Rotational Collision Number Research Articles

On the rotational collison number for air at elevated temperatures

A detailed review of the experimental data for the rotational collision number Zrot for air, O2 and N2 has been made to finalize a temperature correction for the absorption due to rotational relaxation for incorporation in a draft standard on air absorption being prepared by the Sl−57 Committee on Propagation. Subject Classification: [43]35.20, [43]35.35.

Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam

Accurate measurements of the density distribution in Ar and N2 shock waves have been made in a shock tube for the Mach number range from 1.55 to 9 and 10 respectively by the absorption of an electron beam. A modified absorption law has been used for data reduction. The density profiles were corrected for the influence of shock curvature and density rise behind the shock wave. The measurements in Ar agree to within 1% with those of Schmidt (1969) in the mean range of Ms but give a slightly smaller density gradient for Ms = 9. Comparison with various theories shows very good agreement with Bird's Monte Carlo simulation in the whole Mach number range for a simple repulsive intermolecular force law. Further, the agreement with the Mott-Smith density profile for the same interaction law is also good, and surprisingly is found to be better for lower than for higher Mach numbers. Qualitative agreement is obtained with the solutions of Hicks & Yen for hard-sphere and Maxwell molecules. The Navier-Stokes and BGK solutions are found to differ significantly from the present experiments even for the lowest measured Mach number (1·55), whereas the Burnett equation gives better agreement, especially with respect to the asymmetry of the profiles.The measured N2 profiles agree on the whole with the shock-tube measurements of other investigators but show substantial deviations from the low density wind-tunnel experiments of Robben & Talbot (1966b) for higher Mach numbers. Bird's ‘energy sink model’ (1971) is in agreement with the measured density profiles for a realistic interaction law and a suitable rotational collision number. Rotational relaxation in nitrogen is found to be very fast for all Mach numbers. Consequently the coupling between rotational and translational relaxation is very strong.

Rigid and nonrigid classical rotator models for rotational relaxation in HeH 2

Rotational relaxation times and collision numbers of hydrogen in a bath of He atoms are calculated by a classical trajectory method for a range of temperatures between 300 and 1500 K using three models for the vibrational motion of hydrogen. The first model treats the molecule as a rigid rotator, the second as a classical vibrating rotator and the third as a classical rotator but quantum vibrator with an initial vibrational energy set equal to the zero point of energy of hydrogen. Analysis of the relaxation times obtained from the three models leads to the conclusion that the rigid rotator model is the most suitable one for the classical mechanical calculation of rotational relaxation times of hydrogen.

Classical trajectory study of rotational relaxation of molecular hydrogen: Dependence on the potential surface

Rotational relaxation times and collision numbers of molecular hydrogen are calculated by a classical trajectory method for five temperatures from 300–1500 K using two different potential surfaces. The differences in functional form of the two potentials are examined in order to explain the significant differences in the computed values. Comparisons are made with recent experimental results.

Rotational relaxation in mixtures of tetradeuteromethane with helium, neon, argon and xenon

Sound-absorption measurements have been made in mixtures of CD 4 with He, Ne, Ar and Xe to investigate the effect of the noble gases on the rotational relaxation of CD 4. The measurements were carried out in the pressure range of 100 to 150 torr, at 308 K and a frequency of 3 MHz. The relaxation times and rotational collision numbers obtained show the same tendency as was found in CH 4—noble-gas mixtures. The collision numbers Z rot, defined as the ratio of the rotational relaxation time and the mean time between two elastic collisions, increase with increasing mass of the noble gas. We found the following numbers: Z rot (CD 4CD 4) = 10.0 ± 0.3, Z rot (CD 4He) = 2.6±0.7, Z rot (CD 4Ne) = 4.1±0.6, Z rot (CD 4Ar) = 7.3±0.6, Z rot (CD 4Xe) = 14±3. A comparison between these experimental results and theoretical predictions by the rough-sphere model is given.

