10:15 AM - 10:30 AM
[PPS06-18] Effect of porosity on restitution coefficient and sticking properties of snowball simulating Saturn’s rings
Keywords:Saturn's ring, restitution coefficient, sticking
Saturn's rings have a width of tens of thousands of kilometers and a thickness of hundreds of meters, and they are composed of water ice particles with a diameter of mm to meters. The average relative impact velocity among ring particles is estimated to be < several cm/s, so at such low velocities, sticking of ice particles may occur by surface adhesion force. Numerical simulations indicated that the restitution coefficient must be about 0.6 to maintain a thin annular ring. Therefore, it is necessary to investigate the collisional outcomes of ice particles during low velocity collision such as fracture, rebound and sticking. Although previous laboratory experiments were conducted by using non-porous or frosted ice particles, ring particles are predicted by Cassini's observations to be highly porous ice particles such as ice aggregates. Then, this observation is inconsistent with non-porous ice. Therefore, it is necessary to examine whether the ice aggregates can maintain the thin annular rings of Saturn.
The purpose of this study is to clarify the velocity dependence of restitution coefficient of porous ice and the threshold velocity for sticking of porous ice, we then try to estimate the internal structure of ring particles suitable for maintaining thin annular Saturn rings. Therefore, low-velocity impact experiments were performed between a porous ice ball and a porous ice plate, and we investigated the porosity dependence of the relationship between the impact velocity and the restitution coefficient and the threshold velocity for sticking.
The restitution coefficient was measured by letting a ball fall freely on a plate. Porous ice spheres (the radius of 1.5cm, the porosity of 47%, 53% and 60%) were made by compacting ice particles (the average size of 20µm) into spherical molds. A porous ice plate was used for the target plate which was made in the same way as porous ice spheres (the radius of 1.5 cm, the thickness of 2 cm, the porosity of 43% to 62%). The restitution coefficient was determined by measuring the time interval among collisions using a laser displacement meter. The impact velocity was changed from 2.33 to 76.4 cm / s.
The restitution coefficient of the porous ice ball continued to decrease with the increase of the impact velocity. The restitution coefficient decreased as the porosity increased at high impact velocities, but the porosity dependence was not recognized at low impact velocities of < 10cm/s. This velocity dependence of the restitution coefficient can be expressed by the empirical equation, e = e0 * vi -b, where e is the restitution coefficient and vi is the impact velocity, and e0, b was 0.47, 0.17 at the porosity of 47%, 0.59, 0.36 at 53%, and 0.36, 0.27 at 60%, respectively. But, the low velocity data was obtained in the second and subsequent collisions, suggesting that these multiple collisions might cause a change in the surface state.
We find that mixed region where both rebound and sticking occur was observed as the impact velocity decreased. At lower velocities, the rebound was no longer observed. The threshold velocities for mixing region were 10.3 cm/s at the porosity of 47%, 12.9 cm/s at 53%, and 9.68 cm/s at 60%, respectively. And the threshold velocities for sticking were 3.53 cm/s at the porosity of 47%, 1.27 cm/s at 53%, and 9.22 cm/s at 60%, respectively.
From these results, we infer that rebound does not occur at low impact velocities of < 1cm/s. However, the circumstance temperature of Saturn is about 100 K, which is lower than the temperature at which the experiment was conducted. Then, threshold velocity for sticking considered to be lower. Therefore, by extrapolating the empirical equation obtained in this study assuming that the equation is independent of temperature, it was found that the impact velocity corresponding to the restitution coefficient of 0.6 was 0.24 cm/s at the porosity of 47%, 0.95 cm/s at 53%, and 0.15 cm/s at 60%, respectively.
This velocity range was almost consistent with those of ring particles estimated from the numerical simulation ( less than 0.3 to 0.5 cm/s).
The purpose of this study is to clarify the velocity dependence of restitution coefficient of porous ice and the threshold velocity for sticking of porous ice, we then try to estimate the internal structure of ring particles suitable for maintaining thin annular Saturn rings. Therefore, low-velocity impact experiments were performed between a porous ice ball and a porous ice plate, and we investigated the porosity dependence of the relationship between the impact velocity and the restitution coefficient and the threshold velocity for sticking.
The restitution coefficient was measured by letting a ball fall freely on a plate. Porous ice spheres (the radius of 1.5cm, the porosity of 47%, 53% and 60%) were made by compacting ice particles (the average size of 20µm) into spherical molds. A porous ice plate was used for the target plate which was made in the same way as porous ice spheres (the radius of 1.5 cm, the thickness of 2 cm, the porosity of 43% to 62%). The restitution coefficient was determined by measuring the time interval among collisions using a laser displacement meter. The impact velocity was changed from 2.33 to 76.4 cm / s.
The restitution coefficient of the porous ice ball continued to decrease with the increase of the impact velocity. The restitution coefficient decreased as the porosity increased at high impact velocities, but the porosity dependence was not recognized at low impact velocities of < 10cm/s. This velocity dependence of the restitution coefficient can be expressed by the empirical equation, e = e0 * vi -b, where e is the restitution coefficient and vi is the impact velocity, and e0, b was 0.47, 0.17 at the porosity of 47%, 0.59, 0.36 at 53%, and 0.36, 0.27 at 60%, respectively. But, the low velocity data was obtained in the second and subsequent collisions, suggesting that these multiple collisions might cause a change in the surface state.
We find that mixed region where both rebound and sticking occur was observed as the impact velocity decreased. At lower velocities, the rebound was no longer observed. The threshold velocities for mixing region were 10.3 cm/s at the porosity of 47%, 12.9 cm/s at 53%, and 9.68 cm/s at 60%, respectively. And the threshold velocities for sticking were 3.53 cm/s at the porosity of 47%, 1.27 cm/s at 53%, and 9.22 cm/s at 60%, respectively.
From these results, we infer that rebound does not occur at low impact velocities of < 1cm/s. However, the circumstance temperature of Saturn is about 100 K, which is lower than the temperature at which the experiment was conducted. Then, threshold velocity for sticking considered to be lower. Therefore, by extrapolating the empirical equation obtained in this study assuming that the equation is independent of temperature, it was found that the impact velocity corresponding to the restitution coefficient of 0.6 was 0.24 cm/s at the porosity of 47%, 0.95 cm/s at 53%, and 0.15 cm/s at 60%, respectively.
This velocity range was almost consistent with those of ring particles estimated from the numerical simulation ( less than 0.3 to 0.5 cm/s).