Influence of excitation of internal degrees of freedom of molecules on the process of weak evaporation or condensation

A study is made of the process of weak evaporation (or condensation) with allowance for excitation of vibrational and rotational degrees of freedom of diatomic molecules. The solution to the corresponding Knudsen layer problem is obtained on the basis of a model kinetic equation of the type of the Morse equation [1]. A relation is obtained that establishes the connection between the rate of evaporation (or condensation) and the parameters of the surface and the gas above it. The boundary conditions of slip for the equations of gas dynamics are analyzed. The results are compared with the evaporation or condensation in the case of a monatomic gas. The introduction of accommodation coefficients for an evaporating surface is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 98–110, November–December, 1979.     

Analytical calculation of the parameters of a molecular gas on a surface in the Smoluchowski problem

An analytical solution of the classical Smoluchowski problem on the temperature jump in molecular (monatomic, diatomic, and polyatomic) gases is presented. The gas occupies a half–space above a flat wall, with a constant temperature gradient and evaporation rate from the gas—condensed phase interface set far from this wall. The distribution function is explicitly constructed both in the half–space and at its boundary. Formulas for the concentration and temperature at the interface are derived; in the case of diatomic and polyatomic gases, formulas for temperatures determined by translational and rotational degrees of freedom of molecules are obtained. Numerical calculations are performed.     

Slip coefficients and macroparameter jumps of a diatomic gas with rotational degrees of freedom on a weakly curved spherical surface

Using the half-space moment method, the problem of the slip of a diatomic gas along a rigid spherical surface is solved within the framework of a model kinetic equation previously proposed which takes into account the rotational degrees of freedom of the gas. Second-order slip coefficients (correctionsC _m ^′ , β _R ^′ , and β _R to the isothermal and thermal slip which are linear with respect to the Knudsen number Kn) are obtained. The gas macroparameter jump coefficientsC _v andC _q, which are of the second order in the Knudsen number and characterize the discontinuity of the normal mass and heat fluxes on the gas-rigid phase interface, are calculated. These coefficients are given as functions of the tangential momentum accommodation coefficient, the translational and rotational energy accommodation coefficients, and the Prandtl number. The coefficients are calculated for certain diatomic gases. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 163–173, January–February, 2000.     

Boundary conditions for gases on a body surface

The influence of boundary conditions on the distribution of macroscopic parameters of various types is studied using the problem of heat transfer for monatomic and diatomic gases as an example. The calculations are made on the basis of model kinetic equations [1, 2]. A boundary condition that takes into account mutual transitions of rotational and translational energies of particles when they collide with a body surface is proposed for diatomic gas. Comparison with the experimental results made it possible to determine the coefficients appearing in the boundary conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 141–148, September–October, 1986.     

Slip and Macroparameter Jumps of a Polyatomic Gas with Rotational Degrees of Freedom on a Weakly Curved Spherical Surface

The problem of the slip of a temperature-inhomogeneous polyatomic gas along a spherical surface of small curvature is solved. The solution is obtained using the half-space moment method on the basis of a previously proposed model kinetic equation which takes into account the rotational degrees of freedom of the polyatomic gas. Both the first- and second-order (in the Knudsen number) slip coefficients and the polyatomic gas macroparameter jump coefficients on the phase interface are obtained. These coefficients are given as functions of the tangential momentum accommodation coefficients, the translational and rotational energy accommodation coefficients, and the Prandtl number. The kinetic coefficients are calculated for certain polyatomic gases.     

Similitude of hypersonic flows of low-density gas over blunt bodies

Laws of similitude of hypersonic flows of monatomic gases have been obtained earlier from asymptotic analysis of the equations as S and confirmed by experimental data and numerical results [1], For diatomic gases, dimensionless numbers have not been deduced by analyzing the equations but by general arguments based on analogy with monatomic gases; they were used to compare experimental and calculated results in [1–3]. In the present paper, dimensionless numbers are derived on the basis of model kinetic equations for a diatomic gas, and limits of their applicability are established. Numerical calculations confirm the exact and approximate laws of similitude and permit a comparison with experimental results. The influence of the laws of viscosity on the drag for a sphere as a function of the Reynolds number Re₀ determined using the viscosity at the stagnation point is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 130–135, March–April, 1981.     

