Dusty Bodies Research Articles

Polymer presence in boundary layer flow and heat transfer of dusty fluid over a stretching surface

PurposeTo explore the fusion of dust particles and of polymers in a viscous liquid is the main purpose of this article. Newtonian fluid as a base fluid is considered and the mutual presence of polymers and dusty bodies is investigated. It discusses the steady laminar flow and heat transportation of a polymeric dusty liquid induced by a uniformly heated, penetrable and stretchable surface inside the boundary layer.Design/methodology/approachThe mathematical system incorporates separate equations of energy and momentum for dusty bodies and for fluid. The classical Oldroyd-B model is chosen for exploring polymer presence. For the fluid phase, this model adds another stress to the conservation law of momentum. Appropriate similarity variables are introduced to transform the system of partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs). The problem is solved by introducing a numerical iterative procedure which turned out to be fastly converging.FindingsExpeditious changes inside the boundary layer cause polymers to deform. No changes outside the boundary layer are noticed on account of polymer stretching. The dependence of heat transfer rate and skin friction on the parameter of polymer concentration and Weissenberg number is analyzed and displayed graphically against interaction parameters for temperature and velocity, dust particles’ mass concentration, Eckert and Prandtl numbers. Combining effects of polymers and dust particles cause skin friction to decrease and heat transfer rate to increase. Increasing values of interaction parameter for velocity, dust particles’ mass concentration and Eckert number reduces the drag coefficient and local Nusselt number. On the other hand, the Prandtl number and interaction parameter of temperature magnify the heat flux at the wall.Research limitations/implicationsThis article studies the infinite extensibility of polymers. FENE and FENE-P models can be used to investigate the polymer presence in dusty fluids in the future.Originality/valueIn this article, the authors’ aim is to study the combined presence of polymers and dusty bodies. Keeping the existing literature in view, this type of fusion is not studied yet. Polymer inclusion in a viscous dusty fluid is studied and the behavior of fluid flow and heat transportation is investigated within the boundary layer over a permeable linearly stretching sheet.

The Nucleus of comet 67P/Churyumov–Gerasimenko – Part I: The global view – nucleus mass, mass-loss, porosity, and implications

The radio science experiment RSI on-board Rosetta determined the mass of the nucleus of comet 67P/Churyumov–Gerasimenko at the start of the prime mission from 2014 August to November (GM = 666.2 ± 0.2 m3 s−2 or 9982 ± 3 × 1012 kg) and shortly before the end of the mission from 2016 July to September (GM = 665.5 ± 0.1 m3 s−2 or 9971.5 ± 1.5 × 1012 kg). The mass-loss is ΔM = 10.5 ± 3.4·109 kg, about 0.1 per cent of the nucleus mass. Almost 50 per cent of the mass-loss occurred during the 32 d before and 62 d after perihelion. The nucleus mass combined with the new very precise nucleus volume of 18.56 ± 0.02 km3 yields a bulk density of 537.8 ± 0.6 kg m−3. This low bulk density suggests that the nucleus is highly porous. The porosity is constrained by the observed bulk density, the density of ices, mostly water ice, and the density of compacted nucleus dust material. For a range of compacted dust material density from 2000 to 3500 kg m−3, the porosity varies between 65–79 per cent when the dust-to-ice mass ratio Fnucleus for the nucleus body lies in the range 3 ≤ Fnucleus ≤ 7. The nucleus is thus a highly porous very dusty body with very little ice. The total mass-loss ΔM puts hard constraints on the models of interpretation of the observations from other instruments on Rosetta. The loss from gas, based on ROSINA and MIRO observations, suggests that Fcoma, the dust-to-gas mass ratio of cometary matter in the coma beyond the Hill sphere of the nucleus is of the order of Fcoma ≤ 0.5 and therefore at least six times, and perhaps as much as 14 times, smaller than Fnucleus. It seems that the lost gas mass was overestimated by the instruments. The lost gas mass shall be 5.25 × 109 kg for Fcoma = 1. For any other gas mass values > 5.25 × 109 kg Fcoma is < 1. Most of the lifted dust mass will not leave the cometary Hill sphere but falls back to the nucleus. For 3 ≤ Fnucleus ≤ 7 and Fcoma = 0.5, the fallback mass is between 1.8·ΔM and 4.3·ΔM.

