Tangential Momentum Accommodation Coefficient Research Articles

Theory of the spinning rotor gauge in the slip regime

The spinning rotor gauge has found increasing use in ultrahigh vacuum measurements, but it also could be attractive in higher pressure regimes provided an accurate theory were available for interpretation of the measurements (that is, the torque or the deceleration rate as a function of the pressure). In this article we numerically solve the Stokes equation with slip boundary conditions for the rotor geometry by using a Green’s function based approach. We verify that the numerical technique provides accurate results, and then we discuss how the rotor gauge can be used for measurements of the viscosity, the velocity slip coefficient, and the tangential momentum accommodation coefficient. A companion article describes experimental measurements and results for several gases.

Measurements of the tangential momentum accommodation coefficient in the transition flow regime with a spinning rotor gauge

Gas-surface interactions which are described with the accommodation coefficients play an important role in the determination of the mass, momentum, and thermal energy transport in rarefied gas flows, aerosol mechanics, and vacuum technology. While the thermal accommodation coefficient has been extensively studied, the investigations of the other coefficients have been limited, partly because of the difficulties that are associated with the available theories and control of surfaces. To further understand the tangential momentum accommodation coefficients, experimental investigations of the rotational motion of a freely suspended sphere in a variety of gases and over a range of pressures were undertaken. It was found that the experimental results are generally well described by recent theoretical works that have provided numerical solutions of the linearized Boltzmann equation. Further, the theory can be used to interpret experimental data in terms of the tangential momentum accommodation coefficient, α over the entire range of the Knudsen number. The values of α are near 1 for most of the gas types and vary only slightly with the pressure.

The theory of the rotating disc vacuum gauge

The rarefield gas dynamic of momentum transfer from a spinning disc to a stationary coaxial parallel disc is considered in the absence of molecular collisions with a surface tangential momentum accommodation coefficient of unity. The analysis is performed for the case of low and high rotation speeds, with an approximation derived for the intermediate case. Analytical studies are complemented by simulation using a Monte Carlo technique to give accurate results throughout the domain. The results are in excellent agreement with detailed experiments. It is concluded that the resulting rotating disc vacuum gauge can be used as an absolute instrument for measuring pressure in high vacua.

Experiments on surface light-induced drift for various systems

Abstract Surface light-induced drift of a low-pressure gas results from velocity-selective optical excitation combined with state-dependent molecule-surface interaction. This effect has been studied for CH 3 F and OCS, rovibrationally excited by a CO 2 laser, interacting with various surfaces. For the R(4, 3) transition of 13 CH 3 F, an increase in tangential momentum accommodation coefficient α upon excitation is found ranging from δα = 1.0 × 10 -3 for stainless steel to δα = 14 × 10 -3 for LiF(100) at 295 K. For this transition, the effect was also studied as a function of temperature for a quartz surface, resulting in a 40% decrease of δα as the temperature is raised from 300 to 700 K. Experiments for the P(5) transition of OCS yield δα = -0.53 × 10 -3 on a quartz surface at 295 K.

Application of a satellite aerodynamics model based on normal and tangential momentum accommodation coefficients

Tangential and normal momentum accommodation coefficients are reviewed as a parametrization of the gas-surface interaction for modelling aerodynamic forces on artificial Earth satellites. By reference to experimental data and other studies, a simple empirical relationship for the normal momentum coefficients, σ', is deduced whilst the tangential coefficient, σ, is taken to be invariant with the angle, ξ, between the incident stream and the surface normal. Parameters within these coefficients are estimated by least-squares reduction of orbital elements of ANS-1 (1974-70 A). Derived results are σ = 0.93 and σ' = 1.11–0.17sec ξ, yielding a drag coefficient for a sphere of 2.05 ± 0.03, which is less than 10% below the accepted values of 2.2 for heights near 300 km.

