A Smoking Gun for Planetesimal Formation: Charge Driven Growth into a New Size Range
DDraft version January 25, 2021
Typeset using L A TEX twocolumn style in AASTeX62
A Smoking Gun for Planetesimal Formation: Charge Driven Growth into a New Size Range
Jens Teiser, Maximilian Kruss, Felix Jungmann, and Gerhard Wurm University of Duisburg-EssenFaculty of PhysicsLotharstr. 1-21D-47057 Duisburg, Germany (Received; Revised; Accepted)
Submitted to ApJLABSTRACTCollisions electrically charge grains which promotes growth by coagulation. We present aggregationexperiments with three large ensembles of basalt beads (150 µ m − µ m), two of which are charged,while one remains almost neutral as control system. In microgravity experiments, free collisions withinthese samples are induced with moderate collision velocities (0 − . − ). In the control system,coagulation stops at (sub-)mm size while the charged grains continue to grow. A maximum agglomeratesize of 5 cm is reached, limited only by bead depletion in the free volume. For the first time, charge-driven growth well into the centimeter range is directly proven by experiments. In protoplanetary disks,this agglomerate size is well beyond the critical size needed for hydrodynamic particle concentrationas, e.g., by the streaming instabilities. INTRODUCTIONThe first stage of planet formation is dominated byhit-and-stick collisions between small dust and ice grainsat small collision velocities (Wurm & Blum 1998; Blum& Wurm 2008; Johansen et al. 2014; Gundlach & Blum2015). Although this first step is fast and efficient, thereare several obstacles, which stop this evolution. Withincreasing agglomerate size, the relative velocities be-tween the colliding aggregates increase (Weidenschilling& Cuzzi 1993). This leads to restructuring and com-paction (Weidling et al. 2009; Meisner et al. 2012).If now two of these compact aggregates collide slowly( < − ), they rather bounce off than stick to eachother. This has been introduced as the bouncing barrier(G¨uttler et al. 2010; Zsom et al. 2010). Several experi-ments showed that self-consistent growth indeed comesto a halt at a particle size in the millimeter range (Krusset al. 2016, 2017; Demirci et al. 2017). Slight shifts inaggregate size are possible depending on temperaturesor magnetic fields (Kruss & Wurm 2018, 2020; Demirciet al. 2019) but the bouncing barrier is a robust finding. Corresponding author: Jens [email protected]
Collisions and growth in a protoplanetary disk aregoverned by the interaction between gas and solids. Hy-drodynamic processes therefore have a strong effect onparticle evolution. Beyond inducing collisions, they canespecially change the local particle concentration (Jo-hansen et al. 2007; Johansen & Youdin 2007; Chiang& Youdin 2010; Squire & Hopkins 2018). If a criticalsolid-to-gas ratio is reached, the mutual gravity betweenthe solids might lead to the direct formation of a plan-etesimal (Youdin & Goodman 2005; Simon et al. 2016;Klahr & Schreiber 2020). This way, barriers in colli-sional growth could be prevented.However, while these drag instabilities can be veryefficient, they require a minimum size of solids to bepresent (Dr¸a˙zkowska & Dullemond 2014; Carrera et al.2015). Typically, they work best for so-called pebbleswith the Stokes-number (ratio between the orbital pe-riod and gas-grain-coupling time) St ∼
1. Dependingon the disk model and the location in the protoplane-tary disk, this Stokes number typically translates intoparticle sizes of the order of a decimeter though some-what smaller sizes might still work (Yang et al. 2017)under certain conditions. Obviously, to explain planetformation, a severe size gap must be bridged between themillimeter size resulting from the bouncing barrier and a r X i v : . [ a s t r o - ph . E P ] J a n Teiser et al. the decimeter required for the hydrodynamic processesto work.This bridge might be a charge dominated growthphase. Collisions and friction between particles leadto charge separation upon contact (Lacks & MohanSankaran 2011). For a long time, this was attributedeither to different materials in contact (different surfaceenergies) or due to different sizes (Lee et al. 2015). Ex-periments showed that charge separation also occurs forparticles of the same size and material (Jungmann et al.2018).While the detailed physical processes are poorly un-derstood, the resulting charge distributions in granularsamples are well characterized. For a granular samplewith particles of the same size and material, a broadcharge distribution is the result. By