Analog Experiments on Tensile Strength of Dusty and Cometary Matter

The tensile strength of small dusty bodies in the solar system is determined by the interaction between the composing grains. In the transition regime between small and sticky dust (µm) and non cohesive large grains (mm), particles still stick to each other but are easily separated. In laboratory experiments we find that thermal creep gas flow at low ambient pressure generates an overpressure sufficient to overcome the tensile strength. For the first time it allows a direct measurement of the tensile strength of individual, very small (sub)-mm aggregates which consist of only tens of grains in the (sub)-mm size range. We traced the disintegration of aggregates by optical imaging in ground based as well as microgravity experiments and present first results for basalt, palagonite and vitreous carbon samples with up to a few hundred Pa. These measurements show that low tensile strength can be the result of building loose aggregates with compact (sub)-mm units. This is in favour of a combined cometary formation scenario by aggregation to compact aggreates and gravitational instability of these units.

A homogeneous nucleus for comet 67P/Churyumov–Gerasimenko from its gravity field

Cometary nuclei consist mostly of dust and water ice. Previous observations have found nuclei to be low-density and highly porous bodies, but have only moderately constrained the range of allowed densities because of the measurement uncertainties. Here we report the precise mass, bulk density, porosity and internal structure of the nucleus of comet 67P/Churyumov-Gerasimenko on the basis of its gravity field. The mass and gravity field are derived from measured spacecraft velocity perturbations at fly-by distances between 10 and 100 kilometres. The gravitational point mass is GM = 666.2 ± 0.2 cubic metres per second squared, giving a mass M = (9,982 ± 3) × 10(9) kilograms. Together with the current estimate of the volume of the nucleus, the average bulk density of the nucleus is 533 ± 6 kilograms per cubic metre. The nucleus appears to be a low-density, highly porous (72-74 per cent) dusty body, similar to that of comet 9P/Tempel 1. The most likely composition mix has approximately four times more dust than ice by mass and two times more dust than ice by volume. We conclude that the interior of the nucleus is homogeneous and constant in density on a global scale without large voids. The high porosity seems to be an inherent property of the nucleus material.

MACROSCOPIC DUST IN PROTOPLANETARY DISKS—FROM GROWTH TO DESTRUCTION

The collision dynamics of dusty bodies are crucial for planetesimal formation. Especially decimeter agglomerates are important in the different formation models. Therefore, in continuation of our experiments on mutual decimeter collisions, we investigate collisions of centimeter onto decimeter dust agglomerates in a small drop tower under vacuum conditions (p<5*$10^{-1}$ mbar) at a mean collision velocity of 6.68 +- 0.67m/s. We use quartz dust with irregularly shaped micrometer grains. Centimeter projectiles with different diameters, masses and heights are used, their typical volume filling factor is $\Phi_{p,m}$=0.466+-0.02. The decimeter agglomerates have a mass of about 1.5kg, a diameter and height of 12cm and a mean filling factor of $\Phi_{t,m}$=0.44+-0.004. At lower collision energies only the projectile gets destroyed and mass is transferred to the target. The accretion efficiency decreases with increasing obliquity and increasing difference in filling factor, if the projectile is more compact than the target. The accretion efficiency increases with increasing collision energy for collision energies under a certain threshold. Beyond this threshold at 298+-25 mJ catastrophic disruption of the target can be observed. This corresponds to a critical fragmentation strength Q*=190+-16 mJ/kg, which is a factor of four larger than expected. Analyses of the projectile fragments show a power law size distribution with average exponent of -3.8+-0.3. The mass distributions suggest that the fraction of smallest fragments increases for higher collision energies. This is interesting for impacts of small particle on large target bodies within protoplanetary disks, as smaller fragments couple better to the surrounding gas and re-accretion by gas drag is more likely.

