Ss. Hsiau et Ml. Hunt, SHEAR-INDUCED PARTICLE DIFFUSION AND LONGITUDINAL VELOCITY FLUCTUATIONS IN A GRANULAR-FLOW MIXING LAYER, Journal of Fluid Mechanics, 251, 1993, pp. 299-313
In flows of granular material, collisions between individual particles
result in the movement of particles in directions transverse to the b
ulk motion. If the particles were distinguishable, a macroscopic overv
iew of the transverse motions of the particles would resemble a self-d
iffusion of molecules as occurs in a gas. The present granular-flow st
udy includes measurements of the self-diffusion process, and of the co
rresponding profiles of the average velocity and of the streamwise com
ponent of the fluctuating velocity. The experimental facility consists
of a vertical channel fed by an entrance hopper that is divided by a
splitter plate. Using differently-coloured but otherwise identical gla
ss spheres to visualize the diffusion process, the flow resembles a cl
assic mixing-layer experiment. Unlike molecular motions, the local par
ticle movements result from shearing of the flow; hence, the diffusion
experiments were performed for different shear rates by changing the
sidewall conditions of the test section, and by varying the flow rate
and the channel width. In addition, experiments were also conducted us
ing different sizes of glass beads to examine the scaling of the diffu
sion process. A simple analysis based on the diffusion equation shows
that the thickness of the mixing layer increases with the square-root
of downstream distance and depends on the magnitude of the velocity fl
uctuations relative to the mean velocity. The results are also consist
ent with other studies that suggest that the diffusion coefficient is
proportional to the particle diameter and the square-root of the granu
lar temperature.