Characterizing the rheology of fluidized granular matter

In this study we characterize the rheology of fluidized granular matter subject to secondary forcing. Our approach consists of first fluidizing granular matter in a drum half filled with grains via simple rotation and then superimposing oscillatory shear perpendicular to the downhill flow direction. The response of the system is mostly linear, with a phase lag between the grain motion and the oscillatory forcing. The rheology of the system can be well characterized by the GDR MiDi model if the system is forced with slow oscillations. The model breaks down when the forcing time scale becomes comparable to the characteristic time for energy dissipation in the flow.

Figure 1

Schematic of the experimental apparatus. The drum is half filled with glass beads of diameter $d$ and density $\rho$ and the grains are fluidized by rotating the drum with angular frequency $\Omega$. A secondary shear is applied by oscillating the drum with frequency $f$ and the oscillating motion of the grains at the surface is recorded with a high speed camera. The plot to the right shows the motion of the drum [dark (blue)] and 2-mm grains [light (orange)] measured for $f=2.5$ Hz plus sinusoidal fits (black solid lines).

Figure 2

Phase lag $\delta \varphi \left(f\right)$ vs oscillation frequency for representative particle sizes $d$ and rotation rates $\Omega$. The units for $d$ and $\Omega$ are mm and Hz, respectively.

Figure 3

Dimensionless response curves are shown for our model and the experimental data. The black solid line is data from the model and the black dashed line is an extension of the linear regime found in the model and is meant as a guide to the eye. The symbols are experimental data. The units for $d$ and $\Omega$ are mm and Hz, respectively.