(409a) Modeling the Mixing of High Concentrations of Bidisperse Cohesive Particles Under Gravity

The mixing of granular materials is generally a difficult task. First of all, differences in the constituent particles that would affect their dynamics, such as size, density, and roughness, will generally result in similar particles gathering together [1]. Probably the best-known instance of such behavior is the Brazil nut effect, in which large particles rise to the top of a collection of differently-sized particles that is subjected to vertical shaking. Secondly, small particles (typically less than 100 microns in diameter) tend to agglomerate due to cohesive forces (such as the van der Waals force) exceeding the particle's weight [2]. Naturally, this clustering prevents good mixing. Lastly, it generally takes a good deal of energy to mix solids, as they do not flow as easily as most fluids. A certain amount of stress must be applied to granular materials to get them to flow, and even then, it is not uncommon to find areas where the flow is stagnant or plug-like.

The primary purpose of the present study is to examine the influence of particle cohesion on the homogeneity of mixtures of cohesive particles featuring a large range of particle sizes. As a model problem, we consider discrete element method (DEM) simulations [3] 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. Results have already been presented for simulations in which the particles were not subjected to gravity, so that the Brazil nut (or similar) effect did not occur and cohesion was the only source of particle segregation leading to poor mixing. These simulations provided insight into the influence of cohesion on mixing, but the applicability of the results to real particle mixtures remains to be seen and may be limited. So simulations that feature particles subject to gravity have been performed, and the findings are presented here.

With gravity, the large particles rise to the top and the small particles fall to the bottom as assemblies are sheared. As presented before, when the large and small particles were initially separated side-by-side, layers of large particles reached the top before significant mixing could be achieved in the horizontal direction, and so ?reasonably good mixing? could never be achieved. As such, full attention has been given to simulations with initial configurations featuring all of small particles on top of the large particles.

The homogeneity of a given mixture has been measured using the total solid volume fraction, the average size of clusters of small particles [4], and the variance in the concentration of the different sizes of particles. Of those statistics, results suggest that the total volume fraction serves as the best measure of homogeneity. As the large particles spread from the bottom to the top, the mixture naturally becomes more homogeneous, and before the large particles reach the very top, the volume fraction reaches its maximum. As shearing proceeds further, some of the large particles rise out of the mixture and the volume fraction drops. As one may expect, increasing the shear rate results in the peak volume fraction being reached faster. However, the peak volume fraction itself has a complex dependence on shear rate. Also, the maximum volume fraction grows as particle cohesion is reduced, but the rate at which it is reached has a complex dependence on the strength of particle cohesion.

[1] 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.

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

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

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