Free cooling of granular particles with rotational degrees of freedom

Free cooling of granular particles with rotational degrees of freedom

Martin Huthmann

Doctoral thesis

Date of Examination: 1999-11-04

Date of issue: 2001-11-06

Advisor: Zippelius, Annette Prof. Dr.

Referee: Kree, Reiner Prof. Dr.

Persistent Address: http://hdl.handle.net/11858/00-1735-0000-0022-5D52-0

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Abstract

English

Aim of this theses is to elucidate the role of rotational degrees of freedom in a system of freely cooling granular particles. To gather more general aspects rough spherical particles and, as an example for non-spherical particles, needles are considered. The simplest collision rules which allow for exchange of translational and rotational energy are chosen and the dynamics is formulated in terms of a pseudo-Liouville operator. An ED-algorithm to perform simulations is used and results are compared to the analytical theory. Two main results are found. i) For short time or not too high inelasticities the system remains spatially homogeneous, but changes arise in the distribution function for the momenta. The changes are twofold: (i) Due to the dissipative character of collisions the average kinetic energy decreases and (ii) the shape of the distribution function is no longer Maxwellian with a single temperature. The latter is experessed by a ratio, in general different from one, of the average translational energy to the average rotational energy and the emergence of higher cumulants, which are zero in a pure Maxwellian state. The change of the distribution function to an asymptotic fixed shape is fast compared to the decay of the average energy. ii) For sufficiently large inelasticites, densities and system sizes the assumption of homogeneity breaks down. Large scale structures in the translational velocity field arise, whereas longrange organization in the rotational velocity field seems not to ! occur, or is at least much less pronounced. Clusters form and dissolve again, so also the density does not remain homogeneous. In this stae most of the translational energy is stored in the translational velocity field and deviations from Haff's law are found. Also the rotational energy does no longer obey Haff's. For spheres it is shown that it adjusts to the now different translational temperature according to the law found for the homogeneous cooling state.