Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-22T19:24:35.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of Vibrations on Convective Instability of ReactionFronts in Porous Media

Published online by Cambridge University Press:  13 September 2010

H. Aatif ,
K. Allali  and
K. El Karouni
Get access

Abstract

The aim of this paper is to study the effect of vibrations on convective instability ofreaction fronts in porous media. The model contains reaction-diffusion equations coupledwith the Darcy equation. Linear stability analysis is carried out and the convectiveinstability boundary is found. The results are compared with direct numericalsimulations.

Keywords

linear stability analysisreaction frontsporous mediumnumerical simulations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 5: Reaction-diffusion waves , 2010 , pp. 123 - 137
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allali, K., Ducrot, A., Taik, A., Volpert, V.. Convective instability of reaction fronts in porous media. Math. Model. Nat. Phenom., 2 (2007), no. 2, 20–39. CrossRefGoogle Scholar
D. Aronson, H. Weinberger. Nonlinear Diffusion in Population Genetics, Combustion and Nerve Propagation. Lecture Notes in Math Vol. 446, pringer-Verlag, Berlin, 1975.
Bhadauria, B.S., Bhatia, P.K.Debnath, L.. Convection in Hele-Shaw cell with parametric excitation. Int. Journal of Non-Linear Mechanics, 40 (2005), 475–484.CrossRefGoogle Scholar
Boulal, T., Aniss, S., Belhaq, M., Rand, R.. Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer. Phys. Rev. E. 52 (2007), 76, 56320. Google Scholar
N.F. Britton. Reaction-Diffusion Equations and Their Applications to Biology. Academic Press, New York, 1986.
Brunet, E.Derrida, B.. Shift in the velocity of a front due to a cutoff. Phys. Rev. E, 56 (1997), 2597–2604.CrossRefGoogle Scholar
Ebert, U.Van Saarloos, W.. Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts. Physica D 146 (2000), 1–99.CrossRefGoogle Scholar
M. Freidlin. Markov Processes and Differential Equations: Asymptotic Problems. Birkhauser, Basel, 1996.
Gershuni, G.Z., Kolesnikov, A.K., Legros, J.C.Myznikova, B.I.. On the vibrational convective instability of a horizontal, binary-mixture layer with Soret effect. Journal of Fluid Mechanics, 330 (1997), 251–269.CrossRefGoogle Scholar
G.Z. Gershuni, E.M. Zhukhovitskii. The Convective Stability of Incompressible Fluids. Keter Publications, Jerusalem, (1976), 203–230.
Gresho, P.M., Sani, R.L.. The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech., 40 (1970), no. 4, 783–806. CrossRefGoogle Scholar
Murray, B.T., Coriell, S.R.McFadden, G.B.. The effect of gravity modulation on solutal convection during directional solidification. Journal of Crystal Growth, 110 (1991), 713–723.CrossRefGoogle Scholar
J.D. Murray. Mathematical Biology. Springer-Verlag, Berlin, 1989.
Or, A.C.. Finite-wavelength instability in a horizontal liquid layer on an oscillating plane. J. Fluid Mech., 335 (1997), 213–232.CrossRefGoogle Scholar
Rogers, J.L., Schatz, M.F., Bougie, J.L., Swift, J.B.. Rayleigh-Bénard convection in a vertically oscillated fluid layer. Phys. Rev. Lett. 84 (2000), no. 1, 87–90. CrossRefGoogle Scholar
Rosenblat, S.Tanaka, G.A.. Modulation of thermal convection instability. Phys. Fluids, 7 (1971), 1319–1322.CrossRefGoogle Scholar
Volmar, U.E.Muller, H.W.. Quasiperiodic patterns in Rayleigh-Bénard convection under gravity modulation. Phys. Rev. E, 56 (1997), 5423–5430.CrossRefGoogle Scholar
Volpert, V.Petrovskii, S.. Reaction-diffusion waves in biology. Physics of Life Reviews, 6 (2009), 267–310.CrossRefGoogle ScholarPubMed
A. Volpert, Vit. Volpert, Vl. Volpert. Traveling wave solutions of parabolic system. American Mathematical Society, Providence, RI, (1994) 448 pp.
Wadih, M., Roux, B.. The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech., 40 (1970), no. 4, 783–806. Google Scholar
Wheeler, A.A., McFadden, G.B., Murray, B.T., Coriell, S.R.. Convective stability in the Rayleigh-Bénard and directional solidification problems: high-frequency gravity modulation. Phys. Fluids A, 3 (1991), no. 12, 2847–2858. CrossRefGoogle Scholar
Wolf, G.H.. Dynamic stabilization of interchange instability of a liquid-gas interface. Phys. Rev. Lett., 24 (1970), 444–446.CrossRefGoogle Scholar
Woods, D.R.Lin, S.P.. Instability of a liquid film flow over a vibrating inclined plane. J. Fluid Mech., 294 (1995), 391–407.CrossRefGoogle Scholar
Ya.B. Zeldovich, G.I. Barenblatt, V.B. Librovich, G.M. Makhviladze. The Mathematical Theory of Combustion and Explosions. Consultants Bureau, Plenum, New York, 1985.
Zeldovich, Ya.B.Frank-Kamenetsky, D.A.. The theory of thermal propagation of flames. Zh. Fiz. Khim., 12 (1938), 100–105.Google Scholar
Zenkovskaya, S.M.. Action of high-frequency vibration on filtration convection. J. Appl. Mech. Tech. Phys., 32 (1992), 83–86.Google Scholar
Zenkovskaya, S.M.Rogovenko, T.N.. Filtration convection in a high-frequency vibration field. J. Appl. Mech. Tech. Phys., 40 (1999), 379–385.CrossRefGoogle Scholar