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>
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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. 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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. 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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.

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 predicted over time-scales, <img alt="Equation 28" src="/files/ftp_upload/56632/56632eq28.jpg" />, that are on the order of, or smaller than <img alt="Equation 29" src="/files/ftp_upload/56632/56632eq29.jpg" /> <img alt="Equation 30" src="/files/ftp_upload/56632/56632eq30.jpg" /> where <img alt="Equation 31" src="/files/ftp_upload/56632/56632eq31.jpg" /> is the vibration frequency of the grain media container.
The proposed technique provides simultaneous, integrated, superposed experimental information on single-particle and multiple-particle, random and time-averaged dynamics extant over time scales ranging from the inverse PIV camera sample rate, <img alt="Equation 32" src="/files/ftp_upload/56632/56632eq32.jpg" /> to the length of any given experimental run, <img alt="Equation 33" src="/files/ftp_upload/56632/56632eq33.jpg" /> For the results presented here, <img alt="Equation 34" src="/files/ftp_upload/56632/56632eq34.jpg" /> camera frames per second and <img alt="Equation 35" src="/files/ftp_upload/56632/56632eq35.jpg" /> = 10.12 s.
The results are organized as follows. First, we show, using a representative video clip, that all measurements are obtained under strongly non-equilibrium conditions in which the vibrated grain media move in collective, fluid-like flow; see Supplemental Movies 1a-c . The existence of local thermodynamic equilibrium, LTE, observed at an arbitrary, spatially limited camera interrogation area on the surface of the granular flow, is then demonstrated; see Figure 3. Evidence of weak non-equilibrium departures from LTE &#8212; taking place on individual particle scales, and produced by the cyclic injection of vibrational energy into the grain media &#8212; is then presented; see Figure 4. Finally, as a means of demonstrating that long-time-scale, non-equilibrium granular flows can be reasonably predicted using coarse-grained versions of exact, discrete, particle-scale mass and momentum conservation laws, here, the Navier-Stokes (NS) equations, we present a comparison of observed time-averaged grain flow fields against those predicted by the NS equations; see Figure 6.
In our experiments, we investigate the vibration-driven dynamics of eight different grain media, each media type characterized by a given shape, or mixture of shapes, mass density, and characteristic, fixed set of dimensions. In all experiments, the media bowl is filled with a fixed total mass of grain media, and the vibration frequency and amplitude of the bowl are fixed at 29.3 Hz and 2 mm, respectively. As depicted in supplemental movie 1a, observed grain flow patterns, are for all eight media, qualitatively similar: a slow, steady, three-dimensional helical flow, reflecting a dominant, radially-inward component, in which media flows from the outer bowl boundary radially inward toward the bowl&#39;s inner boundary, combined with a weak azimuthal component. Thus, in contrast to light- and neutron-scattering measurements, measurements of single-particle- and multi-particle-scale statistical mechanics must here be carried out in the presence of non-equilibrium flow.
Vibrated grain systems allow what we believe to be the first experimental demonstration of local thermodynamic equilibrium within non-equilibrium fluid flows. As shown in Figure 3, normalized histograms of measured horizontal peculiar grain speeds, obtained at a fixed 4 mm x 4 mm interrogation area on the grain pile surface, are well-fit by Maxwell-Boltzmann (MB) distribution functions. MB distributions, in turn, provide strong evidence of several fundamental dynamical properties: i) they are consistent with the existence of collision-time-scale (dissipationless) Hamiltonian dynamics, ii) they are likewise consistent with existence of velocity-independent interparticle potential energies, as well as a potential-independent kinetic energies, and iii) they provide strong evidence of local, macroscopic, mechanical equilibrium. Importantly, all of these features can be interpreted as macroscale embodiments of dynamical properties traditionally assumed in equilibrium liquid-state molecular hydrodynamic systems.
In order to expose the statistical mechanics of individual grains, the local peculiar grain velocity must be extracted from the measured local grain velocity: i) First, periodic spectral components within the local measured velocity, reflecting solid-like elastic vibration of the grain pile, must be filtered from the (PIV-) measured, time-varying velocity observed at the interrogation point. ii) Next, the local filtered velocity record, representing the purely fluid-like flow component of the grains&#39; dynamics, is used to determine the local, time average velocity (over the entire experimental period, <img alt="Equation 36" src="/files/ftp_upload/56632/56632eq36.jpg" /> iii) Finally, the local average (filtered) velocity is subtracted from the time-varying local filtered velocity. The resulting time-varying velocity record thus represents the local peculiar fluid velocity, as observed at the interrogation point.