Variations in the normal and tangential momentum accommodation coefficients from analysis of atmospheric lift and drag forces on ANS-1 (1974-70A)

Abstract Studies of aerodynamic lift and drag in hyperthermal free molecular flow regimes usually adopt Schamberg's model for gas-surface interaction, utilising the thermal accommodation coefficient. Most authors assume near-diffuse reflection characteristics with constant re-emission speed for all angles of incidence. For modelling atmospheric forces a more natural approach is to utilise normal and tangential momentum coefficients, σ1 and σ respectively. Experimental laboratory data has yielded qualitatively the dependence on the angle of incidence which to good approximation can be represented as ω ≜ ω ′ 0 , ω 1 ≜ ω 0 1 − ω 1 1 sec ϵ i where σ0, σ10 and σ1l are constants and ξi is the angle subtended between the incident flow and the surface normal. Adopting these relationships the effects of atmospheric lift on the satellite inclination, i, and atmospheric drag on the semi-major axis, a, and eccentricity, e, have been investigated. Applications to ANS1 (1974-70A) show that the observed perturbation in i can be ascribed to non-zero σ1l whilst perturbations in a and e produce a constraint equation between the three parameters.

Summary Abstract: Electronic factors in thiophene adsorption and hydrodesulfurization on MoS2 surfaces

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Motion of a spherical particle in a rarefied gas. Part 1. A liquid particle in its saturated vapour

The results of a theoretical investigation of the low-speed motion of a volatile spherical particle in its saturated vapour at arbitrary values of the Knudsen number, evaporation coefficient and tangential momentum accommodation coefficient are presented. The problem is solved on the basis of the Bhatnagar, Gross & Krook (1954) linearized kinetic equation with the model collision integral. The variational method developed for the solution of the axisymmetric problems (Cercignani & Pagani 1968) is employed to calculate the drag. Phase changes on the particle surface have been shown to reduce the drag by an order depending on the Knudsen number. Incomplete accommodation of molecules colliding with the particle also results in the reduction of the drag over the whole range of Knudsen numbers.

A kinetic analysis of thermal force on a spherical particle of high thermal conductivity in a monatomic gas

A linearized version of the hierarchy kinetic model equation was solved by applying a singular perturbation method and the half-range Hermite polynomials. The solution retains correct results up to O(Kn2) and suggests that, if the thermal conductivity of the spherical particle is infinite and the impinging molecules suffer complete energy accomodation at the surface, the thermal force of O(Kn2) disappears (or thermal force is very small) in the near continuum regime. The present results also indicate that the thermal force is sensitive to the variation in the energy accomodation coefficient for the accommodation coefficient of tangential momentum nearly equal to unity. With the effect of such accommodation coefficients, the present results are used to explain the existing experimental results from the viewpoint of kinetic theory as long as the Knudsen number is small.

Energy and momentum accommodation coefficients on platinum and silver

Acoustical measurements of energy (EAC) and tangential momentum accommodation coefficients (TMAC) indicate that stable and reproducible Pt and Ag surfaces are obtained by heating in a vacuum. EAC and TMAC values are given for He and Ne on the heat-cleaned Pt and Ag surfaces and for these gases on Pt and Ag surfaces after exposure to various adsorbent gases. AC values are also given for the various adsorbent gases on themselves on the heat-cleaned Pt and Ag surfaces.

Acoustical measurement of energy and momentum accommodation coefficients on polycrystalline platinum

The acoustical method of measuring energy (EAC), and tangential momentum (TMAC) accommodation coefficients [F. Douglas Shields, J. Chem. Phys. 62, 1248–1252 (1975)] has been used to measure the accommodation coefficients of Ne and He on vacuum flashed Pt and on Pt after exposure to O2, N2, CO, and CO2. Vacuum flashing the Pt at 1400 K in the presence of misch metal getter resulted in a surface that was reproduced a number of times after exposure to various adsorbants. The combined value of TMAC + EAC for this surface was 0.80 ± 0.04 for Ne and 0.64 ± 0.04 for He. These values are significantly greater than values measured earlier in a similar way for W [F. Douglas Shields, J. Chem. Phys. 72, 3767 (1979); 76, 3809 (1982); 76, 3814 (1982)]. Exposing the flashed surface to O2 raised the combined values of TMAC + EAC to 1.28 for Ne and 1.00 for He. Flashing the surface at 1100 K removed some of the O2 and flashing at 1400 K restored the original AC values. In contrast to this, exposure to N2 did not change th...