Effect of rotational degrees of freedom of molecules on energy flux in attenuated gas

On the basis of model kinetic equations a solution is obtained by a numerical method for the flow of attenuated gas around a sphere. The effect of rotational degrees of freedom on the energy flux to the body is investigated. Values of the ratio between the energy flux Q and its free-molecular value Q* for monatomic and diatomic gases are compared; for the comparison, the dimensionless temperature of the body, the gas velocity at infinity, and the law of viscosity must be the same in the two cases. For sufficiently cold bodies (when the body temperature is below the equilibrium temperature for a diatomic gas) the difference between Q/Q* for monatomic and diatomic gases is insignificant. For a diatomic gas when the body temperature is close to equilibrium, the ratio Q/Q* is found to have a nonmonotonic dependence on the Knudsen force.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 119–124, September–October, 1977.     

On the Stress Tensor Jump at the Interface between a Polyatomic Gas and a Condensed Phase

For the components of the hydrodynamic stress tensor the boundary condition at the interface between a polyatomic gas and a condensed phase is obtained. The boundary-value problem is solved within the framework of the previously proposed kinetic model by the method of semi-spatial moments, taking into account the rotational degrees of freedom of the gas molecules. The gas-kinetic coefficient C _p entering into the boundary condition for the stress tensor components depends on the accommodation coefficient of the tangential momentum, q, the accommodation coefficients of the translational, _t , and rotational, _r , energy components, and the Prandtl number. This coefficient is calculated for several polyatomic gases.     

Numerical investigation of rarefied diatomic gas flows through a plane channel into a vacuum

Rarefied flows through a plane microchannel into a vacuum are numerically investigated on the basis of the model kinetic equation for a diatonic gas (nitrogen). The dependence of the gas flow rate through the channel on the Knudsen number, the wall temperature, and the channel length is determined. The energy flux transferred to the cold diatomic gas from the hot channel walls is calculated. The results for diatomic and monatomic gases are compared.     

Effect of Temperature on Slip Coefficients of Molecular Gases

Results obtained by accurate analytical methods applied to the problem of molecular-gas slip over a rigid spherical surface are reported. The Boltzmann equation is modified to take into account rotational degrees of freedom in the BGK model is used as a master kinetic equation. The calculated slip coefficients are shown to depend on the Prandtl number and on the gas temperature. Slip coefficients for several molecular gases are plotted as functions of temperature. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 58–65, January–February, 2006.     

Kinetics of electron recombination in a molecular gas expanding into a cavity

The kinetics of recombination in a diatomic or polyatomic gas dispersing into a cavity is investigated in a model gas with one ionization potential and one electron affinity. In addition to the recombination reaction in triple collisions, which play the most important role in the case of a monatomic gas [1], dissociative recombination, ion-atom charge transfer, and reactions involving negative ions are considered. The qualitative differences in the kinetics of recombination of a molecular gas (in comparison with a monatomic gas) are due to the smallness of the relative electron concentrations at the instant of disturbance of ionization equilibrium and to the important contribution of dissociative recombination reactions and the kinetics of formation and recombination of negative ions.In addition, owing to the greater specific heat of a polyatomic gas and the corresponding lower rate of cooling on dispersion, recombination due to collision of three charged particles is not, as distinct from the case of a monatomic gas, decisive for the asymptotic values of the adiabatic exponent and residual ionization. For this reason the values of the adiabatic exponent can be assigned irrespective of a in the solution of the equations of the kinetics of recombination of diatomic and polyatomic gases. Expressions for the instant of failure of the equilibrium relationship between electrons and, respectively, positive and negative ions are obtained.The relationship between the charged-particle concentration in a gas in ionization nonequilibrium and the time for known values of the reaction rate constants is expressed by quadratures. The values of the rate constants of some ionization processes are known only in order of magnitude. However, available data on rate constants indicate that for practically any initial data for dispersion of the products of explosion or combustion of chemical compounds ionization equilibrium is upset at a time when there is still an equilibrium ratio of concentrations of electrons and negative ions.     

A model kinetic equation for a gas with rotational degrees of freedom

A model kinetic equation for a gas with rotational degrees of freedom is obtained. By averaging of the distribution function over quantities corresponding to the rotational degrees of freedom this equation is reduced to a closed system of two kinetic equations, each of which is analogous to the kinetic equation of a monatomic gas.     

