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Gas flow through layers of porous materials plays a crucial role in technical applications, geology, petrochemistry and space sciences (e.g. fuel cells, catalysis, shale gas production and outgassing of volatiles from comets). In many applications the Knudsen regime is predominant, where the pore size is small compared to the mean free path between intermolecular collisions. In this context common parameters to describe the gas percolation through layers of porous media are the probability of gas molecule transmission and the Knudsen diffusion coefficient of the medium. We show how probabilistic considerations on layer partitions lead to the analytical description of the permeability of a porous medium to gas flow as a function of layer thickness. The derivations are made on the preconditions that the reflection at pore surfaces is diffuse and that the pore structure is homogenous on a scale much larger than the pore size. By applying a bi-hemispherical Maxwell distribution, relations between the layer transmission probability, the half-transmission depth and the Knudsen diffusion coefficient are obtained. For packings of spheres, expressions of these parameters in terms of porosity and grain size are derived and compared with former standard models. A verification of the derived equations is given by means of numerical simulations, also giving evidence that our analytical model for sphere packing is more accurate than the former classical models.

According to current theories of the formation of stellar systems, comets belong to the oldest and most pristine class of bodies to be found around a star. When approaching the Sun, the nucleus shows increasing activity and a pressure increase inside the material causes sublimated and trapped gas molecules to stream away from their regions of origin towards the surface. The present work studies two essential mechanisms of gas transport through a porous layer, namely the Darcy and the Knudsen flow. Gas flow measurements are performed in the laboratory with several analogue materials, which are mimicking dry cometary surface properties. In this first series of measurements, the aim was to separate gas transport properties from internal sources like local sublimation or release of trapped gases. Therefore, only dry granular materials were used and maintaining a low temperature environment was unnecessary. The gas permeability and the Knudsen diffusion coefficient of the sample materials are obtained, thereby representing the relative importance of the respective flow mechanism. The experiments performed with air at a stable room temperature show that the grain size distribution and the packing density of the sample play a major role for the permeability of the sample. The larger the grains, the bigger the permeability and the Knudsen diffusion coefficient. From the latter, we estimated effective pore diameters. Finally, we explain how these parameters can be adapted to obtain the gas flow properties of the investigated analogue materials under the conditions to be expected on the comet.

The success of the Rosetta mission to comet 67P/Churyumov–Gerasimenko has revolutionized our view of comets, while opening a plethora of new questions. In order to find the answers to them and harness the full potential of the new data, an international consortium named “Cophylab – Comet Physics Laboratory” (Cophylab.space) was launched in 2018. In this project several experiment campaigns were initialized to study cometary properties in a controlled environment. The idea was to isolate individual properties and processes in dedicated laboratory experiments. One of the experiment campaigns was designed to characterize gas flow properties of dry porous materials in a first step, with the aim of developing a model that improves our understanding of the outgassing of comets.Before the initial model is extended to consider the sublimation of volatile components, it needs to be validated by alternative methods, such as numerical simulations. For this purpose, we chose the finite element method, to test the combination of the Darcy and Knudsen flow model, which was used in the preceding study.Our approach was to use the results of the experiment as input in the simulations and compare the output with the measurements. This comparison confirmed the validity of the model and its assumptions. In particular, the sample is assumed to be homogenous and isotropic on a macroscopic scale, so that it can be described by a set of averaged parameters. While this description is relatively accurate for samples with well-defined grain shapes (e.g. spherical glass beads), significant discrepancies occur for inhomogeneous materials such as lunar, Asteroid or Martian analogues.We investigated various aspects that were initially neglected in the evaluation of the measurements, such as channel building in the sample, boundary effects and non-ideal geometry of the experimental setup, which will be complemented by inhomogeneities that occur naturally in random close packing or ballistic deposition samples. Furthermore, we assessed the models range of applicability through a thorough review of the different flow regimes encountered in the measurements. Our findings indicate that boundary effects, as well as non-ideal geometry have a significant influence particularly in samples with larger grains. For finer grained samples on the other hand, inhomogeneities are the most probable cause for discrepancies. The grain size also plays an important role regarding the flow regime and its corresponding parameters.The work for this study was performed in the framework of a master’s thesis, as part of the Cophylab project, which is funded by the D-A-CH program (DFG GU1620/3-1 and BL 298/26-1 / SNF 200021E 177964 / FWF I 3730-N36)