Rotational relaxation of molecular hydrogen

The rotational relaxation rate in molecular hydrogen has been determined experimentally between 300 and 1900°K by time of flight analysis of molecular beams from supersonic free jets. Over their common temperature range from 295 to 1073°K our results are in reasonable agreement with the ultrasonic measurements of Winter and Hill which show a rotational collision number Zr between 300 and 400. In terms of momentum transfer collisions Zr is relatively insensitive to temperature. This observation suggests that rotation-rotation transfers play an important role.

Rotational collision numbers and the heat conductivity of nitrogen gas from thermal transpiration measurements to 1250 K

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Transport Properties of a Gas of Diatomic Molecules. V. GPS Calculation of the Rotational Relaxation Time of the Ar–N2 System

The moments of the probability density function for rotationally inelastic scattering of the Ar–N2 system were computed, in Paper XVI of a series on molecular collisions, by both generalized phase shift (GPS) and classical trajectory (CT) methods. In the present paper, it is shown that inclusion of the term of zero order in h/ in a semiclassical expansion of the generalized phase shift modifies the classical limit expressions for the moments. The Ar–N2 system is reconsidered and the first and second moments calculated to the lowest nonzero order in the anisotropy of the interaction potential. The results of this calculation indicate a marked improvement of the first moment over the previous GPS results as compared with the CT results. The development is extended by integrating the moments over the impact parameter and the translational and rotational energies to obtain rotational collision numbers for the Ar–N2 system. These collision numbers are compared with those obtained by classical trajectory methods.

Thermal Creep in Gases

The development of a pressure gradient in a gas-filled capillary due to the application of a temperature gradient is known as thermal transpiration. In the near-continuum limit (small Knudsen number) the mechanism for the transpiration effect is a creeping motion of the gas in a thin layer adjacent to the surface. Measurements performed in the near-continuum limit are compared with a number of theoretical calculations for the thermally induced creep velocity. The experimental data for He, Ne, Ar, Kr, and N2 agree best with the recent theoretical work of Loyalka and indicate little or no dependence on gas type, in contrast with another recent theory which indicates a marked dependence on the thermal accommodation coefficients. In addition, the effect of the thermal creep coefficient upon the evaluation of rotational collision numbers from thermal transpiration measurements is discussed.

Viscosity of Carbon Dioxide in the Temperature Range 25–700°C

The paper presents new relative measurements of the viscosity of carbon dioxide at a pressure P=1 atm and in the temperature range 25–700°C. The accuracy of the reported viscosity data is estimated as ±0.1% at 25°C and ±0.3% at 700°C. The rotational collision number for carbon dioxide is computed with the aid of the kinetic theory for polyatomic gases and reliable thermal conductivity data.

Vibrational and Rotational Relaxation in Ammonia

Ultrasonic absorption has been measured in ammonia in the temperature range 300–773°K over the f/p range 1–100 MHz/atm. This data was analyzed to obtain vibrational and rotational relaxation times and collision numbers. The vibrational collisions numbers are unusually small and decrease only slightly with increasing temperature. The maximum in the collision number predicted by Shin's theory for polar molecules is not observed. The temperature dependence of the rotational collision numbers is in good agreement with the classical calculation of Zeleznik for polar diatomic molecules.

17-Moment Theory of Sound Propagation in Polyatomic Gases

The problem of combined translational and internal relaxation of sound waves in polyatomic gases is studied using the 17-moment approximation. When applied to the sound problem, the moment equations, which are valid for any number of internal degrees of freedom, yield a generalized complex matrix eigenvalue equation which is solved numerically for the absorption coefficient and propagation speed as a function of the rarefaction parameter (the approximate ratio of collision frequency to sound frequency). The physical parameters in the equations are the self-diffusion coefficient (assumed the same for each internal mode), the internal relaxation times, and the internal specific heats. Our solutions for the combined absorption for the case of a single internal mode are compared to those obtained assuming the total absorption is the sum of that due to the translational and internal effects separately, and to that obtained by using the combination rule of Greenspan. Comparison is also made between the combined dispersion calculated by the 17-moment method and the Greenspan rule. In addition, absorption curves are calculated for the case of two internal degrees of freedom for various combinations of internal collision numbers. When applied to rotational relaxation in N2 our theory yields, for a rotational collision number of 5.26, good agreement with experiment over the range of values of the rarefaction parameter for which a continuum theory is expected to be valid.

