This work was supported by the Office of Naval Research (ONR N00014-15-1-0020)[Tkacik and Keanini] and performed at the University of North Carolina at Charlotte&#39;s Motorsports Research Lab. Polishing media was donated by Rosler.

<ol>
	<li>Berne, B. J., Pecora, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Dynamic Light Scattering. , (1976).</li><li>Boon, J. P., Yip, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Molecular Hydrodynamics. , (1980).</li><li>Brown, J. C., Pusey, P. N., Goodwin, J. W., Ottewill, R. H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Light+scattering+study+of+dynamic+and+time-averaged+correlations+in+dispersions+of+charged+particles.">Light scattering study of dynamic and time-averaged correlations in dispersions of charged particles.</a> J. Phys. A: Math Gen. 5 (8), 664-682 (1975).</li><li>Wainwright, T. E., Alder, B. J., Gass, D. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Decay+of+time+correlations+in+two+dimensions.">Decay of time correlations in two dimensions.</a> Phys. Rev. A. 4, 233-236 (1971).</li><li>Evans, D. J., Morriss, G. P. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Statistical Mechanics of Nonequilibrium Liquids. , (2007).</li><li>Levesque, D., Verlet, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Computer+"experiments"+on+classical+fluids,+III.+time-dependent+self+correlation+functions.">Computer "experiments" on classical fluids, III. time-dependent self correlation functions.</a> Phys. Rev. A. 2, 2514-2528 (1970).</li><li>Levesque, D., Ashurst, W. T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Long-time+behavior+of+the+velocity+autocorrelation+function+for+a+fluid+of+soft+repulsive+particles.">Long-time behavior of the velocity autocorrelation function for a fluid of soft repulsive particles.</a> Phys. Rev. Lett. 33, 277-280 (1970).</li><li>Lovesey, S. W., Lovesey, S. W., Springer, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Dynamics of solids and liquids by neutron scattering. , (1977).</li><li>Forster, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Hydrodynamic fluctuations, broken symmetry, and correlation functions. , (1990).</li><li>Mountain, R. D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Generalized+hydrodynamics.">Generalized hydrodynamics.</a> Adv. Mol. Relax. Processes. 9, 225-291 (1977).</li><li>Zwanzig, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Time-correlation+functions+and+transport+coefficients+in+statistical+mechanics.">Time-correlation functions and transport coefficients in statistical mechanics.</a> Ann. Rev. Phys. Chem. 16, 67-102 (1965).</li><li>Keanini, R. G., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Macroscopic+liquid-state+molecular+hydrodynamics.">Macroscopic liquid-state molecular hydrodynamics.</a> Sci. Rep. 7, 41658 (2017).</li><li>Kushick, J., Berne, B. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Role+of+attractive+forces+in+self-diffusion+in+dense+Lennard-Jones+fluids.">Role of attractive forces in self-diffusion in dense Lennard-Jones fluids.</a> J. Chem. Phys. 59 (7), 3732-3736 (1973).</li><li>Mullany, B., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+application+of+computational+fluid+dynamics+to+vibratory+finishing+processes.">The application of computational fluid dynamics to vibratory finishing processes.</a> CIRP Annals. , (2017).</li><li>Fleischhauer, E., Azimi, F., Tkacik, P. T., Keanini, R. G., Mullany, B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Application+of+particle+imaging+velocimetry+(PIV)+to+vibrational+finishing.">Application of particle imaging velocimetry (PIV) to vibrational finishing.</a> J. Mater. Process. Technol. 229, 322-328 (2016).</li><li>Navare, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Experimental and computational evaluation of a vibratory finishing process. , (2017).</li><li>Bolmatov, V., Brazhkin, V., Trachenko, K. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+phonon+theory+of+liquid+thermodynamics.">The phonon theory of liquid thermodynamics.</a> Sci. Rep. 2, 421 (2012).</li><li>Elton, D. C., Fernandez-Serra, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+hydrogen-bond+network+of+water+supports+propagating+optical+phonon-like+modes.">The hydrogen-bond network of water supports propagating optical phonon-like modes.</a> Nat. Commun. 7, 10193 (2016).</li><li>Pathria, R. K., Beale, P. D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Statistical mechanics. , (2011).</li><li>Gibbs, J. W. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Elementary principles in statistical mechanics. , (1902).</li><li>Toda, M., Kubo, R., Saito, N. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Statistical physics I. , (1992).</li><li>Kubo, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Statistical+mechanical+theory+of+irreversible+processes.">Statistical mechanical theory of irreversible processes.</a> I. J. Phys. Soc. Japan. 12, 570-586 (1957).</li><li>Kubo, R., Toda, M., Hashitsume, N. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Statistical physics II: nonequilibrium statistical mechanics. , (1991).</li></ol>

The authors have nothing to disclose.

