We present a technique to achieve low-velocity to intermediate-velocity collisions between fragile dust aggregates in the laboratory. For this purpose, two vacuum drop-tower setups have been developed that allow collision velocities between <0.01 and ~10 m/sec. The collision events are recorded by high-speed imaging.
For the purpose of investigating the evolution of dust aggregates in the early Solar System, we developed two vacuum drop towers in which fragile dust aggregates with sizes up to ~10 cm and porosities up to 70% can be collided. One of the drop towers is primarily used for very low impact speeds down to below 0.01 m/sec and makes use of a double release mechanism. Collisions are recorded in stereo-view by two high-speed cameras, which fall along the glass vacuum tube in the center-of-mass frame of the two dust aggregates. The other free-fall tower makes use of an electromagnetic accelerator that is capable of gently accelerating dust aggregates to up to 5 m/sec. In combination with the release of another dust aggregate to free fall, collision speeds up to ~10 m/sec can be achieved. Here, two fixed high-speed cameras record the collision events. In both drop towers, the dust aggregates are in free fall during the collision so that they are weightless and match the conditions in the early Solar System.
It is generally accepted that planet formation starts with the non-gravitational accumulation of microscopically small dust grains into larger dust aggregates (see review by Blum & Wurm)1. The dust particles collide within their protoplanetary disks due to Brownian motion, relative drift motions, and turbulence of the nebular gas (see review by Johansen et al.)2. If the collision velocities are sufficiently low, the dust particles stick together to form larger agglomerates. A wealth of laboratory measurements over the past years have led to a dust-aggregate collision model that predicts the outcome of a pair of dust aggregates with arbitrary masses and collision velocities3. The basic collisional results are sticking (in general for small aggregate masses and low collision velocities), bouncing, and fragmentation (for high impact speeds). However, the transitions between these phases are not sharp and there are other outcomes, like, e.g. mass transfer or erosion. Applying this model to a typical protoplanetary disk predicts the growth of cm-sized dust aggregates within a few thousand years4. The presence of cm-sized dust aggregates has been extensively investigated by astronomical observations over the past years and can now be considered as established (see review by Testi et al.)5 so that we conclude that the principle mechanism by which the first macroscopic bodies in young planetary systems form has been identified.
However, the further growth to bodies of at least kilometer sizes is not so clear. For the terrestrial-planet region, two hypotheses are currently discussed (see also the recent reviews on this matter by Johansen et al.2 and Testi et al.5): (i) concentration of the cm-sized dust aggregates by, e.g. the streaming instability6 and subsequent gravitational collapse7,8 and (ii) growth of a few ”lucky winners” to larger sizes with subsequent mass accretion by the mass-transfer process9,10,11. In both models, cm-sized dust aggregates undergo an enormous number of mutual collisions at low to moderate velocities. It is unclear what the possible outcomes of these collisions (besides bouncing) are.
To improve the dust-aggregate collision model by Güttler et al.3 and to investigate in more detail the collisions among macroscopic dust aggregates in the relevant velocity regimes, we set up two drop towers in our laboratory, in which individual aggregate-aggregate collisions can be studied in great detail under vacuum and microgravity conditions. Both drop towers possess a free-fall height of 1.5 m, which limits the observation time to ~0.5 sec. Thus, we observe the collisions by high-speed cameras with megapixel format and up to 7,500 frames per second. For maximum contrast and high recording speeds, bright-field illumination is chosen. Lighting is thus provided by high-intensity LED panels and homogenized by diffuser screens. Thus, the high-speed cameras view the colliding dust aggregates as dark objects in front of an illuminated screen. To avoid flickering, the LEDs are DC powered.
To achieve low collision velocities, the two dust aggregates are placed above one another in a double release mechanism. Releasing the upper aggregate a time of t before the lower one results in a relative velocity of v = g t, with g = 9.81 m/sec2 being the gravitational acceleration of the Earth. The two high-speed cameras, which view the collision from two directions 90° apart, are typically released in between the two dust aggregates (typically t/2 after the upper particle). The cameras run in continuous-recording mode, which is terminated by the impact of the camera holders into sand buckets. The maximum frame rate in this operational mode is 1,000 images per second at megapixel resolution. With this setup, velocities down to below 0.01 m/sec have been achieved. Due to limitations of the mechanical setup of the double release mechanism, the maximum relative collision speed is ~3 m/sec. Collisions involving dust aggregates with up to 5 cm in size have been investigated in this drop tower. For higher collision velocities up to ~10 m/sec, a second drop tower is used, which is equipped with an electromagnetic accelerator that is capable to smoothly accelerate dust aggregates up to 5 m/sec in a vertical upward direction. The other dust aggregate is held by a double-wing trap-door release mechanism and can be released rotation-free into free fall at any given time. Here, it does not make sense to use free-falling cameras. We rather use two stationary high-speed cameras with up to 7,500 frames per second and megapixel resolution. Due to the larger diameter of this drop tower, dust aggregates up to (and possibly above) 10 cm in size can be used.