A profound understanding of gas flow in porous media is of great interest for various technological and scientific fields. Its investigation by laboratory measurements, however, poses several challenges. In particular, the determination of macroscopic flow parameters from pressure and gas flow measurements is prone to various error influences, some of which are very difficult to analyze experimentally. Computer simulations are a solution in this context as they facilitate modifications of the underlying geometry and boundary conditions in a flexible way. Here we present a simulation framework for the analysis of a recent experiment for determining the Knudsen diffusion coefficient and viscous permeability of various porous granular materials. By combining the finite element method with analytical models and other numerical methods, we were able to identify previously neglected physical effects that increase the uncertainty of the measurements. In particular, the porosity increase due to finite sample dimensions, in a layer of about a grain diameter thickness near the container wall, creates a deviation of the measured pressure gradient. This deviation amounts to ca. 5% for a sample width of about 100 grains and a porosity of 0.5, and is indirectly proportional to the porosity. The second most prominent error source, the sample support sieve, causes a slight constriction of the flow volume. Simulations of this effect show an error around 4%–7%, dependent on the grain size. Based on these findings we recommend an overall sample dimension of 100 grains or larger. As an example of failures of the sample homogeneity, we elaborate how channels through the sample influence the flow properties. Respective suggestions for keeping all discussed effects negligible are discussed in detail. Our methodology demonstrates how the combination of finite element computations with analytical representations of the involved macroscopic parameters can assess the validity and accuracy of laboratory experiments.

To validate the physical model used to describe gas flow through porous, granular media in recent experiments [1], we conducted a finite element analysis (FEA). The main parameters of a sample, such as gas permeability, Knudsen diffusion coefficient and porosity were determined from the experiment and used as an input for the simulations, with the aim of replicating the pressure evolution (measured quantity) depending on external gas flow. While the results matched well for samples with large and spherical grains, the deviations were significant for materials with small and irregularly shaped grains. An improvement of the model could be achieved with complementary simulation methods and a more detailed analysis of the samples. 1. Introduction In the past decades, multiple cometary space missions (e.g. Deep Impact and Rosetta) have provided us with better data and understanding of the solar system’s primordial objects. The most recent project is a cooperation of six European institutions, called “Cometary Physics Laboratory (CoPhyLab)” and has already produced a plethora of results (see webpage https://cophylab.space/index.php?id=27). In this work we investigated gas flow through porous media with a simulation approach, in order to compare it with the experiment and validate its physical model. 2. Experiment The basis and motivation of this work was the experiment performed by [1] (see Figure 1), where the gas flux through a set of artificial and natural porous materials was analysed. To describe the flux J [mol∙m-2∙s-1] of dry air in the given pressure range, a combination of viscous flow and free molecular diffusion was chosen as the physical model: The gas permeability B­0 (viscous flow) and Knudsen diffusion coefficient DK (molecular diffusion) are the main parameters which describe a sample’s ability to allow gas to flow through it. They were determined by measuring the steady state pressure difference across the inlet and outlet of the sample for different gas flux levels. The porosity of the materials was measured through packing experiments. 3. Simulation Since the physical model describes the gas flow on a macroscopic level, with the main parameters being determined as average values across the whole sample, a FEA is the ideal method. The simulations were computed with the software “COMSOL Multiphysics®”, in which the sample was modelled as a cylinder (see Figure 2). The built-in physics module “Darcy’s Law” was selected to provide the governing equations and all input parameters were taken from the measurements (sample dimensions, B0, DK, porosity, viscosity etc.). In stationary studies, the pressure at the sample outlet and the inward mass flux of the measurements were defined as boundary conditions for the simulation, with the pressure in the rest of the sample being the free variable. For transient studies, the empty volumes of the vacuum chamber, as well as the pressure dependent performance characteristic of the pump were taken into consideration to be able to compare the dynamic process. Furthermore, variation studies of the main parameters were carried out to investigate their individual influence on the pressure evolution. Boundary effects such as the facilitation of gas flow due to lower porosity at the container wall or opening of channels in the sample, or impediment due to the holding sieve, were also analysed by adapting the material parameters for the respective boundary layers. 4. Results For the comparison of stationary simulation results with those of the experiment, the measured pressure at the inlet face of the sample was taken as a boundary condition and for transient simulations also the outlet face pressure (see Figure 3 for an exemplary comparison of results). The deviations were relatively small for synthetic material with large grain sizes (i.e. glass beads with a diameter above 200 µm). However, for smaller grain sizes and natural materials the discrepancies were quite large (up to 35%) and featured no apparent correlation regarding the amount of gas flow. Regarding parameter variation studies, it is important to note that the creation of physical samples where only one parameter varies is very difficult, because many of the parameters are directly or indirectly coupled with each other. Nevertheless, the results indicated that in regimes of low B0 and DK, as is the case for small grain size samples, a variation of either parameter has a large influence on the pressure evolution. This is particularly important when considering measurement and regression errors. When boundary layers were added for the analysis of boundary effects (higher permeability and diffusion at the cylinder wall or in a channel), most of the gas flowed through it and the pressure difference across the sample was minimal. Deviations between simulations with and without the holding sieve, manifested themselves as temporary spikes when the gas flow was increased, with steady state differences below 2%. 5. Summary and Outlook The results indicate that the applied model is well consistent with the measurements of homogenous samples (e.g. synthetic materials with large, spherical grains). However, in the case of small and irregularly shaped grains, the material’s anisotropy could explain the discrepancies. To improve the existing model, it is necessary to analyse the physical samples on a smaller scale and better understand the interdependencies of the governing parameters. This can be achieved by creating virtual samples and using alternative simulation methods (i.e. Monte Carlo), which work on a microscopic scale. 6. Acknowledgements This work was carried out in the framework of the CoPhyLab project funded by the D-A-CH programme (GU 1620/3-1 and BL298/26-1/SNF 200021E 177964/FWF I 3730-N36). References [1] M. Schweighart, W. Macher, G. Kargl, B. Gundlach, H. L. Capelo, Viscous and Knudsen gas flow through dry porous cometary analogue material, Monthly Notices of the Royal Astronomical Society, 2021;, stab934, https://doi.org/10.1093/mnras/stab934

