Kinetics of the deactivation of the vibrations of highly excited oscillators in an inert gas medium,taking account of spontaneous radiation

In the diffusion approximation, the article discusses the kinetics of the process of deactivation of the vibrations of radiating anharmonic and harmonic oscillators in an inert gas medium. Limiting solutions are given for the purely radiational deactivation of a classical Morse oscillator and of a harmonic oscillator. It is shown that, with an increase in the effect of spontaneous radiation, the role of the anharmonic character of the vibrations in the process of deactivation increases; the initial (or arbitrary) distribution relaxes more slowly the higher its energy level, i.e., the greater the effect of the anharmonic character of the vibrations. The results are of importance for systems with a considerable population of the upper vibrational levels of the molecules, which may arise as a result of a chemical reaction or by the optical pumping of a gas.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 62–67, July–August, 1972.The author thanks N. N. Magretova for carrying out the numerical calculation.     

Diffusion equation in the theory of vibrational relaxation of diatomic molecules

A kinetic equation is obtained for the distribution function of anharmonic oscillators with respect to the vibrational energy; it enables one in the diffusion approximation to describe the vibrational relaxation of diatomic molecules in a medium of inert gas when there is a weak interaction between the oscillators and a thermal bath. The main difference from the equation for harmonic oscillators is in the appearance in the diffusion coefficient of an adiabaticity function that characterizes the variation of the adiabaticity factor because of the anharmoni-city of the vibrations. It follows from the form of this function that the greatest difference between the relaxation of anharmonic and harmonic oscillators is to be expected in the case of adiabatic interaction of oscillators with particles of the inert gas.     

Vibrational-translational relaxation of anharmonic oscillators at low temperatures

An approximate analytic solution is found to the problem of the vibrational-translational relaxation of anharmonic oscillators at translational temperatures which are small compared with the energy difference between adjacent levels of the oscillator. The deviation of the obtained distribution from the Boltzmann distribution in the relaxation process is analyzed. A study is made of the behavior of the vibrational energy near equilibrium at temperatures such that dissociation has only a small effect on the rate of vibrational relaxation.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 3–8, March–April, 1976.The author wishes to thank M. B. Zheleznyak and A. Kh. Mnatsakanyan for a useful discussion of the work.     

Analysis of Nonequilibrium Dissociation Kinetics in a Boundary Layer Using Various Reaction Models

Values of the nonequilibrium macroscopic reaction rate for a nonisothermal boundary layer of a monatomic diluent gas are calculated using a number of models for thermal dissociation of diatomic molecules — anharmonic Morse oscillators. Analysis is performed for conditions where the diffusive transfer of excited molecules has a significant effect on the population of their upper vibrational levels, which does not only amount to change in vibrational temperature. Under the joint influence of diffusive transfer of molecules, vibrational exchanges, and reactions involving vibrationally excited particles, the local vibrational distribution functions are substantially nonequilibrium. The kinetic models considered take into account the possible contribution of the energy of molecular translational and rotational degrees of freedom to the energy required to overcome the reaction threshold. The effect of multiquantum vibrational—translational exchanges on the distribution of dissociating molecules in their upper vibrational levels is taken into account approximately.     

Vibrational relaxation of diatomic molecules in a non-Boltzmann thermostat

The action of resonance IR laser radiation on a molecular gas leads, at high-power absorption intensity, to a breakdown in the equilibrium (Boltzmann) energy distribution in the internal degrees of freedom [1]. Under realistic conditions, molecular gases usually are (due to small amounts of impurities or isotopic components) multicomponent systems. In this case resonance IR laser radiation (or other methods of selective action), disturbing the distribution function of the primary gas, does not interact directly with impurities. The problem thus arises of determining the distribution function of the impurity gas interacting with the nonequilibrium (non-Boltzmann) thermostat. The present paper, devoted to the solution of this problem, treats the distribution function of harmonic oscillators A, consisting of a small amount of impurities in a system of harmonic oscillators B with given nonequilibrium distribution functions of vibrational energy. The behavior of a system in a nonequilibrium thermostat was first considered in [2, 3] where, as well as in [4, 5], it was shown that in a non-Maxwellian thermostat with a small amount of harmonic oscillator impurities, a Boltzmann distribution in harmonic oscillator vibrational energies is established under stationary conditions, with a temperature differing from the gas-kinetic temperature of the thermostat, defined in terms of the mean-square velocity. The behavior of a small amount of impurities (heavy monoatomic particles and harmonic oscillators) in a non-Maxwellian thermostat of a light gas was further investigated in [6–8]. Unlike the papers mentioned, the present one considers the behavior of a small amount of harmonic oscillator impurities in a thermostat with a Maxwellian velocity distribution and with a nonequilibrium (non-Boltzmann) distribution in vibrational energies.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1978.     

