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Register a new userMulti-Particle Collisions in Microgravity: Coefficient of Restitution and Sticking Threshold for Systems of Mm-Sized Particles
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The current model of planet formation lacks a good understanding of the growth of dust particles inside the protoplanetary disk beyond mm sizes. In order to investigate the low-velocity collisions between this type of particles, the NanoRocks experiment was flown on the International Space Station (ISS) between September 2014 and March 2016. We present the results of this experiment. We quantify the damping of energy in systems of multiple particles in the 0.1 to 1 mm size range while they are in the bouncing regime, and study the formation of clusters through sticking collisions between particles. We developed statistical methods for the analysis of the large quantity of collision data collected by the experiment. We measured the average motion of particles, the moment of clustering, and the cluster size formed. In addition, we ran simple numerical simulations in order to validate our measurements. We computed the average coefficient of restitution (COR) of collisions and find values ranging from 0.55 for systems including a population of fine grains to 0.94 for systems of denser particles. We also measured the sticking threshold velocities and find values around 1 cm/s, consistent with the current dust collision models based on independently collected experimental data. Our findings have the following implications that can be useful for the simulation of particles in PPDs and planetary rings: (1) The average COR of collisions between same-sized free-floating particles at low speeds (< 2 cm/s) is not dependent on the collision velocity; (2) The simplified approach of using a constant COR value will accurately reproduce the average behavior of a particle system during collisional cooling; (3) At speeds below 5 mm/s, the influence of particle rotation becomes apparent on the collision behavior; (4) Current dust collision models predicting sticking thresholds are robust.
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Planetisimals are thought to be formed from the solid material of a protoplanetary disk by a process of dust aggregation. It is not known how growth proceeds to kilometre sizes, but it has been proposed that water ice beyond the snowline might affect this process. To better understand collisional processes in protoplanetary disks leading to planet formation, the individual low velocity collisions of small ice particles were investigated. The particles were collided under microgravity conditions on a parabolic flight campaign using a purpose-built, cryogenically cooled experimental setup. The setup was capable of colliding pairs of small ice particles (between 4.7 and 10.8 mm in diameter) together at relative collision velocities of between 0.27 and 0.51 m s ^-1 at temperatures between 131 and 160 K. Two types of ice particle were used: ice spheres and irregularly shaped ice fragments. Bouncing was observed in the majority of cases with a few cases of fragmentation. A full range of normalised impact parameters (b/R = 0.0-1.0) was realised with this apparatus. Coefficients of restitution were evenly spread between 0.08 and 0.65 with an average value of 0.36, leading to a minimum of 58% of translational energy being lost in the collision. The range of coefficients of restitution is attributed to the surface roughness of the particles used in the study. Analysis of particle rotation shows that up to 17% of the energy of the particles before the collision was converted into rotational energy. Temperature did not affect the coefficients of restitution over the range studied.
The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice non-trivial (non-Gaussian) fluctuations of the measured values. For a fixed impact velocity, the probability density of the coefficient of restitution, $p(epsilon)$, is formed by two exponential functions (one increasing, one decreasing) of different slope. This behavior may be explained by a certain roughness of the particle which leads to energy transfer between the linear and rotational degrees of freedom.
The coefficient of restitution of colliding viscoelastic spheres is analytically known as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While beeing analytically exact, this result is not suitable for applications in efficient event-driven Molecular Dynamics (eMD) or Monte Carlo (MC) simulations. Based on the analytic result, here we derive expressions for the coefficient of restitution which allow for an application in efficient eMD and MC simulations of granular Systems.
In this paper we present results of two novel experimental methods to investigate the collisional behavior of individual macroscopic icy bodies. The experiments reported here were conducted in the microgravity environments of parabolic flights and the Bremen drop tower facility. Using a cryogenic parabolic-flight setup, we were able to capture 41 near-central collisions of 1.5-cm-sized ice spheres at relative velocities between 6 and $22 mathrm{cm s^{-1}}$. The analysis of the image sequences provides a uniform distribution of coefficients of restitution with a mean value of $overline{varepsilon} = 0.45$ and values ranging from $varepsilon = 0.06$ to 0.84. Additionally, we designed a prototype drop tower experiment for collisions within an ensemble of up to one hundred cm-sized projectiles and performed the first experiments with solid glass beads. We were able to statistically analyze the development of the kinetic energy of the entire system, which can be well explained by assuming a granular `fluid following Haffs law with a constant coefficient of restitution of $varepsilon = 0.64$. We could also show that the setup is suitable for studying collisions at velocities of $< 5 mathrm{mm s^{-1}}$ appropriate for collisions between particles in Saturns dense main rings.
Context: Understanding the collisional properties of ice is important for understanding both the early stages of planet formation and the evolution of planetary ring systems. Simple chemicals such as methanol and formic acid are known to be present in cold protostellar regions alongside the dominant water ice; they are also likely to be incorporated into planets which form in protoplanetary disks, and planetary ring systems. However, the effect of the chemical composition of the ice on its collisional properties has not yet been studied. Aims: Collisions of 1.5 cm ice spheres composed of pure crystalline water ice, water with 5% methanol, and water with 5% formic acid were investigated to determine the effect of the ice composition on the collisional outcomes. Methods: The collisions were conducted in a dedicated experimental instrument, operated under microgravity conditions, at relative particle impact velocities between 0.01 and 0.19 m s^-1, temperatures between 131 and 160 K and a pressure of around 10^-5 mbar. Results: A range of coefficients of restitution were found, with no correlation between this and the chemical composition, relative impact velocity, or temperature. Conclusions: We conclude that the chemical composition of the ice (at the level of 95% water ice and 5% methanol or formic acid) does not affect the collisional properties at these temperatures and pressures due to the inability of surface wetting to take place. At a level of 5% methanol or formic acid, the structure is likely to be dominated by crystalline water ice, leading to no change in collisional properties. The surface roughness of the particles is the dominant factor in explaining the range of coefficients of restitution.
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