Tandem mass spectrometry (MS/MS): a promising new analytical technique for specific component determination in complex mixtures

Publisher Summary This chapter presents the results of the recent analytical and experimental investigations of heat transfer in rarefied gases. It concentrates on the heat transfer through the electrically neutral nonreacting gases. The effects of ionization, dissociation, etc., that may arise in high-speed high temperature gas flows are not considered. The term “rarefied” means that the molecular mean free path is not small compared to a characteristic dimension . The parameter that describes the degree of rarefaction is the Knudsen number. In defining the Knudsen number, it is important to select the appropriate characteristic mean free path and length. When the Knudsen number is very small, then, in the vicinity of the body, the number of collisions between the molecules is large compared to the number of collisions between the molecules and the body. In this case, the usual continuum concepts are applicable and the Navier-Stokes equations and the Fourier heat conduction law are valid. When the Knudsen number becomes sufficiently large, then the continuum concepts must be modified for calculating the heat transfer. At very high Knudsen numbers where the number of collisions between the molecules and the wall is much larger than the number of collisions between the molecules, the flow is termed “free molecule.”

Heat Transfer in Rarefied Gases

An experimental apparatus has been developed to determine thermal accommodation coefficients for a variety of gas-surface combinations. Results are obtained primarily through measurement of the pressure dependence of the conductive heat flux between parallel plates separated by a gas-filled gap. Measured heat-flux data are used in a formula based on Direct Simulation Monte Carlo (DSMC) simulations to determine the coefficients. The assembly also features a complementary capability for measuring the variation in gas density between the plates using electron-beam fluorescence. Surface materials examined include 304 stainless steel, gold, aluminum, platinum, silicon, silicon nitride, and polysilicon. Effects of gas composition, surface roughness, and surface contamination have been investigated with this system; the behavior of gas mixtures has also been explored. Without special cleaning procedures, thermal accommodation coefficients for most materials and surface finishes were determined to be near 0.95, 0.85, and 0.45 for argon, nitrogen, and helium, respectively. Surface cleaning by in situ argon-plasma treatment reduced coefficient values by up to 0.10 for helium and by ∼0.05 for nitrogen and argon. Results for both single-species and gas-mixture experiments compare favorably to DSMC simulations.

An experimental assembly for precise measurement of thermal accommodation coefficients

Heat flow and temperature and density distributions in a rarefied gas between two parallel plates at rest with different uniform temperatures are analyzed numerically on the basis of the full nonlinear Boltzmann equation for hard‐sphere molecules and the Maxwell‐type boundary condition by a finite difference method where the collision term is computed direct numerically. The accurate results are presented for the case in the density measurement by Teagan and Springer [Phys. Fluids 11, 497 (1968)], where the temperature ratio is 1.326, the value of the accommodation coefficient is 0.826, and the ratio of mean free path to plate spacing (Knudsen number Kn) is 0.0658≤Kn≤0.7582. It is found that there is a considerable difference between the present density distribution and the experimental data. The reason for this discrepancy is also discussed. The accurate numerical results of the linearized problem are also presented for comparison.

Heat flow and temperature and density distributions in a rarefied gas between parallel plates with different temperatures. Finite‐difference analysis of the nonlinear Boltzmann equation for hard‐sphere molecules

For understanding the behavior of a gas close to a channel wall it is important to model the gas-wall interactions as detailed as possible. When using molecular dynamics simulations these interactions can be modeled explicitly, but the computations are time consuming. Replacing the explicit wall with a wall model reduces the computational time but the same characteristics should still remain. Elaborate wall models, such as the Maxwell-Yamamoto model or the Cercignani-Lampis model need a phenomenological parameter (the accommodation coefficient) for the description of the gas-wall interaction as an input. Therefore, computing these accommodation coefficients in a reliable way is very important. In this paper, two systems (platinum walls with either argon or xenon gas confined between them) are investigated and are used for comparison of the accommodation coefficients for the wall models and the explicit molecular dynamics simulations. Velocity correlations between incoming and outgoing particles colliding with the wall have been used to compare explicit simulations and wall models even further. Furthermore, based on these velocity correlations, a method to compute the accommodation coefficients is presented, and these newly computed accommodation coefficients are used to show improved correlation behavior for the wall models.

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Computation of accommodation coefficients and the use of velocity correlation profiles in molecular dynamics simulations

The heat conduction and density distributions were experimentally determined for rarefied gases at rest contained between two unequally heated parallel plates Both argon and nitrogen were used as test gases Particular attention was focused on obtaining measurements in the transition regime where the ratio of plate spacing to mean free path was between 1 and 20 The gas density distribution was measured by observing the luminescence produced by a high‐energy electron beam traversed between the plates The experimental results for argon were compared with the analytical results of Wang Chang and Uhlenbeck, Gross and Ziering, and Lees In computing these results the thermal accommodation coefficient measured in the free‐molecule regime was used with the assumption that its value remained constant over the entire pressure range The average agreement between the heat conduction data and the results of the four‐moment methods of Lees and Gross‐Ziering was about 2%, while the measured density profiles agreed with the results of these analyses within 3% Both the heat conduction and density distribution data differ by ∼10‐20% from the results of Gross‐Ziering's eight‐moment method

Heat transfer and density distribution measurements between parallel plates in the transition regime

A simple plane horizontal layer type apparatus is described for measuring thermal conductivities of gases over a wide pressure range. Experimental results obtained with argon, nitrogen, and air indicate that thermal conductivities and thermal accommodation coefficients can be determined with the apparatus within about 2% accuracies at pressures ranging from free molecule to continuum conditions.

Plane Layer Type Apparatus for Gas Thermal Conductivity Measurements

A thermocouple gauge is described which is capable of indicating pressure in the complete pressure range between 10−3 Torr and atmospheric pressure. The experimental results obtained from a test gauge are presented and found to be in good agreement with analysis. The gauge utilizes the free molecule and transition gaseous heat conduction that exists in a gas contained between the foils of multifoil thermal insulation up to pressures in the 100 Torr range. The resulting pressure variation of the thermal conductivity of multifoil insulation is used to indicate the pressure.

William P. Teagan

Papers

Heat transfer and density distribution measurements between parallel plates in the transition regime

Plane Layer Type Apparatus for Gas Thermal Conductivity Measurements

Multifoil Thermocouple Gauge for Measuring Pressures up to 1 atm