In order to use vibrated grain piles as macroscopic analogs for investigating molecular hydrodynamic processes, an experimentalist must, on one hand, learn and use four basic measurements, and on the other, master a few basic elements of equilibrium and non-equilibrium statistical mechanics. Focusing first on experimental measurements, these include: i) measurement of individual grain dynamics through measurement of the single-particle velocity autocorrelation function, ii) measurement of time-average/long-time-scale sur...

Molecular hydrodynamics studies the dynamics and statistical mechanics of individual molecules and collections of molecules within fluids. Among the many experimental techniques developed for studying molecular hydrodynamic systems1,2, light scattering1,2,3, molecular dynamic simulations4,5,6,7 and, to a lesser extent, inelastic neutron scattering8 have been most commonly used. Unfortunately, significant limitations attach to the latter two techniques. Molecular dynamics (MD) simulations, for example: i) are limited to small spatial and temporal <img alt="Equation 1" src="/files/ftp_upload/56632/56632eq1.jpg" /> domains containing relatively few molecules <img alt="Equation 2" src="/files/ftp_upload/56632/56632eq2.jpg" />, ii) require use of approximate inter-particle potentials, iii) typically introduce periodic boundary conditions, invalid under non-equilibrium bulk flow conditions, and iv) cannot, at present, answer the fundamental question of how molecular-scale dynamics, involving either single molecules or collections of molecules, are affected by, and couple back to, bulk, non-equilibrium fluid flow. The main limitation associated with neutron scattering is tied to the difficulty of accessing the limited number of neutron beam sources available.
In order to provide context for the analog experimental technique presented in this article, we highlight light scattering techniques applied to simple dense-gas and liquid-state fluids. In a typical light scattering experiment, a polarized laser light beam is directed to a small interrogation volume containing a stationary fluid sample. Light scattered from molecules within the sample is then detected at some fixed angle relative to the incident beam. Depending on the molecular dynamic regime of interest, detection and analysis of the scattered light signal incorporates either light filtering or light mixing detection methods. As outlined by Berne and Pecora1, filtering techniques, which probe fluid state molecular dynamics on time scales shorter than <img alt="Equation 3" src="/files/ftp_upload/56632/56632eq3.jpg" /> s, introduce a post-scattering interferometer or diffraction grating, and allow scanning of the spectral density of the scattered light. Optical mixing techniques, used for slow-time-scale dynamics, <img alt="Equation 4" src="/files/ftp_upload/56632/56632eq4.jpg" /> s, by contrast, incorporate a post-scattering autocorrelator or spectrum analyzer, in which the spectral content of the scattered signal is extracted from the measured scattered light intensity.
Generally, laser probes, at least those operating in the visible range of the spectrum, have wavelengths much longer than the characteristic spacing between liquid-state molecules. Under these circumstances, the probe beam excites five collective, slow-time-scale, long-wave-length hydrodynamic modes2,9,10 (slow relative to the characteristic collision frequency): two viscously damped, counter-propagating sound waves, two uncoupled, purely diffusive vorticity modes, and a single diffusive thermal (entropy) mode. The sound modes are excited in the (longitudinal) direction of the incident beam, while the vortical modes are excited in the transverse direction.
Considering purely experimental scattering techniques, two fundamental questions, lying at the heart of the equilibrium and non-equilibrium statistical mechanics of molecular, liquid-state systems, remain beyond light and neutron scattering measurements: 
1) Rigorous arguments9,11 show that the random, collision- and sub-collision-time-scale dynamics of individual liquid-state molecules, subject to either classical Newtonian dynamics or quantum dynamics, can be recast in the form of generalized Langevin equations (GLE). GLE&#39;s, in turn, comprise a central theoretical tool in the study of the non-equilibrium statistical mechanics of molecules in dense gases and liquids. Unfortunately, since the dynamics of individual (non-macromolecular) molecules cannot be resolved by either scattering technique, there is presently no direct way, beyond MD simulations, to test the validity of GLE&#39;s. 
2) A fundamental hypothesis lying at the heart of macroscopic continuum fluid dynamics, as well microscale molecular hydrodynamics, posits that on length- and time-scales large relative to molecular diameters and collision times, but small relative to continuum length- and time-scales, local thermodynamic equilibrium (LTE) prevails. In continuum flow and heat transfer models, like the Navier-Stokes (NS) equations, the LTE assumption is required9 in order to couple intrinsically non-equilibrium, continuum-scale flow and energy transport features &#8212; like viscous shear stresses and thermal conduction &#8212; to strictly equilibrium thermodynamic properties, like temperature and internal energy. Likewise, while microscale momentum and energy transport are intrinsically non-equilibrium processes, reflecting the appearance of coupled, microscale mass, momentum, and energy currents, models of these microscale processes assume that the currents represent small perturbations from LTE9. Again, to the best of our knowledge, there have been no direct experimental tests of the LTE assumption. In particular, it appears that no molecular hydrodynamic scattering experiments have been attempted within dense, moving, non-equilibrium fluid flows.
In this paper, we outline an analog experimental technique in which the macroscopic, single particle and collective particle dynamics of vibrated grain piles, measured using standard Particle Imaging Velocimetry (PIV), can be used to indirectly predict, interpret, and expose single- and multi-molecule hydrodynamics in dense gases and liquids. The physical and theoretical elements that enable the proposed technique are stated in a recent paper published by our group12. Experimentally, the macroscopic system must exhibit: (i) a sustained tendency toward local, macroscale statistical mechanical equilibrium, and (ii) small, linear departures from equilibrium that mimic (weak) non-equilibrium fluctuations observed in molecular hydrodynamic systems. Theoretically: (i) classical microscale models describing the equilibrium and weakly-non-equilibrium statistical mechanics of dense, interacting N-particle systems must be recast in macroscale form, and (ii) the resulting macroscale models must reliably predict single- and multiple-particle dynamics, from short, particle-collision-time-scales to long, continuum-flow-time-scales.
Here, we present a detailed experimental protocol as well as representative results obtained by the new technique. In contrast to MD simulations and light and neutron scattering methods, the new technique allows, for the first time, detailed study of molecular hydrodynamic processes within flowing, strongly non-equilibrium, dense gases and liquids.

