Gas Rarefaction Research Articles

Heterogeneous activation of rarefied hydrogen in thin tubes

The direct simulation Monte Carlo method was used to study the rarefied gas flow through a cylindrical channel, taking into account heterogeneous reactions of dissociation-recombination on the surface. The main emphasis was placed on the study of the influence of heterogeneous processes on the degree of dissociation of the flow, coming out of the channel. The study was conducted for different relations of the channel length to its radius, coefficients of dissociation and recombination, and in a wide range of gas rarefaction degrees: from free molecular to transitional regimes. The obtained results may be useful for optimization of gas-dynamic sources ​of activated gas, based on thin tubes.

Sphere oscillating in a rarefied gas

Flow generated by an oscillating sphere in a quiescent fluid is a classical problem in fluid mechanics whose solution is used ubiquitously. Miniaturisation of mechanical devices to small scales and their operation at high frequencies in fluid, which is common in modern nanomechanical systems, can preclude the use of the unsteady Stokes equation for continuum flow. Here, we explore the combined effects of gas rarefaction and unsteady motion of a sphere, within the framework of the unsteady linearised Boltzmann–BGK (Bhatnagar–Gross–Krook) equation. This equation is solved using the method of characteristics, and the resulting solution is valid for any oscillation frequency and arbitrary degrees of gas rarefaction. The resulting force provides the non-continuum counterpart to the (continuum) unsteady Stokes drag on a sphere. In contrast to the Stokes solution, where the flow is isothermal, non-continuum effects lead to a temperature jump at the sphere surface and non-isothermal flow. Unsteady effects and heat transport are found to mix strongly, leading to marked differences relative to the steady case. The solution to this canonical flow problem is expected to be of significant practical value in many applications, including the optical trapping of nanoparticles and the design and application of nanoelectromechanical systems. It also provides a benchmark for computational and approximate methods of solution for the Boltzmann equation.

Lattice Boltzmann based simulation of gas flow regimes in low permeability porous media: Klinkenberg’s region and beyond

Tight gas reservoirs are of prominent importance among unconventional petroleum reservoirs. Due to the complicated flow dynamics of gas in tight porous media and compressibility effects, corrections have to be applied to the Darcy equation so that it can properly predict gas flow dynamics. As the mean pore diameter of tight rocks (e.g. shales) decreases, the ratio of the mean free path to the pore diameter, known as the non-dimensional Knudsen number, rises, the gas rarefaction effects becomes important, and the condition of no-slip on the pore surface is violated. Proper treatments of these complexities have been attempted by using classical continuum fluid mechanics and kinetic theory of gases approaches. The most well-known slip condition correction was presented by Klinkenberg in 1941. Many researchers have tried to correct and extend Klinkenberg's model beyond the slip flow regime. In this research the slip condition of the rarefied gas in low permeability simple porous media is studied by the lattice Boltzmann method and new corrections to Klinkenberg's coefficients are investigated. These corrections allow the extension of Klinkenberg model to higher ranges of Knudsen numbers. All the simulations in this work were performed by codes developed by the authors.

Unsteady rarefied gas flow in a microchannel driven by a pressure difference

The kinetic S-model is used to study the unsteady rarefied gas flow through a plane channel between two parallel infinite plates. Initially, the gas is at rest and is separated by the plane x = 0 with different pressure values on opposite sides. The gas deceleration effect of the channel walls is studied depending on the degree of gas rarefaction and the initial pressure drop, assuming that the molecules are diffusely reflected from the boundary. The decay of the shock wave and the disappearance of the uniform flow region behind the shock wave are monitored. Special attention is given to the gas mass flux through the cross section at x = 0, which is computed as a function of time. The asymptotic behavior of the solution at unboundedly increasing time is analyzed. The kinetic equation is solved numerically by applying a conservative finite-difference method of second-order accuracy in space.

On real statistics of relaxation in gases

By example of a particle interacting with ideal gas, it is shown that the statistics of collisions in statistical mechanics at any value of the gas rarefaction parameter qualitatively differ from that conjugated with Boltzmann’s hypothetical molecular chaos and kinetic equation. In reality, the probability of collisions of the particle in itself is random. Because of that, the relaxation of particle velocity acquires a power-law asymptotic behavior. An estimate of its exponent is suggested on the basis of simple kinematic reasons.

