State Variables in Granular Materials: an Investigation of Volume and Stress Fluctuations.

摘要

This thesis is devoted to the investigation of granular materials near the transition between solid-like and fluid-like behavior. We aim to understand the collective dynamics in dense driven systems, the role of geometry in the volume fluctuations, and the equilibration of granular temperatures. The experiments are conducted using two-dimensional materials composed of a single layer of disks which are supported by a thin layer of air. In driven granular systems, particle dynamics have commonly been quantified by the diffusion, even though this measure discards information about collective particle motion known to be important in dense systems. We draw inspiration from fluid mixing, and utilize the braid entropy, which provides a direct topological measure of the entanglement of particle trajectories and has been used to quantify mixing. We find that as the density or pressure increases, the dynamics slow and the braiding factor exhibits intermittency signifying a loss of chaos in the trajectories on the experimental timescale. In the same system, we experimentally measure the local volume fraction distribution, which we find to be independent of the boundary condition and the inter-particle friction coefficient. We extend the granocentric model to account for randomness in particle separations, which are important in dynamic systems. This model is in quantitative agreement with experimentally-measured local volume fraction distributions, indicating that geometry plays a central role in determining the magnitude of local volume fluctuations. Finally, we test whether the zeroth law (temperature-equilibration) of several ensemble-based granular temperatures is satisfied by two granular systems in contact. We calculate the compactivity and angoricity which are the temperature-like quantities associated with the volume and stress ensembles; we observe the compactivity does not satisfy the zeroth law test, while the angoricity does equilibrate between the two systems.