental effect on fatigue that strongly depends both on inclusion content and on the size of the largest inclusions. Ladle treatment of liquid steel has long been recognized as the processing stage responsible for the inclusion of cleanliness. A multiscale modeling has been proposed to investigate the inclusion behavior. The evolution of the inclusion size distribution is simulated at the process scale due to coupling a computational fluid dynamics calculation with a population balance method integrating all mechanisms, i.e., flotation, aggregation, settling, and capture at the top layer. Particular attention has been paid to the aggregation mechanism and the simulations at an inclusion scale with fully resolved inclusions that represent hydrodynamic conditions of the ladle, which have been specifically developed. Simulations of an industrial-type ladle highlight that inclusion cleanliness is mainly ruled by aggregation. Quantitative knowledge of aggregation kinetics has been extracted and captured from mesoscale simulations. Aggregation efficiency has been observed to drop drastically when increasing the particle size ratio.