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://scholar.google.com/scholar?hl=en&safe=off&q=author%3aBerne%2C+BJ+%22Dynamic+Light+Scattering%22">Dynamic Light Scattering</a>. , John Wiley and Sons Ltd. (1976).</li>
<li>Boon, J. P., Yip, S. <a target="_blank" href="http://scholar.google.com/scholar?hl=en&safe=off&q=author%3aBoon%2C+JP+%22Molecular+Hydrodynamics%22">Molecular Hydrodynamics</a>. , McGraw-Hill. (1980).</li>
<li>Brown, J. C., Pusey, P. N., Goodwin, J. W., Ottewill, R. H. <a target="_blank" href="http://iopscience.iop.org/article/10.1088/0305-4470/8/5/004">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="https://journals.aps.org/pra/abstract/10.1103/PhysRevA.4.233">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://scholar.google.com/scholar?hl=en&safe=off&q=author%3aEvans%2C+DJ+%22Statistical+Mechanics+of+Nonequilibrium+Liquids%22">Statistical Mechanics of Nonequilibrium Liquids</a>. , ANU E Press. (2007).</li>
<li>Levesque, D., Verlet, L. <a target="_blank" href="https://journals.aps.org/pra/abstract/10.1103/PhysRevA.2.2514">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="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.33.277">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. <a target="_blank" href="http://scholar.google.com/scholar?hl=en&safe=off&q=author%3aLovesey%2C+SW+%22Dynamics+of+solids+and+liquids+by+neutron+scattering%22">Dynamics of solids and liquids by neutron scattering</a>. Lovesey, S. W., Springer, T. , Springer-Verlag. (1977).</li>
<li>Forster, D. <a target="_blank" href="http://scholar.google.com/scholar?hl=en&safe=off&q=author%3aForster%2C+D+%22Hydrodynamic+fluctuations%2C+broken+symmetry%2C+and+correlation+functions%22">Hydrodynamic fluctuations, broken symmetry, and correlation functions</a>. , Perseus. (1990).</li>
<li>Mountain, R. D. Generalized hydrodynamics. Adv. Mol. Relax. Processes. 9, 225-291 (1977).</li>
<li>Zwanzig, R. <a target="_blank" href="http://www.annualreviews.org/doi/abs/10.1146/annurev.pc.16.100165.000435">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="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5282555/">Macroscopic liquid-state molecular hydrodynamics.</a> Sci. Rep. 7, 41658(2017).</li>
<li>Kushick, J., Berne, B. J. <a target="_blank" href="http://aip.scitation.org/doi/abs/10.1063/1.1680543">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="https://www-sciencedirect-com.remotexs.ntu.edu.sg/science/article/pii/S0007850617300872">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="https://www-sciencedirect-com.remotexs.ntu.edu.sg/science/article/pii/S0924013615301242">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://scholar.google.com/scholar?hl=en&safe=off&q=%22Experimental+and+computational+evaluation+of+a+vibratory+finishing+process%22">Experimental and computational evaluation of a vibratory finishing process</a>. , University of North Carolina at Charlotte. Charlotte, NC. MSME thesis (2017).</li>
<li>Bolmatov, V., Brazhkin, V., Trachenko, K. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((The+phonon+theory+of+liquid+thermodynamics%5BTitle%5D)+AND+%22Sci.+Rep%22%5BJournal%5D)">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/pubmed?term=((The+hydrogen-bond+network+of+water+supports+propagating+optical+phonon-like+modes%5BTitle%5D)+AND+%22Nat.+Commun%22%5BJournal%5D)">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://scholar.google.com/scholar?hl=en&safe=off&q=author%3aPathria%2C+RK+%22Statistical+mechanics%22">Statistical mechanics</a>. , 3rd ed, Elsevier. (2011).</li>
<li>Gibbs, J. W. <a target="_blank" href="http://scholar.google.com/scholar?hl=en&safe=off&q=author%3aGibbs%2C+JW+%22Elementary+principles+in+statistical+mechanics%22">Elementary principles in statistical mechanics</a>. , University Press. (1902).</li>
<li>Toda, M., Kubo, R., Saito, N. <a target="_blank" href="http://scholar.google.com/scholar?hl=en&safe=off&q=author%3aToda%2C+M+%22Statistical+physics+I%22">Statistical physics I</a>. , 2nd ed, Springer-Verlag. (1992).</li>
<li>Kubo, R. <a target="_blank" href="http://journals.jps.jp/doi/abs/10.1143/JPSJ.12.570">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://scholar.google.com/scholar?hl=en&safe=off&q=author%3aKubo%2C+R+%22Statistical+physics+II%3A+nonequilibrium+statistical+mechanics%22">Statistical physics II: nonequilibrium statistical mechanics</a>. , Springer. (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&amp;nbsp;</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&amp;nbsp;</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.remotexs.ntu.edu.sg/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="https://cloudflare-jove-com.remotexs.ntu.edu.sg/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.remotexs.ntu.edu.sg/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.remotexs.ntu.edu.sg/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.remotexs.ntu.edu.sg/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.remotexs.ntu.edu.sg/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.remotexs.ntu.edu.sg/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 ...

