Rarified Gas Research Articles

Localised sublimation under cometary dust mantles

Observations of cometary surfaces have indicated that the amount of exposed surficial water ice is insufficient to supply the measured water production rates within the inner solar system. The measured water production rates are also a small fraction of that which would arise from freely subliming pure water ice bodies of similar surface area. A plausible mechanism, given the now well-established, high porosity of comets is that water ice is subliming below the visible surface with the produced gas escaping through the pores in a non-subliming hot dust matrix. If this process leads to an additional heating of the evolving gas, this may provide an elegant explanation for the temperature of the gas required to match measured terminal velocities. We investigate this process using a series of numerical models based on the Direct Simulation Monte Carlo (DSMC) method for rarified gas dynamics. We show that inhomogeneities in the source are not evident in the flow field once the thickness of the porous layer reaches a specific size and that lateral flow through the porous layer (parallel to the surface) can broaden the apparent source size when the source is small and isolated. The temperatures of the gas flow at the visible surface can be significantly increased and will respond to the temperature distribution within the non-volatile porous layer. The influence of the structural properties of the porous layer (how the porous layer is mechanically constructed) is shown to have only limited influence on the final gas parameters at the surface.

КВАЗІОДНОВИМІРНА МАТЕМАТИЧНА МОДЕЛЬ ПРОЦЕСІВ В ХОЛЛІВСЬКОМУ ТА ПЛАЗМОВО-ІОННОМУ ДВИГУНІ

Plasma-ion thrusters with a radial magnetic field in ionization chamber and Hall effect thrusters are electrostatic electric propulsion thrusters with closed electron drift. Axial symmetry in the dynamics of the components of propellant in these thrusters allows to write the equations of plasma-dynamics for electrons, ions and neutral atoms in two-dimensional axial-radial form. Attempts to reduce the equations to simpler one-dimensional form by simply removing the components with radius differentiation lead to the loss in the description of important effects, responsible for values of thruster performance. At the same time, a significant disadvantage of gas dynamics equation set is its fundamental openness – the correspondence between the number of unknown variables and equations is achieved approximately basing on some assumptions. In traditional form of gas dynamics, such closeness is made under the assumption of thermodynamic equilibrium with velocity distribution functions of components close to Maxwell one, which is the limit result of collisions. The use of such approximation to plasma components dynamics in electric propulsion thrusters is impossible due to the rarefaction of the substance in them. A mathematical model of two-component plasma-dynamics is represented in stationary form to describe the processes in the Hall effect thruster channel and the ionization chamber of plasma-ion thruster with radial magnetic field. Due to the impossibility of using the method of local thermodynamic equilibrium to describe the rarefied substance in electric propulsion thruster, a more advanced form of equations is used. A more reliable means of approximate closure of the set of equations is proposed in the description of the rarified gas. An approach to the description of the specifics of electrons energy transfer from the plasma to the walls of the channel, as well as the non-mirror reflection of electrons from the potential barrier within the Langmuir layer is shown. A method of averaging the parameters over the cross section of the channel is proposed, which allows to convert the equation into a quasi-one-dimensional form with the preservation of charge, momentum and energy losses on the channel walls.

Treatments of Micro-channel Flows Revisited: Continuum Versus Rarified Gas Considerations

There are numerous treatments of micro-channel flows available that point out the breakdown of the Navier–Stokes equations under molecular flow conditions when continuum conditions should still apply. The wrong conclusion regarding the validity of the Navier–Stokes equations comes about from the missing mass diffusion terms in the continuity equation. This term also affects the Navier–Stokes equations and yields improved theoretical results for flows with strong pressure and temperature gradients. Rarified gas treatments are often applied, although the fluid mechanics conditions are still such, that continuum equations should work. In the paper, the missing mass diffusion term is added, and it is shown that those extended fluid mechanics equation (EFME) allows micro-channel flows to be treated in the so-called slip regime. Hence, the continuum approach for flow treatment holds in micro-channel flows, in the flow regimes where modeling of wall interactions is applied these days. The paper also describes the treatments of micro-channel flows in the slip-flow regime by the rarified gas flow treatment method of Shapiro and Seleznev, and the results are compared with the corresponding results of the EFME. Good agreement was obtained, but differences exist regarding the wall interactions, which are explained, and suggested to use both methods to obtain a deeper insight into molecule–wall interactions in micro-channel flows. The EFME claim that large pressure and temperature gradients are the reasons for the differences between experimental and theoretical results of micro-channel flows. Such differences also exist in other fluid flows with strong property gradients, e.g., in shock waves. Flows of this kind are also treated in this paper in a way to show that the EFME have a wide range of applications.