The Comet Physics Laboratory (CoPhyLab) is an international research program to study the physical properties of cometary analog materials under simulated space conditions. The project is dedicated to studying, with the help of multiple instruments and the different expertise and background from the different partners, the physics of comets, including the processes inside cometary nuclei, the activity leading to the ejection of dust and gas, and the sub-surface and surface evolution of cometary nuclei when exposed to solar illumination. CoPhyLab will provide essential information on the formation and evolution of comets and insights into the origins of primitive Solar System bodies. To this end, we constructed a new laboratory that hosts several small-scale experiments and a large-scale comet-simulation chamber (L-Chamber). This chamber has been designed and constructed to host ice���dust samples with a diameter of up to 250 mm and a variable height between 100 and 300 mm. The cometary-analog samples will be kept at temperatures below 120 K and pressures around 10���6 mbar to ensure cometary-like conditions. In total, 14 different scientific instruments are attached to the L-Chamber to study the temporal evolution of the physical properties of the sample under different insolation conditions. Due to the implementation of a scale inside the L-Chamber that can measure weight changes of the samples with high precision, the cooling system is mechanically decoupled from the sample holder and cooling of the samples occurs by radiation only. The constructed chamber allows us to conduct uninterrupted experiments at low temperatures and pressures up to several weeks.

The experiment WAVES aboard the Juno spacecraft, which will arrive at its target planet Jupiter in 2016, was devised to study the plasma and radio waves of the Jovian magnetosphere. We analyzed the WAVES antennas, which consist of two non-parallel monopoles operated as a dipole. For this investigation we applied two independent methods: the experimental technique, rheometry, which is based on a down-scaled model of the spacecraft to measure the antenna properties in an electrolytic tank; and numerical simulations, based on commercial computer codes, from which the quantities of interest (antenna impedances and effective length vectors) are calculated. In this article we focus on the results for the low-frequency range up to about 4MHz, where the antenna system is in the quasi-static regime. Our findings show that there is a significant deviation of the effective length vectors from the physical monopole directions, caused by the presence of the conducting spacecraft body. The effective axes of the antenna monopoles are offset from the mechanical axes by more than 30° and effective lengths show a reduction to about 60% of the antenna rod lengths. The antennas' mutual capacitances are small compared to the self-capacitances, and the latter are almost the same for the two monopoles. The overall performance of the antennas in dipole configuration is very stable throughout the frequency range up to about 4–5MHz, and therefore can be regarded as the upper frequency bound below which the presented quasi-static results are applicable.