first glimpse, itis similar to a Gaussian distribution, but with heaviertails (Haeberle et al. 2018). The peak position (meancharge) and the full width at half maximum (FWHM)are typically used to characterize the charge distribu-tion of a granular sample. For multiple collisions ofparticles of the same size and same material the re-sulting charge distribution peaks at zero charge (Wurmet al. 2019). Within the scope of this paper, the term”strongly charged” then refers to the FWHM of a cor-responding charge distribution.Agitating a granular system for a duration of about10 min establishes a charge distribution within the sys-tem which does not change significantly when the ag-itation is continued. It only depends on sample andatmospheric parameters as was shown in experimentswith monodisperse basalt beads by Wurm et al. (2019).Larger beads are charged more strongly (larger FWHM)than smaller beads.Additionally, the charging of a granular samplestrongly depends on the surrounding gas pressure. Fora constant granular sample the width of the reachedcharge distribution follows a curve similar to Paschen’slaw of electrical breakthrough in gases. The width(FWHM) of the charge distributions reaches a minimumat a characteristic pressure (100 Pa − few 100 Pa), de-pending on the sample. At larger pressures, the reachedwidth increases gently, while it increases sharply forpressures smaller than the characteristic value. CHARGE DRIVEN AGGREGATION ANDSTABILITYIt is obvious that two grains of opposite charge attracteach other as a first step in aggregation. This effectivelychanges the collisional cross section. It is not obvious apriori though why an initial charge on individual grainsshould be beneficial for the aggregation process later on, once agglomerates have formed. In fact, once two grainsof the same absolute charge, but opposite sign, collideand stick to each other this dimer is overall neutral.The long-range Coulomb interaction of net charges isno longer present and the collisional cross section willno longer be strongly enhanced.However, insulating grains do not discharge upon con-tact. This even holds for metal spheres, if their surfaceis not extremely cleaned from any contamination (Gencet al. 2019; Kaponig et al. 2020). A dimer or a more com-plex aggregate still hold charges on their surface. It hasto be noted at this point that collisions lead to chargeseparation (not neutralization) in the first place andgrains charged this way have a complex charge patternwith patches of negative and positive charges on theirsurface (Grosjean et al. 2020; Steinpilz et al. 2020b).This is also valid for grains which are net neutral. Thetypical configuration are therefore multipoles even on asingle grain.Certainly, there are ways to discharge and neutral-ize grains, which depends on the environment (watercontent, gas pressure, temperature, radiation, materialconductivity). In the experiments here, discharge takeshours, under protoplanetary disk conditions it might beyears (Steinpilz et al. 2020a; Jungmann et al. 2018, 2021)(and running experiments by Steinpilz et al., personalcommunication).So, while these multipole configurations in aggregatesmight not attract other grains from far away, chargesremain highly important during contact. As Coulombforces decrease with distance of two charges r c as 1 /r c ,two oppositely charged spots on a surface close to thecontact point can dominate the sticking force, indepen-dent of the net charge budget of the grains. Therefore,collisions lead to sticking at much higher collision ve-locities for charged grains (Jungmann et al. 2018). Itis important to note that in an ensemble of grains netcharge is only a proxy that is easily accessible to confirmthat grains have a surface charge pattern. Nevertheless,the multipoles determine sticking forces.Aggregates are also more stable, i.e. higher colli-sion velocities are required to destroy them comparedto uncharged aggregates (Steinpilz et al. 2020a). Chargepatches glue aggregates together. A simple analog forthis situation is a salt crystal, which is overall neutralbut the alternating charges still provide strong attrac-tion. This way, we expect collisionally charged grains togrow far beyond the bouncing barrier. Therefore, thereis a high potential in charge driven growth.It is still unclear though, how large agglomerates cangrow this way. In Steinpilz et al. (2020a), cm-sizecharged agglomerates were observed but their direct for- harge driven growth pressure valveelectrodes cameravoice coilparticlereservoir cell 3cell 2 Figure 1.
