Observing Brownian motion in vibration-fluidized granular matter

TL;DR

This study demonstrates that a vibro-fluidized granular system can exhibit Brownian motion characteristics similar to equilibrium systems, allowing the use of fluctuation-dissipation concepts to define an effective temperature and viscosity.

Contribution

It extends the fluctuation-dissipation framework to non-equilibrium granular matter, showing that such systems can behave like thermal baths under vibration.

Findings

Granular medium exhibits Brownian-like motion.

Fluctuation-dissipation relation holds approximately.

Effective temperature and viscosity can be defined.

Abstract

At the beginning of last century, Gerlach and Lehrer observed the rotational Brownian motion of a very fine wire immersed in an equilibrium environment, a gas. This simple experiment eventually permitted the full development of one of the most important ideas of equilibrium statistical mechanics: the very complicated many-particle problem of a large number of molecules colliding with the wire, can be represented by two macroscopic parameters only, namely viscosity and the temperature. Can this idea, mathematically developed in the so-called Langevin model and the fluctuation-dissipation theorem be used to describe systems that are far from equilibrium? Here we address the question and reproduce the Gerlach and Lehrer experiment in an archetype non-equilibrium system, by immersing a sensitive torsion oscillator in a granular system of millimetre-size grains, fluidized by strong external vibrations. The vibro-fluidized granular medium is a driven environment, with continuous injection and dissipation of energy, and the immersed oscillator can be seen as analogous to an elastically bound Brownian particle. We show, by measuring the noise and the susceptibility, that the experiment can be treated, in first approximation, with the same formalism as in the equilibrium case, giving experimental access to a ''granular viscosity'' and an ''effective temperature'', however anisotropic and inhomogeneous, and yielding the surprising result that the vibro-fluidized granular matter behaves as a ''thermal'' bath satisfying a fluctuation-dissipation relation.