CAUTION: Depending on the hazardousness of the used particles, which can be found in the corresponding Safety Data Sheets, mouth protection and safety gear must be worn by the person working with the dust. It is also recommended to use a suction system to keep the ambient air dust-free.
1. Preparation of cm-sized Dust Aggregate Samples
SiO2-monomer grain type | Manufacturer | Particle diameter | Particle shape | Example figure |
Monodisperse | Micromod | 1.52 ± 0.06 µm | Spherical | Figure 1 (left) |
Polydisperse | Sigma-Aldrich | 0.1 – 10 µm | Irregular | Figure 1 (right) |
Table 1. Characteristics of the SiO2 particles used in the dust-aggregate collision experiments.
Figure 1. Electron-microscopy images of the monodisperse (left) and polydisperse (right) SiO2 particles used for the production of macroscopic dust aggregates. Please click here to view a larger version of this figure.
Figure 2. Photograph of the variation of dust-aggregate sample sizes and shapes. The following samples are shown: dust cylinders with 1 cm, 2 cm, and 5 cm diameter (back row), dust spheres with 1 cm and 2 cm diameter (center row), and 2-3 mm-sized Al2O3 spheres (front). Please click here to view a larger version of this figure.
Figure 3. Reconstruction of the internal structure of a cylindrical dust-aggregate sample of 5 cm height and 5 cm diameter after XRT analysis. The gray scale denotes the volume filling factor, which is the ratio of the mass density of the sample and the material density of the monomer-dust particles. From the XRT reconstruction, it is clearly visible that this high-porosity sample was assembled using mm-sized dust aggregates. Please click here to view a larger version of this figure.
2. Principle of Drop Tower Setup
3. Performing Experiments
4. Example Experiments
5. Data Analysis
Figure 4. Example of the analysis of bouncing collisions. The coefficient of restitution, i.e. the ratio of the rebound velocity and the impact velocity, is plotted as a function of the collision velocity. Circles show data for spherical dust aggregates of 2 cm diameter13 (see Figure 2), triangles denote collisions between cylindrical dust aggregates of 5 cm diameter and 5 cm height (see Figure 2) and two different volume filling factors of 0.3 and 0.4, respectively12. The data show a trend of decreasing coefficient of restitution with increasing impact velocity. Please click here to view a larger version of this figure.
Using the well-characterized dust-aggregate samples described in the protocol (see Figures 1-3), any collision observed in one of the laboratory drop towers will yield scientifically valuable information on the outcomes of similar collisions in protoplanetary disks. We have so far systematically investigated the collision outcomes of 2 cm sized spherical dust aggregates (with volume filling factors of 0.5) in the velocity range between 0.008 and 2.02 m/sec13 and of 5 cm sized cylindrical dust aggregates (with volume filling factors between 0.3 and 0.5) in the velocity range between 0.004 and 2 m/sec12. We found bouncing between the dust aggregates as the dominating outcome for velocities below ~0.4 m/sec for both types of dust aggregates (see Movie 6 for an example). In Figure 4, the coefficient of restitution of these bouncing collisions is shown. The circles denote the experiments with 2 cm sized spherical samples13 and the triangles represent results from collisions among 5 cm sized dust cylinders with two different packing densities12. Although the coefficients of restitution of individual experiments scatter widely, the average value of the coefficient of restitution decreases with increasing collision velocity.
Both dust aggregates typically fragment upon impact for velocities above ~1 m/sec (see Movie 7 for an example). For velocities between ~ 0.4 and ~1 m/sec, fragmentation of only one of the two colliding dust aggregates can occur. In this case, the non-fragmenting dust aggregate gains a few percent of mass by mass transfer13. The above-mentioned velocity limits are not sharp but denote approximately where the boundaries between the different regimes lie2,11. For collisions between dust aggregates of different sizes and moderate velocities, impacts will generally not lead to the fragmentation of the larger of the two dust aggregates. On the opposite, the larger bodies increase their mass by transfer of part of the mass of the smaller impactors (see Movie 8).
For the cases, in which the two dust aggregates bounce off one another, the transfer from the translational kinetic energy before the collision (mind that the dust aggregates do not rotate before the collision) into translational kinetic energy, rotational kinetic energy, and other (dissipative) energy channels (e.g. compaction of the dust aggregates) can be determined. We found that for central collisions (in which the rotational energy can be neglected) the relative amount of dissipated energy strongly increases with increasing velocity and is higher for lower volume filling factors of the dust aggregates12. This behavior can be modeled by molecular-dynamics simulations12.
