Granular flow: physical experiments and their implications for microstructural theories

Abstract

Positions, velocities and rotations of individual particles obtained from high-speed motion pictures of essentially two-dimensional flows of plastic spheres in an inclined glass-walled chute were used to test critical assumptions of microstructural theories for the flow of granular materials. The measurements provide a well-defined set of observations for refining and validating computer simulations of granular flows, and point out some important limitations of physical experiments. Two nearly steady, uniform, collisional flows of 6-mm-diameter plastic spheres over a fixed bed of similar spheres inclined at 42.75° were analysed in detail. Particle fluxes were about 2230 particles s−1 and 1280 particles s−1. The nominal depth in both flows was about 18 particle diameters. Profiles of mean downstream velocity and mean rotations, translational temperature and rotational temperature, and bulk density in the flows show slip at the bed of 17 and 26% of the mean flow velocity for the high- and low-flux flows, respectively; mean rotation rates $\overline{\omega}_x$ and $\overline{\omega}_y$ less than 9% of $\overline{\omega}_z$ ($\hat{e}_x$ parallel to the bed, $\hat{e}_x$ normal to the sidewall); translational temperature nearly independent of distance from the bed; rotational temperature decreasing with distance from the bed; and density decreasing almost linearly with distance from the bed. The continuum hypothesis (i.e. small gradients in mean-flow properties) is satisfied throughout the flow except near the fixed bed, where large gradients in the mean rotation $\overline{\omega}_z$ and downstream velocity occur over a few particle diameters. The distributions of velocities and rotations are approximately Maxwellian, except near the fixed bed. Testing microstructural theories with physical experiments is severely hampered by limitations on material properties of particles, flow lengthscale and the spatial and temporal resolution of observations. Only a small volume of the parameter space for collision-dominated flows can reasonably be explored by physical experiment. Extraneous forces due to air drag, sidewall friction and electrical effects are not included in theories but must be addressed in physical experiments. Properly designed experiments are the essential link between computer simulations and theory, because they focus attention on particular features critical to testing the simulations, which in turn provide detailed particle-scale information needed to test theories.