We have investigated the flow of dry granular materials through vertical channels in the regime of dense slow flow using video imaging of the particles adjacent to a transparent wall. Using an image processing technique based on particle tracking velocimetry, the video movies were analysed to obtain the velocities of individual particles. Experiments were conducted in two- and three-dimensional channels. In the latter, glass beads and mustard seeds were used as model granular materials, and their translational velocities were measured. In the former, aluminium disks with a dark diametral stripe were used and their translational velocities and spin were measured. Experiments in the three-dimensional channels were conducted for a range of the channel width W, and for smooth and rough sidewalls. As in earlier studies, we find that shearing takes place predominantly in thin layers adjacent to the walls, while the rest of the material appears to move as a plug. However, there are large velocity fluctuations even in the plug, where the macroscopic deformation rate is negligibly small. The thickness of the shear layer, scaled by the particle diameter dp, increases weakly with W/dp. The experimental data for the velocity field are in good agreement with the Cosserat plasticity model proposed recently. We also measured the mean spin of the particles in the two-dimensional channel, and its deviation from half the vorticity. There is a clear, measurable deviation, which too is in qualitative agreement with the Cosserat plasticity model. The statistics of particle velocity and spin fluctuations in the two-dimensional channel were analysed by determining their probability distribution function, and their spatial and temporal correlation. They were all found to be broadly similar to previous observations for three-dimensional channels, but some differences are evident. The spatial correlation of the velocity fluctuations are much stronger in the two-dimensional channel, implying a pronounced solid-like motion superimposed over an uncorrelated fluid-like motion. The strong spatial correlation over large distances has led us to propose a mechanism for the production of velocity fluctuations in the absence of a macroscopic deformation rate.
An Experimental Study on a Turbulent Flow in a Two-Dimensional Curved Channel. (Space-Time Correlation and Spectra of Velocity Fluctuations).