Beyond a tendency to revert, at all locations, toward LTE, macroscopic dynamical systems &#8211; if they are to serve as true analogs of liquid-state molecular hydrodynamic systems - must possess a second set of crucial property: weak random fluctuations from local equilibrium, taking place on collision and sub-collision-time-scales, that are consistent with generalized Langevin dynamics. Here, as shown in Figure 4, the normalized single-grain (peculiar) velocity autocorrelation function, <img alt="Equation 37" src="/files/ftp_upload/56632/56632eq37.jpg" />, exhibits the same qualitative structure long-predicted in MD simulations of dense gases and liquids2,13: i) a rapid, non-exponential, sub-collision-time-scale decay to slightly negative values, followed by ii) an extended, slow, approach back toward zero. Physically, and again consistent with MD-predicted single-molecule dynamics in dense fluids2,4 the long negative tail in shown in Figure 4 appears to reflect the collective influence of neighboring grains on the motion of individual grains12. In theoretical terms, the short-time-scale temporal structure of&#160;<img alt="Equation 38" src="/files/ftp_upload/56632/56632eq38.jpg" /> is fully consistent with, and explainable in terms of, generalized Langevin dynamics2.
Another dynamical ingredient necessary to establishing a predictive macroscopic analog to liquid-state molecular hydrodynamic systems centers on collective hydrodynamics. First, on long time-scales &#8211; long relative to <img alt="Equation 39" src="/files/ftp_upload/56632/56632eq39.jpg" /> - and on large length-scales &#8211; large relative to the characteristic grain dimension, <img alt="Equation 40" src="/files/ftp_upload/56632/56632eq40.jpg" /> - macroscopic system hydrodynamics must exhibit the same modal response structure predicted and observed in liquid-state molecular systems2,9,10. As noted above, the response of dense fluid systems to both spontaneous fluctuations and externally-imposed disturbances - for example, particle beams in scattering experiments and small-amplitude vibrations in our experiments &#8211; consists of two viscously-damped counter-propagating sound modes, two, uncoupled, diffusive vortical modes, and a diffusive thermal (entropy) mode. Second, the long-time-scale, large-length-scale collective dynamics of macroscopic N-particle systems must &#8211; as molecular systems do &#8211; follow the NS equations (including, again, mass and energy conservation).
At present, with respect to macroscopic modal response, we have only indirect experimental evidence of damped fluid-state acoustic modes: as shown in Figure 5, solid-state acoustic standing waves, driven at the imposed vibration frequency, <img alt="Equation 41" src="/files/ftp_upload/56632/56632eq41.jpg" /> as well as at harmonics of <img alt="Equation 41" src="/files/ftp_upload/56632/56632eq41.jpg" /> are observed in our vibrated grain piles. Unfortunately, due to limitations in the present experimental system, we do not observe acoustic modes in spectra of the local peculiar fluid velocity. In order to excite such modes, new experiments will be carried out in which the media bowl will be subject to cyclic impact. Based on the unambiguous existence of solid-state acoustic modes, we anticipate that this approach will expose fluid-state acoustic modes.
By contrast, we have strong evidence that the collective, macroscopic, long-time and large-scale dynamics of vibrated grain piles do obey the NS equations. As shown in Figure 6, PIV-measured steady state velocity distributions measured on the surface of a vibrated pile are well predicted by the NS equations14. Here, as detailed in Mullany et al.14, the equations are solved numerically within a rectangular, two-dimensional domain corresponding to the surface FOV used in PIV velocity field measurements14. The simulations use experimentally measured effective grain viscosities and impose spatially-varying velocity boundary conditions, determined by PIV measurements, on three of four domain boundaries. Although the simulation assumes strictly two dimensional flow, where the actual flow is three-dimensional, and neglects the presence of the media bowl&#39;s central hub (the latter giving the bowl a donut/toroidal shape), average errors between predicted and actual velocity magnitudes are only on the order of 15%.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/56632/56632fig1.jpg" /> 
