Analog Experiments on Tensile Strength of Dusty and Cometary Matter
aa r X i v : . [ a s t r o - ph . E P ] J un Analog Experiments on Tensile Strength of Dusty and Cometary Matter
Grzegorz Musiolik, Caroline de Beule, Gerhard Wurm a Fakultät für Physik, Universität Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany
Abstract
The tensile strength of small dusty bodies in the solar system is determined by the interaction between the composinggrains. In the transition regime between small and sticky dust ( µ m) and non cohesive large grains (mm), particlesstill stick to each other but are easily separated. In laboratory experiments we find that thermal creep gas flow at lowambient pressure generates an overpressure su ffi cient to overcome the tensile strength. For the first time it allows adirect measurement of the tensile strength of individual, very small (sub)-mm aggregates which consist of only tens ofgrains in the (sub)-mm size range. We traced the disintegration of aggregates by optical imaging in ground based aswell as microgravity experiments and present first results for basalt, palagonite and vitreous carbon samples with upto a few hundred Pa. These measurements show that low tensile strength can be the result of building loose aggregateswith compact (sub)-mm units. This is in favour of a combined cometary formation scenario by aggregation to compactaggreates and gravitational instability of these units.
1. Introduction
The solar system swarms with small dusty bodies.Cometary activity close to the sun bears witness to theirdusty nature. Small bodies are partly modified by or dueto collisions over the last billion of years (Krivov et al.,2006). However, especially for comets most dust fea-tures are likely inherited from the origin within the so-lar nebula. Cometary dust was studied in detail by the
Stardust mission to comet 81P / Wild 2 (Brownlee et al.,2006; Hörz et al., 2006; Trigo-Rodríguez et al., 2008).More generally, ideas of dusty growth come from exper-iments or modeling of early phases of planet formation(Blum & Wurm , 2008; Johansen et al., 2014).Comet flybys of space probes, e.g at Borrelly,Wild 2, and Churyumov-Gerasimenko show thatcomets are highly porous (Brownlee et al., 2006;Davidsson & Gutiérrez, 2004; Davidsson & Gutierrez,2004; Pätzold et al., 2016) and mainly built up of par-ticles with sizes from tens of nanometers to a millimeter(Hörz et al., 2006; Fulle et al., 2015). With densities of0.18-0.3 g / cm , 0.38-0.6 g / cm , and 0.533 g / cm , re-spectively, they are much less dense than pure waterice. High porosities can be the result of quite di ff erentinternal structures. One extreme might be macroporesbetween otherwise solid, monolithic, large fragments. Email address: [email protected] (GrzegorzMusiolik)
This resembles a rubble-pile structure. In this case, thebuilding blocks of the pile might be rather solid withan increased strength due to collisional processing andformation of aqueous alteration minerals which fill thepores as e.g. suggested by Trigo-Rodríguez & Blum(2009). The drill on the lander Philae on cometChuryumov-Gerasimenko as part of the
Rosetta mis-sion, e.g. seemed to have hit solid ground 3 cm belowthe surface (Spohn et al., 2015). This would be in favourof such ideas.Also the dust can provide porosity on di ff erenctscales. On one side there might be very compact dustaggregates, which are then building the larger bodyagain with macro-pore rubble-pile structure. On theother side a homogeneous micro-porosity between mi-crometer dust grains with low volume filling factor canalso provide a global high porosity. An analysis byGustafson & Adolfsson (1996) shows that packing fac-tors of meteors can even be as low as 0.12, which meansthat the major part of volume might be cavities.Some of this structure can be inferred from obser-vations e.g. of the dust production during the activephase or particle entry and ablation into Earth’s at-mosphere or IDP analysis (Borovicka , 1993; Flynn,1989; Trigo-Rodríguez et al., 2003; Fulle et al., 2015;Brownlee et al., 1985). Most of the cometary inter-planetary dust particles (IDPs) collected in the strato-sphere are dense aggregates; typically from 10 µ m to Preprint submitted to Elsevier July 24, 2018 µ m in size and consisting of up to 1 µ m grains(Brownlee et al., 1985; Mannel et al., 2016). Fulle et al.