KINETIC-THEORY ANALYSIS OF FLOW-INDUCED PARTICLE DIFFUSION AND THERMAL CONDUCTION IN GRANULAR MATERIAL FLOWS

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.