Granular Mixtures

  1. Uecker, H., W. T. Kranz, T. Aspelmeier and A. Zippelius, PRE 80, 041303 (2009)

Real granular systems a practically never monodisperse. Nevertheless, most of the theoretical work on granular matter is precisely concerned with monodisperse particles. This is done, of course, for practical reasons but already bidisperse systems show new phenomena. Most strikingly, even for the homogeneous cooling state (HCS), the temperatures do not equilibrate between the species but tend towards a fixed temperature ratio instead. Although this came as a surprise when it was first discovered, we argue that it is quite easily explained.

Temperature $T(a)$ as a function of radius $a$ for a uniform size distribution and (red) force controlled driving, (blue) energy controlled driving, and (green) velocity controlled driving. The circles are results from an event driven simulation.

In addition to the heat flux that works against any temperature difference and that is also present in fluids of elastic particles (e.g., molecules), there is also the heat flux due to dissipation. The latter is different for the two species in most cases. The balance of these (unequal) fluxes will (special combinations of parameters set aside) never lead to energy equipartition.

The argument does not change for driven granular fluids, although here, one has the freedom to chose how the species should be driven. For highly polydisperse fluids, where no two particles are the same, this leads to a whole range of partial temperatures depending on the particle distribution.

  • Last modified: 2013/04/29 12:01
  • by root