Vibrational distribution functions and relaxation rate in anharmonic-oscillator systems

Analytical expressions were derived for the vibrational distribution function in a system of anharmonic oscillators under conditions where the supply of vibrational energy considerably exceeded the equilibrium value. Distribution was found by considering the effect of vibrational-vibrational and vibrational-translational energy exchange, as well as spontaneous radiative transitions. Analytical expressions were also obtained for the relaxation rate of vibrational energy. It was shown that where there is a strong deviation from equilibrium this rate can significantly exceed the corresponding value for a model of harmonic oscillators and is determined by the probability of vibrational-vibrational exchange in the molecules.     

Quasiequilibrium model of the kinetics of coupled modes of CO2 molecules

The correct allowance for the influence of anharmonicity in the vibrational spectrum of CO₂ on the level distribution of molecules under nonequilibrium conditions, when the vibrational temperature departs significantly from the gas temperature, has become especially urgent in connection with obtaining generation on a number of long-wavelength transitions of CO₂ molecules [1, 2]. The shifts in the levels of coupled modes (symmetric and deformation) are due mainly to Fermi resonance and can reach a considerable value, comparable with the gas temperature even for low levels. In [3] the main features of the quasisteady level distribution of coupled modes were clarified within the framework of the Treanor model of vibrational kinetics. The influence of the ascending flux of quanta, excited by VV exchange under nonequilibrium conditions, on the vibrational distribution was considered in [4–6]. In the present paper we propose a quasiequilibrium model of CO₂ kinetics, obtained without presuming quasisteadiness of the ascending flux of quanta, and making it possible, in contrast to [3–6] to describe the dynamics of the variation of the distribution of molecules among multiplets as a result of processes of VV exchange and VT relaxation between multiplets, with allowance for possible processes of pumping by outside sources. With a Boltzmann population distribution within the multiplets, having the translational temperature of the gas, the problem of studying relaxation in coupled modes is reduced to the equations for an effective anharmonic oscillator with levels corresponding to the multiplets of CO₂ molecules. In this case the levels of the effective oscillator are degenerate with a multiplicity equal to the number of levels in the corresponding multiplet, and they have an anharmonicity constant dependent on the gas temperature. The population distribution of the effective oscillator can be studied by methods developed for the investigation cf a one-mode anharmonic oscillator. The proposed quasiequilibrium model was used for a numerical calculations of the temporal evolution of the distribution function of CO₂ molecules over the levels of coupled modes under the conditions of an extremely maintained discharge.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 16–22, May–June, 1986.     

Nonequilibrium dissociation of diatomic molecules in flows with convective and diffusive particle transport

The nonequilibrium effects in the kinetics of the thermal dissociation which occurs in a streaming gas of diatomic molecules are investigated. Expressions are obtained for the macroscopic reaction rate and the vibrational energy distribution of the molecules, taking into account the influence of the gas motion. Cases of flows with convective and diffusive particle transport are considered. The dissociating molecules are simulated by cutoff harmonic oscillators. The vibrational kinetics is described in the framework of the so-called diffusion approximation.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 147–153, November–December, 1985.     

Relaxation of anharmonic molecules

The inclusion of anharmonic effects is important in vibrational population inversions in CO-lasers [1, 2], in relaxation processes in jets [3], in thermal dissociation [1], in the kinetics of chemical reactions with high thresholds [4], etc. Usually these effects are studied by including anharmonic corrections to the kinetic constants in the discrete model of single-quantum transitions or in the diffusion approximation [1, 2]. In [5] a method was given of solving the relaxation equations fro arbitrary forms of the rate constants and the spectrum of the molecule. The method is valid when the ratio of the population densities of neighboring levels varies smoothly with quantum number. It was shown in [5] that this approximation can be used to construct analytical solutions for a wide class of problems. In the present paper the method of [5] is extended to the case of equations with variable coefficients. The properties of the solutions for VT-relaxation of anharmonic molecules are analyzed, and the inclusion of sources is considered. A simple method of taking into account multiple-quantum transitions is given, as well as an extension of the method to an arbitrary mixture of gases. The population densities are calculated and the possibility of using our solutions in relaxation gas dynamics is discussed.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, No. 3, pp. 22–31, May–June, 1986.     

Relaxation of the symmetric vibration mode of the CO2 molecule

The applicability of the Landau-Teller energy-relaxation equation of a harmonic oscillator is verified for the CO₂ molecule in which there is Fermi resonance. It is shown that the distribution over the split levels of the symmetric mode formed by vibrational exchange processes and transitions within multiplets is analogous to the Treanore distribution for a singlemode anharmonic oscillator.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 8–17, May–June, 1975.     

