(8b) Modeling the Mixing of High Concentrations of Bidisperse Cohesive Particles and An Inviscid Binder

Granular materials consist of particles and voids, which may be occupied by an interstitial fluid (e.g. air or binder) or a vacuum. The volume taken up by voids can be quite large; in the case of random arrangements of monodisperse particles, voids take up at least 36% of the total volume [1]. In theory, a way to get a greater solids loading would be to use a mixture of big and small particles, with the latter particles small enough that they would fit in the voids between the big particles. However, the mixing of granular materials has proven to be a more difficult prospect than it may seem.

First of all, virtually any differences between constituent particles can result in segregation [2]. Likely the best known example of this is the so-called Brazil nut effect, where the vertical shaking of a system of differently sized particles results in the large particles rising to the top. Even if such segregation can be avoided, if the particles are sufficiently small (smaller than about 100 microns), they will tend to agglomerate, as the van der Waals attraction between the particles exceeds their weight [3]. As a result, the small particles will generally naturally exist as clusters, and thus will not be able to fit in the gaps between the large particles. That being said, this effect can theoretically be lessened if the mixing is done with such intensity that the clusters are broken up during the mixing process. Furthermore, the particles can be treated with a surfactant that reduces their cohesiveness.

The primary purpose of the present study is to examine the influence of particle cohesion on the homogeneity of mixtures of cohesive particles featuring large difference in size between the largest and smallest particles. As a model problem, we consider discrete element method (DEM) simulations [4] of bidisperse collections of cohesive particles with a diameter ratio of 7:1 undergoing shear flow as a means of mixing. Simulations were performed with different particle cohesive strengths and shear rates. Furthermore, the effects of including an inviscid binder were investigated by either including or ignoring buoyancy effects in the simulations. From each simulation we have extracted the total solid volume fraction, the average cluster size of the small particles [5], and the system-wide variance in the small particle concentration as order metrics to describe the homogeneousness of the mixtures.

Our simulations reveal that the buoyant forces of a liquid binder with a density equal to that of the particles prevented the Brazil nut effect, and thus if such a binder can be used without any adverse effects, it should be used to help promote homogeneous mixing. When including the binder, over the shear rates and levels of cohesion investigated, increasing the shear rate significantly improved the homogeneity of the mixtures. Also, reducing the cohesiveness of the small particles proved to bring about the greatest improvement in homogeneity, as the small particle clusters were easier to break up. Somewhat surprisingly, though, reducing the cohesiveness of the large particles resulted in extremely inhomogeneous mixtures, likely due to the small particles being attracted to each other more than to the big particles, or similarly the big particles being unable to pull apart the small particle clusters. Between the three order metrics used, the average cluster size proved to best quantify the homogeneousness of the mixtures.

[1] S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Springer, New York, 2002.

[2] G. Plantard, H. Saadaoui, P. Snabre, B. Pouligny, Surface-roughness-driven segregation in a granular slurry under shear, Europhys. Lett. 75 (2) (2006) 335-341.

[3] J.P.K. Seville, C.D. Willett, P.C. Knight, Interparticle forces in fluidisation: a review, Powder Technol. 113 (2000) 261-268.

[4] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechníque 29 (1) (1979) 47-65.

[5] S. Gallier, A Stochastic Pocket Model for Aluminum Agglomeration in Solid Propellants, Propellants Explos. Pyrotech. 34 (2009) 97-105.