Reaction-Diffusion Equations for Chemically Reacting Gas Mixtures

Marzia Bisi

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 3, page 805-817
  • ISSN: 0392-4041

Abstract

top
In this paper we aim at describing the hydrodynamic limit of a mixture of chemically reacting gases. Starting from kinetic Boltzmann-type equations, we derive Grad's 13-moments equations for single species. Then, after scaling such equations in terms of a suitable Knudsen number, we apply an asymptotic Chapman-Enskog procedure in order to build up hydrodynamic equations of Navier-Stokes type.

How to cite

top

Bisi, Marzia. "Reaction-Diffusion Equations for Chemically Reacting Gas Mixtures." Bollettino dell'Unione Matematica Italiana 1.3 (2008): 805-817. <http://eudml.org/doc/290471>.

@article{Bisi2008,
abstract = {In this paper we aim at describing the hydrodynamic limit of a mixture of chemically reacting gases. Starting from kinetic Boltzmann-type equations, we derive Grad's 13-moments equations for single species. Then, after scaling such equations in terms of a suitable Knudsen number, we apply an asymptotic Chapman-Enskog procedure in order to build up hydrodynamic equations of Navier-Stokes type.},
author = {Bisi, Marzia},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {805-817},
publisher = {Unione Matematica Italiana},
title = {Reaction-Diffusion Equations for Chemically Reacting Gas Mixtures},
url = {http://eudml.org/doc/290471},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Bisi, Marzia
TI - Reaction-Diffusion Equations for Chemically Reacting Gas Mixtures
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/10//
PB - Unione Matematica Italiana
VL - 1
IS - 3
SP - 805
EP - 817
AB - In this paper we aim at describing the hydrodynamic limit of a mixture of chemically reacting gases. Starting from kinetic Boltzmann-type equations, we derive Grad's 13-moments equations for single species. Then, after scaling such equations in terms of a suitable Knudsen number, we apply an asymptotic Chapman-Enskog procedure in order to build up hydrodynamic equations of Navier-Stokes type.
LA - eng
UR - http://eudml.org/doc/290471
ER -

References

top
  1. BISI, M. - DESVILLETTES, L., From reactive Boltzmann equations to reaction-diffusion systems, J. Stat. Phys., 124 (2006), 881-912. Zbl1134.82323MR2264629DOI10.1007/s10955-005-8075-x
  2. BISI, M. - GROPPI, M. - SPIGA, G., Grad's distribution functions in the kinetic equations for a chemical reaction, Continuum Mech. Thermodyn., 14 (2002), 207-222. Zbl0996.76093MR1896837DOI10.1007/s001610100066
  3. BISI, M. - GROPPI, M. - SPIGA, G., Fluid-dynamic equations for reacting gas mixtures, Appl. Math., 50 (2005), 43-62. Zbl1099.82015MR2117695DOI10.1007/s10492-005-0003-5
  4. BISI, M. - GROPPI, M. - SPIGA, G., Kinetic Modelling of Bimolecular Chemical Reactions, in "Kinetic Methods for Nonconservative and Reacting Systems", (G. Toscani Ed.), "Quaderni di Matematica" [Mathematics Series], Aracne Editrice, Roma, 16 (2005), 1-143. Zbl1121.82032MR2244535
  5. BISI, M. - SPIGA, G., Diatomic gas diffusing in a background medium: kinetic approach and reaction-diffusion equations, Commun. Math. Sci., 4 (2006), 779-798. Zbl1120.82011MR2264820
  6. CERCIGNANI, C., Rarefied Gas Dynamics. From Basic Concepts to Actual Calculations, Cambridge University Press, Cambridge (2000). Zbl0961.76002MR1744523
  7. CHAPMAN, S. - COWLING, T. G., The mathematical theory of non-uniform gases, Springer, New York (1994). Zbl0063.00782MR116537
  8. DE MASI, A. - FERRARI, P. A. - LEBOWITZ, J. L., Reaction-diffusion equations for interacting particle systems, J. Stat. Phys., 44 (1986), 589-644. Zbl0629.60107MR857069DOI10.1007/BF01011311
  9. DESVILLETTES, L. - MONACO, R. - SALVARANI, F., A kinetic model allowing to obtain the energy law of polytropic gases in the presence of chemical reactions, Eur. J. Mech. B Fluids, 24 (2005), 219-236. Zbl1060.76100MR2118066DOI10.1016/j.euromechflu.2004.07.004
  10. GIOVANGIGLI, V., Multicomponent Flow Modeling, Birkhäuser, Boston (1999). Zbl0956.76003MR1713516DOI10.1007/978-1-4612-1580-6
  11. GROPPI, M. - SPIGA, G., Kinetic approach to chemical reactions and inelastic transitions in a rarefied gas, J. Math. Chem., 26 (2000), 197-219. Zbl1048.92502
  12. GROPPI, M. - SPIGA, G., Kinetic theory of a chemically reacting gas with inelastic transitions, Trans. Th. Stat. Phys., 30 (2001), 305-324. Zbl1174.82327
  13. KOLLER, W. - SCHÜRRER, F., Conservative solution methods for extended Boltzmann equations, Riv. Mat. Univ. Parma, (6) 4* (2001), 109-169. Zbl1005.82023MR1881106
  14. POLEWCZAK, J., A review of the kinetic modelings for non-reactive and reactive dense fluids, Riv. Mat. Univ. Parma, (6) 4* (2001), 23-55. Zbl1009.82018MR1881104
  15. PRIGOGINE, I. - XHROUET, E., On the perturbation of Maxwell distribution function by chemical reactions in a gas, Physica, 15 (1949), 913-932. Zbl0037.41003
  16. ROSSANI, A. - SPIGA, G., A note on the kinetic theory of chemically reacting gases, Physica A, 272 (1999), 563-573. MR1730976DOI10.1016/S0378-4371(99)00336-2
  17. SHIZGAL, B. - KARPLUS, M., Non-equilibrium contributions to the rate of reaction. Perturbation of the velocity distribution function, J. Chem. Phys., 52 (1970), 4262- 4278. MR273964DOI10.1063/1.1673637
  18. SPIGLER, R. - ZANETTE, D. H., Asymptotic analysis and reaction-diffusion approximation for BGK kinetic models of chemical processes in multispecies gas mixtures, J. Appl. Math. Phys. (ZAMP), 44 (1993), 812-827. Zbl0784.76108MR1241634DOI10.1007/BF00942811
  19. ZANETTE, D. H., Linear and nonlinear diffusion and reaction-diffusion equations from discrete-velocity kinetic models, J. Phys. A: Math. Gen., 26 (1993), 5339-5349. Zbl0808.60073MR1248718

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.