Ramjet acceleration of microscopic black holes within stellar material

In this work we present a case that Microscopic Black Holes (MBH) of mass $10^{16}\text{ kg}$ to $3 \times 10^{19}\text{ kg}$ experience acceleration as they move within stellar material at low velocities. The accelerating forces are caused by the fact that a MBH moving through stellar material leaves a trail of hot rarified gas. The rarified gas behind a MBH exerts lower gravitational force on the MBH than the dense gas in front of it. The accelerating forces exceed the gravitational drag forces when MBH moves at Mach number $\mathscr {M}<\mathscr {M} _{0}$. The equilibrium Mach number $\mathscr {M}_{0}$ depends on MBH mass and stellar material characteristics. Our calculations open the possibility of MBH orbiting within stars including Sun at Mach number $\mathscr {M}_{0}$. At the end of this work we list some unresolved problems which result from our calculations.

Photophoresis of aerosol particles with nonuniform gas–surface accommodation in the free molecular regime

The problem of calculating the photophoretic force acting on an aerosol particle, with nonuniform distributions of accommodation coefficients over the particle's surface in a rarified equilibrium gas medium in the free molecular regime, is considered within the framework of perturbation theory, using the assumption that the variations of accommodation coefficients are sufficiently small. In general, the expression for the force acting on a convex particle involves four contributions. The energy accommodation coefficient and the radiometric accommodation coefficient for normal momentum are used.The formulae for calculating all four contributions to the photophoretic force are presented for a uniform spherical particle with finite thermal conductivity and a nonuniform axisymmetric distribution of accommodation coefficients over its surface. According to our estimates, the photophoretic force is defined with good accuracy by only two contributions: the “delta-alpha” force and “delta-T” force. The other contributions are small corrections to these two prevailing forces of order 1% or less.The ratio between the “delta-alpha” and “delta-T” forces depends on the particle size, Knudsen number, and the differences in the accommodation coefficients. For micron-sized spherical particles, the photophoretic “delta-alpha” force exceeds the “delta-T” force, and also exceeds gravity if the variation in the radiometric accommodation coefficient over the particle's surface is more than 0.055. Thus, levitation of particles in the Earth's stratosphere is possible due to gravito-photophoresis. For centimetre-sized particles, the “delta-T” force is a few orders of magnitude larger than the “delta-alpha” force due to the influence of IR radiation on the particles' temperature.

Sub-Doppler Resonances Caused by Rabi Oscillations on Atomic Transitions in Thin Gas Cells

Excitation of atoms from the ground quantum level to a metastable state by traveling monochromatic radiation in a thin gas cell, the internal thickness of which is much smaller than its radius, is studied theoretically. Sub-Doppler resonances are detected and analyzed that arise in the population of a metastable atomic level due to light-induced Rabi oscillations on a given optical transition and specific features of transit-time relaxation of atoms in a considered cell with a rarified gas upon scanning the radiation frequency. Such nontrivial resonances can be recorded in fluorescence of atoms with the help of an additional probe light beam. A method is proposed for a direct measurement of the Rabi frequency from spectral intervals between detected sub-Doppler resonances. The results obtained can be applied in atomic spectroscopy for the precision determination of components of dipole moment matrix elements, as well as for the Einstein coefficients and oscillator strengths related to these components, for quantum transitions between the ground and metastable levels of atoms.