<table>
	<tbody>
		<tr>
			<td>Vibratory Polishing Bowl</td>
			<td>Raytech</td>
			<td>AV-75</td>
			<td></td>
		</tr>
		<tr>
			<td>Flow Meter</td>
			<td>Peristaltic Pumps</td>
			<td>913 Mity Flex</td>
			<td></td>
		</tr>
		<tr>
			<td>Scale</td>
			<td>Pelouze</td>
			<td>4040</td>
			<td></td>
		</tr>
		<tr>
			<td>Triaxial Accelerometer</td>
			<td>PCB Piezotronics</td>
			<td>PCB 356B11</td>
			<td>Accelerometer with Sensor Signal Conditioner</td>
		</tr>
		<tr>
			<td>Data Acquisition Computer</td>
			<td>IBM</td>
			<td>Thinkpad</td>
			<td>Used with high speed camera</td>
		</tr>
		<tr>
			<td>High Speed Camera</td>
			<td>Redlake</td>
			<td>Motionxtra HG-XR</td>
			<td></td>
		</tr>
		<tr>
			<td>Zoom Lens</td>
			<td>Tamron</td>
			<td>Model A18</td>
			<td>18-250mm F/3.5-6.3&#160;</td>
		</tr>
		<tr>
			<td>High intensity Light</td>
			<td>ARRI</td>
			<td>EB 400/575 D</td>
			<td></td>
		</tr>
		<tr>
			<td>Data Processing Computer</td>
			<td>Dell</td>
			<td>Dell Precision Tower 7910</td>
			<td></td>
		</tr>
		<tr>
			<td>PIV Software&#160;</td>
			<td>Dantec Dynamics</td>
			<td>Dynamic Studio 2013</td>
			<td>version 3.41.38</td>
		</tr>
		<tr>
			<td>Data Acquisition Hardware</td>
			<td>National Instruments</td>
			<td>SCXI</td>
			<td>SCXI-1000 Chasis with SCXI 1100 Card and SCXI 1303 Adapter</td>
		</tr>
		<tr>
			<td>Data Acquisition Software</td>
			<td>National Instruments</td>
			<td>LabVIEW 2012</td>
			<td></td>
		</tr>
		<tr>
			<td>Data Processing Software</td>
			<td>MATHWORKS</td>
			<td>MATLAB</td>
			<td></td>
		</tr>
		<tr>
			<td>Polishing Media</td>
			<td>Rosler</td>
			<td>RSG 10/10S</td>
			<td>Multiple media types used (mixed, spherical, triangular)</td>
		</tr>
		<tr>
			<td>Polishing Solution</td>
			<td>Rosler</td>
			<td>FC KFL (3%)</td>
			<td>3% soap solution with water</td>
		</tr>
		<tr>
			<td>Ruled Scale</td>
			<td>Swiss Precision Instruments</td>
			<td>13-911-3</td>
			<td></td>
		</tr>
		<tr>
			<td>Graduated Cylinder</td>
			<td>Global Scientific</td>
			<td>601082</td>
			<td></td>
		</tr>
	</tbody>
</table>

