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ABSTRACT
We consider premixed gaseous flames propagating between parallel plates (Hele-Shaw cell) and qualitatively analyze how the resulting losses of momentum and heat affect the flame stability for wavelengths of wrinkling that noticeably exceed the plate spacing. Modelling the flame as an effective interface and using Euler-Darcy equations for the gas on both sides, we firstly show that friction to adiabatic walls modify the Landau-Darrieus instability in two ways: a damping coefficient is brought in, along with a Saffman-Taylor type of instability. Being due to friction-induced pressure gradients, the latter may even dominate the stabilizing influence of gravity for downwardly propagating fronts in narrow channels.
Because they ultimately make the gas density resume its upstream value, heat losses tend to moderate these effects, as well as the Landau-Darrieus instability and the influence of gravity, but the long wavelengths of wrinkling may remain unstable in downward propagations when heat losses are acounted for. This last conclusion is reached upon analysis of the weak-expansion limit.
We also outline a flame-dynamics type of experiment to estimate the heat and momentum exchanges that are involved in our analysis.
