Abstract
Two kinetic theories for bimolecular chemical reactions in dilute gases are analyzed and compared. Reactive scattering kernels are constructed, satisfying microreversibility principles and yielding a physically plausible link between the two models. Mathematical properties and in particular the role played by microreversibility conditions and by certain elastic collisional terms on existence of solutions are also investigated.
Similar content being viewed by others
REFERENCES
I. Prigogine and E. Xhrouet, On the perturbation of Maxwell distribution function by chemical reaction in gases,Physica XV:913–932 (1949).
R. Kapral, Kinetic theory of chemical reactions in liquids, inAdvances in Chemical Phys-ics, I. Prigogine and S. A. Rice, eds,Vol. 48, John Wiley and Sons, New York,1981, pp.71–181.
J. C. Light, J. Ross, and K. E. Shuler, Rate coefficients, reaction cross sections and microscopic reversibility, inKinetic Processes in Gases and Plasmas, A. R. Hochstim, ed., Academic Press, New York, 1969,pp. 281–320.
A. Rossani and G. Spiga, A note on the kinetic theory of chemically reacting gases,Physica A,272:563–573 (1999).
J. Ross and P. Mazur, Some deductions from a formal statistical mechanical theory of chemical kinetics,J. Chem. Phys. 35:19–28 (1961).
M. T. Marron, Simple collision theory of reactive hard spheres,J. Chem. Phys. 52:4060–4061 (1970).
N. Xystris and J. S. Dahler, Kinetic theory of simple reacting spheres,J. Chem. Phys. 68:387–401 (1978).
S. Bose and P. Ortoleva, Reacting hard sphere dynamics: Liouville equation for con-densed media,J. Chem. Phys. 70:3041–3056 (1979).
M. Groppi and G. Spiga, Kinetic approach to chemical reactions and inelastic transitions in a rare ed gas,J. Math. Chem. 26:197–219 (2000).
F. Schürrer, P. Griehsnig, and G. Kügerl, The nonlinear Boltzmann equation including internal degrees of freedom,Phys. Fluids A 4:2739–2746 (1992).
P. Griehsnig, F. Schürrer, and G. Kügerl, The kinetic theory for particles with internal degrees of freedom, inRare ed Gas Dynamics: Theory and Simulations, Vol. 159,. Progress in Astronautics and Aeronautics, D. Shizgal and D. P. Weaver, eds.(AIAA, Washington, DC,1992), p. 581.
A. V. Bobylev, J. A. Carrillo, and I. M. Gamba, On some properties of kinetic and hydrodynamic equations for inelastic interactions,J. Stat. Phys. 98:743–773 (2000).
J. Polewczak, The kinetic theory of simple reacting spheres: I. Global existence results in a dilute-gas limit,J. Stat. Phys. 100:327–362 (2000).
N. Xystris and J. S. Dahler, Enskog theory of chemically reacting fluids,J. Chem. Phys. 68:374–386 (1978).
C. Cercignani, The Boltzmann Equation and its Applications,(Springer, New York, 1988).
J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases, (North–Holland, Amsterdam,1972).
H. Grad, Asymptotic theory of the Boltzmann equation, II, inRare ed Gas Dynamics I, J. L. Laurmann, ed.(Academic Press,1963),pp. 26–59.
P. Andries, K. Aoki, and B. Perthame, A consistent BGK-type model for gas mixtures,J. Stat. Phys. 106:993–1018 (2002).
R. L. DiPerna and P. L. Lions, On the Cauchy problem for the Boltzmann equation: Global existence and weak stability,Ann. Math. 130:321–366 (1989).
S. Mischler and B. Wennberg, On the spatially homogeneous Boltzmann equation,Ann. Inst. Henri Poincaré 16:467–501 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Groppi, M., Polewczak, J. On Two Kinetic Models for Chemical Reactions: Comparisons and Existence Results. Journal of Statistical Physics 117, 211–241 (2004). https://doi.org/10.1023/B:JOSS.0000044059.59066.a9
Issue Date:
DOI: https://doi.org/10.1023/B:JOSS.0000044059.59066.a9