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

Nanyang Technological University

Education

Research

JoVE Core

JoVE Journal

Physics

Engineering

Chemistry

Civil Engineering

Unit 1

Vectors and Scalars

Fluid Dynamics

Gases

SCIENTISTS IN ACTION

8.5K Views.  University of North Carolina at Charlotte. Een experimenteel toegankelijk analoge methode voor de studie van moleculaire hydrodynamische processen in dichte vloeistoffen wordt gepresenteerd. De techniek maakt gebruik van particle image velocimetry universele, hoge-restitutie graan palen en kunt direct, macroscopische observatie van dynamische processen bekend en voorspelde bestaan in sterk interactie, hoge dichtheid gassen en vloeistoffen.

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

A Microfluidic-based Hydrodynamic Trap for Single Particles

The ability to confine and manipulate single particles in free solution is a key enabling technology for fundamental and applied science. Methods for particle trapping based on optical, magnetic, electrokinetic, and acoustic techniques have led to major advancements in physics and biology ranging from the molecular to cellular level. In this article, we introduce a new microfluidic-based technique for particle trapping and manipulation based solely on hydrodynamic fluid flow. Using this method, we demonstrate trapping of micro- and nano-scale particles in aqueous solutions for long time scales. The hydrodynamic trap consists of an integrated microfluidic device with a cross-slot channel geometry where two opposing laminar streams converge, thereby generating a planar extensional flow with a fluid stagnation point (zero-velocity point). In this device, particles are confined at the trap center by active control of the flow field to maintain particle position at the fluid stagnation point. In this manner, particles are effectively trapped in free solution using a feedback control algorithm implemented with a custom-built LabVIEW code. The control algorithm consists of image acquisition for a particle in the microfluidic device, followed by particle tracking, determination of particle centroid position, and active adjustment of fluid flow by regulating the pressure applied to an on-chip pneumatic valve using a pressure regulator. In this way, the on-chip dynamic metering valve functions to regulate the relative flow rates in the outlet channels, thereby enabling fine-scale control of stagnation point position and particle trapping. The microfluidic-based hydrodynamic trap exhibits several advantages as a method for particle trapping. Hydrodynamic trapping is possible for any arbitrary particle without specific requirements on the physical or chemical properties of the trapped object. In addition, hydrodynamic trapping enables confinement of a "single" target object in concentrated or crowded particle suspensions, which is difficult using alternative force field-based trapping methods. The hydrodynamic trap is user-friendly, straightforward to implement and may be added to existing microfluidic devices to facilitate trapping and long-time analysis of particles. Overall, the hydrodynamic trap is a new platform for confinement, micromanipulation, and observation of particles without surface immobilization and eliminates the need for potentially perturbative optical, magnetic, and electric fields in the free-solution trapping of small particles.