Schematic view of test cells 2 and 3. The uppercell (3) is a vacuum chamber ( p ≈
20 Pa), while cell 2 is atnormal pressure. mation from individual grains was not traced and tookplace prior to the free-floating phase in an agitated gran-ular bed. The effects of charging were shown by means ofnumerical simulations matching the experiments in thatcase. The key question thus remains: Is charge drivencoagulation able to provide the necessary aggregate sizesfor drag instabilities to take over? EXPERIMENTTo investigate how large agglomerates can form by col-lisions of small charged particles, a microgravity exper-iment is currently being developed for sub-orbital plat-forms. Here, we report on the first shorter time mi-crogravity experiments during this development, whichwere conducted at the Bremen Drop Tower (ZARM).Using the catapult mode, microgravity with residual ac-celeration of < − g and a duration of 9 . Experimental setup
The central part of the experimental setup consistsof three test cells, two of which are shown in Fig. 1.All cells have the same geometry with a free volumeof 50 mm ×
50 mm ×
42 mm and an additional particlereservoir of 14 mm depth and 25 mm length. While cells2 and 3 are placed in the same unit, cell 1 is placed in asingle unit with half the height. Test cell 3 (the upperone in Fig. 1) is designed as a vacuum chamber with a pressure of 20 Pa, while the other two cells are at normalpressure.The side walls of the test cells are copper electrodeswhich are part of a capacitor at which a DC-voltage of4 kV can be applied. The experiments are observed witha Raspberry Pi camera (30 frames/s, resolution: 1640 × µ m and 180 µ m diameter (White-house Scientific). A total amount of 6 g is used in eachcell. To reduce collisions between basalt beads and dif-ferent materials, the top and the bottom of each testcell (including the particle reservoir) are coated withthe same basalt beads.3.2. Experiment protocol
The test cells can be agitated with a harmonic mo-tion using a voice coil mounted underneath. Prior tothe catapult launch this agitation is used to charge thebasalt beads for test cells 2 and 3 by collisions and fric-tion due to constant agitation on ground. The durationis 20 min with a frequency of 14 Hz and an amplitude of4.6 mm (peak to peak), similar to the experiment pro-tocol in Steinpilz et al. (2020a). During this period thesample mostly remains within the sample reservoir andthe beads are exposed to numerous collisions and fric-tion among each other. Even in case the particles leavethe reservoir, they are only exposed to particle-particlecollisions, as the bottom of the test cells is coated withbasalt beads and tilted by an angle of 4 ◦ , so basicallyno particles hit the side walls.The sample was left at rest for about 10 min betweenthis agitation period and the catapult launch, whichdoes not change the charge distribution significantly. Incontrast to cells 2 and 3, test cell 1 was not agitatedon ground, so a sample with minimum charge is usedas control experiment. In microgravity, the agitation isused to distribute the sample at the beginning and tokeep up a sufficient collision rate to see growth on theshort timescales available at the drop tower.The experiment protocol has been changed for thedifferent experiments, so that different aspects of theplanned long-duration experiments could be tested on ashort timescale. A high voltage at the capacitor platescan be used to estimate the charges in aggregates, butimmediately stops further growth processes as the vol-ume is cleared from particles. Agitation can be used toinduce a high collision rate, but no charge measurementor particle tracking is possible during this agitation. The Teiser et al. different parameters used in the presented experimentsare described in section 4.3.3.
Collision velocities
Due to the limitations of the optical system and thelarge particle concentration within the test cells, it isnot possible to track single particles. However, the col-lision velocities can be estimated using the parametersof the agitation cycle. As the agitation follows a har-monic, frequency f and maximum amplitude A directlytranslate in a maximum velocity of the test cells via v max = 2 πf · A . For the parameters used in Fig. 2( f = 14 Hz, A = 1 . v max = 0 .
11 m s − . In case of perfectly elas-tic collisions between the particles and the experimentwalls (top and bottom), a resting particle could get amaximum velocity of v col = 2 v max or even larger in caseof an initial velocity towards the wall.Indeed, non-charged basalt beads collide rather elas-tically with a coefficient of restitution (cid:15) = v after /v before of the order of (cid:15) = 0 . RESULTSThe experiments presented were planned to qualify anexperiment hardware for suborbital flights and to testparts of the experiment protocol. Here, we present threedifferent experiment protocols, which were used to showdifferent aspects of the upcoming long-duration experi-ments. 4.1.
First growth
The first experiment protocol was used to check if arather homogeneous particle distribution can be gen-erated by agitation in microgravity. Here, the sample
Figure 2.