FROM PLANETESIMALS TO DUST: LOW-GRAVITY EXPERIMENTS ON RECYCLING SOLIDS AT THE INNER EDGES OF PROTOPLANETARY DISKS

Transporting solids of different sizes is an essential process in the evolution of protoplanetary disks and planet formation. Large solids are supposed to drift inward; high-temperature minerals found in comets are assumed to have been transported outward. From low-gravity experiments on parabolic flights we studied the light-induced erosion of dusty bodies caused by a solid-state greenhouse effect and photophoresis within a dust bed's upper layers. The gravity levels studied were 0.16g, 0.38g, 1g, and 1.7g. The light flux during the experiments was 12 +/- 2 kW/m^2 and the ambient pressure was 6 +/- 0.9 mbar. Light-induced erosion is strongly gravity dependent, which is in agreement with a developed model. In particular for small dusty bodies ((sub)-planetesimals), efficient erosion is possible at the optically thin inner edges of protoplanetary disks. Light-induced erosion prevents significant parts of a larger body from moving too close to the host star and be being subsequently accreted. The small dust produced continues to be subject to photophoresis and is partially transported upward and outward over the surface of the disk; the resulting small dust particles observed over the disk's lifetime. The fraction of eroded dust participates in subsequent cycles of growth during planetesimal formation. Another fraction of dust might be collected by a body of planetary size if this body is already present close to the disk edge. Either way, light induced erosion is an efficient recycling process in protoplanetary disks.

LOW-VELOCITY COLLISIONS OF CENTIMETER-SIZED DUST AGGREGATES

Collisions between centimeter- to decimeter-sized dusty bodies are important to understand the mechanisms leading to the formation of planetesimals. We thus performed laboratory experiments to study the collisional behavior of dust aggregates in this size range at velocities below and around the fragmentation threshold. We developed two independent experimental setups with the same goal to study the effects of bouncing, fragmentation, and mass transfer in free particle-particle collisions. The first setup is an evacuated drop tower with a free-fall height of 1.5 m, providing us with 0.56 s of microgravity time so that we observed collisions with velocities between 8 mm/s and 2 m/s. The second setup is designed to study the effect of partial fragmentation (when only one of the two aggregates is destroyed) and mass transfer in more detail. It allows for the measurement of the accretion efficiency as the samples are safely recovered after the encounter. Our results are that for very low velocities we found bouncing as could be expected while the fragmentation velocity of 20 cm/s was significantly lower than expected. We present the critical energy for disruptive collisions Q*, which showed up to be at least two orders of magnitude lower than previous experiments in the literature. In the wide range between bouncing and disruptive collisions, only one of the samples fragmented in the encounter while the other gained mass. The accretion efficiency in the order of a few percent of the particle's mass is depending on the impact velocity and the sample porosity. Our results will have consequences for dust evolution models in protoplanetary disks as well as for the strength of large, porous planetesimal bodies.

Dust ejection from planetary bodies by temperature gradients: Laboratory experiments

Laboratory experiments show that dusty bodies in a gaseous environment eject dust particles if they are illuminated. We find that even more intense dust eruptions occur when the light source is turned off. We attribute this to a compression of gas by thermal creep in response to the changing temperature gradients in the top dust layers. The effect is studied at a light flux of 13 kW/m 2 and 1 mbar ambient pressure. The effect is applicable to protoplanetary disks and Mars. In the inner part of protoplanetary disks, planetesimals can be eroded especially at the terminator of a rotating body. This leads to the production of dust which can then be transported towards the disk edge or the outer disk regions. The generated dust might constitute a significant fraction of the warm dust observed in extrasolar protoplanetary disks. We estimate erosion rates of about 1 kg s −1 for 100 m parent bodies. The dust might also contribute to subsequent planetary growth in different locations or on existing protoplanets which are large enough not to be susceptible to particle loss by light induced ejection. Due to the ejections, planetesimals and smaller bodies will be accelerated or decelerated and drift outward or inward, respectively. The effect might also explain the entrainment of dust in dust devils on Mars, especially at high altitudes where gas drag alone might not be sufficient.

