# Darrieus–Landau instability

The Darrieus–Landau instability is an intrinsic flame instability that occurs in premixed flames due to the thermal expansion of the gas produced by the combustion process. It was predicted independently by Georges Jean Marie Darrieus and Lev Landau.[1][2]

The instability analysis behind the Darrieus–Landau instability considers a planar, premixed flame front subjected to very small perturbations.[3] It is useful to think of this arrangement as one in which the unperturbed flame is stationary, with the reactants (fuel and oxidizer) directed towards the flame and perpendicular to it with a velocity u1, and the burnt gases leaving the flame also in a perpendicular way but with velocity u2. The analysis assumes that the flow is an incompressible flow, and that the perturbations are governed by the linearized Euler equations and, thus, are inviscid. With these considerations, the main result of this analysis is that, if the density of the burnt gases is less than that of the reactants, which is the case in practice due to the thermal expansion of the gas produced by the combustion process, the flame front is unstable to perturbations of any wavelength. Another result is that the rate of growth of the perturbations is inversely proportional to their wavelength; thus small flame wrinkles (but larger than the characteristic flame thickness) grow faster than larger ones. In practice, however, diffusive and buoyancy effects that are not taken into account by the analysis of Darrieus and Landau may have a stabilizing effect.[4][5][6][7]

## References

1. ^ Darrieus, G. (1938). "Propagation d'un front de flamme". La Technique Moderne and Congrés de Mécanique Appliquée Paris.
2. ^ Landau, L. D. (1944). "On the theory of slow combustion". Acta Physicochim.
3. ^ Clavin, Paul; Searby, Geoff (2016). Combustion Waves and Fronts in Flows. Cambridge: Cambridge University Press. doi:10.1017/cbo9781316162453. ISBN 9781316162453.
4. ^ Markstein, G. H. Non-steady flame Propagation,(1964). P22, Pergarmon, New York.
5. ^ Frankel, M. L.; Sivashinsky, G. I. (December 1982). "The Effect of Viscosity on Hydrodynamic Stability of a Plane Flame Front". Combustion Science and Technology. 29 (3–6): 207–224. doi:10.1080/00102208208923598. ISSN 0010-2202.
6. ^ Matalon, M.; Matkowsky, B. J. (1982/11). "Flames as gasdynamic discontinuities". Journal of Fluid Mechanics. 124: 239–259. doi:10.1017/S0022112082002481. ISSN 1469-7645. Check date values in: `|date=` (help)
7. ^ Pelce, P.; Clavin, P. (1982/11). "Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames". Journal of Fluid Mechanics. 124: 219–237. doi:10.1017/S002211208200247X. ISSN 1469-7645. Check date values in: `|date=` (help)