Influence of the potential well on the breakage rate of colloidal aggregates in simple shear and uniaxial extensional flows.

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.