(2015) also conclude from measurements of dustejected from comet Churyumov-Gerasimenko that onlya small fraction of the dust is really highly porous.Related to the morphology, it is the tensile strengthwhich therefore might be a quantity to constrain earlyplanet formation scenarios. For solid monolithic"rocky" material, values for tensile strength are way toolarge to allow shedding of a dust population. If largerbodies are composed of particles on the order of 1 µ min a homogeneous way, their tensile strength is still onthe order of 1 kPa (Blum et al., 2006). This assumes thatparticles only stick together by surface forces and not bychemical bonding, i.e. are not sintered together but thatthey are packed densely. Such values might be expectedfrom a pure collisional formation of cometesimals witha homogeneous porosity also on large size scales. Frommeteor observations Trigo-Rodríguez & Llorca (2006,2007) conclude that cometary particles of sizes from 10 to 10 microns entering the atmosphere themselves havetensile strengths of 0.4 to 10 kPa. Tsuchiyama et al.(2009) measured the tensile strength for ∼ µ m car-bonaceous chondrites to 0.3-30 Mpa. All this gives clearevidence that on the small scale dust is rather compactand firmly sticks to each other.Recently discussed are gravitational collapse scenar-ios for planet (comet) formation where aggregates ofmm to cm size form first by collisions in agreement toa large tensile strength. However, these are then con-centrated gently and mostly bound together by gravitylater (Johansen et al., 2014). In this case, the overalltensile strength of the nucleus’ surface is determined bythe contacts between these larger granules. The ten-sile strength measured for such dust granule bodies inanalog laboratroy experiments is only at the 1 Pa level(Skorov & Blum, 2012; Blum et al., 2014; Brisset et al.,2016).These values might be set in the context of pro-cesses occuring during active cometary phases. Whencomets approach the inner solar system the sublima-tion of ices (H O, CO , CO) leads to a near surfacepressure. If this pressure is larger than the tensilestrength of the overlaying material, dust is ejected. Sub-limation of ice might provide a pressure on the orderof a few Pa (Skorov & Blum, 2012). Groussin et al.(2015) estimate the tensile strength of di ff erent partsof comet Churyumov-Gerasimenko to values betweena few Pa and 1kPa at maximum. Combined with themeasured tensile strength of loosly bound compact ag-gregates, Skorov & Blum (2012); Blum et al. (2014);Groussin et al. (2015) conclude that these are indica- tions of an early gravitational instability scenario forcomets. In any case all these findings indicate the ex-istence of di ff erent size scales. Constituents with highertensile strength are assembled to larger bodies with alower tensile strength.Obviously, the relation between the grain size and thetensile strength is important. Nonetheless, besides thework by Skorov & Blum (2012); Blum et al. (2014) onlarge assemblies of dust aggregates there are no dedi-cated laboratory experiments. Tensile strength has neverbeen explicitly measured before for an individual smallaggregate with only few grains within. A question im-portant to judge on formation scenarios would e.g. be:What size distribution of sticky aggregates can buildlarger assemblies of what tensile strength? This gen-eral question is far beyond this paper but we approachthis problem here by new laboratory experiments. Wedeveloped a technique and used it for the first time todetermine the tensile strength of small individual dustaggregates which are only (sub)-mm in size with con-stituents on the same size scale.Our experiments are based on thermal creep gas flowat low pressure. While we use it as technique here tomeasure tensile strength for small aggregates the inter-pretation of this work might go beyond. Thermal creepis not restricted to a laboratory environment. Particledisintegration by thermal creep might occur naturallyduring planet formation and evolution on the surface ofilluminated bodies (Kelling et al., 2011; Kocifaj et al.,2011; de Beule et al. , 2014). Therefore, this work notonly shows laboratory measurements but also allowsspeculations on the existence of a potentially disastrousprocess, the knudsen barrier, for weak bodies under cer-tain conditions (Wurm, 2007).