An accelerated discrete velocity method for flows of rarefied ternary gas mixtures in long rectangular channels

An accelerated discrete velocity method is presented for rarefied three-component gas mixtures flowing through long rectangular ducts. The scheme is developed on the basis of the McCormack linearized kinetic model. Diffusion equations are derived for the velocity and the heat flow vector. The kinetic and diffusion equations are solved in a coupled iteration. Simulations are carried out for He–Ar–Xe mixture to test the computational performance of the scheme for pressure driven flow. It is shown that the accelerated method requires a fewer number of iterations and smaller computational time in a large part of the gas rarefaction from the transition region to the hydrodynamic limit than the non-accelerated one. These quantities are studied as a function of the convergence parameter also. The flow rates as a function of the rarefaction parameter and representative velocity profiles are shown. A good agreement is found between the total flow rate and the corresponding slip flow value at large rarefaction parameters. The present approach can be useful for fast computation of flows of ternary gas mixtures in long rectangular channels.

Heat transfer in ternary rarefied gas mixtures between two parallel plates

An approach is presented to calculate the heat transfer problem in ternary rarefied gas mixtures between two parallel plates. The study is based on the McCormack linearized kinetic model, which is solved by the discrete velocity method. The heat flux is determined and tabulated for He–Ar–Xe and Ne–Ar–Xe mixtures in a wide range of the gas rarefaction at various values of the mole-fractions by using the experimental potential. Results with the hard-sphere model are also delivered for the first mixture. The heat flux is sensitive to the mole-fractions and the intermolecular potential. Representative distributions of the perturbations of the density and the temperature of the components are shown. The results indicate that the deduction of the heat flux should be based on the full treatment of the three component gas mixture.

A fast iterative discrete velocity method for ternary gas mixtures flowing through long tubes

An accelerated discrete velocity method is presented for flows of three-component gas mixtures through long tubes. The gas is modeled by the McCormack linearized kinetic equation. Two diffusion equations are derived from the kinetic one. These equations are solved during the kinetic iteration by a linear algebraic approach. Test simulations are performed for flows of He–Ar–Xe mixture driven by pressure or temperature gradients in a wide range of the gas rarefaction. The accelerated method requires fewer number of iterations and smaller computational times than the non-accelerated one in the early transition, slip and near-hydrodynamic domains. The efficiency of the accelerated scheme compared to the standard one increases with increasing rarefaction parameter. The computational performance in terms of the iteration criterion is also analyzed. In typical simulations, the convergent results can be reached in approximately less than two minutes by using the new method in a wide range of the gas rarefaction on a present-day computer.

Combined Effects of Surface Roughness Mode and Accommodation Coefficient of Air-Bearing Film in the Head/Disk Interface

In a modern hard disk drive (HDD), when the spacing between slider and disk is on the order of 1 or 2 nm, the gaseous rarefaction effects, surface roughness, and surface accommodation effects must be taken into account. Effects of gaseous rarefaction with either surface roughness or surface accommodation were reported in literature. However, only a few of the published works have considered the combined effects simultaneously. This paper investigates the combined effects of the surface roughness mode and the surface accommodation as well as the gaseous rarefaction effects on the static characteristics of the air-bearing film in both the cases of symmetric molecular interaction and asymmetric molecular interaction.

Unbalance response of micro gas bearing-rotor system considering rarefaction effect

The unbalance response of micro gas bearing-rotor system is calculated using the fourth-order Runge–Kutta method based on the motion equation of the rotor, in which the nonlinear gas film force is obtained from solving the modified Reynolds equation using the alternating direction implication algorithm. The study shows that the proper eccentric mass of the rotor can improve the stability of micro gas bearing-rotor system. Compared with the result without considering the gas rarefaction effect, the stability threshold speed of micro rotor system considering the gas rarefaction effect is increased. Meanwhile for the same mass eccentricity, the peak value emerges at the lower rotation speed, which shows that the unbalance eccentric mass will influence the motion of micro rotor system more greatly when the gas rarefaction effect is taken into account.

