Abstract
Equations for fully fluidized granular materials are proposed and are solved in a simple case. In fully fluidized granular materials, the granular particles slip or collide with each other and energy is dissipated. In describing the energy dissipation process characteristic to granular materials, a measure of random motion of granular particles is introduced as a new internal variable. We derive the constitutive equations by using a simple kinematical model of the collision of particles. The set of equations for fully fluidized granular materials obtained has properties similar to the equations that describe turbulence. For reasonable assumptions, these equations predict the results of Bagnold, namely that the shear and normal stress depend upon the square of the velocity gradient. In case of steady one-dimensional gravity flow the calculated flow profiles resemble experimental ones.
Résumé
Des équations pour des matériaux granulés entièrement fluides sont proposées et résolues dans un cas simple. Par le frottement et les collisions des particules entre elles, de l'énergie est dissipée. Pour décrire l'énergie de dissipation, on introduit une mesure du mouvement aléatoire des particules comme nouvelle variable intense. Un module cinématique simple de la collision des particules permet d'établir les équations. Ces équations ont des propriétés semblables aux équations de la turbulence. Sous des hypothèses raisonnables, elles prédisent les résultats de Bagnold, à savoir que l'abrasion et la tension normale dépendent du gradient de la vitesse. Pour un flux de granité stable, les profils de flux calculés ressemblent à ceux obtenus expérimentalement.
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Ogawa, S., Umemura, A. & Oshima, N. On the equations of fully fluidized granular materials. Journal of Applied Mathematics and Physics (ZAMP) 31, 483–493 (1980). https://doi.org/10.1007/BF01590859
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DOI: https://doi.org/10.1007/BF01590859