Gallery: Free space in the DEM simulation
Our DEM simulations of silo drainage allow us to track the position of every particle, and as such they provide us with an excellent source of data for examining how particles move and rearrange at a microscopic level during flow. For other phases of matter, such as gases or crystals, microscopic models of the particle motion can be used to infer macroscopic properties of flow, but for amorphous packings, such a description is lacking. Perhaps the only candidate in the literature is the idea of a particle-sized “void” of free space in the random packing, into which a single particle may move, thereby replacing the void. Flow in a packing could be mediated by the presence of many voids moving in the opposite direction to the particles. Originally proposed by Eyring in 1936, this mechanism has been posulated in many contexts, such as theories of the glass transition, shear flow in metallic glasses, and compaction in vibrated granular materials, but is now considered somewhat unrealistic.
The DEM data allows us to directly test for the presence of voids during granular drainage. For each snapshot in the DEM data, the simulation region was covered by a fine three-dimensional mesh, and at each point, the sphere of maximum size that could be inserted there between the particles was calculated. The diagram above shows all the free spaces with diameter larger than half a particle, for four different frames as the flow starts. The free spaces are plotted using a color gradient, with gray representing spheres which have half the diameter of a particle, and dark blue representing spheres which have the same size as a particle. The free surface is shown as the dark blue line at the top of the packing. For all four frames, we see many more gray regions, showing that most of the free space is distributed throughout the container in volumes much smaller than a particle. A statistical analysis shows that at any instant, there are only a few complete voids in the container, and these are mainly concentrated around the orifice, providing very strong evidence that the concept of voids is inaccurate, and a more collective notion of particle flow is required.
We can also see that as flow takes place, more free space is visible in the regions of highest strain; see our analysis of local density for more information.