Prediction of declining solar activity trends during solar cycles 25 and 26 and indication of other solar minimum

In this work we present a case that Microscopic Black Holes (MBH) of mass $10^{16}\ kg$ to $3 \cdot 10^{19}\ kg$ experience acceleration as they move within stellar material at low velocities. The accelerating forces are caused by the fact that a MBH moving through stellar material leaves a trail of hot rarified gas. The rarified gas behind a MBH exerts lower gravitational force on the MBH than the dense gas in front of it. The accelerating forces exceed the gravitational drag forces when MBH moves at Mach number $\mathcal{M}<\mathcal{M}_0$. The equilibrium Mach number $\mathcal{M}_0$ depends on MBH mass and stellar material characteristics. Our calculations open the possibility of MBH orbiting within stars including Sun at Mach number $\mathcal{M}_0$. At the end of this work we list some unresolved problems which result from our calculations.

Conjugate thermal creep flow in a thin microchannel

In the present work, we analyze asymptotically and numerically the conjugate heat transfer between a rarified gas flow and the lower wall of a thin horizontal microchannel. The laminar motion of the gas is originated only by the thermal creep or transpiration effect on the lower wall of the microchannel. It is well known the need to impose, in general, a variable temperature regime at the lower wall to induce the transpiration effect. Usually, it can be reached by setting a linear temperature profile as a boundary condition. However, in our case, we prefer to avoid this simplification taking into account that in practical applications, the temperature profile at the lower wall can be unknown. This case can occur, for instance, in a heat sink or a similar device with a well defined heat dissipation rate. Under this physical configuration, we can assume then that the bottom or external face of this heat sink with finite thermal conductivity is exposed to a uniform heat flux. On the other hand, the upper wall of the microchannel is subjected to a prescribed condition. The above conditions are sufficient to consider the simultaneous or conjugate heat transfer analysis of the heat conduction equation for the heat sink and the mass, momentum and energy equations for the gaseous-phase. Resulting governing equations are written in dimensionless form, assuming that the Reynolds number associated with the characteristic velocity of the thermal creep and the aspect ratio of the microchannel, are both very small. The velocity and temperature profiles for the gas phase and the temperature profiles for the solid wall are predicted as functions of the involved dimensionless parameters and the main results confirm that the phenomenon of conjugate thermal creep exists whenever the temperature of the lower wall varies linearly or nonlinearly.

Effects of nanoscale pore structure on permeability and relative permeability loss analyzed by GPU enhanced Multiple-Relaxation-Time LBM

Pore scale and the pore structure have significant effects on mass transfer properties through the porous media. In this article the effects of nanoscale pore structure (0.01<Kn<0.1) on permeability and permeability damage were studied by the GPU enhanced Multiple-Relaxation-Time (MRT) Lattice Boltzmann Model (LBM). Six mono-sized-bead packed nanoscale pores and six two-sized-bead packed same porosity different structure (SPDS) nanoscale pores were made to analyze scale and pore structure effects on permeability. The water predicted permeability and air predicted permeability in these nanoscale pores were estimated, and a modified slip boundary condition was implemented to mimic rarified gas effect in this scale. Simulation results are coherent with Klinkenberg effect that air predicted permeability is larger than water predicted permeability in every pore sample. Further analyses showed that pore dimension evenness degree (PDED, the ratio of max pore diameter to min pore diameter) is an essential factor of permeability. Larger PDED increases pore structure complexity, total surface area and tortuosity, but decreases permeability; smaller PDED has opposite effects. PDED is a new pore structure parameter presented in this article. GPU speed up results showed that CUDA parallel significantly accelerated calculation. The highest speed up ratio of CUDA parallel to single CPU was 468.

Gas flow through rough microchannels in the transition flow regime.

A multiple-relaxation-time lattice Boltzmann model of Couette flow is developed to investigate the rarified gas flow through microchannels with roughness characterized by fractal geometry, especially to elucidate the coupled effects of roughness and rarefaction on microscale gas flow in the transition flow regime. The results indicate that the surface roughness effect on gas flow behavior becomes more significant in rarefied gas flow with the increase of Knudsen number. We find the gas flow behavior in the transition flow regime is more sensitive to roughness height than that in the slip flow regime. In particular, the influence of fractal dimension on rarefied gas flow behavior is less significant than roughness height.

