459652 Discrete Element Model of Concentrated Colloidal Dispersions: Linking Viscosity to Cluster Properties
We use the Discrete Element Method (DEM) to model the dynamic behavior of waterborne polystyrene latex subjected to a high shear. The interaction of the particles with the fluid is accounted for using the two-way coupling technique. The interaction between the particles that are stabilized, adhesive and elastic is described by the combination of the Derjaguin-Landau-Verwey-Overbeek (DLVO) and Johnson-Kendall-Roberts (JKR) theories. The model is spatially three-dimensional and allows therefore capturing not only the characteristic coagulation time, but also the size and structure of the produced clusters. Moreover, we developed a method for the evaluation of the viscosity of concentrated dispersions.
The results of the model in terms of both the characteristic coagulation time and the size of the produced clusters are in a good agreement with literature experimental data and established theories. The coagulation is shown to be faster for more concentrated and less stabilized dispersions and the clusters tend to be larger for more adhesive particles subjected to a smaller shear. Based on the balance of forces acting on a single cluster, we generalized these results into a simple expression relating the cluster size to the key parameters, such as the shear rate, primary particle size and surface energy. The viscosity of the dispersion is shown to be affected primarily by the particle volume fraction, which is in an agreement with the semi-empirical description by the Krieger-Dougherty equation for a simplified hard-sphere system. For more complicated systems, there is no established description. However, our model predicts the rise of viscosity for adhesive coagulating particles and it is also able to capture the viscosity growth during the autocatalytic coagulation of the stabilized latex. Combining these results together, it is possible to link the viscosity of the coagulating dispersion to the properties of the produced clusters, such as their size and structure. This provides a powerful tool for the prediction of the rheological properties of colloidal dispersions based on their structure.
The results of this work bring a theoretical insight into the complicated behavior of concentrated dispersions. Moreover, they can serve as a basis for the operation of real processes that handle colloidal latexes.
 Kroupa, M.; Vonka, M.; Kosek, J. Modeling the Mechanism of Coagulum Formation in Dispersions. Langmuir 2014, 30, 2693–2702.
 Kroupa, M.; Vonka, M.; Soos, M.; Kosek, J. Size and Structure of Clusters Formed by Shear Induced Coagulation: Modeling by Discrete Element Method. Langmuir 2015, 31, 7727–7737.
 Kroupa, M.; Vonka, M.; Soos, M.; Kosek, J. Utilizing the Discrete Element Method for the Modeling of Viscosity in Concentrated Suspensions. Submitted 2016.