2. Experimental setup: Ground based
For the experiments, free moving small aggregatesare needed. As we intend to measure low tensilestrength, these aggregates are rather fragile by defini-tion. We used two di ff erent approaches for our measure-ments. One setup works in the ground based laboratory.The other setup was used in drop tower experiments.Both are complementary. In this section, we describethe ground based experiments.On the ground, free moving aggregates of di ff erentsizes can be generated in the following way: At lowambient pressure dust samples are placed on a heater.This leads to thermal creep through the aggregates andan overpressure between the dust and the heater, whichlevitates dust aggregates (Kelling & Wurm, 2009). Asthis support is adjusting itself to only compensate the2eight and is distributing stress over a larger area andpartially volume, even low-tensile-strength aggregatescan be levitated by this method.Thermal creep is strong enough if the ratio betweenthe mean free path of the gas molecules and the grain orpore size within the aggregate is comparable to or largerthan 1. Therefore, low ambient pressure is needed tolevitate the aggregates.The main part of the setup thus consists of a heaterplaced within a vacuum chamber (Fig.1). Before theexperimental run, the heater is kept at room temperatureand for the test experiments basaltic dust with grainsizes smaller than 125 µ m is placed in its center (Fig.1(1)). The vacuum chamber is evacuated to 200 Pa andthe heater is heated to 620 K (Fig.1 (2)). Eventually,dust aggregates start to levitate over the hot surface(Fig.1 (3)). At this stage, the heater is tilted and thelevitating aggregates slip down from the hot surfaceand are in free fall (Fig.1 (4)). No longer exposed tothe hot surface, the aggregates rapidly cool from theoutside in due to thermal radiation (Fig.1 (5)). Hence,the maximum temperature is inside the aggregate. Inthe same way as thermal creep leads to levitation forthe aggregates with hot bottom and cool top, gas is nowpumped into the aggregate by thermal creep.On small millisecond timescales, an overpressurebuilds up inside the aggregate. This e ff ect is also knownas Knudsen compressor (Knudsen, 1909). If the pres-sure is larger than the tensile strength, the aggregateis explosively disintegrating (Fig.1 (6)). The aggre-gate disintegration is observed by a camera with 25000frames per second at a resolution of 6 µ m. This tem-poral and spatial resolution allows to measure the initialacceleration at the start of disintegration. With observedfragment size and known density this directly translatesinto a tensile strength at the moment the aggregate frag-mented. Figure 2 shows three snapshots of a time se-quence of one of such disintegration observed.
3. Experimental setup: Microgravity
The ground based experiments described above allowan observation at high frame rates and high spatialresolution. Therefore, the accelerated motion upondisintegration can be measured (in 2d) and the valuesfor the tensile strength can directly be determined.Due to the nature of high resolution imaging, only fewaggregates which fragment just at the right momentcan be observed with this method. No informationis gained about a broader aggregate sample, which F G (1) (2) (3)(4) (5) (6) thermal creepHeater Figure 1: Principle of the laboratory experiment. A dust sample isplaced on a heater within a vacuum chamber (200 Pa) forming ag-gregates (1). The heater is set to 620 K (2) and based on thermalcreep described by (Kelling & Wurm, 2009), the aggregates start tolevitate over the hot surface (3). The heater is then tilted and the freeaggregates slip into free fall (4). Now their outside can cool and atemperature maximum is established inside the aggregate (5). Ther-mal creep then leads to a gas flow from the cool surroundings to thewarm inside. On short timescales, this generates an overpressure anddisintegration of the aggregates occurs (6).
Figure 2: Unprocessed data of a basaltic dust aggregate disintegratingin free fall due to an overpressure induced by thermal creep in thelaboratory experiment. might disintegrate at locations not observed or whichmight not fragment at all. To sample a larger numberof aggregates it would be beneficial if tensile strengthscould be deduced from low resolution imaging of thefragments after the explosion. Then a larger field ofview could be observed and statistical sampling wouldbe possible. We therefore also carried out first droptower experiments where aggregate fragments can betraced over long timescales of seconds.A sketch of the experiment is shown in Fig.3. Inthis case, suspended aggregates of particle sampleswere generated by light induced ejections from aparticle bed. This ejection mechanism is described,e.g. by Wurm & Krauss (2006); Kelling et al. (2011);de Beule et al. (2013); de Beule et al. (2014), and werefer to these papers for details. In the context of thiswork, it is only important that the released aggregateswere part of an illuminated dust bed. An infrared laserbeam (955 nm) illuminated a 3.4 cm spot on the dust3 acuum chambercamera dust bed b r i gh tf i e l d Figure 3: Setup of the microgravity experiment. Suspended dust ag-gregates are provided by the e ff ect of light induced erosion in mi-crogravity. Once the aggregates left the dust bed and the radiation,they cool from outside-in and an overpressure evolves inside, leadingeventually to disintegration. bed with 7 cm diameter. The light flux was 5.4 and 12.7kW / m . We used basalt and palagonite samples in thiswork.The palagonite was tempered for 1 hour at 900 K toavoid e ff ects of adhering water during the experiments.Furthermore, in a parallel setup a red laser beam (655nm) with a 5.5 mm spot and a flux of 12.6 kW / m wasused for a sample of vitreous carbon spheres.We estimate the temperature of the dust bed to420 K - 650 K (Kocifaj et al., 2011). The sample wasin a vacuum chamber at 400 Pa ambient pressure. Onceagglomerates leave the surface, they are free to radiateinto space and cool from the outside-in, especially ifthey leave the laser beam. As in the ground basedexperiments, a radial temperature gradient within theaggregates evolves.The experiments reported here were carried out undermicrogravity at the drop tower in Bremen. This allowssu ffi cient time for aggregate observations and trajectoryreconstruction.