Analysis of the diodic effect of flows of rarefied gases in tapered rectangular channels

Pressure driven flows of rarefied single gases through long tapered rectangular channels are studied computationally. A part of the results is compared to the available experimental data. The flow is modeled by the linearized Bhatnagar-Gross-Krook kinetic equation. The mass flow rate and the distributions of the pressure and the rarefaction parameter are deduced. Calculations are performed in the whole range of the gaseous rarefaction. The diodicity has a maximum at intermediate values of the Knudsen number and increases with large to small cross section ratio. The diodic effect is explained phenomenologically. The pressure profile depends on the flow direction and varies strongly near the small height. The mass flow rates of CO2, N2 and Ar gases in a mini/microchannel at moderate rarefactions are compared to the numerical results. An end-correction to the numerical calculation is applied. A relatively good agreement is found between the computational and experimental flow rates. The agreement is improved if the end-correction is used. The experimental diodicity is reproduced well with the numerical simulation. The results presented in the paper might be useful for the development and optimal design of pumping systems based on the diode effect.

Argon metastables in HiPIMS: validation of the ionization region model by direct comparison to time resolved tunable diode-laser diagnostics

The volume plasma interactions of high power impulse magnetron sputtering (HiPIMS) discharges operated with a Ti target is analyzed in detail by combining time-resolved diagnostics with modeling of plasma kinetics. The model employed is the ionization region model (IRM) with an improved and detailed treatment of the kinetics of the argon metastable (Arm) state, called m-IRM. The diagnostics used is tunable diode-laser absorption spectroscopy (TD-LAS) of the Arm state, which gives the line-of-sight density integrated along the laser path parallel to the target surface. The TD-LAS recordings exhibit quite complex temporal evolutions Arm(t), with distinct features that are shown to reflect the time evolution of the plasma (the electron density and temperature), and of the argon gas (gas rarefaction and refill). The Arm(t) function is thus a tracer for the most important aspects of internal discharge physics, and therefore suitable for model testing and validation. The IRM model is constructed to be locked to obey specific experimental macroscopic discharge parameters, specifically the discharge current ID(t) and the voltage UD(t). It has to this purpose been run with the appropriate process gas pressures (from 0.67 to 2.67 Pa), with the experimentally applied voltage pulse profiles UD(t), and with the resulting current pulse profiles ID(t) (with maxima from 0.5 to 70 A). It is shown that the model reproduces the features in the TD-LAS measurements: both the Arm(t) evolution in single pulses, and how the pulse shapes change with gas pressure and with pulse amplitude. The good agreement between the measurements and model output is in this work taken to validate the basic assumptions of the m-IRM. In addition, the m-IRM results have been used to unravel the connections between volume plasma kinetics and various features recorded in the TD-LAS measurement, and to generalize the foremost characteristics of the studied discharges.

An Overview on Time‐Resolved Optical Analysis of HiPIMS Discharge

The progress in the time‐resolved characterization of HiPIMS discharges performed during the last decade in our group is overviewed. Optical emission and absorption spectroscopy, as well as laser‐induced fluorescence‐based techniques have been mainly utilized. The results covering such important aspects of the HiPIMS discharge as the density evolution of the discharge species, their ionization and excitation, propagation of secondary electrons in the discharge volume, dynamics of velocity distribution of the discharge species, gas rarefaction, etc. are discussed.

Conductive heat transfer in rarefied polyatomic gases confined between parallel plates via various kinetic models and the DSMC method

The conductive heat transfer through rarefied polyatomic gases confined between parallel plates maintained at different temperatures is investigated. The approach is based on three kinetic models namely the Holway, Rykov and Andries models, as well on the DSMC scheme supplemented by the Borgnakke–Larsen collision model. Results are presented for the total as well as for the translational and rotational parts of the heat flux and of the density and temperature fields in a wide range of the Knudsen number and for small, moderate and large temperature differences. The effect of the thermal accommodation at the boundaries is also examined for two diffuse-specular reflection scenarios at the walls. All three kinetic models provide results which are in very good agreement between them and they also compare very well with corresponding DSMC results. Comparisons with experimental results are performed verifying the validity of the simulations. The total heat fluxes of diatomic and polyatomic gases have been found to be about 30%–50% and 50%–75% respectively higher than the corresponding monatomic ones, with the highest differences occurring in the free molecular limit. The translational and rotational temperature distributions (as well as the total temperature) are very close to each other for each set of parameters examined and they are close to the corresponding monatomic ones, when the translational and rotational accommodation coefficients are the same. On the contrary they depart from each other when the two coefficients are different. In most cases as the gas–surface interaction becomes more diffusive the dimensionless total heat flux is monotonically increased. However, for adequately large temperature differences and sufficiently high gas rarefaction levels a non-monotonic behavior has been observed. It has been also found that in polyatomic gases the dimensional heat flux is not necessarily increased as the molar mass is decreased, which is always the case in monatomic gases.

