Towards dense, realistic granular media in 2D

The development of an applicable theory for granular matter—with both qualitative and quantitative value—is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.

In most systems, low density co-exists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional nonlinear phenomena and material properties are important in realistic granular media, involving, e.g.:

1. multi-particle interactions and elasticity

2. strong dissipation,

3. friction,

4. long-range forces and wet contacts,

5. wide particle size distributions and

6. various particle shapes.

Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some cannot.

This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions and corrections given are qualitatively true also in 3D.

Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier–Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws—one by one—in order to account for the realistic physical effects and properties listed above.