4. Data analysis
With the given frame rate of 25000 fps in the groundbased experiments, the initial acceleration can be re-solved which is shown in Fig.4 for one fragment. Wesubtract the gravitational acceleration and rescaled the
Figure 4: Example of a fragment position with time in both dimen-sions observed after a particle disintegration. Gravitational accelera-tion was subtracted. Overplotted are linear (red, dashed) and parabolic(black, solid) fits. positions by an arbitrary linear motion to center the tra-jectory somewhat. The latter is only for visual reasonsand is neither showing the trajectory in the center ofmass system nor it has an e ff ect on the determinationof the acceleration. After removal of the gravity de-pendence, the trajectory of a fragment can be dividedinto three distinct parts: a linear motion before disin-tegration as part of the aggregate, an accelerated partduring disintegration and a second linear part after theexpansion. Therefore, we approximately fit the result-ing curves with two linear parts before and after theexplosion with a parabola in between. Due to the ex-pansion of the gas within the aggregate the accelerationdecreases with time. The approximation of a parabolawith constant acceleration therefore underestimates theinitial acceleration by a small factor. However, withinthe accuracy of the data the deviation from a parabolacannot be quantified. We consider the deviation negli-gible compared to the current uncertainties. We furtherassume that the velocity is continuous at the connec-tions and set the end points, so that the linear tracks be-fore and after the acceleration have the lowest squared4i ff erence to the data.The mean force acting on a fragment can be derivedfrom the acceleration data (parabolic part of the track)if the mass of the fragment is known. Taking the crosssection of the fragment this also gives a measure of thepressure acting during the explosion which equals thetensile strength. Mass and cross section are estimatedfrom the observed size of the fragment. We approximatethe grains by spherical particles of equivalent observedcross section. From this size we estimate the mass byassuming a bulk density of 2.89 g cm − . For 10 frag-ments analyzed for one fragmentation we get the meanvalue for the tensile strength ∆ P acc = . ± . . (1)The observation of such explosions is not trivial and weonly consider this as first measurement here to show thecapability of the technique. Also, the data lack a 3dinformation. Therefore, accelerations are systematicallyunderestimated. During the further analysis we take a look at disinte-grating aggregates at 1000 fps from the drop tower ex-periments. Here, it is no longer possible to resolve theacceleration as shown above. With the help of a simpledisintegration model, as detailed below, we neverthelesscan estimate the value for the tensile strength. The ideais to determine the kinetic energy of all fragments andcompare this to the energy released by the expansion ofthe gas due to the overpressure.Fig.5 shows an example for a recorded fragment trajec-tory. From the first image, where the particle is observedto 50 images later, the motion can be described by aconstant velocity. Note, that there are di ff erent scalescompared to Fig.4. All fragments can be described by alinear motion, which allows a straight forward determi-nation of the kinetic energies. On very long timescalesthe fragments change their trajectories, as particles cou-ple to the gas and residual flows within the experimentchamber. This is not important here and is not consid-ered further.The motion of the visible center of mass of the aggre-gate before fragmentation is also determined. The mo-tion of the fragment after the disintegration can then bedescribed in the center of mass system. Fig.6 shows thefinal data of an explosion reduced to the size and veloc-ity of the fragments in the center of mass system. Asmentioned above, we define the size of the grains by theradius of a sphere with equivalent observed cross sec-tion. To estimate the mass we use a bulk density of 2.89 Figure 5: Example of a fragment position with time in both dimen-sions observed after a particle disintegration. x and y refers to cameracoordinates. Overplotted are linear fits. g / cm for basalt, 1.45 g / cm for vitreous carbon and 2.5g / cm for the palagonite sample. Adding the mass of allindividual grains or smaller aggregates after disintegra-tion often di ff ers from the deduced mass, which can bededuced independently in the same way for the originalaggregate. The di ff erence is typically a factor of about0.5. We attribute the "missing" half of the mass to theporosity of the aggregate with 50% being a typical valuefor dust samples consistent with our observation.Fig.7 shows the velocity of fragments after disintegra-tion of the aggregate over their mass. In total, 7 dis-integrations are shown. There is a clear trend that par-ticles with larger mass move slower. The spread hasdi ff erent origins. Particles can move towards or awayfrom the observer and would be misleadingly attributedas slower in a 2d projection. Also, some fragmentsmight pick up rotational energy. Related to this, thereis a variation among the fragments in shape which in-fluences the energy that a fragment can get. The dot-ted lines have a slope of − / − / ff er-ent events. To complete the data, the size distributionsof the dust samples were measured with a Mastersizer3000 (Malvern Instruments) and are shown in Fig.8. Wenote that the basalt sample of the ground based experi-ment was sieved to below 125 µ m.
