Abstract
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.
Highlights
As a guide to what is presented, both in the paper and in the Supplementary material, we highlight the main results: (1) We show experimentally that a large family of vibrated, high-restitution grains exist in local statistical mechanical equilibrium; see subsection entitled ‘Macroscale Equilibrium Statistical Mechanics’ below
In contrast to microscale theoretical predictions, we observe hydrodynamic organization on sub- and near-collision time-scales; molecular dynamic (MD) models predict this effect on slightly longer time-scales
(4) Similar to atomic liquids and dense gases exposed to weak external perturbations, the low-frequency, collective response of vibrated grain piles is characterized by excitation of hydrodynamic modes
Summary
This paper reports a set of experimental and theoretical contributions to the study of dense, liquid-like, vibration-driven granular systems. Grains remain closely packed so that these short wave modes survive randomization, at least for a time This effect, signaled by a negative dip in the near-collision time-scale ψ(t) and representing an approximate indicator of the liquid state, is seen in four of the eight grains tested; see Fig. 3. Amplitude spectra determined from simultaneous bowl acceleration and PIV grain velocity measurements, shown, expose several hydrodynamic features either experimentally observed or simulated, or expected in atomic liquids and dense gases: (i) damped acoustic modes, (ii) long-time-average fluid flow, and (iii) generalized Langevin single-grain dynamics. Vibrated grain piles exhibit the same dynamical hierarchy observed in dense gases and simple liquids: (i) on sub-, near-, and supra-collision-time-scales, generalized Langevin single-grain response and low-frequency, multiple-grain, collective hydrodynamic response, here to vibrational forcing, and (ii) as described on longer time-scales, organized, emergent flow. Analytical model outlined in Supplement 2, we obtain three-dimensional, helical flows that are qualitatively similar to those measured
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