Eur. Phys. J. B 5, 223-229 (1998)
https://doi.org/10.1007/s100510050438

Nonlinear dynamics of density waves in granular flows through narrow vertical channels

Groupe Matière Condensée et Matériaux (UMR 6626.) , Université Rennes 1, 35042 Rennes Cedex, France

Corresponding author: ^a valance@truffaut.uni-rennes1.fr

Received: 11 March 1998
Accepted: 3 July 1998
Published online: 15 September 1998

Abstract

We study granular flows through narrow channels driven by gravity in the framework of the kinetic theory for dissipative dense gases. We derive equations of motion for quasi-one-dimensional systems. In a certain range of flow density, the steady homogeneous regime is found to be unstable against the formation of density waves. We show moreover that near the onset of the instability, the governing equation for the flow density is a mixture of the Korteweg-de-Vries equation, which leads to soliton, and the Bürger equation which exhibits spatio-temporal chaos. The competition between chaos and solitons may lead either to regular spatially ordered density waves or to chaotic dynamics. We argue that these two types of dynamics can be encountered experimentally according to the channel width and the dissipative properties of the granular media.