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
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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.
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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)
P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Progr. Energy Comb. Sci. 11, 1–59 (1985)
F. Desprez and M. Garbey, Numerical simulation of a combustion problem on a Paragon Machine, to appear in Parallel Computing
D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Plenum Press, New York, 1969
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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)
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)
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H. J. Viljoen, J. E. Gatica, and V. Hlavacek, Bifurcation analysis of chemically driven convection, Chem. Eng. Sci. (2) 45, 503–517 (1990)
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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)
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Ya. B. Zeldovich and D. A. Frank-Kamenetsky, Theory of thermal propagation of flames, Zh. Fiz. Khim. 12, 100 (1938)
A. P. Aldushin and S. G. Kasparyan, Thermodiffusional instability of a combustion front, Soviet Physics-Doklady, Akademii Nauk SSSR (5) 24, 29 (1979)
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)
P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Progr. Energy Comb. Sci. 11, 1–59 (1985)
F. Desprez and M. Garbey, Numerical simulation of a combustion problem on a Paragon Machine, to appear in Parallel Computing
D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Plenum Press, New York, 1969
M. Garbey, A. Taïk, and V. Volpert, Linear stability analysis of reaction fronts in liquids, Quart. Appl. Math. 54, 225–247 (1996)
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)
L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon, Oxford and New York, 1987
O. Manley and M. Marion, Attractor dimension for a simple premixed flame propagation model, Combustion Sci. and Tech. 88, 15 32 (1992)
M. Marion, Attractors and Turbulence for some Combustion Models, Mathematics and its Applications, vol. 35, to appear
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)
S. B. Margolis, An asymptotic theory of condensed two-phase flame propagation, SIAM J. Appl. Math. 43, 351–369 (1983)
M. Matalon and B. J. Matkowsky, Flames in fluids: Their interaction and stability, Combustion Science and Tech. 34, 295–316 (1983)
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)
B. J. Matkowsky and G. I. Sivashinsky, Acceleration effects on the stability of flame propagation, SIAM J. Appl. Math. 37, 669–685 (1979)
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)
A. H. Nayfeh, Perturbation Methods, Wiley, New York, 1973
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)
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)
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)
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)
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)
D. A. Vasquez, J. W. Wilder, and B. F. Edwards, Hydrodynamic instability of chemical waves, J. Chem. Phys. (3) 98, 2138–2143 (1993)
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)
H. J. Viljoen, J. E. Gatica, and V. Hlavacek, Bifurcation analysis of chemically driven convection, Chem. Eng. Sci. (2) 45, 503–517 (1990)
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)
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)
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
Ya. B. Zeldovich and D. A. Frank-Kamenetsky, Theory of thermal propagation of flames, Zh. Fiz. Khim. 12, 100 (1938)
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