Redistribution of particles across the nucleus of comet 67P/Churyumov-Gerasimenko

We present an investigation of the surface properties of areas on the nucleus of comet 67P/Churyumov-Gerasimenko. Aims. We aim to show that transport of material from one part of the cometary nucleus to another is a significant mechanism that influences the appearance of the nucleus and the surface thermal properties. Methods. We used data from the OSIRIS imaging system onboard the Rosetta spacecraft to identify surface features on the nu- cleus that can be produced by various transport mechanisms. We used simple calculations based on previous works to establish the plausibility of dust transport from one part of the nucleus to another. Results. We show by observation and modeling that “airfall” as a consequence of non-escaping large particles emitted from the neck region of the nucleus is a plausible explanation for the smooth thin deposits in the northern hemisphere of the nucleus. The consequences are also discussed. We also present observations of aeolian ripples and ventifacts. We show by numerical modeling that a type of saltation is plausible even under the rarified gas densities seen at the surface of the nucleus. However, interparticle cohesive forces present difficulties for this model, and an alternative mechanism for the initiation of reptation and creep may result from the airfall mechanism. The requirements on gas density and other parameters of this alternative make it a more attractive explanation for the observations. The uncertainties and implications are discussed.

Statistical theory of rarified gases in the coulomb model of substance: Adiabatic approximation and initial atoms

In the framework of the adiabatic approximation for a subsystem of nuclei with the average distance between them significantly exceeding the dimensions of the initial atom, we consider a nonrelativistic Coulomb system consisting of electrons and nuclei of one type for the temperature range where we can restrict ourself to using the ground state to describe the electron subsystem. We show that the equilibrium properties of such a system are equivalent to the thermodynamic properties of the one-component system of initial atoms interacting between themselves via a short-range potential that is the effective potential of the nucleus-nucleus interaction. In the framework of the applicability of Boltzmann statistics, we present quantum group expansions for the thermodynamic properties of a chemically reacting rarified gas that correspond to the method of initial atoms.

Asymptotic Burnett model of the gas flow in a thin shock layer near a cylinder

Using the two-layer ideology of the theory of a viscous shock layer assuming the presence in the structure of the flow between the streamlined surface and the overrunning unperturbed stream of two (each with its own specific) characteristic areas-layers (smeared-out shock + shock layer itself), the complete Burnett equations are simplified in accordance with the problem of the cross-sectional flow-around of a round cylinder by the hypersound flow of rarified gas. The unitary asymptotic composite system of equations is formulated describing the flow in the entire thin shock layer including both of its above-mentioned structural areas (of the sublayer). Unlike the full Burnett equations, the obtained equation of the Burnett thin shock layer has an order not exceeding the order of the corresponding Navier-Stokes problem of the hypersonic thin shock layer, for which the research tool is sufficiently well developed.

Average charge states of heavy and superheavy ions passing through a rarified gas: Theory and experiment

The average charge states $\overline{q}$ of heavy and superheavy ions (atomic numbers $Z=80$--114) passing through He gas are studied experimentally and theoretically. Experimental data were measured at the gas-filled recoil separator, i.e., the TransActinide Separator and Chemistry Apparatus (TASCA) at GSI Darmstadt, for ion energies of a few hundred keV/u at gas pressures of 0.2 to 2.0 mbar. An attempt is made to describe experimental $\overline{q}$ values by means of atomic calculations of the binding energies and electron-loss and electron-capture cross sections. The influence of the gas-density effect is included in the calculations. The calculated $\overline{q}$ reproduce the experimental values for elements with $Z=80$--114 within 20%. A comparison with different semiempirical models is presented as well, including a local fit of high accuracy, which is often used in superheavy-element experiments to estimate the average charge states of heavy ions, e.g., at the gas-filled recoil separator TASCA. The $\overline{q}$ values for elements with $Z=115$, 117, 119, and 120 at He-gas pressure of 0.8 mbar are predicted.

