An Introduction to Granular Flow

Abstract

The flow of granular materials such as sand, snow, coal, and catalyst particles is a common occurrence in natural and industrial settings. They are important since a large fraction of the materials handled and processed in the chemical, metallurgical, pharmaceutical, and food-processing industries are granular in nature. The mechanics of these materials' flows is not well understood. This book describes the theories for granular flow based mainly on continuum models, although alternative discrete models are also discussed briefly. The level is appropriate for advanced undergraduates or beginning graduate students. The goal is to inform the reader about observed phenomena and some available models and their shortcomings and to visit some issues that remain unresolved. There is a selection of problems at the end of the chapters to encourage exploration, and extensive references are given.

On the turbulent boundary layer of a dry granular avalanche down an incline. I. Thermodynamic analysis

“…When in motion, the interactions among the solid grains result from short--term instantaneous elastic and inelastic collisions and long-term enduring frictional contact and sliding. They play a structural role in the macroscopic behavior, and are characterized as the microstructural effect (Aranson and Tsimring, 2009;Ausloos et al, 2005;GDR MiDi, 2004;Mehta, 2007;Pöschel and Brilliantiv, 2013;Rao and Nott, 2008). Depending on dominant microstructural grain-grain interactions, the quasi-static, dense and collisional flow states are defined, by which the avalanche is classified as a flow with rapid speed (flow in collisional state) (Pudasaini and Hutter, 2007;Pöschel and Brilliantiv, 2013;Rao and Nott, 2008).…”

Higher-order moment theories for dilute granular gases of smooth hard spheres

“…We consider a dilute granular gas composed of smooth-inelastic-identical hard-spheres of mass m and diameter d. The binary collision between two such spheres having precollisional velocities c and c 1 leads to the following velocity transformation after the collision (see e.g., Brilliantov & Pöschel 2004;Rao & Nott 2008):…”

“…The velocities c ′′ and c ′′ 1 are the pre-collisional velocities in an inverse collision and are related to the c and c 1 as follows (see e.g., Brilliantov & Pöschel 2004;Rao & Nott 2008).…”

“…While writing (2.10), the symmetry properties of the Boltzmann collision operator (Brilliantov & Pöschel 2004;Rao & Nott 2008) have been employed. It should be noted from the transfer equation (2.9) that irrespective of the value of ψ chosen for defining a moment by (2.7), the transfer equation (2.9) will always contain an additional moment of one more order in the flux term.…”

“…It is worth pointing out that the stress and heat flux appearing in (2.12) and (2.13)-in general-have non-vanishing collisional contributions in addition to the usual kinetic contribution given by (2.14) (Brey et al 1997;Garzó & Dufty 1999;Rao & Nott 2008;Garzó 2013). However, for dilute granular gases, the kinetic contributions to the stress and heat flux dominate over their respective collisional transfer contributions, and therefore the collisional transfer contributions to the stress and heat flux can be neglected for dilute granular gases (Brilliantov & Pöschel 8 V. K. Gupta et al 2004).…”