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      Macroscopic liquid-state molecular hydrodynamics

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          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.

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          Most cited references 17

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          Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems

           Ryogo Kubo (1957)
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            Hydrodynamic equations and correlation functions

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              Time-Correlation Functions and Transport Coefficients in Statistical Mechanics

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                Author and article information

                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group
                2045-2322
                31 January 2017
                2017
                : 7
                Affiliations
                [1 ]The University of North Carolina at Charlotte, Department of Mechanical Engineering and Engineering Science , Charlotte, NC, 28223, USA
                Author notes
                Article
                srep41658
                10.1038/srep41658
                5282555
                28139711
                Copyright © 2017, The Author(s)

                This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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