Figure 1: Vibratory System Experimental Set-Up with Camera and Lighting. This system consists of an annular polyurethane bowl having an outer diameter of 600 mm, with a single-speed (1740 rpm), unbalanced motor. The camera and lighting system are suspended above the vibratory bowl and attached to support structures or tripods not in contact with the vibratory system. This ensures that the motion of the bowl does not cause movement in the camera or the light. The peristaltic pump provides steady fluid flow to lubricate the media. <a href="https://cloudflare.jove.com/files/ftp_upload/56632/56632fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
Supplemental Movie 1: Typical Grain Flow Video. (a) A typical clip of the grain flow as captured by the high speed camera. (b) Slow motion video of media undergoing tangential flow around a stationary workpiece (c) Slow motion video of media undergoing normal flow into a stationary workpiece. The PIV-measured velocity fields in (c) are compared against theoretically computed velocity fields in Figure 6. <a href="http://cloudflare.jove.com/files/ftp_upload/56632/supplementalmovie1.zip">Please click here to download these files.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/56632/56632fig2.jpg" /> 
Figure 2: Example Processing and Post Processing Images. (a) A typical FOV single image taken by the high speed camera. (b) A typical calibration image with a scaled ruler. (c) Zoomed in view of velocity vector map overlaid on the first frame of the double frame images used to calculate the vectors. The vectors represent the particle movement between first and second frames of the double frame. The velocity ranges from ~0 m/s (dark red) to 0.17 m/s (yellow) in this figure. <a href="https://cloudflare.jove.com/files/ftp_upload/56632/56632fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/56632/56632fig3.jpg" /> 
Figure 3: Experimental evidence of local statistical mechanical equilibrium. Distributions of horizontal peculiar (random) grain speeds, measured at the point shown in (f), are fit by two dimensional Maxwell-Boltzmann (MB) speed distributions. (a-e) depicts Speeds (v), and probability density functions (pdf) are in units of cm s-1 and s cm-1, respectively, and the red scales represent 1 cm by grain type. The grains shown are: (a) RS19K; (b) mixed media; (c) RS1010; (d) RCP0909; and (e) RS3515. This figure has been modified from Keanini et al. in Science Reports (2017)12. <a href="https://cloudflare.jove.com/files/ftp_upload/56632/56632fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/56632/56632fig4.jpg" /> 
Figure 4: Single grain, short-time-scale dynamics. The velocity autocorrelation function, <img alt="Equation 42" src="/files/ftp_upload/56632/56632eq42.jpg" />, for single grains, plotted as a function of the characteristic number of grain collisions, <img alt="Equation 43" src="/files/ftp_upload/56632/56632eq43.jpg" />, where t is the time lag and <img alt="Equation 31" src="/files/ftp_upload/56632/56632eq31.jpg" /> is the vibration frequency. Collision-time-scale, single grain dynamics exhibit trends qualitatively mimicking those predicted in molecular liquids and dense gases, including: (i) trapped particle dynamics, here determined by the continuum response of the grain fluid to vibrational forcing12, (ii) rapid, non-exponential decay in <img alt="Equation 38" src="/files/ftp_upload/56632/56632eq38.jpg" />, consistent with generalized Langevin dynamics12, and (iii) manifestation of dense gas, liquid, and mixed liquid-solid thermodynamic phases12. This figure has been modified from Keanini et al. in Science Reports (2017)12. <a href="https://cloudflare.jove.com/files/ftp_upload/56632/56632fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/56632/56632fig5.jpg" /> 
Figure 5: Vibrational response to vibration. Amplitude spectra15, determined from local PIV grain velocity measurements and from simultaneous container acceleration measurements, are shown in (a and b), respectively. The PIV measurement location is shown in Figure 3f; grain container accelerations are obtained from the exterior of the container. Resonant acoustic waves within the grain pile-container system, manifested by peaks in the spectrum (a), nominally coincide with resonant acoustic modes excited within the empty container, shown in (b). The fluid dynamics of both individual grains and of the entire grain pile are exposed by filtering the solid-like acoustic response. This figure has been modified from Keanini et al. in Science Reports (2017)12. <a href="https://cloudflare.jove.com/files/ftp_upload/56632/56632fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/56632/56632fig6.jpg" /> 
Figure 6: Comparison between PIV measured and PIV predicted velocity fields. (a) PIV- measured velocity field for normal flow around a stationary workpiece (FOV has been limited to 91 mm x 198 mm to match the CFD specified area) overlaid on image of vibrating media used to create the vector map ; (b) CFD-predicted velocity field for normal flow around stationary workpiece. This figure 6b has been modified from the MSME thesis of J. Navare16. <a href="https://cloudflare.jove.com/files/ftp_upload/56632/56632fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