In this article, we present a microfluidic-based method for particle confinement based on hydrodynamic flow. We demonstrate stable particle trapping at a fluid stagnation point using a feedback control mechanism, thereby enabling confinement and micromanipulation of arbitrary particles in an integrated microdevice.

The ability to confine and manipulate single particles in free solution is a key enabling technology for fundamental and applied science.  Methods for ...

Bioengineering

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Surface acoustic waves (SAWs) can be used to drive liquids in portable microfluidic chips via the acoustic counterflow phenomenon. In this video we present the fabrication protocol for a multilayered SAW acoustic counterflow device. The device is fabricated starting from a lithium niobate (LN) substrate onto which two interdigital transducers (IDTs) and appropriate markers are patterned. A polydimethylsiloxane (PDMS) channel cast on an SU8 master mold is finally bonded on the patterned substrate. Following the fabrication procedure, we show the techniques that allow the characterization and operation of the acoustic counterflow device in order to pump fluids through the PDMS channel grid. We finally present the procedure to visualize liquid flow in the channels. The protocol is used to show on-chip fluid pumping under different flow regimes such as laminar flow and more complicated dynamics characterized by vortices and particle accumulation domains.

In this video we first describe fabrication and operation procedures of a surface acoustic wave (SAW) acoustic counterflow device. We then demonstrate an experimental setup that allows for both qualitative flow visualization and quantitative analysis of complex flows within the SAW pumping device.

Surface acoustic waves (SAWs) can be used to drive liquids in portable microfluidic chips via the acoustic counterflow phenomenon. In this video we ...

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

The behavior of confined colloidal suspensions with attractive interparticle interactions is critical to the rational design of materials for directed assembly1-3, drug delivery4, improved hydrocarbon recovery5-7, and flowable electrodes for energy storage8. Suspensions containing fluorescent colloids and non-adsorbing polymers are appealing model systems, as the ratio of the polymer radius of gyration to the particle radius&#160;and concentration of polymer control the range and strength of the interparticle attraction, respectively. By tuning the polymer properties and the volume fraction of the colloids, colloid fluids, fluids of clusters, gels, crystals, and glasses can be obtained9.&#160;Confocal microscopy, a variant of fluorescence microscopy, allows an optically transparent and fluorescent sample to be imaged with high spatial and temporal resolution in three dimensions. In this technique, a small pinhole or slit blocks the emitted fluorescent light from regions of the sample that are outside the focal volume of the microscope optical system. As a result, only a thin section of the sample in the focal plane is imaged. This technique is particularly well suited to probe the structure and dynamics in dense colloidal suspensions at the single-particle scale: the particles are large enough to be resolved using visible light and diffuse slowly enough to be captured at typical scan speeds of commercial confocal systems10. Improvements in scan speeds and analysis algorithms have also enabled quantitative confocal imaging of flowing suspensions11-16,37.&#160;In this paper, we demonstrate confocal microscopy experiments to probe the confined phase behavior and flow properties of colloid-polymer mixtures. We first prepare colloid-polymer mixtures that are density- and refractive-index matched. Next, we report a standard protocol for imaging quiescent dense colloid-polymer mixtures under varying confinement in thin wedge-shaped cells. Finally, we demonstrate a protocol for imaging colloid-polymer mixtures during microchannel flow.

Confocal microscopy is used to image quiescent and flowing colloid-polymer mixtures, which are studied as model systems for attractive suspensions. Image analysis algorithms are used to calculate structural and dynamic metrics for the colloidal particles that measure changes due to geometric confinement.

The behavior of confined colloidal suspensions with attractive interparticle interactions is critical to the rational design of materials for directed ...

