Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-22T10:42:33.736Z Has data issue: false hasContentIssue false
  • English
  • Français

Double-diffusive instabilities of autocatalytic chemical fronts

Published online by Cambridge University Press:  28 March 2007

J. D'HERNONCOURT ,
A. DE WIT  and
A. ZEBIB
J. D'HERNONCOURT
Affiliation:
Nonlinear Physical Chemistry Unit and Center for Nonlinear Phenomena and Complex Systems, CP 231, Université Libre de Bruxelles, 1050 Brussels, [email protected]; [email protected]
A. DE WIT
Affiliation:
Nonlinear Physical Chemistry Unit and Center for Nonlinear Phenomena and Complex Systems, CP 231, Université Libre de Bruxelles, 1050 Brussels, [email protected]; [email protected]
A. ZEBIB
Affiliation:
Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854-8058, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Convective instabilities of an autocatalytic propagating chemical front in a porous medium are studied. The front creates temperature and concentration gradients which then generate a density gradient. If the front propagates in the direction of the gravity field, adverse density stratification can lead to Rayleigh–Taylor or Rayleigh–Bénard instabilities. Differential diffusivity of mass and heat can also destabilize the front because of the double-diffusive phenomena. We compare the stability boundaries for the classical hydrodynamic case of a bounded layer without reaction and for the chemical front in the parameter space spanned by the thermal and solutal Rayleigh numbers. We show that chemical reactions profoundly affect the stability boundaries compared to the non-reactive situation because of a delicate coupling between the double-diffusive and Rayleigh–Taylor mechanisms with localized density perturbations driven by the reaction. In the reactive case, a linear stability analysis identifies three distinct stationary branches of the instability. They bound a region of stability that shrinks with increasing Lewis number, in marked contrast to the classical double-diffusive layer. In particular a region of global and local stable stratification is susceptible to a counter-intuitive mechanism of convective instability driven by chemistry and double-diffusion. The other two regions display an additional contribution of localized Rayleigh–Taylor instabilities. Displaced-particle arguments are employed in support of and to elucidate the entire stability boundary.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 576 , 10 April 2007 , pp. 445 - 456
Copyright
Copyright © Cambridge University Press 2007

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

REFERENCES

Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradient. J. Fluid Mech. 37, 289–306.CrossRefGoogle Scholar
DeWit, A. Wit, A. 2001 Fingering of chemical fronts in porous media. Phys. Rev. Lett. 87, 054502.Google Scholar
DeWit, A. Wit, A. 2004 Miscible density fingering of chemical fronts in porous media: Nonlinear simulations. Phys. Fluids 16, 163–175.Google Scholar
D'Hernoncourt, J., Zebib, A. & DeWit, A. Wit, A. 2006 Reaction driven convection around a stably stratified chemical front. Phys. Rev. Lett. 96, 154501.CrossRefGoogle ScholarPubMed
Kalliadasis, S., Yang, J. & DeWit, A. Wit, A. 2004 Fingering instabilities of exothermic reaction–diffusion fronts in porous media. Phys. Fluids 16, 1395–1409.CrossRefGoogle Scholar
Khan, A. A. & Zebib, A. 1981 Double diffusive instability in a vertical layer of a porous medium. J. Heat Transfer 103, 179–181.CrossRefGoogle Scholar
Nield, D. A. 1968 Onset of thermohaline convection in porous media. Water Resour. Res. 11, 553–560.CrossRefGoogle Scholar
Nield, D. A. & Bejan, A. 1992 Convection in Porous Media. Springer.CrossRefGoogle Scholar
Pojman, J. A. & Epstein, I. R. 1990 Convective effects on chemical waves. 1. Mechanisms and stability criteria. J. Phys. Chem. 94, 4966–4972.CrossRefGoogle Scholar
Pojman, J. A. & Epstein, I. R. 1998 An Introduction to Nonlinear Chemical Dynamics. Oxford University Press.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Vasquez, D. A., Wilder, J. W. & Edwards, B. F. 1996 Chemical wave propagation in Hele-Shaw cells and porous media. J. Chem. Phys. 104, 9926.CrossRefGoogle Scholar