Couette flow and heat transfer between parallel plates in a rarefied gas

The effectiveness of the self-similar interpolation method in its simplest form is demonstrated by solving the problem of a planar Couette flow in a rarefied gas between plates with different temperatures. An analytic representation of the solution is compared with the results obtained by the DSMC method. The most interesting result is the nonmonotonicity of the heat flow and the change in its sign accompanying the modification in the gas rarefaction, i.e., in the Knudsen number Kn.

Method to control deposition rate instabilities—High power impulse magnetron sputtering deposition of TiO2

The authors describe how changes in shutter state (open/closed) affect sputter plasma conditions and stability of the deposition rate of Ti and TiO2 films. The films were grown by high power impulse magnetron sputtering in pure Ar and in Ar/O2 mixture from a metallic Ti target. The shutter state was found to have an effect on the pulse waveform for both pure Ar and reactive sputtering of Ti also affecting stability of TiO2 deposition rate. When the shutter opened, the shape of pulse current changed from rectangular to peak-plateau and pulse energy decreased. The authors attribute it to the change in plasma impedance and gas rarefaction originating in geometry change in front of the magnetron. TiO2 deposition rate was initially found to be high, 1.45 Å/s, and then dropped by ∼40% during the first 5 min, while for Ti the change was less obvious. Instability of deposition rate poses significant challenge for growing multilayer heterostructures. In this work, the authors suggest a way to overcome this by monitoring the integrated average energy involved in the deposition process. It is possible to calibrate and control the film thickness by monitoring the integrated pulse energy and end growth when desired integrated pulse energy level has been reached.

Rarefied gas deceleration in a channel in the case of expansion into a vacuum

The time-dependent problem of the development of a rarefied flow in a plane channel formed by two parallel infinite plates is considered on the basis of a kinetic model. At the initial moment of time the gas at rest occupies half the channel and borders on a vacuum. The effect of gas deceleration at the channel walls is studied as a function of the gas rarefaction degree under the conditions of the diffuse reflection of molecules from the boundary. Emphasis is placed on the calculations of the time dependence of the integral gas mass flux through the boundary separating the gas from the vacuum at the initial moment. The deceleration of the conditional expansion wave front and the conditional front of gas expansion into the vacuum is traced. The kinetic equation is numerically solved using a first-order difference method.

Rarefied gas flow through a slit and channel of finite length due to a large pressure difference. A benchmark problem

The rarefied gas flow through a slit and channel of finite length is presented as a benchmark problem. Computation of gas flow rate and flow field through a slit and channel of finite length has been carried out in case of a large pressure difference in a wide range of gas rarefaction. We used the direct simulation Monte Carlo method based on the majorant frequency scheme. Input and output parameters in computation correspond to parameters of the benchmark problem. A comparison of results in solving this problem obtained by various methods has been made and recommendations for future research prospective have been proposed.

Various Shapes of Plasma Spokes Observed in HiPIMS

A time-resolved analysis of the emission of power impulse magnetron sputtering plasmas reveals inhomogeneities in the form of rotating spokes. The shape of these spokes depends on the target material in a characteristic manner; the peculiar shape of the emission profiles is explained by the localization of the sputtering process as being governed by Ar gas rarefaction and the local dynamics of secondary electrons generation. This general picture is able to explain the observed emission patterns for different target materials as presented.

Gas flow in micro tree-shaped hierarchical network

A lattice Boltzmann model of gas flow in tree-shaped microchannel network is developed and numerically analyzed to investigate the behaviors of gas flow and boundary velocity slip in tree-shaped hierarchical network. The rarefaction effect, multiscale effect and bifurcation effect are all examined and analyzed. The velocity and pressure distributions, Poiseuille number and effective slip length in hierarchical networks are presented. The results indicate that the gas flow behavior in tree-shaped microchannel network is dependent on the rarefaction effect, multiscale effect and bifurcation effect. The boundary slip velocity along the streamwise decreases in a stepwise fashion, but the velocity slip degree owing to rarefaction effect intensifies with increasing branching level. The abrupt rise and fall of slip velocity as well as slight pressure recovery is observed at the bifurcations. In multi-scale tree-shaped hierarchical network, increases in branching level lead to larger Knudsen number, which induce larger effective slip length and smaller Poiseuille number. In addition, the gas rarefaction effects are enhanced when the width exponent of tree-shaped microchannel tends to be smaller in the hierarchical network.