Collisions between spheres are a common ingredient in a variety of scientific problems, and the coefficient of restitution is a key parameter to describe the outcome of those. We present a new collision model that treats adhesion and viscoelasticity self-consistently, while energy losses arising from plastic deformation are assumed additive. Results show that viscoelasticity can significantly increase the energy that is dissipated in a collision, enhancing the sticking velocity. Furthermore, collisions well above the sticking velocity remain dissipative. We systemically compare the model to a large and unbiased set of published laboratory experiments to show its general applicability. The model is well capable of reproducing the important relation between impact velocity and coefficient of restitution as measured in the experiments, covering a wide range of materials, particle sizes, and collision velocities. Furthermore, the fitting parameters from those curves provide physical parameters like the surface energy, yield strength, and characteristic viscous relaxation time. Our results show that all three aspects-adhesion, viscoelastic dissipation and plastic deformation-are required for a proper description of the kinetic energy losses in sphere collisions.

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 . The analysis of the image sequences provides a uniform distribution of coefficients of restitution with a mean value of and values ranging from ε=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 Haff's law with a constant coefficient of restitution of ε=0.64. We could also show that the setup is suitable for studying collisions at velocities of <5 mm s−1 appropriate for collisions between particles in Saturn's dense main rings

Context. In the very first steps of the formation of a new planetary system, dust agglomerates grow inside the protoplanetary disk that rotates around the newly formed star. In this disk, collisions between the dust particles, induced by interactions with the surrounding gas, lead to sticking. Aggregates start growing until their sizes and relative velocities are high enough for collisions to result in bouncing or fragmentation. With the aim of investigating the transitions between sticking and bouncing regimes for colliding dust aggregates and the formation of clusters from multiple aggregates, the Suborbital Particle and Aggregation Experiment (SPACE) was flown on the REXUS 12 suborbital rocket. Aims. The collisional and sticking properties of sub-mm-sized aggregates composed of protoplanetary dust analogue material are measured, including the statistical threshold velocity between sticking and bouncing, their surface energy and tensile strength within aggregate clusters. Methods. We performed an experiment on the REXUS 12 suborbital rocket. The protoplanetary dust analogue materials were micrometre-sized monodisperse and polydisperse SiO 2 particles prepared into aggregates with sizes around 120 µm and 330 µm, respectively and volume filling factors around 0.37. During the experimental run of 150 s under reduced gravity conditions, the sticking of aggregates and the formation and fragmentation of clusters of up to a few millimetres in size was observed. Results. The sticking probability of the sub-mm-sized dust aggregates could be derived for velocities decreasing from ∼22 to 3 cm s −1 . The transition from bouncing to sticking collisions happened at 12.7 +2.1 −1.4 cm s −1 for the smaller aggregates composed of monodisperse particles and at 11.5 +1.9 −1.3 and 11.7 +1.9 −1.3 cm s −1 for the larger aggregates composed of mono-and polydisperse dust particles, respectively. Using the pull-off force of sub-mm-sized dust aggregates from the clusters, the surface energy of the aggregates composed of monodisperse dust was derived to be 1.6×10 −5 J m −2 , which can be scaled down to 1.7×10 −2 J m −2 for the micrometre-sized monomer particles and is in good agreement with previous measurements for silica particles. The tensile strengths of these aggregates within the clusters were derived to be 1.9 +2.2 −1.2 Pa and 1.6 +0.7 −0.6 Pa for the small and large dust aggregates, respectively. These values are in good agreement with recent tensile strength measurements for ∼mm-sized silica aggregates. Conclusions. Using our data on the sticking-bouncing threshold, estimates of the maximum aggregate size can be given. For a minimum mass solar nebula model, aggregates can reach sizes of ∼1 cm.

Context. 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. Aims. To better understand collisional processes in protoplanetary disks leading to planet formation, the individual low velocity collisions of small ice particles were investigated. Methods. 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. Results. 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.