Fast Imaging Technique to Study Drop Impact Dynamics of Non-Newtonian Fluids

In the field of fluid mechanics, many dynamical processes not only occur over a very short time interval but also require high spatial resolution for detailed observation, scenarios that make it challenging to observe with conventional imaging systems. One of these is the drop impact of liquids, which usually happens within one tenth of millisecond. To tackle this challenge, a fast imaging technique is introduced that combines a high-speed camera (capable of up to one million frames per second) with a macro lens with long working distance to bring the spatial resolution of the image down to 10 &#181;m/pixel. The imaging technique enables precise measurement of relevant fluid dynamic quantities, such as the flow field, the spreading distance and the splashing speed, from analysis of the recorded video. To demonstrate the capabilities of this visualization system, the impact dynamics when droplets of non-Newtonian fluids impinge on a flat hard surface are characterized. Two situations are considered: for oxidized liquid metal droplets we focus on the spreading behavior, and for densely packed suspensions we determine the onset of splashing. More generally, the combination of high temporal and spatial imaging resolution introduced here offers advantages for studying fast dynamics across a wide range of microscale phenomena.

Drop impact of non-Newtonian fluids is a complex process since different physical parameters influence the dynamics over a very short time (less than one tenth of a millisecond). A fast imaging technique is introduced in order to characterize the impact behaviors of different non-Newtonian fluids.

In the field of fluid mechanics, many dynamical processes not only occur over a very short time interval but also require high spatial resolution for ...

Microfluidic Devices for Characterizing Pore-scale Event Processes in Porous Media for Oil Recovery Applications

Microfluidic devices are versatile tools for studying transport processes at a microscopic scale. A demand exists for microfluidic devices that are resistant to low molecular-weight oil components, unlike traditional polydimethylsiloxane (PDMS) devices. Here, we demonstrate a facile method for making a device with this property, and we use the product of this protocol for examining the pore-scale mechanisms by which foam recovers crude oil. A pattern is first designed using computer-aided design (CAD) software and printed on a transparency with a high-resolution printer. This pattern is then transferred to a photoresist via a lithography procedure. PDMS is cast on the pattern, cured in an oven, and removed to obtain a mold. A thiol-ene crosslinking polymer, commonly used as an optical adhesive (OA), is then poured onto the mold and cured under UV light. The PDMS mold is peeled away from the optical adhesive cast. A glass substrate is then prepared, and the two halves of the device are bonded together. Optical adhesive-based devices are more robust than traditional PDMS microfluidic devices. The epoxy structure is resistant to swelling by many organic solvents, which opens new possibilities for experiments involving light organic liquids. Additionally, the surface wettability behavior of these devices is more stable than that of PDMS. The construction of optical adhesive microfluidic devices is simple, yet requires incrementally more effort than the making of PDMS-based devices. Also, though optical adhesive devices are stable in organic liquids, they may exhibit reduced bond-strength after a long time. Optical adhesive microfluidic devices can be made in geometries that act as 2-D micromodels for porous media. These devices are applied in the study of oil displacement to improve our understanding of the pore-scale mechanisms involved in enhanced oil recovery and aquifer remediation.

The goal of this procedure is to easily and rapidly produce a microfluidic device with customizable geometry and resistance to swelling by organic fluids for oil recovery studies. A polydimethylsiloxane mold is first generated, and then used to cast the epoxy-based device. A representative displacement study is reported.

Microfluidic devices are versatile tools for studying transport processes at a microscopic scale. A demand exists for microfluidic devices that are ...