Analytical model of explosions in a rarefied atmosphere

A new model of explosion products expansion in rarified gas is obtained. This model is based on an approach taking into account the energy dissipation in the “snowplow” model, thus making it possible to obtain an exact analytical solution and results which are in good agreement with experimental data. A comparison of the new model with the currently existing models (Simple Snowplow Model, Stuart’s model and Holway’s model) is indicative of the fact that the latter can be described in the framework of the new model. Alongside with that, the new model is able to take into account yet more processes not considered in the existing models. A comparison with the Spolokh-1 experiment demonstrates good agreement with data obtained in this experiment.

Stability properties of phase transition layers in the diffuse ISM revisited

AbstractIn a thermally bistable medium, cold, dense gas is separated from warm, rarified gas by thin phase transition layers, or fronts, in which radiative heating/cooling, thermal conduction, and convection of material are balanced. While these fronts have received only scant attention in the literature, and are not resolved by most current numerical simulations, they have been shown to have important ramifications for transport processes and structure formation in the diffuse interstellar medium. Here, we discuss calculations of their hydrodynamic and magnetohydrodynamic stability properties.

Rigorous validity of the Boltzmann equation for a thin layer of a rarefied gas

We consider a thin layer of a rarified gas modeled by a large hard-sphere system and show that, as long as the thickness of the layer is much larger than the interaction length, the limiting behavior is described, at least for short times, by a Boltzmann equation with two-dimensional position variable and three-dimensional velocity.By the analysis of the Lorentz gas we argue that, if the thickness of the layer is of the same order of the interaction length, this is not the case.

Effects of ion–neutral chemical reactions on dynamics of lightning-induced electric field

Secondary lightning phenomena in the upper atmosphere called sprites attract interest from the viewpoint of atomic–molecular and plasma physics. Lightning-induced electric field accelerates the ionospheric electrons up to tens of electron-volts, inducing electrical breakdown as well as strong optical emissions, through electron impact ionization of molecules. A large-scale structure of sprites is constructed by collective dynamics of filamentary streamer discharges in a rarified gas, which in turn is controlled by the distribution of the background electric field. In this paper, we firstly reanalyze the relationship between quasi-static field formation and local ion chemistry with first-order perturbation techniques. Secondly, we investigate with a full ion chemical model the effects of electron attachment to oxygen molecules on its density in moderate cases of undervoltage lightning electric fields rather than the cases of intense ionization in streamers. We estimate the minimum values that are provided by the chemical balance with electron detachment from negative ions. We also investigate the recovery timescale of the electron density and find that the scale (⩾1 s) is occasionally much larger than the interval of each lightning stroke (≈10 ms). We suggest that the subsequent sprite event as well as the field formation could be well affected by the ghost of the primary event. We discuss further the negative ion chemistry triggered by electron attachment in the nighttime mesosphere.

Power and exponential asymptotic forms of correlation functions

Using the Ornstein.Zernike equation, we obtain two asymptotic equations, one describing the exponential asymptotic behavior and the other describing the power asymptotic behavior of the total correlation function h(r). We show that the exponential asymptotic form is applicable only on a bounded distance interval l L and reproduces the form of the interaction potential. In this case, as the density of a rarified gas decreases, L → l, the exponential asymptotic form vanishes, and only the power asymptotic form remains. Conversely, as the critical point is approached, L → ℞, and the applicability domain of the exponential asymptotic form increases without bound.

Superradiant resonant Rayleigh scattering of light by the Bose-Einstein condensate of rarified atomic gases

Based on the earlier model, the superradiant Rayleigh scattering of the high-intensity short light pulses by the Bose-Einstein condensate of rubidium vapor is studied. It is demonstrated that only six states with a certain momentum are filled when the resonance detuning is about the Rabi frequency. The first two states describe the atomic motion along the condensate due to absorption, whereas the remaining four states describe the atomic motions at angles of 45° and 135° to the condensate axis owing to the reemission of the photon. The condensate pulsations between the state with zero momentum and the last four states are revealed. The corresponding shape of the coherent Rayleigh pulse is found for various resonance detunings.