Energy and tangential momentum accommodation coefficients on gas covered tungsten

The sum of the energy (EAC) and tangential momentum (TMAC) accommodation coefficients has been measured acoustically for Ne on W exposed to the following adsorbates: CO, CO2, O2, N2, H2O, and D2; for He on W with O2 and D2 as adsorbates; and for each of these adsorbates on itself on W. An effort has been made to infer separate values of EAC and TMAC from the measured values of their sum. Good agreement is obtained with EAC values obtained from thermal conductivity cell measurements if TMAC is assumed to have a value of 0.75 for He and Ne on all the gas covered surfaces, and a value of 1.0 for all the adsorbates except D2 on itself on W. The acoustical method which was used has the capability of determining AC values under gas dynamic conditions where the surface and the gas are at essentially the same temperature. For CO2, since the acoustical measurments were made at frequencies far above the vibrational relaxation frequency, the EAC value obtained is for the translational and rotational energy only. The measurements in D2 reveal rotational relaxation.

Energy and tangential momentum accommodation coefficients of Ne and He on different vacuum flashed tungsten surfaces

The acoustical method has been used to determine energy and tangential momentum accomodation coefficients on three different polycrystalline tungsten surfaces. To obtain the second surface, the first was highly oxidized and then cleaned by vacuum flashing at 2150 K. The third surface, manufactured by the same chemical deposition process as the first, was specified as having half the microscopic roughness of the first. Photographs made with the scanning electron microscope indicate that though the oxidation dramatically increased the roughness of the surface, this roughness was removed in the flashing process. The electron micrographs also showed that flashing dramatically increased the grain size in the third surface. This third surface, though supposedly smoother, was found to have larger AC values than the first. This has been attributed to a shorter accumulated flashing time at the time the measurements were made and, therefore, smaller grain size. The microscopic roughness does not appear to be an important factor in determining AC values after the surface is flashed. The problem of simultaneously determining energy and tangential momentum accomodation coefficients is discussed.

More on the acoustical method of measuring energy and tangential momentum accommodation coefficients

Additional measurements of the energy (EAC) and tangential momentum accommodation coefficients (TMAC) of He and Ne on polycrystalline tungsten have been made using an acoustic technique previously reported. The measurements were made after the tungsten surface had been exposed to the atmosphere and after it had been flashed in a vacuum at 1240, 1460, 1770, and 2000 K. Three stable, reproducible surfaces were detected. These have been associated with an atomic oxygen film, upper molecular oxygen film, and an unknown film produced by atmospheric exposure. Comparison with molecular beam scattering experiments indicates that TMAC corresponds to the fraction of molecules scattered diffusely from polycrystalline surfaces and EAC to the diffuse fraction from single crystal surfaces.

Satellite drag coefficients calculated from measured distributions of reflected helium atoms

The primary objectives of this study were to obtain the necessary data and develop a calculation procedure that would facilitate predicting the atmospheric-helium contribution to the drag of a satellite having a predominantly convex exterior. Molecular-beam techniques were used to measure, for several incidence angles, the spatial and energy distributions of 7000 m/s helium atoms scattered from a 6061-T6 aluminum plate and an anodized 1235-0 aluminum surface. From these measured distributions, tangential and normal momentum accommodation coefficients were calculated as functions of incidence angle. Using these calculated accommodation coefficients, one can predict drag coefficients for satellites having predominantly convex exteriors. For spherical satellites, drag coefficients of 2.64 and 2.62 were predicted for the subject surfaces.

Thermal transpiration in a circular capillary with a small temperature difference

The results of an experimental investigation of the thermal transpiration effect (the thermomolecular pressure difference or t.p.d. effect) in a single glass capillary with a length-to-radius ratio of 250 are presented. The temperatures of the gas in the ‘cold’ and ‘hot’ chambers were 273·2°K and 293°K, respectively. A modified relative method has been used. To measure the t.p.d. effect, a capacitance differential digital micromanometer with sensitivity 4·5 × 10−5N/(m2Hz) was used. The gases investigated were He, Ne, Ar, Xe, H2, D2, N2, CO2, CH4 and SF6. It was discovered that in the intermediate flow regime the thermal-creep flow rate does not depend on the (non-isothermal) tangential momentum accommodation coefficient. From the experimental data on the viscous slip flow regime, the Eucken factors and the accommodation coefficients are calculated. For inert gases the Eucken factor is found to be equal to 2·5 within the experimental error, while the accommodation coefficients differ significantly from unity.

