Kinetic Theory Analysis of Flow-Induced Particle Diffusion and Thermal Conduction in Granular Material Flows

Abstract

The present study on granular material flows develops analytical relations for the flow-induced particle diffusivity and thermal conductivity 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 isotropically distributed throughout the flow. The particle diffusivity and 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 predict diffusion in a granular-flow mixing layer, and to compare qualitatively with recent experimental measurements. The analytical expression for the effective thermal conductivity is used to define an apparent Prandtl number for a simple-shear flow; this result is also qualitatively 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 need for more detailed experimental measurements.