Boltzmann equation for a dissociating gas
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The incorporation of three-body collisions for dissociation/recombination into the Boltzmann equation is discussed. Conditions are assumed such that collisions are completed in the sense of scattering theory, so the collision operator is determined by scattering and reaction cross sections. The resulting equation has anH-theorem, and the equilibrium solution requires the law of mass action in addition to the Maxwellian dependence on momentum. A brief discussion is given of the normal solution and the transport coefficients.
Key wordsBoltzmann equation three-body collisions reactions dissociation recombination
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- 1.E. G. D. Cohen, On the generalization of the Boltzmann equation to general order in the density,Physica 28:1025 (1962); Cluster expansions and the hierarchy. I. Non-equilibrium distribution functions,Physica 28:1045 (1962); Cluster expansions and the hierarchy. II. Equilibrium distribution functions,Physica 28:1060 (1962); The generalization of the Boltzmann equation to higher densities,Acta Physica Austr. Suppl. X:157 (1973).Google Scholar
- 2.Iu. L. Klimontovich and D. Kremp, Quantum kinetic equations in systems with bound states,Physica 109A:517 (1981); J. A. McLennan, Kinetic equations for a quantum gas wtih bound states,J. Stat. Phys. 28:521 (1982); S. Lagan and J. A. McLennan, Kinetic theory for a weakly-associated diatomic gas with reactions,Physica 128A:178 (1984).Google Scholar
- 3.L. Waldmann, Die Boltzmann Gleichung fur Gase mit Rotierenden Molekulen,Z. Naturforsch. 12A:660 (1957); R. F. Snider, Quantum-mechanical modified Boltzmann equation for degenerate internal states,J. Chem. Phys. 32:1051 (1960).Google Scholar
- 4.C. S. Wang Chang, G. E. Uhlenbeck, and J. de Boer, The heat conductivity and viscosity of polyatomic gases, inStudies in Statistical Mechanics II, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1964).Google Scholar
- 5.M. S. Green, Surface integral form for three-body collision in the Boltzmann equation,Phys. Rev. 136A:905 (1964).Google Scholar
- 6.J. Ross and P. Mazur, Some deductions from a formal statistical mechanical theory of chemical kinetics,J. Chem. Phys. 35:19 (1961); B. Shizgal and M. Karplus, Non-equilibrium contributions to the rate of reactions. II. Isolated multicomponent systems,J. Chem. Phys. 52:4262 (1970).Google Scholar
- 7.L. Waldmann, Transporterscheinungen in Gasen von Mittlerem Druck, inEncyclopedia of Physics, Vol. 12 (Springer-Verlag, Berlin, 1958).Google Scholar
- 8.R. G. Newton,Scattering Theory of Waves and Particles (Springer-Verlag, New York, 1982), p. 500.Google Scholar
- 9.S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, 1970).Google Scholar
- 10.J. O. Hirschfelder, Heat transfer in chemically reacting mixtures. I,J. Chem. Phys. 26:274 (1957); J. N. Butler and R. S. Brokaw, Thermal conductivity of gas mixtures in chemical equlibrium,J. Chem. Phys. 26:1636 (1957).Google Scholar
- 11.J. T. Vanderslice, S. Weissman, E. A. Mason, and R. J. Fallon, High-temperature transport properties of dissociating hydrogen,Phys. Fluids 5:155 (1962); K. S. Yun and E. A. Mason, Collision integrals for the transport properties of dissociating air at high temperatures,Phys. Fluids 5:380 (1962); K. S. Yun, S. Weissman, and E. A. Mason, High temperature transport properties of dissociating nitrogen and dissociating oxygen,Phys. Fluids 5:672 (1962).Google Scholar