Tangential momentum accommodation on smooth gold and silver thin film surfaces

Tangential momentum transfer occurs between a moving solid surface and a stationary free molecular gas, and can be characterized by a tangential momentum accommodation coefficient σ. Experimental measurements have been done to evaluate these coefficients for helium, argon and nitrogen on gold and silver surfaces. The moving surface was a magnetically suspended rotating sphere and momentum transfer was monitored as an angular deceleration due to drag. Clean gold and silver surfaces were obtained by sublimation onto the sphere substrate. For thin silver layers σ varied from 0.92 to 0.98 and was insensitive to gas molecule species. For thick films, σ values were less consistent; however some lower values were found down to 0.80 for nitrogen on gold.

Experimental investigation of rarefied gas flow in different channels

An experimental investigation of flows of a large number of inert and polyatomic gases in various channels, a non-ideal orifice, flat slits with different surface roughnesses and wall materials, capillary packets with molten walls and a capillary sieve, has been made.The unsteady flow method and a highly sensitive capacitance micromanometer were used (the sensitivity being ∼ 3 × 10−4N/m2Hz). Measurements were made in a range of Knudsen numbers 5 × 104–10−3at ∼ 293 °K, and some measurements for flow through a non-ideal orifice were carried out at 77.2°K.It was found that, both in the viscous slip-flow and free-molecule regimes for the channels with molten walls, the experimental conductivities were higher (by ∼ 15%) than theoretical ones calculated assuming diffuse molecular scattering by the walls. We have also observed that the channel conductivity essentially depends on the channel surface roughness and on the kind of gas. The larger the roughness height, the lower the conductivity. From the experimental data the tangential momentum accommodation coefficients were calculated.

Poiseuille flow at arbitrary Knudsen numbers and tangential momentum accommodation

A Poiseuille-flow problem in a cylindrical capillary in the whole range of Knudsen numbers with incomplete tangential momentum accommodation of molecules incident on the wall has been worked out. The linear non-homogeneous integral equation for the macroscopic gas velocity flow has been solved by the Bubnov-Galerkin method. For a limited range of Knudsen numbers, generally known results have been obtained.An experimental investigation of the rare gases helium, neon and argon in the range of Knudsen numbers 103−10−3 has been made on packets consisting of 10 and 100 glass capillaries with molten walls. Comparison of theoretical and experimental data enables us to define both slip constants and tangential momentum accommodation coefficients. In the free-molecule flow regime the accommodation coefficients are 0·935, 0·929 and 0·975 for helium, neon and argon, respectively. In the viscous slip-flow regime these coefficients are equal to 0·895, 0·865 and 0·919, respectively. This difference in the tangential momentum accommodation coefficients is, most probably, due to the variable density of adsorbed molecules coating the capillary wall. Gas viscosity coefficients which coincide with those of Kestin within 0.5% have also been calculated. Argon was used as the calibrating gas.

On the motion of small spheres in gases IV. Diffusion coefficient of porous membranes

The formalism for scattering by spherical particles has been used for a study of the diffusion coefficient and separation efficiency of the porous membranes used in separating isotopes and gas mixtures. The membrane, or barrier, is replaced by the randomly dispersed sphere model, thereby enabling the ideas developed in earlier papers of this series to be employed. Calculations are made in the Knudsen régime, and from an asymptotic solution to the Boltzmann equation for gas flow in the barrier an expression is obtained for the diffusion coefficient in terms of an average over the solution of a certain integral equation whose kernel is determined by the barrier properties. The integral equation is solved by pertubation and variational methods, and the results indicate that, of the conventional gas-surface interaction parameters, it is the tangential momentum accommodation coefficient which is most effective in determining barrier efficiency. The energy accommodation enters only in a minor fashion. In general, it is found that the larger the tangential coefficient, the smaller is the diffusion coefficient, whilst the energy accommodation acts in the opposite sense although to a smaller extent. The limitations of the `dusty-gas' model are stressed by comparison with exact results.