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.

The stability of colloidal dispersions is of crucial importance because the properties of dispersions are strongly affected by the degree of coagulation. Whereas the coagulation kinetics for quiescent (i.e., nonstirred) and diluted systems is well-established, the behavior of concentrated dispersions subjected to shear is still not fully understood. We employ the discrete element method (DEM) for the simulation of coagulation of concentrated colloidal dispersions. Normal forces between interacting particles are described by a combination of the Derjaguin, Landau, Verwey, and Overbeek (DLVO) and Johnson, Kendall, and Roberts (JKR) theories. We show that, in accordance with the expectations, the coagulation behavior depends strongly on the particle volume fraction, the surface potential, and the shear rate. Moreover, we demonstrate that the doublet formation rate is insufficient for the description of the coagulation kinetics and that the detailed DEM model is able to explain the autocatalytic nature of the coagulation of stabilized dispersions subjected to shear. With no adjustable parameters we are able to provide semiquantitative predictions of the coagulation behavior in the high-shear regions for a broad range of particle volume fractions. The results obtained using the DEM model can provide valuable guidelines for the operation of industrial dispersion processes.

The rheological behavior of concentrated suspensions is a complicated problem because it originates in the collective motion of particles and their interaction with the surrounding fluid. For this reason, it is difficult to accurately model the effect of various system parameters on the viscosity even for highly simplified systems. We model the viscosity of a hard-sphere suspension subjected to high shear rates using the dynamic discrete element method (DEM) in three spatial dimensions. The contact interaction between particles was described by the Hertz model of elastic spheres (soft-sphere model), and the interaction of particles with flow was accounted for by the two-way coupling approach. The hydrodynamic interaction between particles was described by the lubrication theory accounting for the slip on particle surfaces. The viscosity in a simple-shear model was evaluated from the force balance on the wall. The obtained results are in close agreement with literature data for systems with hard spheres. Namely, the viscosity is shown to be independent of shear rate and primary particle size for monodisperse suspensions. In accordance with theory and experimental data, the viscosity grows rapidly with particle volume fraction. We show that this rheological behavior is predominantly caused by the lubrication forces. A novel approach based on the slip of water on a particle surface was developed to overcome the divergent behavior of lubrication forces. This approach was qualitatively validated with literature data from AFM measurements using a colloidal probe. The model presented in this work represents a new, robust, and versatile approach to the modeling of viscosity in suspensions with the possibility to include various interaction models and study their effect on viscosity.

in Wiley Online Library (wileyonlinelibrary.com) Sustaining stable liquid-liquid dispersion with the desired drop size still relies on experimental correlations, which do not reflect our understanding of the underlying physics and have a limited prediction capability. The complex behavior of liquid-liquid dispersions inside a stirred tank, which is equipped with a Rushton turbine, was characterized by a combination of computational fluid dynamics and population balance equations (PBE). PBE took into account both the drop coalescence and breakup. With the increasing drop viscosity, the resistance to drop breakage also increases, which was introduced by the local criteria for drop breakup in the form of the local critical Webber number (We c ). The dependency of We c on the drop viscosity was derived from the experimental data available in the literature. Predictions of Sauter mean diameter agree well with the experimentally measured values allowing prediction of mean drop size as a function of variable viscosity, interfacial tension, and stirring speed.