Restructuring of colloidal aggregates in shear flow: coupling interparticle contact models with Stokesian dynamics

Role of Flow Inertia in Aggregate Restructuring and Breakage at Finite Reynolds Numbers

Forces acting on aggregates depend on their properties, such as size and structure. Breakage rate, stable size, and structure of fractal aggregates in multiphase flows are strongly related to the imposed hydrodynamic forces. While these forces are prevalently viscous for finite Reynolds number conditions, flow inertia cannot be ignored, thereby requiring one to fully resolve the Navier-Stokes equations. To highlight the effect of flow inertia on aggregate evolution, numerical investigation of aggregate evolution in simple shear flow at the finite Reynolds number is conducted. The evolution of aggregates exposed to shear flow is tracked over time. Particle coupling with the flow is resolved with an immersed boundary method, and flow dynamics are solved using a lattice Boltzmann method. Particle dynamics are tracked by a discrete element method, accounting for interactions between primary particles composing the aggregates. Over the range of aggregate-scale Reynolds numbers tested, the breakage rate appears to be governed by the combined effect of momentum diffusion and the ratio of particle interaction forces to the hydrodynamic forces. For higher shear stresses, even when no stable size exists, breakage is not instantaneous because of momentum diffusion kinetics. Simulations with particle interaction forces scaled with the viscous drag, to isolate the effect of finite Reynolds hydrodynamics on aggregate evolution, show that flow inertia at such moderate aggregate Reynolds numbers has no impact on the morphology of nonbreaking aggregates but significantly favors breakage probability. This is a first-of-its-kind study that establishes the role of flow inertia in aggregate evolution. The findings present a novel perspective into breakage kinetics for systems in low but finite Reynolds number conditions.

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.

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.

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.

Floc compaction during ballasted aggregation

Ballasted aggregation, a process using the addition of a ballasting agent to improve the settling performance of flocs, appears particularly appropriate for the treatment of humic rich waters that leads to low-density aggregates. In that context, using an aquagenic humic acid coagulated by ferric chloride in the presence of pozzolana particles as ballasting agent, we show that the origin of improved floc settling in ballasted aggregation is not simply related to an increased specific weight of flocs, but also to a significant restructuring of flocs to a more compact structure induced by the added particles. The floc restructuring is evidenced from the increased lag time before measurable floc growth in the presence of the ballasting agent, the higher fractal dimension of flocs above the micron scale range after incorporation of the particles into the aggregates, and a much smaller sediment volume after settling. A simple model of floc compaction based on the turbulent viscous effects that act on an elastic floc, is described.

Estimating Colloidal Contact Model Parameters Using Quasi-Static Compression Simulations

For colloidal particles interacting in suspensions, clusters, or gels, contact models should attempt to include all physical phenomena experimentally observed. One critical point when formulating a contact model is to ensure that the interaction parameters can be easily obtained from experiments. Experimental determinations of contact parameters for particles either are based on bulk measurements for simulations on the macroscopic scale or require elaborate setups for obtaining tangential parameters such as using atomic force microscopy. However, on the colloidal scale, a simple method is required to obtain all interaction parameters simultaneously. This work demonstrates that quasi-static compression of a fractal-like particle network provides all the necessary information to obtain particle interaction parameters using a simple spring-based contact model. These springs provide resistances against all degrees of freedom associated with two-particle interactions, and include critical forces or moments where such springs break, indicating a bond-breakage event. A position-based cost function is introduced to show the identifiability of the two-particle contact parameters, and a discrete, nonlinear, and non-gradient-based global optimization method (simplex with simulated annealing, SIMPSA) is used to minimize the cost function calculated from deviations of particle positions. Results show that, in principle, all necessary contact parameters for an arbitrary particle network can be identified, although numerical efficiency as well as experimental noise must be addressed when applying this method. Such an approach lays the groundwork for identifying particle-contact parameters from a position-based particle analysis for a colloidal system using just one experiment. Spring constants also directly influence the time step of the discrete-element method, and a detailed knowledge of all necessary interaction parameters will help to improve the efficiency of colloidal particle simulations.

Strength Deterioration of Nonfractal Particle Aggregates in Simple Shear Flow

The restructuring of a nonfractal particle aggregate in simple shear flow was simulated by a Stokesian dynamics approach. We studied the deformation and the resultant strength change of aggregates by the surrounding flow under the condition that the cohesive strength of an aggregate is comparable to the fluid stress. In particular, we focused on how the aggregate deteriorates because of the fluid stress exerted on it periodically. The image analysis was applied to visualized simulation results for the quantitative estimation of irreversible change in an aggregate configuration. We examined the structural change in the aggregate from various perspectives, i.e., the outer shape, the internal strength, and the fluid stress on the surface of the aggregate. The simulation results show that the aggregate gets squashed after an intricate restructuring process and it elongates along with the streamline as experimentally observed in the previous study. Regarding the internal strength, the weakest point locally develops in the aggregate by periodically varying the fluid stress. A combination of rotation and elongation effects of shear flow is complexly involved in the deterioration of the internal strength of the aggregate.

Size and Structure of Clusters Formed by Shear Induced Coagulation: Modeling by Discrete Element Method

The coagulation process has a dramatic impact on the properties of dispersions of colloidal particles including the change of optical, rheological, as well as texture properties. We model the behavior of a colloidal dispersion with moderate particle volume fraction, that is, 5 wt %, subjected to high shear rates employing the time-dependent Discrete Element Method (DEM) in three spatial dimensions. The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory was used to model noncontact interparticle interactions, while contact mechanics was described by the Johnson-Kendall-Roberts (JKR) theory of adhesion. The obtained results demonstrate that the steady-state size of the produced clusters is a strong function of the applied shear rate, primary particle size, and the surface energy of the particles. Furthermore, it was found that the cluster size is determined by the maximum adhesion force between the primary particles and not the adhesion energy. This observation is in agreement with several simulation studies and is valid for the case when the particle-particle contact is elastic and no plastic deformation occurs. These results are of major importance, especially for the emulsion polymerization process, during which the fouling of reactors and piping causes significant financial losses.

Self-assembly of Janus particles under shear

We investigate the self-assembly of colloidal Janus particles under shear flow by employing hybrid molecular dynamics simulations that explicitly take into account hydrodynamic interactions. Under quiescent conditions, the amphiphilic colloids form spherical micellar aggregates of different sizes, where the solvophobic hemispheres are directed towards the core and the solvophilic caps are exposed to the solvent. When sufficiently strong shear is applied, the micelles disaggregate with a consequent decay of the average cluster size. Nonetheless, we find an intermediate shear rate regime where the balance between rearrangement and dissociation favors the growth of the aggregates. Additionally, our simulations show that clusters composed of either 6 or 13 particles are the most stable towards the shear flow due to their high geometric symmetry. Our findings open up a new range of applications for Janus particles, ranging from biotechnology to sensor systems.