Observing the evaporation transition in vibro-fluidized granular matter

TL;DR

This paper investigates the evaporation transition in vibro-fluidized granular matter, using a Fermi configurational approach and kinetic theory to describe the velocity distribution and collective behavior of grains.

Contribution

It introduces a global temperature concept for a non-equilibrium granular system and develops a kinetic model linking microscopic dynamics to macroscopic responses.

Findings

Identification of a Fermi-like statistical behavior in granular matter

Measurement of a lattice-gas packing factor independent of external parameters

Validation of kinetic theory predictions with experimental mean free path data

Abstract

By shaking a sand box the grains on the top start to jump giving the picture of evaporating a sand bulk, and a gaseous transition starts at the surface granular matter (GM) bed. Moreover the mixture of the grains in the whole bed starts to move in a cooperative way which is far away from a Brownian description. In a previous work we have shown that the key element to describe the statistics of this behavior is the exclusion of volume principle, whereby the system obeys a Fermi configurational approach. Even though the experiment involves an archetypal non-equilibrium system, we succeeded in defining a global temperature, as the quantity associated to the Lagrange parameter in a maximum entropic statistical description. In fact in order to close our approach we had to generalize the equipartition theorem for dissipative systems. Therefore we postulated, found and measured a fundamental dissipative parameter, written in terms of pumping and gravitational energies, linking the configurational entropy to the collective response for the expansion of the centre of mass (c.m.) of the granular bed. Here we present a kinetic approach to describe the experimental velocity distribution function (VDF) of this non-Maxwellian gas of macroscopic Fermi-like particles (mFp). The evaporation transition occurs mainly by jumping balls governed by the excluded volume principle. Surprisingly in the whole range of low temperatures that we measured this description reveals a lattice-gas, leading to a packing factor, which is independent of the external parameters. In addition we measure the mean free path, as a function of the driving frequency, and corroborate our prediction from the present kinetic theory.