Correlation of spin and velocity in the homogeneous cooling state of a granular gas of rough particles
1 Max-Planck-Institute for Dynamics and Self Organization, Bunsenstr. 10, 37073 Göttingen, Germany
2 Institute of Theoretical Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
3 Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, UK
4 Cluster of Excellence “Engineering of Advanced Materials”, Friedrich-Alexander-University, Erlangen, Germany
5 Universität Erlangen-Nürnberg, Institute for Multiscale Simulation, Nägelsbachstrasse 49b, Erlangen, Germany
In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a steady-state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analyzed systematically for a wide range of system parameters, including the coefficients of tangential and normal restitution as well as the moment of inertia of the particles. For most parameter values the axis of rotation and the direction of linear momentum are perpendicular like in a sliced tennis ball, while parallel orientation, like in a rifled bullet, occurs only for a small range of parameters. The limit of smooth spheres is singular: any arbitrarily small roughness unavoidably causes significant translation-rotation correlations, whereas for perfectly smooth spheres the rotational degrees of freedom are completely decoupled from the dynamic evolution of the gas.
© EDP Sciences, Springer-Verlag, 2010