Evolution of the particle ensemble in cell 3 dur-ing one experimental run at different times, starting directlyafter the begin of microgravity and ending when the samplehas reached a final state while the test cell is at rest. Thewidth of the chamber of 50 mm can be used as a scale. was agitated with a frequency of 14 Hz, an amplitude of1.2 mm, and a duration of 1 s, starting at the beginningof the microgravity phase. After a short break of 1 s,the agitation was then repeated for a duration of 1 s.Afterwards, the test cells were not moved until the endof the microgravity.Fig. 2 shows the temporal evolution of the particlesin the vacuum chamber (cell 3) for this experiment. Itstarts directly after the last agitation cycle from a welldistributed sample, which blocks the illumination almostcompletely. While the test cell is kept at rest a clusteringprocess can be observed. After around 5 s, the final stateis reached as the grown clusters do not collide anymore.Of the three cells, the vacuum chamber shows themost homogeneous sample distribution in the initialstate and the largest agglomerate sizes in the final state(see also Fig. 4). According to Wurm et al. (2019) basaltbeads charge differently depending on the surroundingpressure. At pressures of about 100 Pa − few 100 Pa thecharge distribution is narrowest. For lower pressure thewidth of the charge distribution rises steeply (Wurmet al. 2019). Additionally, particle motion is not dampedsignificantly by gas drag, as the gas-grain coupling timeexceeds the experiment duration. Therefore, this di- harge driven growth Charges
The charge distribution of single basalt beads cannotbe obtained from the data available, as the spatial andtemporal resolution of the camera system are not suit-able for this. However, the agitation method and there-fore the process of particle charging is almost identicalto previous studies, either with glass beads (Jungmannet al. 2018, 2021; Steinpilz et al. 2020a) or with basaltbeads (Wurm et al. 2019). The width (FWHM) of thecorresponding charge distribution scales with the parti-cle size (Wurm et al. 2019), with many studies treatingcharges on insulators as surface charges only (Lee et al.2018; Grosjean et al. 2020; Steinpilz et al. 2020b). Witha similar charge density on the surface as in Wurm et al.(2019), a charge distribution centered at zero chargewith a FWHM of about 3 · − C can be expected.To roughly estimate the charges on the agglomerateswe performed an experiment in which the beads wereshaken for 5 s during microgravity (f = 14 Hz, A =1.2 mm). As shown in Fig. 4 (middle) cm-sized agglom-erates form in cell 2. After agitation, a voltage of ± electron charges. We note that this is only an esti-mate of the order of magnitude as a detailed analysis isbeyond the scope of this paper and not possible with theavailable data from the short-time experiments. How-ever, this indicates that there are abundant charges onthe clusters which might play a role in the agglomerationprocess. 4.3. Growing tall
The evolution presented in Fig. 2 shows that growthby collisions of charged basalt beads is possible in prin-ciple. On the other hand it becomes clear that the col-lision rate is crucial for the outcome and has to be kepton a high level. This was considered in the experimentshown in Fig. 4. Here, the experiment protocol was × × × × × particle number c h a r g e [ e ] Figure 3.
Absolute estimated charges of resulting clustersformed during microgravity. The large error bars result fromthe high uncertainty of the masses of the agglomerates. changed to maintain a certain collision rate, while ob-servation of the grains is still possible. With the onset ofmicrogravity, the test cells were agitated with f = 14 Hzand A = 1 . f = 1 Hzfor a duration of 4 s, resulting in an amplitude of 3 mmand a maximum velocity of v max = 0 .
02 m s − . After-wards, the test cells were at rest for the last 2 s of mi-crogravity.Fig. 4 shows the final particle distributions duringthis experiment run. It also reveals the systematic dif-ferences between the three test cells. The least chargedsample (top) only shows minor growth in comparisonto the charged sample in the test cell with atmosphericpressure (middle) where larger entities evolve. The vac-uum cell (bottom) shows a striking result. Almost allparticles are incorporated into one large agglomerate,which therefore has a width of 5 cm (from wall to wall),a thickness of about 2 cm and a total mass of about 6 g.The free volume between the larger agglomerates isalso of great interest to interpret the result. In the leastcharged sample, the particles remain widely distributedin the entire volume. Also in the test cell with atmo-spheric pressure there is still a significant amount of sin-gle beads (or only very small agglomerates) in the freevolume between the larger aggregates. This is totallydifferent in cell 3, where the maximum charges can beexpected. Single particles are either incorporated intothe major agglomerate or stick to the walls of the cell.The free volume is almost completely cleared from smallparticles. Due to this particle depletion the growth pro-cess comes to a halt. Therefore, it can be assumed thatthe final distribution does not show the maximum sizesachievable by such collisions. Teiser et al. cell 2cell 1cell 3
Figure 4.
Final particle distributions with continuous agita-tion of 1 Hz under microgravity. Top: sample with minimumcharge (no shaking in advance). Middle: 20 min shaking inadvance, normal pressure. Bottom: 20 min shaking in ad-vance, vacuum (20 Pa).
Stability
Figure 5.
Sequence of a 2.5 mm cluster (average diameter)colliding with the electrode. Its impact velocity is about 2cm/s. The red arrow shows the direction of motion.
