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Observing Brownian motion and measuring temperatures in vibration-fluidized granular matter

Understanding the behaviour of granular media, either at rest or moving under external driving, is a difficult task, although it is important and of very practical interest. Describing the motion of each individual grain is complicated, not only because of the large number of grains, but also because the mechanisms of interaction at the grain level involve complex contact forces. One would like to have, in fact, a description in terms of a few macroscopic quantities. Since a granular medium resembles a liquid or a gas when strongly vibrated or when flowing out of a container, a natural approach is to adopt usual equilibrium statistical mechanics tools in order to test if such a macroscopic description is possible. In other words, an interesting question is to investigate whether one can model granular media, when close to a liquid-like state for example, using viscosity, temperature, and so on, as one does for normal liquids. With this aim in view, we have developed a non-equilibrium version of the classical Brownian motion experiment. In particular, we have observed the motion of a torsion oscillator immersed in an externally vibrated granular medium of glass spheres, and have collected evidence that the motion is Brownian-like. An approximate fluctuation–dissipation relation holds, and we can define temperature-like and viscosity-like parameters.