Ss. Hsiau et Ml. Hunt, KINETIC-THEORY ANALYSIS OF FLOW-INDUCED PARTICLE DIFFUSION AND THERMAL CONDUCTION IN GRANULAR MATERIAL FLOWS, Journal of heat transfer, 115(3), 1993, pp. 541-548
The present study on granular material flows develops analytical relat
ions for the flow-induced particle diffusivity and thermal conductivit
y based on the kinetic theory of dense gases. The kinetic theory model
assumes that the particles are smooth, identical, and nearly elastic
spheres, and that the binary collisions between the particles are isot
ropically distributed throughout the flow. The particle diffusivity an
d effective thermal conductivity are found to increase with the square
root of the granular temperature, a term that quantifies the kinetic
energy of the flow. The theoretical particle diffusivity is used to pr
edict diffusion in a granular-flow mixing layer, and to compare qualit
atively with recent experimental measurements. The analytical expressi
on for the effective thermal conductivity is used to define an apparen
t Prandtl number for a simple-shear flow; this result is also qualitat
ively compared with experimental measurements. The differences between
the predictions and the measurements suggest limitations in applying
kinetic theory concepts to actual granular material flows, and the nee
d for more detailed experimental measurements.