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 ...

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8.4K 조회수.  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.

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

Revealing Dynamic Processes of Materials in Liquids Using Liquid Cell Transmission Electron Microscopy

The recent development for in situ transmission electron microscopy, which allows imaging through liquids with high spatial resolution, has attracted significant interests across the research fields of materials science, physics, chemistry and biology. The key enabling technology is a liquid cell. We fabricate liquid cells with thin viewing windows through a sequential microfabrication process, including silicon nitride membrane deposition, photolithographic patterning, wafer etching, cell bonding, etc. A liquid cell with the dimensions of a regular TEM grid can fit in any standard TEM sample holder. About 100 nanoliters reaction solution is loaded into the reservoirs and about 30 picoliters liquid is drawn into the viewing windows by capillary force. Subsequently, the cell is sealed and loaded into a microscope for in situ imaging. Inside the TEM, the electron beam goes through the thin liquid layer sandwiched between two silicon nitride membranes. Dynamic processes of nanoparticles in liquids, such as nucleation and growth of nanocrystals, diffusion and assembly of nanoparticles, etc., have been imaged in real time with sub-nanometer resolution. We have also applied this method to other research areas, e.g., imaging proteins in water. Liquid cell TEM is poised to play a major role in revealing dynamic processes of materials in their working environments. It may also bring high impact in the study of biological processes in their native environment.

We have developed a self-contained liquid cell, which allows imaging through liquids using a transmission electron microscope. Dynamic processes of nanoparticles in liquids can be revealed in real time with sub-nanometer resolution.

액체 셀 전송 전자 현미경을 사용하여 액체의 재료의 동적 프로세스를 공개

The recent development for in situ transmission electron microscopy, which allows imaging through liquids with high spatial resolution, has attracted ...

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Simulation of the Planetary Interior Differentiation Processes in the Laboratory

A planetary interior is under high-pressure and high-temperature conditions and it has a layered structure. There are two important processes that led to that layered structure, (1) percolation of liquid metal in a solid silicate matrix by planet differentiation, and (2) inner core crystallization by subsequent planet cooling. We conduct high-pressure and high-temperature experiments to simulate both processes in the laboratory. Formation of percolative planetary core depends on the efficiency of melt percolation, which is controlled by the dihedral (wetting) angle. The percolation simulation includes heating the sample at high pressure to a target temperature at which iron-sulfur alloy is molten while the silicate remains solid, and then determining the true dihedral angle to evaluate the style of liquid migration in a crystalline matrix by 3D visualization. The 3D volume rendering is achieved by slicing the recovered sample with a focused ion beam (FIB) and taking SEM image of each slice with a FIB/SEM crossbeam instrument. The second set of experiments is designed to understand the inner core crystallization and element distribution between the liquid outer core and solid inner core by determining the melting temperature and element partitioning at high pressure. The melting experiments are conducted in the multi-anvil apparatus up to 27 GPa and extended to higher pressure in the diamond-anvil cell with laser-heating. We have developed techniques to recover small heated samples by precision FIB milling and obtain high-resolution images of the laser-heated spot that show melting texture at high pressure. By analyzing the chemical compositions of the coexisting liquid and solid phases, we precisely determine the liquidus curve, providing necessary data to understand the inner core crystallization process.

The high-pressure and high-temperature experiments described here mimic planet interior differentiation processes. The processes are visualized and better understood by high-resolution 3D imaging and quantitative chemical analysis.

행성 내부의 분화의 시뮬레이션 실험실에서 처리

A planetary interior is under high-pressure and high-temperature conditions and it has a layered structure. There are two important processes that led to ...

