Experimental evidence and theoretical modeling suggest that piles of confined, high-restitution grains, subject to low-amplitude vibration, can serve as experimentally-accessible analogs for studying a range of liquid-state molecular hydrodynamic processes. Experiments expose single-grain and multiple-grain, collective dynamic features that mimic those either observed or predicted in molecular-scale, liquid state systems, including: (i) near-collision-time-scale hydrodynamic organization of single-molecule dynamics, (ii) nonequilibrium, long-time-scale excitation of collective/hydrodynamic modes, and (iii) long-time-scale emergence of continuum, viscous flow. In order to connect directly observable macroscale granular dynamics to inaccessible and/or indirectly measured molecular hydrodynamic processes, we recast traditional microscale equilibrium and nonequilibrium statistical mechanics for dense, interacting microscale systems into self-consistent, macroscale form. The proposed macroscopic models, which appear to be new with respect to granular physics, and which differ significantly from traditional kinetic-theory-based, macroscale statistical mechanics models, are used to rigorously derive the continuum equations governing viscous, liquid-like granular flow. The models allow physically-consistent interpretation and prediction of observed equilibrium and non-equilibrium, single-grain, and collective, multiple-grain dynamics.
Confined, vibration-driven grain piles exhibit fluid-like properties, in particular, predictable, non-random flow patterns, hydrodynamic modal response to vibrational forcing, and a persistent, spatially uniform tendency toward local statistical mechanical equilibrium. This paper presents a technique that combines particle image velocimetry of vibration-driven grain flow over a submerged, instrumented cylinder and measurement of the flow-induced drag force on the cylinder to determine the grain flows effective kinematic viscosity. The fundamental basis of such measurements is provided by recent work showing that highrestitution grain piles subject to low-amplitude vibration are macroscopic dynamical analogs of liquid-state molecular hydrodynamic systems. Practically, the proposed viscometric method provides a key material property, the kinematic, or equivalently, dynamic viscosity, for use in computational fluid dynamic simulations of a variety of materials processing operations that utilize vibration-driven grain flows.
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