In this work, we report on microgravity studies of particle ensembles simulating ice-particle collisions in Saturn's dense main rings. We have developed an experimental method to study the energy dissipation in a many-body system consisting of approx. one hundred cm-sized glass spheres. The temporal development of the mean particle velocity, ranging from ~10 cm/s (at the beginning) to ~0.35 cm/s (after 9s of experiment duration), can be explained by a constant coefficient of restitution of 0.64. A comparison to values obtained for pure water-ice bodies shows that future cryogenic ice-collision experiments can achieve collision velocities of ~0.1 cm/s, and thus will very well simulate the conditions in Saturn's main rings.
Deep Dive into Laboratory studies of ice-particle collisions in Saturns dense rings.
In this work, we report on microgravity studies of particle ensembles simulating ice-particle collisions in Saturn’s dense main rings. We have developed an experimental method to study the energy dissipation in a many-body system consisting of approx. one hundred cm-sized glass spheres. The temporal development of the mean particle velocity, ranging from ~10 cm/s (at the beginning) to ~0.35 cm/s (after 9s of experiment duration), can be explained by a constant coefficient of restitution of 0.64. A comparison to values obtained for pure water-ice bodies shows that future cryogenic ice-collision experiments can achieve collision velocities of ~0.1 cm/s, and thus will very well simulate the conditions in Saturn’s main rings.
Planetary rings are among the most fascinating objects in our solar system. Especially Saturn's bright rings have impressed astronomers, like G. Galilei and J. D. Cassini, for the past four centuries. Today we know that they radially extend to several hundred thousand kilometers distance from Saturn, although they are locally confined to a thickness of only a few meters [1,2,3]. The radio occultation data [4,5] obtained by deep-space missions (e.g. Voyager and Cassini) show that the rings can be described as 'granular gases' consisting of myriads of cmto m-sized, almost pure water-ice bodies [6,7] moving on Keplerian orbits. Their orbital motion is disturbed by interaction with nearby moons and so-called 'moonlets' leading to an increase of orbital eccentricity, which is counteracted by the dissipation of kinetic energy in frequent inelastic collisions at relative velocities well below 1 cm s -1 [8].
In the past, several kinetic theories [9,10,11,12] were developed and numerical studies [13,14] were carried out to explain the dynamic phenomena, like wakes propagating throughout the rings, instabilities, and overstabilities, observed by the deep-space missions Voyager and Cassini [3,15,16]. In addition, visco-elastic collision models were developed to treat fragmentation processes and mass gain of the constituent particles [17,18,19].
In most of the simulations and kinetic theories, the energy dissipation in individual collisions is described by only one parameter, the coefficient of restitution ε, given by the ratio of relative velocities v ′ (after) and v (before the impact).
We designed an experimental setup to investigate the collision processes within an ensemble of up to one hundred centimeter-sized spheres in microgravity. As a prototype, we built a glass-made test chamber of 150 × 150 × 15 mm 3 volume in which the sample particles can be injected from opposite sides by two electrically slid glass bars afterwards sealing the entry holes of the glass box. The typical injection velocity is ∼ 10 cm s -1 . The experiments were performed at the Bremen drop-tower facility ZARM 1 , where a catapult was utilized to achieve 9 s of microgravity with a residual acceleration of ∼ 10 -5 g 0 , where g 0 = 9.81 m s -2 is the Earth’s gravitational acceleration. During the experiment the particle ensemble was captured by a high-speed, high-resolution CCD camera operated at 115 frames per second (fps) with a resolution of 1024 × 1024 pixels (see Fig. 1 for a sample image).
The design of the test cell allows for free collisions of the particles and the limitation of the height to 1.5 particle diameters ensures an unambiguous analysis of their motion, because the samples cannot pass each other in the line of sight of the camera. In future experiments the studies will be extended to pure water ice samples in a cryogenic environment for a more realistic simulation of Saturn’s dense rings.
In this work, we report on one out of seven experiments conducted with 92 solid glass beads (1 cm diameter). Two sets of 32 glass spheres each were injected into the experiment chamber from opposites sides, while 28 particles were at rest inside the cell. After a short period of equilibration, the kinetic energy of the system decreased due to inelastic collisions. To analyze the particles’ motion all images were convolved with an image of an individual sample sphere giving the most probable positions of all particles’ center coordinates. Afterwards the images were binarized and a particle tracking algorithm was used to determine the trajectories of all particles. From this data, the individual sample velocities could be calculated for each image frame. This means that (although generally possible) the collisions were treated in a statistical way, rather than being analyzed individually.
The results can be found in Fig. 2, which shows that after the equilibration (first 2 s of experiment duration) the velocity decays systematically due to inelastic collisions and excitation of rotational motion. Assuming a constant coefficient of restitution ε = const., describing the energy loss in individual collisions, the mean velocity v as a function of time can be derived to be
Velocity decay over experiment duration. After a short period of equilibration the velocity decay can be fitted by a simple equation which is in accordance with Haff’s Law [20].
Normalized cumulative number of samples with velocity ≤ v for the time interval 6.5 . . . 8.5 s. The mean particle velocity is 3.5 mm s -1 (dashed line) with 50% of all samples covering the velocity range 2 . . . 5 mm s -1 (dotted lines). Hence, the collisions occur in the velocity regime relevant for studying Saturn’s rings.
where v 0 is the initial injection velocity, σ = 4πr 2 is the collisional cross-section, and n is the number density of the particle ensemble. A fit of Eq. ( 1) to the data shows that the low-velocity regime (after approx. 2 s of experiment time) can be well described wit
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