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

Powders and granules are everywhere around us. A life without them is impossible in modern societies. They appear in food and drinks as grains or even flour, sugar, coffee and cocoa. They are needed for daily used objects like the toner for laser printer. Also the plastic industry is not imaginable without them, because plastic is transported in granular form before it is melted and given a new shape. After Ennis et al.¹ at least 40% of the value added to the consumer price index of the United States of America by the chemical industry (agriculture, food, pharmaceuticals, minerals, munitions) is connected to particle technology. Nedderman² even stated that about 50% (weight) of the products and a minimum of 75% of the raw materials are granular solids in the chemical industry. He also declared that there occur many problems concerning storage and transportation of granular materials. One of these is that during transport and handling many collisions take place. To analyze, describe and predict the behavior of a particulate system, Discrete Element Method (DEM) simulations can be performed. For these simulations knowledge of the collision behavior of the particulate system is necessary. The parameter that describes this behavior in DEM simulations is the coefficient of restitution (COR) that has to be determined in experiments.

The COR is a number that characterizes the loss of kinetic energy during the impact as described by Seifried et al.³. They explained that this is caused by plastic deformations, wave propagation and viscoelastic phenomena. Thornton and Ning⁴ also mentioned that some energy might be dissipated by work due to interface adhesion. The COR depends on impact velocity, material behavior, particle size, shape, roughness, moisture content, adhesion properties and temperature as stated in Antonyuk et al.⁵. For a completely elastic impact all absorbed energy is returned after the collision so that the relative velocity between the contact partners is equal before and after the impact. This leads to a COR of e = 1. During a perfectly plastic impact all the initial kinetic energy is absorbed and the contact partners stick together which leads to a COR of e = 0. Furthermore, Güttler et al.⁶ explained that there are two types of collisions. On the one hand, there is the collision between two spheres which is also known as the particle-particle contact. On the other hand, there is the collision between a sphere and a plate that is also called particle-wall contact. With the data for the COR and other material properties like coefficient of friction, density, Poisson's ratio and shear modulus DEM simulations can be performed to determine the post-collisional velocities and orientations of the particles as explained by Bharadwaj et al.⁷. As shown in Antonyuk et al.⁵, the COR can be calculated with the ratio of rebound velocity to impact velocity.

Therefore an experimental setup for free-fall tests to examine the particle-wall contact of particles with a diameter from 0.1 mm to 4 mm was constructed. The advantage of free-fall experiments compared to accelerated experiments as in Fu et al.⁸ and Sommerfeld and Huber⁹ is that rotation might be eliminated. Hence, the transfer between rotational and translational kinetic energy which influences the COR can be avoided. Aspheric particles need to be marked as in Foerster et al.¹⁰ or Lorenz et al.¹¹ to take rotation into account. As the COR is depending on the impact velocity, the impact velocities in the experiments have to match the ones in the real transport and handling processes. In free-fall experiments under atmospheric pressure, the impact velocity is limited by the drag force, having an increasing influence for a decreasing particle size. To overcome this drawback, the experimental setup works under vacuum conditions. A second challenge is to drop just one single particle since then it is possible to characterize all properties that influence the COR beforehand, for instance surface roughness and adhesion. With this knowledge, the COR can be determined according to the properties of the particle. For this, a new release mechanism was developed. Another issue is the adhesive forces of powders with a diameter inferior to 400 µm. Therefore, a dry and ambient temperature environment is necessary to overcome adhesion.

The experimental setup consists of several parts. An exterior view of the existing experimental setup is shown in Figure 1. First, there is the vacuum chamber that is made out of glass. It is composed of a lower part (cylinder), a top cover, a seal ring and a sleeve to connect the parts. The lower part has two openings for a connection with the vacuum pump and the vacuum gauge. The top cover has four openings. Two of them are necessary for the sticks of the release mechanism described below and also two that can be used for further improvements of the experiment. All these openings can be closed with seal rings and screw caps when working under vacuum conditions.

Moreover, a new release mechanism was developed since the use of a vacuum nozzle as in many other experiments documented in literature (for example Foerster et al.¹⁰, Lorenz et al.¹¹, Fu et al.¹² or Wong et al.¹³) is not possible in a vacuum environment. The mechanism is realized by a cylindrical chamber with a conical drill hole that is held by a plate. This is connected to a stick that fits in one of the seal rings of the top cover of the vacuum chamber and guarantees the adjustment of a variable initial height for the free-fall experiments. A scale is drawn on the stick for measuring the height. The closing of the particle chamber is implemented by a conical tip of a pipette that is again connected to a stick. The new release mechanism can be seen in Figure 2 and works as described here: in the initial state the pipette tip is pushed down so that the circumference of the tip touches the edge of the chamber's drill hole. The chamber is closed with the pipette tip such that there is no space for a particle to leave the chamber through the hole. To release the particle, the stick is pulled upwards very slowly together with the tip connected to it. As the diameter of the tip is getting smaller a gap between its circumference and the edge of the drill hole arises through which the particle can leave the chamber. Although one might expect a rotation of the particle with the newly developed release mechanism as the particle could 'roll' out of the chamber, a different behavior appears in the experiments. Figure 3 shows the impact of an aspherical particle from 50 frames before to 50 frames after the impact in steps of 25 frames. From the shape of the particle no rotation is visible before the impact (1-3) whereas afterwards it obviously spins (4-5). Therefore the claimed non-rotational release is taking place with this release mechanism.

Another component of the experimental setup is the baseplate. In fact there are three different kinds of baseplates consisting of different materials. One is made of stainless steel, a second of aluminum and a third of polyvinyl chloride (PVC). These baseplates represent frequently used materials in process engineering for example in reactors and tubes.

To determine the impact and rebound velocities, a high-speed camera with 10,000 fps and a resolution of 528 x 396 pixels is used. This configuration is chosen as there is always one picture near the impact and also the resolution is still satisfactory. The camera is connected to a screen that shows the videos in the instant when they are recorded. This is necessary, because the high speed camera can only save a limited amount of pictures and overwrites the beginning of the video when this amount is exceeded. Furthermore, a strong light source for the illumination of the visual field of the high-speed camera is required. For illumination uniformity a sheet of technical drawing paper is glued on the backside of the vacuum chamber that spreads the light.

Finally, a two-stage rotary vane pump is used to establish a vacuum of 0.1 mbar and a vacuum gauge measures the vacuum to guarantee constant environmental conditions.

For the here presented work glass beads with different particle diameters (0.1-0.2, 0.2-0.3, 0.3-0.4, 0.700, 1.588, 2.381, 2.780, 3.680 and 4.000 mm) are used. The beads are made of soda lime glass and are spherical with a rather smooth surface.