Temperature Dependence of Rotational Collision Numbers from Thermal Transpiration

The temperature dependence of the rotational collision numbers for O2, N2, CO, and CO2 was investigated in the range 475–676°K by the thermal transpiration technique with the use of a novel apparatus design. In all cases the collision number was found to increase with temperature. For O2 and N2, where some comparison with theory is possible, the experimental rate of increase with temperature was found to be faster than the predicted behavior. The results for CO and CO2 are in general agreement with other transpiration measurements and with acoustic absorption results which were obtained at lower temperatures.

Rotational Relaxation in Polar Gases. III. Molecular Dynamics

A 50 molecule sample in contact with a heat bath of similar molecules was used as a model to calculate the rotational collision numbers, Zrot, for HCl and DCl at 300 and 500°K, by the method of molecular dynamics. The mean rotational energy of the sample exhibits an exponential approach to a steady state value; however, there was considerable scatter about the exponential curve. The results for Zrot generally agree with previous theoretical calculations. They are intermediate to experimental acoustic data and the earlier perturbation results.

The rotational relaxation time of atom-diatom systems in the dominant coupling limit

The rotational relaxation time, τ rot, and collision number, Z rot, have been calculated for a gas consisting of a small fraction of nonpolar and rigid diatomic molecules in a heat bath of atoms. The basis for the calculation is a kinetic theory expression for Z rot, derived by Mason et al. following Wang-Chang and Uhlenbeck, and the “phase space” theory of Light et al., going to the classical-mechanical limit. Z rot is found to be a function of two dimensionless parameters, the reduced moment of inertia β = Г (μσ 2 12) and the reduced temperature T ∗ = T ( ε 12k ) with usual symbols for mass and Lennard-Jones interaction parameters. Partial resemblance with results for the rough-sphere model is demonstrated.

Ultrasonic Absorption in Hydrogen Sulfide

Ultrasonic absorption has been measured in H2S in the temperature range 300° to 683°K. This data was analyzed to obtain vibrational and rotational relaxation times. The vibrational collision numbers seem to increase with temperature from 300° to 473°K and then decrease with temperature. This behavior can be explained by the v-r theory of Shields and Burks. The rotational collision numbers compare favorably with thermal-transpiration measurements.

Ultrasonic Absorption in H2S

Ultrasonic absorption has been measured in H2S in the temperature range 300°–683°K. These data were analyzed to obtain vibrational and rotational relaxation times. The vibrational collision numbers seem to increase with temperature from 300° to 473°K and then decrease with temperature. This behavior can be explained by the v-r theory of Shields and Burks. The rotational collision numbers compare favorably with thermal transpiration measurements.

Thermal separation of the ortho and para forms of H 2 and D 2

The kinetic theory of non-spherical molecules is shown to account for the experimental observations on thermal diffusion in pH 2 − oH 2 and oD 2 − pD 2 mixtures, in terms of measured rotational collision numbers.

Rotational Collision Numbers of N2, O2, CO, and CO2 from Thermal Transpiration Measurements

Thermal transpiration results which were determined at an (assumed) characteristic temperature of 504°K are reported for all of the noble gases and for N2, O2, CO, and CO2. The helium data are found to be anomalous when viewed in terms of the dusty-gas model for thermal transpiration. Application of the model in the zeroth differential approximation yields the following rotational collision numbers for the polyatomic molecules: N2, 6.0; O2, 2.2; CO, 1.3; CO2, 1.9.

Rotational Relaxation in Polar Gases. II

A classical calculation of polar gas rotational relaxation times is carried out based on the volume viscosity definition of the relaxation time. The calculation demonstrates that the volume viscosity relaxation time agrees with the relaxation time based on an energy relaxation equation through third order in perturbation. An examination of thermal conductivity data shows that the extraction of rotational collision numbers from such measurements is highly suspect. On the other hand, it might be possible to determine internal diffusion coefficients from thermal conductivity measurements when rotational collision numbers can be obtained from other sources.