Environment

Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions

The microstructure of soft matter directly impacts macroscopic rheological properties and can be changed by factors including colloidal rearrangement during previous phase changes and applied shear. To determine the extent of these changes, we have developed a microfluidic device that enables repeated phase transitions induced by exchange of the surrounding fluid and microrheological characterization while limiting shear on the sample. This technique is &#181;2rheology, the combination of microfluidics and microrheology. The microfluidic device is a two-layer design with symmetric inlet streams entering a sample chamber that traps the gel sample in place during fluid exchange. Suction can be applied far away from the sample chamber to pull fluids into the sample chamber. Material rheological properties are characterized using multiple particle tracking microrheology (MPT). In MPT, fluorescent probe particles are embedded into the material and the Brownian motion of the probes is recorded using video microscopy. The movement of the particles is tracked and the mean-squared displacement (MSD) is calculated. The MSD is related to macroscopic rheological properties, using the Generalized Stokes-Einstein Relation. The phase of the material is identified by comparison to the critical relaxation exponent, determined using time-cure superposition. Measurements of a fibrous colloidal gel illustrate the utility of the technique. This gel has a delicate structure that can be irreversibly changed when shear is applied. &#181;2rheology data shows that the material repeatedly equilibrates to the same rheological properties after each phase transition, indicating that phase transitions do not play a role in microstructural changes. To determine the role of shear, samples can be sheared prior to injection into our microfluidic device. &#181;2rheology is a widely applicable technique for the characterization of soft matter enabling the determination of rheological properties of delicate microstructures in a single sample during phase transitions in response to repeated changes in the surrounding environmental conditions.

We demonstrate the fabrication and use of a microfluidic device that enables multiple particle tracking microrheology measurements to study the rheological effects of repeated phase transitions on soft matter.

The microstructure of soft matter directly impacts macroscopic rheological properties and can be changed by factors including colloidal rearrangement ...

Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films

Droplet impact is a very common phenomenon in nature and attracts attention due to its aesthetic fascination and wide-ranging applications. Previous studies on flowing liquid films have neglected the contributions of spatial structures of waves to the impact outcome, while this has recently been shown to have a significant influence on the drop impact dynamics. In this report, we outline a step-by-step procedure to investigate the effect of periodic inlet forcing of a flowing liquid film leading to the production of spatiotemporally regular wave structures on drop impact dynamics. A function generator in connection with a solenoid valve is used to excite these spatiotemporally regular wave structures on the film surface while the impact dynamics of uniform-sized droplets are captured using a high-speed camera. Three distinct regions are then studied; viz. the capillary wave region preceding the large wave peak, the flat film region, and the wave hump region. The effects of important dimensionless quantities such as film Reynolds, drop Weber and Ohnesorge numbers parameterized by the film flow rate, drop speed, and drop size are also examined. Our results show interesting, hitherto undiscovered dynamics brought about by this application of film inlet forcing of the flowing film for both low and high inertia drops.

A protocol to study the contributions of waves to droplet impact dynamics on flowing liquid films is presented.

Droplet impact is a very common phenomenon in nature and attracts attention due to its aesthetic fascination and wide-ranging applications. Previous ...

Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique

In this paper, we introduce the use of microscale schlieren technique to measure mixing inhomogeneity in a microfluidic device. The microscale schlieren system is constructed from a Hoffman modulation contrast microscope, which provides easy access to the rear focal plane of the objective lens, by removing the slit plate and replacing the modulator with a knife-edge. The working principle of microscale schlieren technique relies on detecting light deflection caused by variation of refractive index1-3. The deflected light either escapes or is obstructed by the knife-edge to produce a bright or a dark band, respectively. If the refractive index of the mixture varies linearly with its composition, the local change in light intensity in the image plane is proportional to the concentration gradient normal to the optical axis. The micro-schlieren image gives a two-dimensional projection of the disturbed light produced by three-dimensional inhomogeneity.
To accomplish quantitative analysis, we describe a calibration procedure that mixes two fluids in a T-microchannel. We carry out a numerical simulation to obtain the concentration gradient in the T-microchannel that correlates closely with the corresponding micro-schlieren image. By comparison, a relationship between the grayscale readouts of the micro-schlieren image and the concentration gradients presented in a microfluidic device is established. Using this relationship, we are able to analyze the mixing inhomogeneity from associate micro-schlieren image and demonstrate the capability of microscale schlieren technique with measurements in a microfluidic oscillator4. For optically transparent fluids, microscale schlieren technique is an attractive diagnostic tool to provide instantaneous full-field information that retains the three-dimensional features of the mixing process.

