Compaction of granular mixtures: a free volume model

Abstract

We describe compaction, induced by weak tapping of a powder, as a process where a grain can jump into a hole, only if the hole is large enough. The distribution of hole sizes is taken to be the Poisson type, with a certain characteristic free volume. For macrodisperse powders, this leads to a classical logarithmic law of compaction, already derived by Knight et al. Here we focus our attention on the case of mixtures, between two populations: large grains ( L) and small grains ( S) with very different sizes, so that the ( S) grains may fill the interstices of the ( L) grains. Geometrically, these mixtures can exist as “gravels” (where the intersices are not completely filled) or “puddings” (where the L grains are not tighlty packed). Dynamically, we expect a cross over curve between L-type compaction and S-type compaction, which is different from the geometrical boundary. This implies that, for certain material ratios ρ = L/ S, the plot of density versus number of tappings should show two distinct branches.