Darrieus–Landau instability

The Darrieus–Landau instability, or density fingering, refers to an instability of chemical fronts propagating into a denser medium, named after Georges Jean Marie Darrieus and Lev Landau. It is a key instrinsic flame instability that occurs in premixed flames, caused by density variations due to thermal expansion of the gas produced by the combustion process. In simple terms, stability inquires whether a steadily propagating plane sheet with a discontinuous jump in density is stable or not.

The analysis behind the Darrieus–Landau instability considers a planar, premixed flame front subjected to very small perturbations. 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 incompressible, and that perturbations are governed by the linearized Euler equations, and are thus inviscid.

With these considerations, the main result of this analysis is that, if the density of burnt gases is less than that of the reactants (true in practice due to thermal expansion of the gas produced by combustion), the flame front is unstable to perturbations of any wavelength. Another result is that the rate of growth of perturbations is inversely proportional to their wavelength; thus small flames (but larger than the characteristic flame thickness) tend to wrinkle, and 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.