Spatial Separation of Molecular Conformers and Clusters

Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold molecular beams. However, these beams often contain multiple conformers and clusters, even at low rotational temperatures. We present an experimental methodology that allows the spatial separation of these constituent parts of a molecular beam expansion. Using an electric deflector the beam is separated by its mass-to-dipole moment ratio, analogous to a bender or an electric sector mass spectrometer spatially dispersing charged molecules on the basis of their mass-to-charge ratio. This deflector exploits the Stark effect in an inhomogeneous electric field and allows the separation of individual species of polar neutral molecules and clusters. It furthermore allows the selection of the coldest part of a molecular beam, as low-energy rotational quantum states generally experience the largest deflection. Different structural isomers (conformers) of a species can be separated due to the different arrangement of functional groups, which leads to distinct dipole moments. These are exploited by the electrostatic deflector for the production of a conformationally pure sample from a molecular beam. Similarly, specific cluster stoichiometries can be selected, as the mass and dipole moment of a given cluster depends on the degree of solvation around the parent molecule. This allows experiments on specific cluster sizes and structures, enabling the systematic study of solvation of neutral molecules.

We present a technique that allows the spatial separation of different conformers or clusters present in a molecular beam. An electrostatic deflector is used to separate species by their mass-to-dipole moment ratio, leading to the production of gas-phase ensembles of a single conformer or cluster stoichiometry.

분자 순응및 클러스터의 공간 분리

Gas-phase molecular physics and physical chemistry experiments commonly use supersonic expansions through pulsed valves for the production of cold ...

The Preparation of Electrohydrodynamic Bridges from Polar Dielectric Liquids

Horizontal and vertical liquid bridges are simple and powerful tools for exploring the interaction of high intensity electric fields (8-20 kV/cm) and polar dielectric liquids. These bridges are unique from capillary bridges in that they exhibit extensibility beyond a few millimeters, have complex bi-directional mass transfer patterns, and emit non-Planck infrared radiation. A number of common solvents can form such bridges as well as low conductivity solutions and colloidal suspensions. The macroscopic behavior is governed by electrohydrodynamics and provides a means of studying fluid flow phenomena without the presence of rigid walls. Prior to the onset of a liquid bridge several important phenomena can be observed including advancing meniscus height (electrowetting), bulk fluid circulation (the Sumoto effect), and the ejection of charged droplets (electrospray). The interaction between surface, polarization, and displacement forces can be directly examined by varying applied voltage and bridge length. The electric field, assisted by gravity, stabilizes the liquid bridge against Rayleigh-Plateau instabilities. Construction of basic apparatus for both vertical and horizontal orientation along with operational examples, including thermographic images, for three liquids (e.g., water, DMSO, and glycerol) is presented.

Horizontal and vertical electrohydrodynamic liquid bridges are simple and powerful tools for exploring the interaction of high intensity electric fields and polar dielectric liquids. The construction of basic apparatus and operational examples, including thermographic images, for three liquids (e.g., water, DMSO, and glycerol) is presented.

폴라 유전체 액체에서 특히 전기 교량의 준비

Horizontal and vertical liquid bridges are simple and powerful tools for exploring the interaction of high intensity electric fields (8-20 kV/cm) and ...

A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation

The dynamic fracture of a body is a late-stage phenomenon typically studied under simplified conditions, in which a sample is deformed under uniform stress and strain rate. This can be produced by evenly loading the inner surface of a cylinder. Due to the axial symmetry, as the cylinder expands the wall is placed into a tensile hoop stress that is uniform around the circumference. While there are various techniques to generate this expansion such as explosives, electromagnetic drive, and existing gas gun techniques they are all limited in the fact that the sample cylinder must be at room temperature. We present a new method using a gas gun that facilitates experiments on cylinders from 150 K to 800 K with a consistent, repeatable loading. These highly diagnosed experiments are used to examine the effect of temperature on the fracture mechanisms responsible for failure, and their resulting influence on fragmentation statistics. The experimental geometry employs a steel ogive located inside the target cylinder, with the tip located about halfway in. A single stage light gas gun is then used to launch a polycarbonate projectile into the cylinder at 1,000 m/sec-1. The projectile impacts and flows around the rigid ogive, driving the sample cylinder from the inside. The use of a non-deforming ogive insert allows us to install temperature control hardware inside the rear of the cylinder. Liquid nitrogen (LN2) is used for cooling and a resistive high current load for heating. Multiple channels of upshifted photon Doppler velocimetry (PDV) track the expansion velocity along the cylinder enabling direct comparison to computer simulations, while High speed imaging is used to measure the strain to failure. The recovered cylinder fragments are also subject to optical and electron microscopy to ascertain the failure mechanism.