an analog macroscopic technique for studying molecular hydrodynamic processes in dense gases and liquids

An analog, macroscopic method for studying molecular-scale hydrodynamic processes in dense gases and liquids is described. The technique applies a standard fluid dynamic diagnostic, particle image velocimetry (PIV), to measure: i) velocities of individual particles (grains), extant on short, grain-collision time-scales, ii) velocities of systems of particles, on both short collision-time- and long, continuum-flow-time-scales, iii) collective hydrodynamic modes known to exist in dense molecular fluids, and iv) short- and long-time-scale velocity autocorrelation functions, central to understanding particle-scale dynamics in strongly interacting, dense fluid systems. The basic system is composed of an imaging system, light source, vibrational sensors, vibrational system with a known media, and PIV and analysis software. Required experimental measurements and an outline of the theoretical tools needed when using the analog technique to study molecular-scale hydrodynamic processes are highlighted. The proposed technique provides a relatively straightforward alternative to photonic and neutron beam scattering methods traditionally used in molecular hydrodynamic studies.

In presenting representative results, we refer to continuum-time-scale processes as those observed and predicted over time-scales, <img alt="Equation 25" src="/files/ftp_upload/56632/56632eq25.jpg" /> that are long relative to the characteristic grain collision time scale, <img alt="Equation 26" src="/files/ftp_upload/56632/56632eq26.jpg" /> <img alt="Equation 27" src="/files/ftp_upload/56632/56632eq27.jpg" /> and particle-time-scale processes as those observed and predi...

Watch this Scientific Journal Video about An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids at JoVE.com

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An experimentally accessible analog method for studying molecular hydrodynamic processes in dense fluids is presented. The technique uses particle image velocimetry of vibrated, high-restitution grain piles and allows direct, macroscopic observation of dynamical processes known and predicted to exist in strongly interacting, high density gases and liquids.

An analog, macroscopic method for studying molecular-scale hydrodynamic processes in dense gases and liquids is described. The technique applies a ...

an-analog-macroscopic-technique-for-studying-molecular-hydrodynamic

Education

Research

JoVE Core

JoVE Journal

Physics

Engineering

Chemistry

Civil Engineering

Unit 1

Vectors and Scalars

Fluid Dynamics

Gases

SCIENTISTS IN ACTION

8.4K Views.  University of North Carolina at Charlotte. An experimentally accessible analog method for studying molecular hydrodynamic processes in dense fluids is presented. The technique uses particle image velocimetry of vibrated, high-restitution grain piles and allows direct, macroscopic observation of dynamical processes known and predicted to exist in strongly interacting, high density gases and liquids.