An experimental study of wave propagation and velocity distributions in a vertically driven time-dependent granular gas

Averaged over appropriate space and time scales the dynamics of highly fluidized granular systems are often reminiscent of molecular fluid flows. As a result, theoretical efforts to describe these systems have borrowed heavily from continuum mechanics, particularly hydrodynamics. This has led to various proposed granular hydrodynamic theories which have been used to simulate granular materials in various states of confinement and excitation. These studies suggest that a continuum model for granular gasses can accurately reproduce the mean density, velocity and temperature profiles for an experimental granular gas.; This thesis contributes to this body of work by presenting an experimental study of the hydrodynamic fields and velocity distributions within a vertically driven quasi-2D granular gas. We have taken pictures as fast as possible of a time-dependent granular gas using a high-speed CCD camera. We have extracted the positions and velocities of 57-564 particles per frame over 400 GB of raw images collected at 3700 fps. We used this data to compute the density, velocity and temperature fields as functions of time and space to a very high resolution. This approach led to the discovery of novel substructures within the hydrodynamic fields which would have been overlooked had we chosen to average over a drive cycle as earlier studies have done. In particular, the high spatial resolution available from our measurements reveals a serrated substructure in the shock waves which has not been reported before. This substructure is the result of collisional momentum transport .; One of the current issues in formulating a granular continuum model is how to incorporate local and non-local dependencies between stress and strain correctly. In this thesis we demonstrate that the collisional transfer of momentum produces a non-local effect in the stress tensor which plays a major role in determining the mean flow. Current models have incorporated only the collisional or ballistic component, but rarely both. Our work here will show that neither component can be ignored. To our knowledge, this thesis represents the first experimental visualization of collisional transport in a granular system. Further, we have identified its essential role in the formation of a granular shock wave. We measure the speed of these shock waves at different densities and show that a theoretical speed of sound prediction is difficult with the currently available models. Our findings suggest that a typical granular hydrostatic pressure equation fails to fully capture the collisional contribution to pressure. We make suggestions for how the theory could be improved.