5. Disintegration model
In the following, we assume that an overpressurewithin the aggregate is responsible for the disintegra-5 igure 6: Velocities (2d projections) and sizes of the fragments in thecenter of mass system for a disintegration of a basalt aggregate. Thesizes of the circles are proportional to the actual sizes of the fragments. tion. It is worth to mention that this occurs on very smallspatial scales but 100 µ m scales for pressure inducedtension were also seen in recent work by de Beule et al.(2015).As a model, we approximate an aggregate as a core-mantle structure. The individual grains form a shell sur-rounding a central pore as seen in Fig.9. If the pres-sure inside the pore-space increases beyond the ten-sile strength due to thermal creep, the aggregate (shell)is disrupted and smaller sub-units down to individualgrains are accelerated by the pressure as long as the ex-pansion takes place. The maximum pressure di ff erencethat can be achieved is given by (Knudsen, 1909) ∆ P max = P o ⎛⎝ √ T i T o − ⎞⎠ (2)where P o is the ambient pressure, T i is the temperaturewithin the pore, and T o =
300 K is the ambient temper-ature. T i depends on the intensity of the correspondinglaser and the duration of exposure, which is not exactlyknown. Assuming values between 1-5 seconds we get T i ∈ [ , ] for the 5.4 kW / m laser (used forbasalt) and T i ∈ [ , ] for the 12.6 kW / m and12.7 kW / m lasers (used for vitreous carbon spheres andJSC-600) referring to Kocifaj et al. (2011). These re-sults lead to overpressures ∆ P max ∈ [ , ] forbasalt and ∆ P max ∈ [ , ] for JSC-600 and the Figure 7: 2d velocity over mass. The velocities for di ff erent disinte-grations are scaled to 1 at a mass of 1 ng in order to compare aggre-gates with di ff erent absolute velocities. In addition, lines proportionalto m − / according to a simple explosion model are shown. The up-per and lower lines are provided to guide the eye. The data cover 7events (4 for basalt, 2 for palagonite (JSC600) and 1 for carbon glassspheres). glass-spheres. The real pressure at disintegration can belower.The actual value for the pressure is deduced from thekinetic energy of the fragments which can be measured.Keeping in mind that velocities v i for fragments withmasses m i are 2d projections only, we get the lower limitof the total kinetic energy in the center of mass system ∆ E kin = ∑ i m i v i (3)which is on the order of 0 . E pres = ∫ ( P i − P o ) dV . (4)As it is not possible to resolve the pressure change dur-ing the expansion in the images taken with 1000 fps, weassume that the shell is expanding by a distance of spa-tial resolution adiabatically or with a constant b = P i V κ where κ is the isentropic exponent. This gives E pres = ∫ V E V I ( bV κ − P o ) dV = b ( V − κ E − V − κ I ) − κ + P o ( V I − V E ) (5)with the initial volume of the pore V I and the volume ofthe pore after the expansion V E . The constant b is givenby b = ( P o + ∆ P ) V κ I . Thus we get ∆ P = [ E pres − P o ( V I − V E )] ( − κ ) V κ I ( V − κ E − V − κ I ) − P o (6)6 igure 8: Volume size distributions in arb. units (probability densitybut not normalized) of the dust samples studied. THERMAL CREEP DISINTEGRATIONV I V E Figure 9: Aggregate model with a central pore surrounded by the in-dividual grains and thin capillaries allowing thermal creep to enter thepore. in total. As the fragmentation occurs in a dry air envi-ronment, we use κ = . [ . R A , . R A ] withthe radius of the aggregate R A this allows to estimate V I . In order to calculate V E we consider radii between [ R A + µ m , R A + µ m ] , which is an estimation basedon the recorded dataset for 25000 fps ground based ex-periments. It represents the range of determined ex-pansion volumes, where fragments are accelerated. Fi-nally, Eq.