The thermal properties of the surface and subsurface layers of planets and planetary objects yield important information that allows us to better understand the thermal evolution of the body itself and its interactions with the environment. Various planetary bodies of our Solar System are covered by so-called regolith, a granular and porous material. On such planetary bodies the dominant heat transfer mechanism is heat conduction via IR radiation and contact points between particles. In this case the energy balance is mainly controlled by the effective thermal conductivity of the top surface layers, that can be directly measured by thermal conductivity probes. A traditionally used method for measuring the thermal conductivity of solid materials is the needle-probe method. Such probes consist of thin steel needles with an embedded heating wire and temperature sensors. For the evaluation of the thermal conductivity of a specific material the temperature change with time is determined by heating a resistance wire with a well-defined electrical current flowing through it and simultaneously measuring the temperature increase inside the probe over a certain time. For thin needle probes with a large length-to-diameter ratio it is mathematically easy to derive the thermal conductivity, while this is not so straightforward for more rugged probes with a larger diameter and thus a smaller length-to-diameter ratio. Due to the geometry of the standard thin needle probes they are mechanically weak and subject to bending when driven into a soil. Therefore, using them for planetary missions can be problematic. In this paper the thermal conductivity values determined by measurements with two non-ideal, ruggedized thermal conductivity sensors, which only differ in length, are compared to each other. Since the theory describing the temperature response of non-ideal sensors is highly complicated, those sensors were calibrated with an ideal reference sensor in various solid and granular materials. The calibration procedure and the results are described in this work.

We present the high-frequency properties of the eight electric field sensors as proposed to be launched on the spacecraft "RESONANCE" in the near future. Due to the close proximity of the conducting spacecraft body, the sensors (antennas) have complex receiving features and need to be well understood for an optimal mission and spacecraft design. An optimal configuration and precise understanding of the sensor and antenna characteristics is also vital for the proper performance of spaceborne scientific instrumentation and the corresponding data analysis. The provided results are particularly interesting with regard to the planned mutual impedance experiment for measuring plasma parameters. Our computational results describe the extreme dependency of the sensor system with regard to wave incident direction and frequency, and provides the full description of the sensor system as a multi-port scatterer. In particular, goniopolarimetry techniques like polarization analysis and direction finding depend crucially on the presented antenna characteristics.

International audience; We present a study of plasma conditions in the atmospheres of the Hot Jupiters HD 209458b and HD 189733b and for an HD 209458b like planet at orbit locations between 0.2 and 1 au around a Sun-like star. We discuss how these conditions influence the radio emission we expect from their magnetospheres. We find that the environmental conditions are such that the cyclotron maser instability (CMI), the process responsible for the generation of radio waves at magnetic planets in the Solar system, most likely will not operate at Hot Jupiters. Hydrodynamically expanding atmospheres possess extended ionospheres whose plasma densities within the magnetosphere are so large that the plasma frequency is much higher than the cyclotron frequency, which contradicts the condition for the production of radio emission and prevents the escape of radio waves from close-in exoplanets at distances

Context. The Microwave Instrument for the Rosetta Orbiter (MIRO) was one of the key instruments of the Rosetta mission, which acquired a wealth of data, in particular as the orbiter moved in the close environment of comet 67P/Churyumov-Gerasimenko (August 2014–September 2016). It was the only instrument of the Rosetta payload that was able to measure temperatures in the near-subsurface layers of the cometary nucleus down to a depth of some centimeters. This range is most relevant for understanding the mechanisms of cometary activity. Aims. We simulate the 3D temperature distribution for two selected regions that were observed by MIRO in March 2015 when the comet was at a distance of about 2 au from the Sun. The importance of a full 3D treatment for a realistic subsurface temperature distribution and the thermal heat balance in the uppermost subsurface is investigated in comparison with analogous 1D simulations. Methods. For this purpose, we developed a numerical heat transfer model of the surface as well as the near-subsurface regions. It enabled us to solve the heat transfer equation in the subsurface volume with appropriate radiation boundary conditions taken into account. The comparison with 1D simulations was made on the basis of the same solar irradiation history. Results. Although the temperature gradient is predominantly normal to the comet surface, we still find that tangential flows may be responsible for local temperature differences of up to 30 K (a few Kelvin on the average) in the uppermost subsurface layers. From the results of the 3D simulations, we calculated the MIRO antenna temperature. A comparison with the actual measurements shows good agreement for the MIRO submillimeter channel, but there is a notable discrepancy for the millimeter channel. This last assessment is not related to the use of the 3D model; potential causes are discussed in some detail with a view to future studies.