Granular Flow Lubrication: Continuum Modeling of Shear Behavior

Abstract

Because at extreme temperatures, conventional liquid lubrication breaks down, researchers have proposed using flows of solid particles as a lubricating mechanism. The particles may be powders, which tend to coalesce and slide over one another in sustained contact, or granules, which collide with one another in fluctuating motion. Distinction between these two regimes is elucidated. The behavior of various granular flows is studied using a granular kinetic lubrication (GKL) model. Our GKL model is a continuum approach that applies proper rheological constitutive equations for stress, conduction and dissipation to thin shearing flows of granular particles, as well as the most rigorous boundary conditions for momentum and energy transport. A robust numerical code, utilizing Newton’s finite differencing method, is developed to apply GKL theory to the problem of simple shearing flow. The code solves two second-order, coupled nonlinear ordinary differential equations with coupled boundary conditions of the first-order. As a result, new parametric curves for the local flow properties of the large-particle granular flows are constructed. Results from the GKL model agree qualitatively with past experiments using glass granules in an annular shear cell.