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

The overall goal of this procedure is to study molecular scale hydrodynamic processes in liquids using an analog technique that measures single and collective particle dynamics in vibrated grain piles. The main advantage of this technique is that it provides experimentally accessible inverse microshell for directly observing complex molecular scale dynamics. Since this technique is strongly coupled in the statistical mechanics of interacting particle systems, it opens a door for experimental investigation in the fundamental questions in this field.

This technique can also be applied to study the statistical mechanics of interacting macroscopic particle systems, such as the vibrating grain piles we are investigating. Generally, individuals using this technique will struggle learning the elements of equilibrium and non equilibrium statistical mechanics that are necessary for interpreting experimental observations in designing experiments. Visual demonstration of this technique is critical since it extends particle imaging velocimetry, normally used for measuring the motion of micron scale particles to the motion of centimeter scale grains.

The experiment uses this vibratory system. It consists of an annular polyurethane bowl attached to a single speed unbalanced motor to generate vibrations. These are attached to a weighted base and separated by a group of springs.

Attach the bowl assembly to its stand with rubber hooks. Inside the bowl, attach a triaxial accelerometer. This is connected to a sensor signal on a table away from the vibratory system.

Next, work with the chosen media for the experiment. In this case, use a ceramic polishing media straight-cut triangle with equal side lengths. Add the media to the vibratory bowl Near the bowl, have a water and finishing compound solution ready to wet the media.

Also, setup a peristaltic pump to move the fluid in the vibratory bowl. Run a plastic tube from the pump to the top of the bowl. Set the pump rate but do not initiate flow.

For imaging, setup a high speed camera. Choose a lens appropriate for the desired surface integration and resolution. Support the camera on a structure that is isolated from the vibratory system.

When mounting the camera, its length should be perpendicular to the media's open surface and 550 millimeters above it. Next, connect the camera to its power supply, a GPS antenna and the computer. At the computer, start the camera software and select the camera.

View the camera's field of view live with the software. At the setup, use any bright light to illuminate the test region. The chosen field of view should be illuminated evenly.

Next, use the camera software to digitally zoom in to 500 times magnification. At the camera, adjust the lens focus ring. The goal is to achieve the best optical focus for data collection.

Then return the digital zoom to no magnification. Continue by setting the camera acquisition rate. Before taking images, place a ruled scale in the field of view.

Use the camera to record a single image of it. Save the image as a TIFF file before deleting it from the camera. Once the camera is ready, prepare to start the vibratory bowl.

Get 150 milliliters of finishing compound solution from the container. Take the 150 milliliters to the vibratory bowl and spread the solution around evenly to provide the initial wetting of the media. Next, place the large container of compound on the floor near the peristaltic pump.

Attach a hose from the pump to the container before activating the pump. At this point, start the vibratory bowl and wait a minimum of one minute. With the flow in steady state, trigger the camera to record action in the field of view for the chosen runtime.

These recorded frames have been made into a video. When the data is collected, stop the vibratory system. Then stop the peristaltic pump.

For processing, save the acquired images as TIFF files on the computer and convert them to greyscale. Then begin work in the particle image of velocimetry software environment. Go to File and from there to Import, then Import Images.

In the Import Wizard dialogue box, select Single Frame, followed by Add Images. Now select the calibration image to add it to the images to import. Click Add Images again, then highlight all of the data images to select them for import.

Continue by clicking Next. On the following screen, input the camera settings, include the frame rate and pixel pitch. When these are entered, click Next and then Finish.

Now go to the contents list. The calibration image should be first. Right click on the second image, select Split Ensemble from Here to make two image sets.

Grab the image set with only the calibration image and drop it on the location labeled New Calibration. Next, right click the calibration image set and select Measure Scale Factor. The calibration image will appear on the screen.

In the image, position the A marker on the end image ruler. Then place the B marker at another position on the ruler. Go to the Absolute distance text box and input the distance between the markers according to the ruler.

Click OK to save the settings and continue. Now select the imported image set without the calibration image. Move to click Analyze.

Select Make Double Frame. Then choose to create image pairs from the style options. To define the interrogation area, open any non calibration image.

Right click on the image and select Particle Density. In the dialogue box that appears, there will be a zoomed view of a probe area. Click the Settings tab and begin to alter the probe size area.

The objective is to consistently have a minimum of three particles in the probe area. Note the probe area size for later use. Return to Analyze and choose the Adaptive Correlation method.

Click OK.Go to the interrogation area tab and click on it. There, select the previously determined interrogation area that allows three or more particles to be identified. Click OK in the Adaptive Correlation dialogue box to perform the analysis.

As the analysis proceeds, visually inspect the first several velocity fields. This is an example of a vector field overlaiD on a greyscale image of the media. In this case, the vector lengths and directions do not appear consistent or reasonable.

Visually inspect the vector maps as they're being produced to ensure the results are realistic. If the results are unsatisfactory, stop the process and alter the user-defined inputs such as interrogation area, then restart the analysis. This is an example of a satisfactory vector field.

Again, overlaid on the greyscale image. When the analysis is completed, a vector field spanning the field of view will be created for each image pair in the set. Particle image velocimetry data allows fitting the speed distribution at a point in the system to the Maxwell Boltzmann distribution.

The image is of the grain used in the experiment. The red bar represents one centimeter. The data in blue represent a normalized histogram of measured horizontal peculiar grain speeds.

The data over many particle types are consistent with dissipation-less Hamiltonian dynamics, velocity independent inter-particle potential energies, and potential independent kinetic energies. Further, they provide evidence for local macroscopic mechanical equilibrium. The velocity autocorrelation function for single grains is a function of the characteristic number of grain collisions can also be extracted from the velocimetry data.

The single grain dynamics qualitatively mimic those predicted in molecular liquids and dense gases. These spectra are determined from particle image velocimetry in simultaneous container acceleration measurements. The resonate acoustic waves in the grain pile container system coincide with resonate acoustic modes in the empty container.

Acoustic modes in the spectra of the local peculiar fluid velocity are not evident due to limitations of the experiment. This method can help answer key questions in the molecular hydrodynamics of liquids such as how predictable, observable fluid flow emerges from the unpredictable liquid state dynamics of molecules. Once mastered, the experimental portion of this procedure can be done in less than an hour.

The PIV processing and data analysis can take anywhere from an hour to a couple of days depending on the data processing system. It's important to recognize that in order to connect observations made in vibrated grain systems to molecular hydrodynamics, elements of equilibrium and non equilibrium statistical mechanics must be learned. Following this development, this technique has been used to experimentally validate fluid dynamic simulations of vibration driven grain flows as well as test measure viscosities in grain fluids against those predicted by non equilibrium statistical mechanics.

After watching this video, you should have a reasonable understanding of how to first setup a PIV system to measure the vibratory grain systems and second how to use these measurements to investigate molecular hydrodynamic systems.