Fracture and fragmentation are late stage phenomena in dynamic loading scenarios and are typically studied using explosives. We present a technique for driving expansion using a gas gun which uniquely enables control of both loading rate and sample temperature.

The dynamic fracture of a body is a late-stage phenomenon typically studied under simplified conditions, in which a sample is deformed under uniform ...

Formation of Thick Dense Yttrium Iron Garnet Films Using Aerosol Deposition

Aerosol deposition (AD) is a thick-film deposition process that can produce layers up to several hundred micrometers thick with densities greater than 95% of the bulk. The primary advantage of AD is that the deposition takes place entirely at ambient temperature; thereby enabling film growth in material systems with disparate melting temperatures. This report describes in detail the processing steps for preparing the powder and for performing AD using the custom-built system. Representative characterization results are presented from scanning electron microscopy, profilometry, and ferromagnetic resonance for films grown in this system. As a representative overview of the capabilities of the system, focus is given to a sample produced following the described protocol and system setup. Results indicate that this system can successfully deposit 11 &#181;m thick yttrium iron garnet films that are &#160;&#62; 90% of the bulk density during a single 5 min deposition run. A discussion of methods to afford better control of the aerosol and particle selection for improved thickness and roughness variations in the film is provided.

This report describes the use of a custom-built system to perform aerosol deposition of thick films of yttrium iron garnet onto sapphire substrates at RT. The deposited films are characterized using scanning electron microscopy, profilometry, and ferromagnetic resonance to give a representative overview of the capabilities of the technique.

에어로졸 증착을 사용하여 두꺼운 고밀도 이트륨 철 가넷 필름의 형성

Aerosol deposition (AD) is a thick-film deposition process that can produce layers up to several hundred micrometers thick with densities greater than 95% ...

Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation

Shape Memory Alloys (SMA) using elastocaloric cooling processes have the potential to be an environmentally friendly alternative to the conventional vapor compression based cooling process. Nickel-Titanium (Ni-Ti) based alloy systems, especially, show large elastocaloric effects. Furthermore, exhibit large latent heats which is a necessary material property for the development of an efficient solid-state based cooling process. A scientific test rig has been designed to investigate these processes and the elastocaloric effects in SMAs. The realized test rig enables independent control of an SMA&#39;s mechanical loading and unloading cycles, as well as conductive heat transfer between SMA cooling elements and a heat source/sink. The test rig is equipped with a comprehensive monitoring system capable of synchronized measurements of mechanical and thermal parameters. In addition to determining the process-dependent mechanical work, the system also enables measurement of thermal caloric aspects of the elastocaloric cooling effect through use of a high-performance infrared camera. This combination is of particular interest, because it allows illustrations of localization and rate effects &#8212; both important for efficient heat transfer from the medium to be cooled.
The work presented describes an experimental method to identify elastocaloric material properties in different materials and sample geometries. Furthermore, the test rig is used to investigate different cooling process variations. The introduced analysis methods enable a differentiated consideration of material, process and related boundary condition influences on the process efficiency. The comparison of the experimental data with the simulation results (of a thermomechanically coupled finite element model) allows for better understanding of the underlying physics of the elastocaloric effect. In addition, the experimental results, as well as the findings based on the simulation results, are used to improve the material properties.

Experimental methods for investigation of solid state cooling processes and characterization of elastocaloric material properties of Shape Memory Alloys (SMA) are presented. A custom-built test rig has been designed for controlling and comprehensive monitoring of elastocaloric cooling processes. Furthermore, it provides a validation platform for thermomechanically coupled modeling approaches.

형상 기억의 조사를 기반으로 Elastocaloric 냉각 프로세스 및 모델 검증을위한 실험 방법

Shape Memory Alloys (SMA) using elastocaloric cooling processes have the potential to be an environmentally friendly alternative to the conventional vapor ...

