Macroscopic rate equations are formulated for vibrational relaxation in mixtures of CO2 with either N2 or a noble gas. A model is used that assumes the bending and symmetric-stretching modes of CO2 to be in equilibrium with each other and to have a common vibrational temperature. The asymmetric-stretching mode is taken to be described by a different vibrational temperature, which, in the case of CO2−N2 mixtures, is taken to be common with the temperature of the nitrogen vibrational mode. The rate equations are then derived on a phenomenological basis. The resulting phenomenological coefficients can be interpreted in terms of characteristic relaxation times and energy exchange ratios, which are a measure of the relative amounts of energy exchanged by the different vibrational modes in V—V transitions. The equations can be used for any linearized problem. Here they are applied to a spectrophone. The resulting phase-lag equations are used to reinterpret spectrophone data that had been thought to lead to false conclusions. It is shown that the data is in fact compatible with the results from other experiments. Well done and well interpreted spectrophone experiments can possibly yield new information about the energy exchange ratio (and hence the important V—V transitions) for CO2−diluent collisions. It might also be possible to obtain more accurate values for the long V—T relaxation times for CO2 collisions with the heavy noble gases. These possibilities are discussed.
Macroscopic equations are formulated for the nonequilibrium interaction of vibrational and radiative rate processes in CO2. A model for CO2 is used that assumes that the energy levels of each vibrational mode are evenly spaced and that each mode can be assigned a vibrational temperature. The bending and symmetric-stretching modes are, however, taken to be in mutual equilibrium so that they have the same vibrational temperature. Collisional rate equations for the V—T and V—V processes are derived on a phenomenological basis. The resulting phenomenological coefficients are interpreted, with the help of basic knowledge of the microscopic physics, in terms of characteristic relaxation times and parameters measuring the relative amounts of energy exchanged by the various modes during V—V transitions. Radiative transfer equations are developed for the three strongest infrared bands, located in the spectrum at 15, 4.3, and 2.7 μ, by appropriately summing a previously derived microscopic transfer equation. It is found that the absorption coefficient is a function of the kinetic and the vibrational temperatures in a manner that depends on the band in question. The source function, which is also different for each band, depends strongly on the temperature of the vibrational modes involved in the transition and weakly on the kinetic temperature. The rate and transfer equations are then incorporated with the conservation equations of gas dynamics for application to linearized nonequilibrium flows of carbon dioxide gas. As a particularly simple example, a solution for the spectrophone is presented, including expressions for the phase lag in the pressure signal that results from radiative excitation via each of the bands individually. One of these expressions can be used in conjunction with experimental results from other sources to draw conclusions about predominant V—V transitions in CO2. The results of doing this using the 4.3-μ band have been reported previously. The utility of a spectrophone can also be extended by exploiting the possibility of selectively exciting CO2 through the different bands and making use of all the phase-lag expressions. All equations were derived without restriction to room temperature, allowing for possible use of spectrophones at higher temperatures. The approach used to derive the macroscopic rate equations can equally well be applied to other polyatomic molecules.
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