Impact of vibrational non-equilibrium on chemical reaction rates
We study non-equilibrium effects caused by dissociation and other chemical reactions in gas mixtures. For that, we employ a general algorithm for deriving a uniform asymptotic solution of the kinetic equation for spatially inhomogeneous reactive gas mixtures developed earlier by the authors. We show that chemical reactions lead to quasi-stationary vibrational distribution function that differs from the quasi-equilibrium one. Under such conditions, the approach based on introduction of reaction rate constants shall be revised. We obtained expressions for reaction rates of pure unimolecular processes that have a dependence on pressure in good agreement with the theory of unimolecular reactions. Considering both unimolecular and collisional mechanisms of elementary reactions leads to new dependencies of reaction rates on gas pressure. Parallel reactions are considered (when one molecule reacts with several others), and a strong correlation between these reactions is demonstrated in the non-equilibrium case. This correlation can be manifested as blocking of one reaction by another. It violates the mass action law.
Kinetic theory, reactive mixture, transport equations, non-equilibrium effects
Исследуются неравновесные эффекты, обусловленные диссоциацией и другими химическими реакциями в газовых смесях. Для этого используется общий алгоритм построения асимптотического решения кинетического уравнения для пространственно неоднородных реагирующих газовых смесей, разработанный авторами ранее. Показано, что химические реакции приводят к квазистационарному колебательному распределению, отличающемуся от квазиравновесного. В этих условиях подход, основанный на введении понятия константы скорости реакции нуждается в пересмотре. Получены выражения для скоростей реакций чисто мономолекулярных процессов, которые имеют зависимость от давления, хорошо согласующуюся с теорией мономолекулярных реакций. Учет как мономолекулярного, так и столкновительного механизма элементарных реакций ведет к новой зависимости скоростей реакций от давления. Рассмотрены параллельные реакции (когда одна молекула реагирует с несколькими другими молекулами), и показана сильная корреляция между этими реакциями в неравновесном случае. Эта корреляция может проявляться как блокирование одной реакции другой. Это явление ведет к нарушению закона действующих масс.
кинетическая теория, реагирующие газовые смеси, процессы переноса, неравновесные эффекты
[1] Kolesnichenko E.G., Gorbachev Yu.E. Gas-dynamic equations for spatially inhomogeneous gas mixtures with internal degrees of freedom. I. General theory. To be published in: Applied Mathematical Modelling. [2] Kolesnichenko[1] Kolesnichenko E.G., Gorbachev Yu.E. Gas-dynamic equations for spatially inhomogeneous gas mixtures with internal degrees of freedom. I. General theory. To be published in: Applied Mathematical Modelling. [2] Kolesnichenko E.G., Losev S.A. Kinetics of relaxation processes in the moving mediums. Himia plasmi, v. 7, Atomizdat, M. 1979. (in Russian) [3] Gerasimov G.Ya. Kolesnichenko E.G. On the nonequilibrium effects influence on the transport processes in the dissociating gas. Pisma v jurnal tehnicheskoi physiki (USSR), 1981, v. 7, No 16, pp.965-967. (in Russian) [4] Gerasimov G.Ya. Kolesnichenko E.G. The transport processes in the nonequilibrium dissociating gas. Izvestia akademii nauk SSSR. Mehanika jidkosti i gaza (USSR), 1983, No 5, p. 159-166. (in Russian) [5] Robinson P.J., Holbrook K.A. Unimolecular reactions. Wiley-Interscience, London, New York, Sydney, Toronto, 1972. [6] Stupochenko E.V., Losev S.A., Osipov A.I. Relaxation in Shock Waves. Berlin, Springer-Verlag, 1967. [7] Vallander S.V., Egorova I.A., Rydalevskaia M.A. Spreading of the Chapman-Enskog method on the gas mixtures with internal degreas of freedom and with chemical reactions. In: Rarefied Gas Aerodynamics, v.2, Leningrad, LSU, 1965. (in Russian) [8] Gordietz B.F., Osipov A.I., Shelepin L.P. Kinetic processes in gases and molecular lasers. Moscow, Nauka, 1980. (in Russian) [9] Kondrat’ev V.N., Nikitin E.E. Kinetics and Mechanism of Gas-Phase Reactions, Moscow, Nauka, 1974, 558 pp. (in Russian) [10] Gordietz B.F., Zhdanok S.A. Analytical description on vibrational kinetics of anharmonic oscillators. In: Nonequilibrium vibrational kinetics. Ed.: M. Capitelly, Springer-Verlag Berlin Heidelberg, 1986. [11] Kolesnichenko E.G. On kinetic equations for chemically reacting gases. Thermophysics of High Temperatures, 1980, v. 18, N 1, pp. 55-62. (in Russian) [12] Prigogine I., Xhrouet E. On the perturbation of Maxwell distribution function by chemical reactions in a gas. Physica, 1949, 15, pp. 913–932. [13] Kolesnichenko E.G. Kinetic equations of the theory of chemically reactive gases. Moscow State University, 1983, 148 pp. (in Russian) E.G., Losev S.A. Kinetics of relaxation processes in the moving mediums. Himia plasmi, v. 7, Atomizdat, M. 1979. (in Russian) [3] Gerasimov G.Ya. Kolesnichenko E.G. On the nonequilibrium effects influence on the transport processes in the dissociating gas. Pisma v jurnal tehnicheskoi physiki (USSR), 1981, v. 7, No 16, pp.965-967. (in Russian) [4] Gerasimov G.Ya. Kolesnichenko E.G. The transport processes in the nonequilibrium dissociating gas. Izvestia akademii nauk SSSR. Mehanika jidkosti i gaza (USSR), 1983, No 5, p. 159-166. (in Russian) [5] Robinson P.J., Holbrook K.A. Unimolecular reactions. Wiley-Interscience, London, New York, Sydney, Toronto, 1972. [6] Stupochenko E.V., Losev S.A., Osipov A.I. Relaxation in Shock Waves. Berlin, Springer-Verlag, 1967. [7] Vallander S.V., Egorova I.A., Rydalevskaia M.A. Spreading of the Chapman-Enskog method on the gas mixtures with internal degreas of freedom and with chemical reactions. In: Rarefied Gas Aerodynamics, v.2, Leningrad, LSU, 1965. (in Russian) [8] Gordietz B.F., Osipov A.I., Shelepin L.P. Kinetic processes in gases and molecular lasers. Moscow, Nauka, 1980. (in Russian) [9] Kondrat’ev V.N., Nikitin E.E. Kinetics and Mechanism of Gas-Phase Reactions, Moscow, Nauka, 1974, 558 pp. (in Russian) [10] Gordietz B.F., Zhdanok S.A. Analytical description on vibrational kinetics of anharmonic oscillators. In: Nonequilibrium vibrational kinetics. Ed.: M. Capitelly, Springer-Verlag Berlin Heidelberg, 1986. [11] Kolesnichenko E.G. On kinetic equations for chemically reacting gases. Thermophysics of High Temperatures, 1980, v. 18, N 1, pp. 55-62. (in Russian) [12] Prigogine I., Xhrouet E. On the perturbation of Maxwell distribution function by chemical reactions in a gas. Physica, 1949, 15, pp. 913–932. [13] Kolesnichenko E.G. Kinetic equations of the theory of chemically reactive gases. Moscow State University, 1983, 148 pp. (in Russian)
