Volume 60, Number 5, December 2002
|Page(s)||684 - 690|
|Section||Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics|
|Published online||01 November 2002|
Segregation in hard-sphere mixtures under gravity. An extension of Edwards approach with two thermodynamical parameters
Dipartimento di Fisica, Università
“Federico II”, INFM and INFN Napoli Via Cintia,
80126 Napoli, Italy
2 Department of Mathematics, Imperial College - London, SW7 2BZ, UK
Accepted: 20 September 2002
We study segregation patterns in a hard-sphere binary model under gravity subject to sequences of taps. We discuss the appearance of the “Brazil nut” effect (where large particles move up) and the “reverse Brazil nut” effects in the stationary states reached by “tap” dynamics. In particular, we show that the stationary state depends only on two thermodynamical quantities: the gravitational energy of the first and of the second species, and not on the sample history. To describe the properties of the system, we generalize Edwards' approach by introducing a canonical distribution characterized by two configurational temperatures, conjugate to the energies of the two species. This is supported by Monte Carlo calculations showing that the average of several quantities over the tap dynamics and over such distribution coincide. The segregation problem can then be understood as an equilibrium statistical-mechanics problem with two control parameters.
PACS: 45.70.Mg – Granular flow: mixing, segregation and stratification / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.20.-y – Classical statistical mechanics
© EDP Sciences, 2002
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.