Brownian Dynamics Simulations of the Shear-Induced Clustering of Electrostatically Stabilized Colloidal Suspensions with Hydrodynamic Interactions

In this work, the aggregation kinetics of charged polystyrene particles exposed to shear flow has been investigated using Brownian Dynamics simulations with the Rotne–Prager-Yamakawa (RPY) approximation of the long-range Hydrodynamic Interactions (HI) over a wide range of particle volume fractions (Φ), Peclet number values (Pe), which measures the relative importance of shear forces with respect to diffusion, and surface potentials (Ψ₀). The strength of the repulsive electrostatic interactions has been quantified by means of the Fuchs stability ratio (W).

It has been observed that, for high values of W and low Pe number values, the aggregation rate is insensitive to the shear rate, being the process dominated by repulsion forces among particles, similarly to what is observed under reaction-limited cluster aggregation (RLCA) regime. As the values of Peclet number increase, the resulting shear is sufficient to overcome the energy barrier to aggregation resulting in a sharp increase in the aggregation dynamics and radius of gyration, consistently with the available experimental results and theoretical predictions¹.

Similar results have been obtained as particle concentrations increases under a given shear rate and for a specific W. Simulations predict that the larger the volume fraction, the higher the collision rate, and the more intense is the disturbance in the flow field induced by particles, which promotes the mobility of the clusters and enhances the resulting aggregation rate. It was also observed that for high values of the Pe number, the curve describing the dimensionless time evolution of the number concentration of clusters for different Φ are almost overlapping throughout the whole simulation time, most likely indicating a similar aggregation mechanism, where concentration instead of shear rate plays a predominant role in determining the process dynamics.

Furthermore, in the early stages of the process, when aggregation occurs mostly between primary particles and small clusters, simulations neglecting HI and employing a pure BD algorithm lead to faster aggregation kinetics if compared to the method which includes the long-range hydrodynamics contributions. However, in the subsequent stages, the process is dominated by particle-cluster and cluster-cluster interactions and the long-range hydrodynamics term becomes predominant, resulting in a rapid increase of the aggregation rate and radius of gyration after a given time. This indicates that the inclusion of long-range HI can reveal unique features of the phenomenon and provide a more exhaustive description of the complex interplay between DLVO-interactions and hydrodynamics under shear flow conditions.

References

(1) Lattuada, M.; Zaccone, A.; Wu, H.; Morbidelli, M. Population-Balance Description of Shear-Induced Clustering, Gelation and Suspension Viscosity in Sheared DLVO Colloids. Soft Matter 2016, 12 (24), 5313–5324.