Movie 1. High-speed movie (played back in slow motion) of the particle-on-a-string (top) and trap-door release mechanism (bottom).
Movie 2. High-speed movie (played back in slow motion) of the double trap-door release mechanism. Both samples are clumps of Al2O3 particles of 2 mm diameter, which remain confined during free fall due to the extremely low disturbance during release.
Movie 3. High-speed movie (played back in slow motion) of the scissor-type double release mechanism.
Movie 4. High-speed movie (played back in slow motion) of the double-wing trap-door release mechanism.
Movie 5. Animation of the timer electronics switching the upper and lower release mechanism as well as the camera release to free fall.
Movie 6. High-speed movie (played back in slow motion) of a bouncing collision between two 5 cm-sized dust-aggregate cylinders. The two dust aggregates are released by the scissor-type double release mechanism and collide with 0.09 m/sec velocity.
Movie 7. High-speed movie (played back in slow motion) of two 2 cm-sized cylindrical dust aggregates colliding at a relative velocity of 7.4 m/sec. Both aggregates fragment completely.
Movie 8. High-speed movie (played back in slow motion) of a 5 mm-sized dust aggregate impacting a 5 cm-sized cylindrical solid target. As the impact velocity of 4.3 m/sec is above the fragmentation speed of the small dust aggregate, this breaks apart and transfers part of its mass to the target, which is clearly visible in the movie.
Movie 9. Determination of the particle trajectories by a semi-automatic particle-tracking algorithm. Here, the collision between two 2 cm-sized spherical dust aggregates is shown.
Due to the high mechanical precision, the failure rate of both drop towers is extremely low. This is of utmost importance, because the sample preparation may take up to several hours, depending on size, shape and porosity of the desired dust aggregates. It should be mentioned that large dust aggregates with very high porosities are extremely fragile and, thus, difficult to handle. It may occur that these dust aggregates break during extraction off the mold or transfer to the drop tower. In these cases, a new sample has to be prepared. Thus, it is important that the small drop tower allows reliable (and predictable) collision velocities down to 0.01 m/sec 11,13. The lowest impact speed so far achieved was 0.004 m/sec. These small impact velocities can only be reached for free particles in a microgravity environment. The laboratory drop tower is a cheap and versatile realization of such a microgravity facility.
Alternative methods to achieve low impact speeds make use of levitation techniques14,15 (e.g. by electromagnetic or aerodynamic levitation) but generally induce a force between the colliding particles, which has to be taken into account in the analysis of the collisions. Moreover, levitation often induces rotational motion14, which, if unwanted, does not allow rotation-free collisions but, on the other hand, might even allow realistic simulations of collisions among rotating particles. In case of aerodynamic levitation, air-cushion effects during the collision may induce unwanted conditions that do not match those in protoplanetary disks. However, levitation allows for unlimited observation time and repeatable experiments so that it has to be considered an alternative to the drop tower if the time limitation is essential. All our efforts so far have been concentrated on SiO2 as a representative of the silicates in the terrestrial-planet formation region of young Solar Systems. As most of the mass of protoplanetary disks is concentrated beyond the condensation point of water ice, it is essential to also study the collision behavior of aggregates consisting of µm-sized H2O-ice grains. We are currently setting up a cryo-vacuum drop tower for this purpose. It must be noted that the temperatures in such simulation experiments must be below ~150 K, which is the temperature of the so-called “snow line” in protoplanetary disks (the “snow line” divides the inner regions where water is in the vapor phase from the outer regions where it is found as solid water ice). We have shown that the formation of µm-sized water-ice particles is feasible and that aggregates thereof can be produced16 so that we are optimistic to have first results on their collision behavior within the next 1-2 years.
The authors have nothing to disclose.
The authors thank the Deutsches Zentrum für Luft- und Raumfahrt (DLR), the Deutsche Forschungsgemeinschaft (DFG), and the TU Braunschweig for continual support of our laboratory activities. The low-velocity drop tower has been established under DLR grant 50WM0936, the high-velocity drop tower has been developed under DFG grant INST 186/959-1 as part of the CRC 963 “Astrophysical Flow Instabilities and Turbulence”.
Monodisperse SiO2 particles | Micromod | 43-00-153 | Particle diameter 1.52 ± 0.06 µm; particle shape spherical |
Polydisperse SiO2 particles | Sigma-Aldrich | S5631 | Particle diameter 0.1 – 10 µm; particle shape irregular |