Decimetre dust aggregates in protoplanetary discs

The growth of planetesimals is an essential step in planet formation. Decimetre-size dust agglomerates mark a transition point in this growth process. In laboratory experiments we simulated the formation, evolution, and properties of decimetre-scale dusty bodies in protoplanetary discs. Small sub-mm size dust aggregates consisting of micron-size SiO$_2$ particles randomly interacted with dust targets of varying initial conditions in a continuous sequence of independent collisions. Impact velocities were 7.7 m/s on average and in the range expected for collisions with decimetre bodies in protoplanetary discs. The targets all evolved by forming dust \emph{crusts} with up to several cm thickness and a unique filling factor of 31% $\pm$3%. A part of the projectiles sticks directly. In addition, some projectile fragments slowly return to the target by gravity. All initially porous parts of the surface, i.e. built from the slowly returning fragments, are compacted and firmly attached to the underlying dust layers by the subsequent impacts. Growth is possible at impact angles from 0$^{\circ}$ (central collision) to 70$^{\circ}$. No growth occurs at steeper dust surfaces. We measured the velocity, angle, and size distribution of collision fragments. The average restitution coefficient is 3.8% or 0.29 m/s ejection velocity. Ejecta sizes are comparable to the projectile sizes. The high filling factor is close to the most compact configuration of dust aggregates by local compression ($\sim 33$%). This implies that the history of the surface formation and target growth is completely erased. In view of this, the filling factor of 31% seems to be a universal value in the collision experiments of all self-consistently evolving targets at the given impact velocities. We suggest that decimetre and probably larger bodies can simply be characterised by one single filling factor.

Light-induced disassembly of dusty bodies in inner protoplanetary discs: implications for the formation of planets

Laboratory experiments show that a solid-state greenhouse effect in combination with thermophoresis can efficiently erode a dust bed in a low-pressure gaseous environment. The surface of an illuminated, light absorbing dusty body is cooler than the dust below the surface (solid-state greenhouse effect). This temperature gradient leads to a directed momentum transfer between gas and dust particles and the dust particles are subject to a force towards the surface (thermophoresis). If the thermophoretic force is stronger than gravity and cohesion, dust particles are ejected. Applied to protoplanetary discs, dusty bodies smaller than several kilometres in size which are closer to a star than ∼0.4 au are subject to a rapid and complete disassembly to submillimetre size dust aggregates by this process. While an inward-drifting dusty body is destroyed, the generated dust is not lost for the disc by sublimation or subsequent accretion on to the star but can be reprocessed by photophoresis or radiation pressure. Planetesimals cannot originate through aggregation of dust inside the erosion zone. If objects larger than several kilometres already exist, they prevail and further grow by collecting dust from disassembled smaller bodies. The pile-up of solids in a confined inner region of the disc, in general, boosts the formation of planets. Erosion is possible in even strongly gas-depleted inner regions as observed for TW Hya. Reprocessing of dust through light-induced erosion offers one possible explanation for growth of large cores of gas-poor giant planets in a gas-starved region as recently found around HD 149026b.

Eolian Erosion of Dusty Bodies in Protoplanetary Disks

We discuss the possibility of the erosion of dusty bodies in protoplanetary disks by a subsonic laminar gas flow. Our analysis is based on wind tunnel experiments on centimeter-size dust targets in an air gas flow of 63 m s-1 at static gas pressures between 0.1 and 4.5 mbar. We compare the results to numerical calculations of gas flow through porous bodies and the resulting drag force on dust aggregates at the surface. Our studies imply that a dusty body can be efficiently eroded if the dynamic gas pressure of the surface flow exceeds gravity and/or cohesion. In protoplanetary disks, we find that objects on circular orbits might be relatively safe against erosion in a laminar gas flow even in a dense disk. However, if a body is stirred up to an eccentric orbit, its motion relative to the gas increases. Such objects can be significantly eroded if they consist of dust. As an extreme, a 100 m body with the rather low eccentricity of an Earth orbit might be eroded in a single orbit. This effect leads to a bias for planetesimals in low-eccentricity orbits, as objects with large eccentricities are destroyed more easily. Erosion of bodies in high-eccentricity orbits, and reaccretion of the dust aggregates by low-eccentricity planetesimals, might provide a special growth mode of planetesimals and protoplanets.

