The Dynamics in Vibro-fluidized Beds: A Diffusing Wave Spectroscopy Study

We demonstrate the densification of a granular model system of polystyrene spheres over time by shaking with varying excitation amplitudes or effective temperatures. This densification is quantified by the mean square displacement (MSD), which is measured by diffuse wave spectroscopy (DWS) of a sinusoidally excited vibrating fluidized granular bed. The DWS method also extracts the inherent heterogeneous dynamics of the system in the bulk and at the wall. Through an empirical model-based extraction we obtain the ballistic and diffusive time constants, as well as caging sizes, which were found to depend on temperature and density. The results obtained from this study reveal a sub-diffusive power-law behavior in the MSD, indicating an arrest of motion and potentially a glassy system, especially in cases where the excitation is low to moderate compared to gravity. The extracted MSD caging sizes are two orders smaller than the Lindeman length found in colloidal systems.