The mixing of cohesive granular materials featuring a large size range in the absence of gravity
We have studied the shear mixing of bidisperse collections of cohesive particles in an effort to develop models that would allow one to predict and control the homogeneity of particle composites. Our focus has been on the effects of interparticle cohesion and shear rate on the microstructure of particle composites. Furthermore, we have focused on particles that have a “large size range,” specifically a 7:1 diameter ratio, such that homogeneous mixtures would include the small particles filling in the gaps formed between big particles, resulting in a correlation between the packing fraction and mixing quality. As a model problem, the cohesion resulting from the van der Waals force acting between particles was considered. Simulations were performed in which initially segregated bidisperse collections of particles were subjected to plane shear under constant applied stress as a method of mixing. Gravity was ignored in these simulations so that the different particles were not driven to different sides of the mixtures and the only hindrance to homogeneous mixing was cohesion. Simulations were performed with a variety of shear rates and particle cohesion strengths for both the large and small particles, and the homogeneity of the resultant mixtures was quantified using two distinct statistics: the estimated mean size of small-particle clusters and the spatial variance in the relative concentrations of the small and large particles. Microstructure images of the mixtures were used to provide additional qualitative measure of homogeneity as well as a measure of the relevance of the order statistics. These data suggested that the cohesiveness (Hamaker constant) of the small particles had the strongest influence on the mixture’s homogeneity. When the small particles were not sufficiently cohesive, they did not significantly agglomerate, and so the resulting mixtures were relatively homogeneous over the range of shear rates and Hamaker constants of the big particles explored here. When the small particles were more cohesive, the small particles formed strong agglomerates and the mixtures become significantly inhomogeneous at lower shear rates. Somewhat surprisingly in these cases, better mixing was not achieved by simply making the large particles less cohesive. Rather, reducing the cohesiveness of the large particles far enough caused the large particles to pack more tightly, making the small-particle agglomerates unable to fit in between them, ultimately resulting in worse mixing. As such, the best mixing in these cases was achieved when the big particles were moderately cohesive. A correlation between solid volume fraction and homogeneity was not observed when particle cohesion was varied, as making either the small or large particles more cohesive led to a decrease in solid volume fraction, regardless of the effect on homogeneity. On the other hand, when homogeneity was found to increase with shear rate, so did the solid volume fraction.
Keywords: Mixing, Cohesion, Shear flow of powders, Discrete element simulation