Influence of the Potential Well on the Breakage Rate of Colloidal Aggregates in Simple Shear and Uniaxial Extensional Flows

Abstract

In this work we build on our previous paper (Harshe, Y. M.; Lattuada, M. Langmuir 2012, 28, 283-292) and compute the breakage rate of colloidal aggregates under the effect of shear forces by means of Stokesian dynamics simulations. A library of clusters made of identical spherical particles covering a broad range of masses and fractal dimension values (from 1.8 to 3.0) was generated by means of a combination of several Monte Carlo methods. DLVO theory has been used to describe the interparticle interactions, and contact forces have been introduced by means of the discrete element method. The aggregate breakage process was investigated by exposing them to well-defined shear forces, generated under both simple shear and uniaxial extensional flow conditions, and by recording the time required to reach the first breakage event. It has been found that the breakage rate of clusters was controlled by the potential well between particles as described by DLVO theory. A semiempirical Arrhenius-type exponential equation that relates the potential well to the breakage rate has been used to fit the simulation results. The dependence of the breakage process on the radius of gyration, on the external shear strength, and on the fractal dimension has been obtained, providing a very general relationship for the breakage rate of clusters. It was also found that the fragment mass distribution is insensitive to the presence of electrostatic repulsive interactions. We also clarify the physical reason for the large difference in the breakage rate of clusters between simple shear and the uniaxial extensional flow using a criterion based on the energy dissipation rate. Finally, in order to answer the question of the minimum cluster size that can break under simple shear conditions, a critical rotation number has been introduced, expressing the maximum number of rotations that a cluster exposed to simple shear could sustain before breakage.

Fractal-like structures in colloid science

“…The yet unraveled interplay between potentials and cluster structures finds here one of its practical outcomes: the nonpossibility to predict the type of breakage and thus the resulting fractal structure for non-DLVO stabilized particles. Recent work based on Stokesian dynamic simulations has however demonstrated that the structure and mass distributions of fragments generated by shearinduced breakage is virtually independent of the depth of the energy well existing between particles in a cluster [72].…”

Shear-Induced Heteroaggregation of Oppositely Charged Colloidal Particles

“…This mechanism is generally referred to as orthokinetic aggregation and, for sufficiently large Péclet numbers, enhances the aggregation rate compared to a Brownian mechanism. Furthermore, as aggregates grow in size, the shear stresses exerted by the flow field on the aggregate structure induce substantial restructuring effects, , thus altering the structure produced upon aggregation. For these reasons, if a critical concentration exists in orthokinetic heteroaggregation over which size stabilization occurs, its value may be different from the one characterizing perikinetic aggregation.…”

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

“…This observation can be explained by flow recirculation patterns that demonstrate inertia in the liquid phase, which cannot be completely neglected when simulating particle interactions even at Reynolds numbers considered very low such as Re = 0.028. This is significant information since many numerical investigations in such conditions [ 19 , 31 ] use Stokesian Dynamics, which is unable to account for such effects. They, therefore, cannot be used for calculating inclusion aggregation kinetics.…”