Disorders in granular matter

A major issue in material science is the formulation of a macroscopic description of material properties based on local characteristics. We consider here the case of a granular medium, for which we show that the applicable treatments depend not only on the nature of the disorder but also on the specific property under consideration. The ordinary transport properties of a porous medium are adequately described by classical homogenization techniques introduced long ago in the study of electrical composites. Poorly connected porous systems or multi-phase flows, where a wide range of scale effects are present, require descriptions—such as percolation or fractals—which take into account large-scale disorder. We consider extensions of this approach to other properties—e.g., hydrodynamic dispersion. In a different context, the properties of solid, unconsolidated granular media cannot be treated by homogenization techniques because of the sensitivity of the properties to the local disorder at contact zones; an example of the latter is that the very broad distribution of stresses in a compressed granular medium is found to depend very sensitively on the local ordering and leads to a very heterogeneous distribution of local forces along continuous chains of grains.