Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Influence of natural convection on stability of reaction fronts in liquids


Authors: M. Garbey, A. Taïk and V. Volpert
Journal: Quart. Appl. Math. 56 (1998), 1-35
MSC: Primary 76E06; Secondary 76E15, 76V05, 80A32
DOI: https://doi.org/10.1090/qam/1604868
MathSciNet review: MR1604868
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the influence of natural convection on stability of reaction fronts in liquids. In our previous article [6] we considered the case where the reactants were in a liquid phase and the product of the reaction was solid. In this paper we study the case where both of them are liquid. We carry out a linear stability analysis and show that the results are essentially different compared to the case of a solid product.


References [Enhancements On Off] (What's this?)

  • [1] A. P. Aldushin and S. G. Kasparyan, Thermodiffusional instability of a combustion front, Soviet Physics-Doklady, Akademii Nauk SSSR (5) 24, 29 (1979)
  • [2] G. I. Barenblatt, Ya. B. Zeldovich, and A. G. Istratov, Diffusive-thermal stability of a laminar flame, Zh. Prikl. Mekh. Tekh. Fiz. (4) 21 (1962) (in Russian)
  • [3] P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Progr. Energy Comb. Sci. 11, 1-59 (1985)
  • [4] F. Desprez and M. Garbey, Numerical simulation of a combustion problem on a Paragon Machine, to appear in Parallel Computing
  • [5] D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Plenum Press, New York, 1969
  • [6] M. Garbey, A. Taïk, and V. Volpert, Linear stability analysis of reaction fronts in liquids, Quart. Appl. Math. 54, 225-247 (1996) MR 1388014
  • [7] A. G. Istratov and V. B. Librovich, Effect of the transfer processes on stability of a planar flame front, J. Appl. Math. Mech. (3) 30, 451-466 (1966) (in Russian)
  • [8] L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon, Oxford and New York, 1987 MR 961259
  • [9] O. Manley and M. Marion, Attractor dimension for a simple premixed flame propagation model, Combustion Sci. and Tech. 88, 15 32 (1992)
  • [10] M. Marion, Attractors and Turbulence for some Combustion Models, Mathematics and its Applications, vol. 35, to appear MR 1119794
  • [11] S. B. Margolis, H. G. Kaper, G. K. Leaf, and B. J. Matkowsky, Bifurcation of pulsating and spinning reaction fronts in condensed two-phase combustion, Combustion Sci. and Tech. 43, 127-165 (1985)
  • [12] S. B. Margolis, An asymptotic theory of condensed two-phase flame propagation, SIAM J. Appl. Math. 43, 351-369 (1983) MR 700343
  • [13] M. Matalon and B. J. Matkowsky, Flames in fluids: Their interaction and stability, Combustion Science and Tech. 34, 295-316 (1983)
  • [14] B. J. Matkowsky and G. I. Sivashinsky, Propagation of a pulsating reaction front in solid fuel combustion, SIAM J. Appl. Math. 35, 465-478 (1978) MR 507948
  • [15] B. J. Matkowsky and G. I. Sivashinsky, Acceleration effects on the stability of flame propagation, SIAM J. Appl. Math. 37, 669-685 (1979) MR 549148
  • [16] B. J. Matkowsky and G. I. Sivashinsky, An asymptotic derivation of two models in flame theory associated with the constant density approximation, SIAM J. Appl. Math. 37, 686-699 (1979) MR 549149
  • [17] A. H. Nayfeh, Perturbation Methods, Wiley, New York, 1973 MR 0404788
  • [18] B. V. Novozhilov, The rate of propagation of the front of an exothermic reaction in a condensed phase, Proc. Academy Sci. USSR, Phys. Chem. Sect. 141, 836-838 (1961)
  • [19] J. A. Pojman, R. Graven, A. Khan, and W. West, Convective instabilities in traveling fronts of addition polymerization, J. Physical Chemistry 96, 7466-7472 (1992)
  • [20] J. A. Pojman and I. R. Epstein, Convective effects on chemical waves. 1. Mechanisms and stability criteria, J. Phys. Chem. (12) 94, 4966-4972 (1990)
  • [21] J. A. Pojman, I. R. Epstein, T. J. McManus, and K. Scowalter, Convective effects on chemical waves. 2. Simple convection in the iodate-arsenous acid system, J. Phys. Chem. (3) 95, 1299-1306 (1991)
  • [22] K. G. Shkadinsky, B. I. Khaikin, and A. G. Merzhanov, Propagation of a pulsating exothermic reaction front in condensed phase, Combustion, Explosion, and Shock Waves 7, 15 (1971)
  • [23] D. A. Vasquez, J. W. Wilder, and B. F. Edwards, Hydrodynamic instability of chemical waves, J. Chem. Phys. (3) 98, 2138-2143 (1993)
  • [24] D. A. Vasquez, B. F. Edwards, and J. W. Wilder, Onset of convection for autocatalytic reaction fronts: Laterally bounded systems, Physical Review A 43, 6694-6699 (1991)
  • [25] H. J. Viljoen, J. E. Gatica, and V. Hlavacek, Bifurcation analysis of chemically driven convection, Chem. Eng. Sci. (2) 45, 503-517 (1990)
  • [26] Vit. A. Volpert, VI. A. Volpert, and J. A. Pojman, Effect of thermal expansion on stability of reaction front propagation, Chem. Eng. Sci. 49, No. 14, 2385-2388 (1994)
  • [27] J. W. Wilder, B. F. Edwards, D. A. Vasquez, and G. I. Sivashinksy, Derivation of a nonlinear front evolution equation for chemical waves involving convection, Physica D, 73, 217-226 (1994)
  • [28] Ya. B. Zeldovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, The Mathematical Theory of Combustion and Explosions, Consultants Bureau, New York, 1985 MR 781350
  • [29] Ya. B. Zeldovich and D. A. Frank-Kamenetsky, Theory of thermal propagation of flames, Zh. Fiz. Khim. 12, 100 (1938)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 76E06, 76E15, 76V05, 80A32

Retrieve articles in all journals with MSC: 76E06, 76E15, 76V05, 80A32


Additional Information

DOI: https://doi.org/10.1090/qam/1604868
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society