Development of an Experimental Setup for the Measurement of the Coefficient of Restitution under Vacuum Conditions

The overall goal of this experimental setup is to measure the coefficient of restitution of colliding particles under vacuum conditions. This method can contribute to solve engineering problems since the coefficient of restitution is present in any engineering operation such as transportation, handling, storage of granular solids in the engineering industry. The main advantage of this method is that it can be applied to fine powders under vacuum conditions without accelerating the particle when it comes into the chamber.

Sven Drucker, a grad student from my lab will be demonstrating the procedure. He works in the framework of a project called Pardem. For working with particles of any size, first remove the sleeve over the vacuum chamber and lift off the top cover.

Then, select the base-plate with the desired wall material into the chamber. Next, turn the lower part of the vacuum chamber sideways and carefully slide the base-plate into position. Next, using tweezers, place exactly one particle of a known size at the center of the base-plate.

Then, adjust the position of a high-speed video camera mounted to a tripod so that the base-plate is in the lowest quarter of the visual field and focus is on the particle. Set the high-speed camera to record 10, 000 frames per second at a resolution of 528 by 396 pixels. Then, take a brief video of the particle for reference purposes.

Don’t forget to remove the particle afterwards. When working with particles that are 700 microns or coarser, first adjust the height of the particle chamber so the desired impact velocity is reached. Measure the height using the scale attached to the holding plate.

Then, close the particle chamber with the tip of a pipet. Now, lift the top cover of the vacuum chamber and put one single sphere inside of the particle chamber using tweezers. This example shows a solid sphere.

However, liquid-filled spheres can also be tested. Place the top cover on the lower part of the vacuum chamber and connect the top cover and the lower part of the vacuum chamber with the sleeve. Now, put on safety goggles before generating the vacuum.

Using the pump, evacuate the chamber until the desired pressure is obtained. The target pressure in this demonstration is 0.1 millibars. Then, close the valve on the side of the chamber and turn off the pump.

At this point, start the video recording. While recording, open the hole of the particle chamber to liberate the particle, and at the same time pull and turn the stick attached to the tip of the pipet. This will prevent stick slip problems due to high friction between the stick and the sealed ring.

After the impact occurs, immediately stop the recording. Only a limited number of frames can be saved, and the first are over-written as soon as the limit is exceeded. Cut the movie around the instant of the impact at the screen, and save it on the memory card.

Anticipate repeating the experiment about 10 times for an accurate main value. When working with finer particles, use essentially the same procedure with a few alterations. Load 50 to 100 spheres onto a folded sheet of paper and load the particles into the chamber off the paper.

When pulling the stick at the initiation of the experiement, pull very slowly to prevent all the particles from dropping at the same time. When cutting the movie, do it in such a way that at least 10 clearly focused impacts are visible. Before evaluating the data, it is first necessary to calibrate the software.

Load a frame with the particle of known size obtained during the setup. Then, count the number of pixels of the horizontal diameter and divide the known distance by the number of pixels to get the conversion factor, distance per pixel. The horizontal is easier to use because of the contrast between the particle and white background.

To calculate the impact velocity, set a reference point of motion on the top of the sphere 10 frames before the point of impact and a second reference point one frame before the impact. Use the number of pixels between the two points and the conversion factor to calculate the traveled distance. Then, divide the distance by the passed time between nine frames to obtain the impact velocity.

To calculate the rebound velocity, use reference points on the top of the sphere, one frame after the impact and ten frames after the impact. Finally, calculate the coefficient of restitution, or COR, as the ratio of rebound velocity to impact velocity. Repeat all these steps to evaluate all the recorded drop test videos.

Glass particles with diameters of 100 microns to four millimeters were dropped from an initial height of 200 millimeters onto a stainless steel base-plate with a thickness of 20 millimeters. The mean value of the COR was about 0.9 for particles 700 microns or larger. This result was independent of the air pressure.

For particles with a diameter less than 400 microns, the COR was nearly constant with a value of 0.9 under vacuum conditions. Under atmospheric pressure, the coefficient of restitution decreased with particle diameter. The results for the impact velocity depended on the particle’s size and atmospheric pressure.

Fine powders were a lot slower under atmospheric pressure, whereas their impact velocity decreased only slightly under vacuum conditions. The data showed some exceptional outliers at 700 microns that may have been created by a false calibration. After watching this video, you should have a good understanding how to measure the coefficient of restitution in free fall experiments under vacuum conditions.

Once mastered, this method can be done in one and a half hours for 10 particles if it is properly applied. Don’t forget that working with a glass cylinder in vacuum conditions is extremely hazardous, and that precautions should always be taken.