Kinetic equations for vibrational relaxation in a mixture of polyatomic gases

Kinetic equations are derived for the relaxation of the vibrational energy in a mixture of polyatomic gases, which are ones with molecules simulated by harmonic oscillators. The most general case is envisaged, where the energy relaxation occurs not only via vibrational-translational transitions but also via multiquantum vibrational exchange involving an arbitrary number of vibrational modes. The analysis also incorporates the possible degeneracy of each mode when the molecules colliding are the same. An expression is derived that extends previous results [1–6] and that relates the vibrational temperatures in the case of quasiequilibrium. Equations are derived for the vibrational relaxation for the CO₂-N₂ case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 29–37, November–December, 1972.We are indebted to L. A. Shelepin for valuable discussions on the results.     

Thermal effects accompanying nonresonant vibrational exchange

Calculation has been made of the thermal effects attending nonresonant vibrational exchange in a molecular gas in a nonequilibrium state. Study has been made of the binary mixture, modeled as a set of harmonic oscillators of various frequencies. Vibrational exchange, the most rapid relaxation process occurring in the system, was assumed to completely determine the distribution of vibrational energy. It is shown that nonresonant vibrational exchange can lead to either heating or cooling in nonequilibrium states of the gaseous mixture. Calculation has been made of the amount of thermal energy liberated or absorbed in these processes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 20–23, March–April, 1975.The author would like to thank N. N. Sobolev for his interest in this work and for his valuable advice concerning it.     

Thermal dissociation of diatomic molecules in a nonisothermal two-temperature boundary layer

Nonequilibrium thermal dissociation in a nonisothermal boundary layer in a mixture of Morse anharmonic oscillators — molecules of a diatomic gas and its atoms — is considered within the framework of the ladder mechanism. The local nonlinear nonequilibrium corrections to the two-temperature macroscopic dissociation rate, which depend, in particular, on the translational and vibrational temperature gradients and the degree of dissociation, are determined.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 191–201, March–April, 1996.     

Physicochemical Model of Hypersonic Rarefied Gas Flow past Bodies

The effect of the internal molecular degrees of freedom on the flow field and heat transfer in hypersonic rarefied gas flow past a cylinder or sphere is investigated using the direct statistical simulation (Monte-Carlo) method. The variable-diameter rough spherical molecule model (VRS-model) is generalized to include the case of energy exchange between the translational and vibrational degrees of freedom. The interaction between diatomic molecules with allowance for vibrational degrees of freedom is simulated as the interaction of classical or quantum-mechanical harmonic and anharmonic oscillators in the external force approximation. A model of the dissociation of a diatomic gas is proposed.     

Dissociation of anharmonic molecules by means of high-power infrared emission

The kinetics of nonequilibrium molecular dissociation when vibrations are excited by high-power infrared emission is investigated for a model of anharmonic oscillators. The case when exchange of vibrational quanta during collision with molecules in the lower states plays a fundamental role in the formation of the vibratory distributionfunction at the upper level is analyzed. Dependences of the “vibration temperature” and the rate constant for nonequilibrium dissociation, as a function of the optical pumping probability are obtained for different pumping conditions. The results are compared with similar calculations for a harmonic model.     

Effect of vibrational excitation of molecules on the velocity of sound in a high-temperature diatomic gas

A formula for the velocity of sound, which is valid not only for barotropic gases, is derived on the basis of methods of the kinetic theory of gases. This formula is specified for various stages of relaxation of a high-temperature diatomic gas in the approximation of the model of anharmonic oscillators. A dependence between the populations of vibrational levels of molecules and the velocity of sound is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 28–34, May–June, 2008.     

Nonlinear stabilization of unstable acoustical vibrations in a bounded heat-evolving medium

The working process in many power units, taking place with the evolution of energy, under determined conditions is acoustically unstable in a linear approximation. The problem of determination of the amplitudes of the unstable waves, set up as a result of the pumping of energy from the unstable mode to the damping mode with their linear interaction is of practical interest. In this paper equations are derived for the fully established amplitudes of plane acoustical vibrations in a three-wave approximation, taking account of boundary impedances, breaking down the internal resonance of the acoustical overtones excited. The discussion regards a high-temperature heat-evolving gas, whose general stability conditions were formulated in [1] and discussed also in [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 34–41, November–December, 1978.     

Gas-dynamic equations involving vibrational relaxation

We derive the gas-dynamic equations in the Navier-Stokes approximation for weak excitation of molecular vibrational states. We determine the distribution function for the density of the numbers determining occupancy of the vibrational states of the molecules. We show that the relaxational pressure is proportional to the deviation of the vibrational energy density from its local-equilibrium value for the temperature of the translational and rotational degrees of freedom of the molecules.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 8–17, July–August, 1972.In conclusion, the author thanks V. N. Zhigulev and V. S. Galkin for a discussion of his results.