Effect of molecular rotations on acoustic properties of a two-fluid medium

The effect of molecular rotations on the dispersion of the speed of sound and the absorption factor is theoretically analyzed for mixtures of diatomic and monatomic gases with disparate molecular masses. Two types of mixtures are considered: 1) the molecules of the diatomic component are significantly lighter than the molecules of the monatomic gas, and 2) the monatomic molecules have a smaller mass. The calculations show that the effect of rotational relaxation on acoustic characteristics in the range of frequencies close to the critical value can by ignored in the first-type mixtures, whereas the energy exchange between the rotational and translational degrees of freedom of molecules has a considerable effect on the propagation of forced acoustic oscillations in the second case. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 97–103, May–June, 1999.     

Expansion of monatomic and diatomic gases from a spherical source into a vacuum in a gravitational field

Steady monatomic and diatomic gas flows from a spherical source into a vacuum in a gravitational field are studied using direct statistical simulation. The qualitative gravitation effect on the flow is shown to be independent of the intermolecular collision model. Three characteristic Jeans parameter ranges can always be distinguished, namely, the subcritical range, on which the flow in a weak gravitational field is similar with the outflow in the absence of gravitation, the supercritical range, on which the outflow velocity remains small even at large distances from the source, and a narrow transitional range between the two former ranges. The presence of internal degrees of freedom of gas molecules displaces the transitional range toward the greater values of the Jeans parameter and leads to an increase in the outflow velocity and the gas temperature; however, in the initial region the latter effect is expressed only slightly. The normalized escape flow is a nonmonotonic function of both the Jeans parameter and the Knudsen number and is different for monatomic and diatomic gases within 50% on the parameter range considered.     

Intense Condensation of a Molecular Gas

The kinetic problem of intense subsonic condensation of a polyatomic gas on a plane surface is solved by the method of semispatial moments. The contribution of the internal degrees of freedom to the total heat capacity is taken into account. The domains of existence of the Boltzmann equation solution are determined for the given method. Analytic expressions for calculating the gas concentration behind the Knudsen layer depending on the Mach number and temperature are derived for the cases of mon-, di-, and triatomic gases.     

Light scattering and sound propagation in polyatomic gases with classical degrees of freedom

In this work we analyze time-dependent problems like sound propagation and light scattering in dilute polyatomic gases with classical internal degrees of freedom by using a kinetic model of the Boltzmann equation that replaces the collision operator with a single relaxation-time term. Comparison of the theoretical results with available experimental data shows that the model equation can be used to describe the acoustic properties and the light scattering spectrum of dilute polyatomic gases as long as the external oscillation frequency is smaller than the frequency required for the translational and the internal degrees of freedom to come to thermal equilibrium.Received: 12 January 2004, Accepted: 2 February 2004, Published online: 16 April 2004PACS: 51.10. + y; 51.40. + p     

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.     

Effects of slip velocity and surface acoustic wave on the laminar flow stability

The stability of slip flows when a surface acoustic wave (SAW) propagating along the walls of a microchannel in the laminar flow regime is investigated. The governing equation which was derived by considering the weakly nonlinear coupling between the deformable wall and streaming slip flow is linearized and then the eigenvalue problem is solved by a numerical code together with the associated interface and slip velocity boundary conditions. The value of the critical Reynolds number was found to be near 1,441 for a Knudsen number being 0.001 (associated with a physical parameter K ₀ characterizing the SAW effect) which is much smaller than the static-wall case for conventional pressure-driven flows.     

Initial and boundary value problems of hyperbolic heat conduction

This is a study on the initial and boundary value problem of a symmetric hyperbolic system which is related to the conduction of heat in solids at low temperatures. The nonlinear system consists of a conservation equation for the energy density e and a balance equation for the heat flux , where e and are the four basic fields of the theory. The initial and boundary value problem that uses exclusively prescribed boundary data for the energy density e is solved by a new kinetic approach that was introduced and evaluated by Dreyer and Kunik in [1], [2] and Pertame [3]. This method includes the formation of shock fronts and the broadening of heat pulses. These effects cannot be observed in the linearized theory, as it is described in [4]. The kinetic representations of the initial and boundary value problem reveal a peculiar phenomenon. To the solution there contribute integrals containing the initial fields as well as integrals that need knowledge on energy and heat flux at a boundary. However, only one of these quantities can be controlled in an experiment. When this ambiguity is removed by continuity conditions, it turns out that after some very short time the energy density and heat flux are related to the initial data according to the Rankine Hugoniot relation. Received October 6, 1998