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

This paper reports an array-designed C84-embedded Si substrate fabricated using a controlled self-assembly method in an ultra-high vacuum chamber. The characteristics of the C84-embedded Si surface, such as atomic resolution topography, local electronic density of states, band gap energy, field emission properties, nanomechanical stiffness, and surface magnetism, were examined using a variety of surface analysis techniques under ultra, high vacuum (UHV) conditions as well as in an atmospheric system. Experimental results demonstrate the high uniformity of the C84-embedded Si surface fabricated using a controlled self-assembly nanotechnology mechanism, represents an important development in the application of field emission display (FED), optoelectronic device fabrication, MEMS cutting tools, and in efforts to find a suitable replacement for carbide semiconductors. Molecular dynamics (MD) method with semi-empirical potential can be used to study the nanoindentation of C84-embedded Si substrate. A detailed description for performing MD simulation is presented here. Details for a comprehensive study on mechanical analysis of MD simulation such as indentation force, Young&#39;s modulus, surface stiffness, atomic stress, and atomic strain are included. The atomic stress and von-Mises strain distributions of the indentation model can be calculated to monitor deformation mechanism with time evaluation in atomistic level.

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

This paper reports the nanomaterial fabrication of a fullerene Si substrate inspected and verified by nanomeasurements and molecular dynamic simulation.

C 프로빙<sub&gt; (84)</sub&gt;은 스캐닝 프로브 현미경 및 분자 역학을 사용하여 실리콘 기판을 - 임베디드

This paper reports an array-designed C84-embedded Si substrate fabricated using a controlled self-assembly method in an ultra-high vacuum chamber. The ...

Studying Dynamic Processes of Nano-sized Objects in Liquid using Scanning Transmission Electron Microscopy

Samples fully embedded in liquid can be studied at a nanoscale spatial resolution with Scanning Transmission Electron Microscopy (STEM) using a microfluidic chamber assembled in the specimen holder for Transmission Electron Microscopy (TEM) and STEM. The microfluidic system consists of two silicon microchips supporting thin Silicon Nitride (SiN) membrane windows. This article describes the basic steps of sample loading and data acquisition. Most important of all is to ensure that the liquid compartment is correctly assembled, thus providing a thin liquid layer and a vacuum seal. This protocol also includes a number of tests necessary to perform during sample loading in order to ensure correct assembly. Once the sample is loaded in the electron microscope, the liquid thickness needs to be measured. Incorrect assembly may result in a too-thick liquid, while a too-thin liquid may indicate the absence of liquid, such as when a bubble is formed. Finally, the protocol explains how images are taken and how dynamic processes can be studied. A sample containing AuNPs is imaged both in pure water and in saline.

This protocol describes the operation of a liquid flow specimen holder for scanning transmission electron microscopy of AuNPs in water, as used for the observation of nanoscale dynamic processes.

스캔 전송 전자 현미경을 사용하여 액체에 나노 크기의 개체의 동적 프로세스를 공부

Samples fully embedded in liquid can be studied at a nanoscale spatial resolution with Scanning Transmission Electron Microscopy (STEM) using a ...

Wicking Tests for Unidirectional Fabrics: Measurements of Capillary Parameters to Evaluate Capillary Pressure in Liquid Composite Molding Processes

During impregnation of a fibrous reinforcement in liquid composite molding (LCM) processes, capillary effects have to be understood in order to identify their influence on void formation in composite parts. Wicking in a fibrous medium described by the Washburn equation was considered equivalent to a flow under the effect of capillary pressure according to the Darcy law. Experimental tests for the characterization of wicking were conducted with both carbon and flax fiber reinforcement. Quasi-unidirectional fabrics were then tested by means of a tensiometer to determine the morphological and wetting parameters along the fiber direction. The procedure was shown to be promising when the morphology of the fabric is unchanged during capillary wicking. In the case of carbon fabrics, the capillary pressure can be calculated. Flax fibers are sensitive to moisture sorption and swell in water. This phenomenon has to be taken into account to assess the wetting parameters. In order to make fibers less sensitive to water sorption, a thermal treatment was carried out on flax reinforcements. This treatment enhances fiber morphological stability and prevents swelling in water. It was shown that treated fabrics have a linear wicking trend similar to those found in carbon fabrics, allowing for the determination of capillary pressure.

An experimental method to measure geometrical parameters and the apparent advancing contact angles describing capillary wicking in unidirectional synthetic and natural fabrics is proposed. These parameters are mandatory for the determination of the capillary pressures that must be taken into account for liquid composite molding (LCM) applications.

During impregnation of a fibrous reinforcement in liquid composite molding (LCM) processes, capillary effects have to be understood in order to identify ...