Simulation of Aggregate Deformation and Breakup in Simple Shear Flows Using a Combined Continuum and Discrete Model

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.

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.

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

A method to couple interparticle contact models with Stokesian dynamics (SD) is introduced to simulate colloidal aggregates under flow conditions. The contact model mimics both the elastic and plastic behavior of the cohesive connections between particles within clusters. Owing to this, clusters can maintain their structures under low stress while restructuring or even breakage may occur under sufficiently high stress conditions. SD is an efficient method to deal with the long-ranged and many-body nature of hydrodynamic interactions for low Reynolds number flows. By using such a coupled model, the restructuring of colloidal aggregates under shear flows with stepwise increasing shear rates was studied. Irreversible compaction occurs due to the increase of hydrodynamic stress on clusters. Results show that the greater part of the fractal clusters are compacted to rod-shaped packed structures, while the others show isotropic compaction.

Breakage rate of colloidal aggregates in shear flow through stokesian dynamics

We study the first breakage event of colloidal aggregates exposed to shear flow by detailed numerical analysis of the process. We have formulated a model, which uses stokesian dynamics to estimate the hydrodynamic interactions among the particles in a cluster, van der Waals interactions and Born repulsion to describe the normal interparticle interactions, and the tangential interactions through discrete element method to account for contact forces. Fractal clusters composed of monodisperse spherical particles were generated using different Monte Carlo methods, covering a wide range of cluster masses (N(sphere) = 30-215) and fractal dimensions (d(f) = 1.8-3.0). The breakup process of these clusters was quantified for various flow magnitudes (γ), under both simple shear and extensional flow conditions, in terms of breakage rate constant (K(B)), mass distribution of the produced fragments (FMD, f(m,k)), and critical stable aggregate mass (N(c)), defined as the largest cluster mass that does not break under defined flow conditions. The breakage rate K(B) showed a power law dependence on the product of the aggregate size and the applied stress, with values of the corresponding exponents depending only on the aggregate fractal dimension and the type of flow field, whereas the prefactor of the power law relation also depends on the size of the primary particles comprising a cluster. The FMD was fitted by Schultz-Zimm distribution, and the parameter values showed an analogous dependence on the product of the aggregate size and the applied stress similar to the rate constant. Finally, a power law relation between the applied stress and corresponding largest stable aggregate mass was found, with an exponent value depending on the aggregate fractal dimension. This unique and detailed analysis of the breakage process can be directly utilized to formulate a breakage kernel used in solving population balance equations.