A Continuum Description of Dense Granular Lubrication Flow

The present paper applies a recent continuum theory due to Aranson and Tsimring (2002, “Continuum Theory of Partially Fluidized Granular Flows,” Phys. Rev. E, 65, p. 061303) for the dense granular flow of particles in sustained contact to lubrication flows. Such third body granular flow may apply to some solid lubrication mechanisms. The continuum theory is unique in that it addresses solidlike behavior and the transition to fully fluidized behavior. The continuum studies are complemented by a discrete particle dynamics model of Iordanoff et al. (2005, “Numerical Study of a Thin Layer of Cohesive Particles Under Plane Shearing,” Powder Technol., 159, pp. 46–54). Three problems are treated: (1) flow due to the gravity of a layer of granular material down an inclined plane, (2) simple shear flow of a layer confined between sliding parallel surfaces, and (3) lubrication flow of a layer confined between a curved surface and a sliding plane. The perspective of this paper is that a continuum model will be more useful than a discrete model in engineering design of solid lubrication systems for the foreseeable future. In the inclined plane problem, the discrete simulations are used to provide material property parameters to the continuum model. In the simple shear problem, for validation, predictions of the continuum model are compared to those of the discrete element computer simulations. Finally, the continuum theory is applied to a more complex lubrication flow.