When applying an electric field some large clusters areaccelerated towards the electrodes and therefore reachhigh impact velocities. This can be used to estimatethe stability of these clusters. Similar to chapter 4.2these clusters were tracked manually and their impactvelocities determined. An example of a cluster collidingand bouncing off the wall is shown in Fig. 5.Collisions between clusters and the (side) walls occurat impact velocities from 10 − m s − to 2 . · − m s − ,while the typical cluster sizes (average diameters) rangefrom 2 . . ≤ − m s − , evenfor particles of a few cm in size (Weidenschilling & Cuzzi1993). As a collision with a solid wall is much more se-vere than mutual collisions between equally sized clus-ters, mutual collisions in protoplanetary disks will notdestroy the grown agglomerates.The relative velocities are larger for particles of differ-ent size, so single particles hitting an agglomerate willbe faster. However, the velocities are still in the range of10 − m s − , which is exactly in the velocity range of thesingle basalt beads during the agitation cycles, resultingin growth. CONCLUSION AND OUTLOOKCharge driven coagulation has already been presentedby Steinpilz et al. (2020a) as a possible mechanism toovercome the bouncing barrier in planet formation. Al-though they could show that the size distribution of harge driven growth
Blum, J., & Wurm, G. 2008, ARA&A, 46, 21Bogdan, T., Teiser, J., Fischer, N., Kruss, M., & Wurm, G.2019, Icarus, 319, 133Carrera, D., Johansen, A., & Davies, M. B. 2015, A&A,579, A43. https://doi.org/10.1051/0004-6361/201425120Chiang, E., & Youdin, A. N. 2010, Annual Review of Earthand Planetary Sciences, 38, 493Demirci, T., Krause, C., Teiser, J., & Wurm, G. 2019,A&A, 629, A66Demirci, T., Teiser, J., Steinpilz, T., et al. 2017, ApJ, 846,48Dr¸a˙zkowska, J., & Dullemond, C. P. 2014, A&A, 572, A78Genc, E., M¨olleken, A., Tarasevitch, D., et al. 2019, Reviewof Scientific Instruments, 90, 075115.https://doi.org/10.1063/1.5093988Grosjean, G., Wald, S., Sobarzo, J. C., & Waitukaitis, S.2020, Physical Review Materials, 4, 082602Gundlach, B., & Blum, J. 2015, ApJ, 798, 34G¨uttler, C., Blum, J., Zsom, A., Ormel, C. W., &Dullemond, C. P. 2010, A&A, 513, A56Haeberle, J., Schella, A., Sperl, M., Schr¨oter, M., & Born,P. 2018, Soft Matter, 14, 4987Johansen, A., Blum, J., Tanaka, H., et al. 2014, inProtostars and Planets VI, ed. H. Beuther, R. S. Klessen,C. P. Dullemond, & T. Henning, 547Johansen, A., Oishi, J. S., Mac Low, M.-M., et al. 2007,Nature, 448, 1022Johansen, A., & Youdin, A. 2007, ApJ, 662, 627 Jungmann, F., Steinpilz, T., Teiser, J., & Wurm, G. 2018,Journal of Physics Communications, 2, 095009Jungmann, F., Bila, T., Kleinert, L., et al. 2021, Icarus,355, 114127Kaponig, M., M¨olleken, A., Tarasevitch, D., et al. 2020,Journal of Electrostatics, 103, 103411Klahr, H., & Schreiber, A. 2020, ApJ, 901, 54Kruss, M., Demirci, T., Koester, M., Kelling, T., & Wurm,G. 2016, ApJ, 827, 110Kruss, M., Teiser, J., & Wurm, G. 2017, A&A, 600, A103Kruss, M., & Wurm, G. 2018, ApJ, 869, 45—. 2020, The Planetary Science Journal, 1, 23Lacks, D. J., & Mohan Sankaran, R. 2011, Journal ofPhysics D Applied Physics, 44, 453001Lee, V., James, N. M., Waitukaitis, S. R., & Jaeger, H. M.2018, Physical Review Materials, 2, 035602Lee, V., Waitukaitis, S. R., Miskin, M. Z., & Jaeger, H. M.2015, Nature Physics, 11, 733Meisner, T., Wurm, G., & Teiser, J. 2012, A&A, 544, A138Schaffer, N., Yang, C.-C., & Johansen, A. 2018, A&A, 618,A75Simon, J. B., Armitage, P. J., Li, R., & Youdin, A. N. 2016,The Astrophysical Journal, 822, 55Squire, J., & Hopkins, P. F. 2018, MNRAS, 823Steinpilz, T., Joeris, K., Jungmann, F., et al. 2020a, NaturePhysics, 16, 225Steinpilz, T., Jungmann, F., Joeris, K., Teiser, J., & Wurm,G. 2020b, New Journal of Physics, 22, 093025