Dust Eruptions by Photophoresis and Solid State Greenhouse Effects

We carried out experiments that show a gas pressure dependent ability of light to eject particles from a dust bed. Dust eruptions also occur upon removal of the light source. This can be attributed to a solid state greenhouse effect and photophoretic forces. This ejection mechanism works at light intensities larger than 6 kW/m2 but in extreme cases might work as low as 1 kW/m2. It can be applied to sunlit dust on Mars where it aids or triggers dust lift-off from the surface into the atmosphere. It is of importance for dusty bodies at the inner edge of protoplanetary disks where it leads to light induced erosion. The effect also offers a base for technical applications of dust removal in low pressure environments.

Growth of planetesimals by impacts at ∼25 m/s

We study central collisions between millimeter-sized dust projectiles and centimeter-sized dust targets in impact experiments. Target and projectile are dust aggregates consisting of micrometer-sized SiO 2 particles. Collision velocities range up to 25 m/s. The general outcome of a collision strongly depends on the impact velocity. For collisions below 13 m/s rebound and a small degree of fragmentation occur. However, at higher collision velocities up to 25 m/s approximately 50% of the mass of the projectile rigidly sticks to the target after the collision. Thus, net growth of a body is possible in high speed collisions. This supports the idea that planetesimal formation via collisional growth is a viable mechanism at higher impact velocities. Within our set of parameters the experiments even suggest that higher impact velocities might be preferable for growth in collisions between dusty bodies. For the highest impact velocities most of the ejecta is within small dust aggregates about 500 μm in size. In detail the size distribution of ejected dust aggregates is flat for very small particles smaller than 500 μm and follows a power law for larger ejected dust aggregates with a power of − 5.6 ± 0.2 . There is a sharp upper cut-off at about 1 mm in size with only a few particles being slightly larger. The ejection angle is smaller than 3° with respect to the target surface. These fast ejecta move with 40 ± 10 % of the impact velocity.

Ejection of dust by elastic waves in collisions between millimeter- and centimeter-sized dust aggregates at16.5to37.5m∕simpact velocities

We report on experiments in which millimeter-sized Si O2 dust aggregates consisting of (sub)-micrometer-sized grains impact into centimeter-sized targets that consist of the same kind of dust particles. The porosity of the granular targets is between 74% and 88%. Impact speeds are between 16.5 and 37.5 m/s with most impacts around 25 m/s . Compaction of the target by the impacting dust aggregate creates a crater which is several millimeters deep and 2-3 cm in diameter. We do not detect a significant amount of ejecta originating at the crater. We do observe a large amount of ejecta though. These are dust granules that are ejected from the whole target surface up to significant distances away from the impact site. This implies that elastic waves induced by the impact are an efficient mechanism to eject material. The estimated mass of these ejecta can be larger than 10 times the projectile mass. The ejecta velocity is uniform across the surface. It is typically 0.5% of the impact velocity. We apply these results to the problem of planetesimal formation. Under microgravity ablation of a dusty body or mass gain in a dust-dust collision might result. This depends on the parameters of the impact. Due to the low ejecta velocities, net growth is also possible in secondary collisions after an eroding primary collision if the body is placed in a gas flow. Thus, for a large number of typical conditions for dust-dust collisions in protoplanetary disks, formation of a larger body results from an impact.

Observation of dust shedding from material bodies in a plasma

Exposure to a space plasma can cause a dusty body, such as a spacecraft or a boulder in Saturn's rings, to release dust into its environment. This is demonstrated in a laboratory experiment with an aluminum sphere covered with micrometer‐sized dust grains. The sphere was rotating and electrically floating like an object in space. Laser light scattering was used to detect dust falling from the body. When a low‐temperature nitrogen plasma was turned on, rapid dust shedding was observed, and when it was turned off, the shedding stopped. The rate of shedding increases with plasma density. The dust is not all released the instant the plasma is turned on but rather takes place over an extended period of time, with individual grains jumping off at random intervals with a certain probability per unit time.