Herein, we describe a procedure that employs microscale schlieren technique to measure mixing inhomogeneity in a microfluidic device. Through calibration, distribution of concentration gradient can be derived from the micro-schlieren image.

In this paper, we introduce the use of microscale schlieren technique to measure mixing inhomogeneity in a microfluidic device. The microscale schlieren ...

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

We have developed a Python-based open-source package to analyze the results stemming from ab initio molecular-dynamics simulations of fluids. The package is best suited for applications on natural systems, like silicate and oxide melts, water-based fluids, and various supercritical fluids. The package is a collection of Python scripts that include two major libraries dealing with file formats and with crystallography. All the scripts are run at the command line. We propose a simplified format to store the atomic trajectories and relevant thermodynamic information of the simulations, which is saved in UMD files, standing for Universal Molecular Dynamics. The UMD package allows the computation of a series of structural, transport and thermodynamic properties. Starting with the pair-distribution function it defines bond lengths, builds an interatomic connectivity matrix, and eventually determines the chemical speciation. Determining the lifetime of the chemical species allows running a full statistical analysis. Then dedicated scripts compute the mean-square displacements for the atoms as well as for the chemical species. The implemented self-correlation analysis of the atomic velocities yields the diffusion coefficients and the vibrational spectrum. The same analysis applied on the stresses yields the viscosity. The package is available via the GitHub website and via its own dedicated page of the ERC IMPACT project as open-access package.

Melts and fluids are ubiquitous vectors of mass transport in natural systems. We have developed an open-source package to analyze ab initio molecular-dynamics simulations of such systems. We compute structural (bonding, clusterization, chemical speciation), transport (diffusion, viscosity) and thermodynamic properties (vibrational spectrum).

We have developed a Python-based open-source package to analyze the results stemming from ab initio molecular-dynamics simulations of fluids. The package ...

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Adsorption of surface-active molecules to fluid-fluid interfaces is ubiquitous in nature. Characterizing these interfaces requires measuring surfactant adsorption rates, evaluating equilibrium surface tensions as a function of bulk surfactant concentration, and relating how surface tension changes with changes in the interfacial area following equilibration. Simultaneous visualization of the interface using fluorescence imaging with a high-speed confocal microscope allows the direct evaluation of structure-function relationships. In the capillary pressure microtensiometer (CPM), a hemispherical air bubble is pinned at the end of the capillary in a 1 mL volume liquid reservoir. The capillary pressure across the bubble interface is controlled via a commercial microfluidic flow controller that allows for model-based pressure, bubble curvature, or bubble area control based on the Laplace equation. Compared to previous techniques such as the Langmuir trough and pendant drop, the measurement and control precision and response time are greatly enhanced; capillary pressure variations can be applied and controlled in milliseconds. The dynamic response of the bubble interface is visualized via a second optical lens as the bubble expands and contracts. The bubble contour is fit to a circular profile to determine the bubble curvature radius, R, as well as any deviations from circularity that would invalidate the results. The Laplace equation is used to determine the dynamic surface tension of the interface. Following equilibration, small pressure oscillations can be imposed by the computer-controlled microfluidic pump to oscillate the bubble radius (frequencies of 0.001-100 cycles/min) to determine the dilatational modulus The overall dimensions of the system are sufficiently small that the microtensiometer fits under the lens of a high-speed confocal microscope allowing fluorescently tagged chemical species to be quantitatively tracked with submicron lateral resolution.

This manuscript describes the design and operation of a microtensiometer/confocal microscope to do simultaneous measurements of interfacial tension and surface dilatational rheology while visualizing the interfacial morphology. This provides the real-time construction of structure-property relationships of interfaces important in technology and physiology.

Adsorption of surface-active molecules to fluid-fluid interfaces is ubiquitous in nature. Characterizing these interfaces requires measuring surfactant ...

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

Samenvatting

Meer video's verkennen