(6) allows us to calculate the tensile strengthas E pres = ∆ E kin . Here we assume that the volume work E pres is fully transferred into kinetic energy of the frag-ments. The results are shown in Fig.10. If the processwas not fully adiabatic, only a fraction of E pres couldbe converted into volume work and thus also into ki-netic energy. With this, the tensile strength ∆ P could berather overestimated by the model due to ∆ P ∼ E pres .As every fragment is accelerated by the samepressure, the acceleration is proportional to 1 / r with a Figure 10: Tensile strength for di ff erent aggregates. The upper limitsare the maximum pressure di ff erences from Eq.(2). The lower limitsresult from the estimation of the smallest expanding volume V E . fragment size r . As all fragments are accelerated overthe same time, also the final (measured) velocities aredepending on 1 / r or 1 / m / . The mass dependence ofthe ejecta velocity seen in Fig.7 is in agreement withthis.For the ground based experiments we can apply bothmethods. As seen above we can directly measurethe acceleration and deduce a tensile strength of ∆ P acc = . ± . . . Using the energy method weget a tensile strength of ∆ P E = . + . − . Pa for the sameaggregate. This is in good agreement and the averagevalues only di ff er by a factor 1.4.
6. Conclusion
We measured the tensile strength of small aggregatesconsisting of basalt, JSC and vitreous carbon on the or-der of ∼ µ m to 500 µ m for the first time. We used high aswell as low temporal and spatial resolution. We showedthat both methods produce similar values. Therefore,low resolution imaging with a wider field of view canprovide statistical information on tensile strength of alarger aggregate sample in future experiments. This isthe first proof of concept that low tensile strength of par-ticle aggregates can be measured. This technique allowsto quantify values in the range expected for cometarymatter. The measured tensile strength is on the order of10 Pa to 100 Pa for three di ff erent materials.While these are first measurements they show thata size scale of 100 µ m is possible as constituent tobuild the weak surface of comets. These constituentsthemselves can be more stable sub-units. In general,7he results are consistent with former work on me-teroid fragmentation and strength measurements by the Stardust mission of 81P / Wild 2 (Brownlee et al., 2006;Trigo-Rodríguez & Llorca , 2006, 2007; Hörz et al.,2006). The results fit also the idea of a gravitationalinstability formation scenario for comets where com-pact aggregates with high tensile strength grow firstand are then assembled to weak larger bodies by grav-ity as suggested by Blum et al. (2014); Groussin et al.(2015); Skorov & Blum (2012). It has to be kept inmind that a minimum aggregate size is needed to con-centrate them. E.g. Bai & Stone (2010); Carrera et. al(2015); Dr ˛a˙zkowska & Dullemond (2014) show thatStokes numbers (ratio between gas-grain friction timeand orbital period) larger than 10 − are needed forstreaming instabilities though this might even be re-duced further (Yang et al., 2016). This number dependson the disk model but especially in the comet formingregion in the outer solar system this might rather cor-respond to cm or larger aggregates. Our results showthat the tensile strength is already low for much smaller100 µ m constituents. So while di ff erent tensile strengthfor the constituent and the aggregate is in support of in-stabilities, there is a mismatch in size scales. In a proba-bly simplified view, the interpretation is that either grav-itational instabilities did not form comets or instabilitieswere able to concentrate much smaller grains than pre-viously expected.
7. Acknowledgements
This project was supported by DLR Space Manage-ment with funds provided by the Federal Ministry ofEconomics A ff airs and Energy (BMWi) under grantnumber DLR 50 WM 1242. G. Musiolik is funded bythe DFG. We thank B. Ste ff entorweihen for help withthe lab experiments. We also appreciate the reviews ofthe two referees. References