Stability of a planar flame front in the slow-combustion regime

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Abstract
The hydrodynamic stability of a planar flame (deflagration) is determined by solving the complete system of equations, including thermal conduction and energy release due to chemical reactions, for the case in which the Lewis number is equal to unity. In the asymptotic limit of large-wavelength perturbations, the developed theory provides a rigorous justification of the Darrieus-Landau assumption that the flame-front velocity is constant, which is the necessary supplementary condition in the model of discontinuous flame front. The analytical solution for the suppression of the flame-front instability is obtained for an arbitrary activation energy. It is shown that the obtained solution does not depend on the specific form of the energy release. The perturbation growth rate is also found numerically by solving the eigenvalue problem.