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Fluid Dynamics Seminar

Monday, Feb 12, 2007, 4:00 PM
Cullimore Lecture Hall, Room 611
New Jersey Institute of Technology

Distributions of particle packings in static and slowly driven amorphous materials: Does the concept of Edwards entropy make sense?

Jerzy Blawzdziewicz

Department of Mechanical Engineering, Yale University

Abstract

Edwards generalization of the equilibrium Gibbs-ensemble theory for granular media has recently been widely used to describe the inherently nonequilibrium states of such systems (e.g. in investigations of static granular configurations and the motion of slowly sheared or vibrated granular materials). Analogous concepts have also been applied to explain the slow dynamics in glass-forming liquids.

Edwards entropy of a granular system is defined as the logarithm of the number of mechanically stable particle packings satisfying given macroscopic conditions. The core assumption of Edwards theory is that all mechanically stable particle packings consistent with a given set of macroscopic constraints are equally probable. However, this assumption has not been directly verified: the available tests are either indirect or they have been carried out for simplified mean-field or discrete models.

I will present results of our numerical simulations in which we have determined the probability distribution of mechanically stable packings in small bidisperse systems of frictionless disks. We have found that the packing probability distribution is very non-uniform, contrary to Edwards assumption. Even in a small packing-fraction interval some packings are many orders of magnitude more probable than the others. We examine possible sources of this non-uniformity, and discuss the relevance of our findings for quasi-thermodynamic descriptions of granular matter.