Voronoi Volumes in Dense Granular Flow

The concept of free volume in amorphous materials has a long history, including void-based theories of viscous flow (Eyring 1936), the glass transition (Turnbull and Cohen 1957), and granular drainage (Mullins 1972), although it has become clear that particle displacements are highly correlated and not mediated by single-particle voids. Recently, we have shown that dense random packings can be made to flow cooperatively at nearly uniform density by diffusing ``spots'' of influence and find good agreement with discrete-element (DEM) simulations of frictional spheres in the case of granular drainage. Spots are presumed to carry a slight excess of interstitial volume, but verifying this would require tracking changes in local volume fraction of only a few percent. In flowing random packings, this is a significant computational challenge, which we address here by computing the evolving Voronoi tesselation with an efficient new algorithm. We study the distribution of local Voronoi volumes in simulations of granular drainage using the spot model and DEM and observe some intriguing differences. The Voronoi volume also provides a sensitive measure of whether a given region is ``liquid-like'' of ``solid-like'' in dense granular flow.