Fast-time instabilities refer to dynamics that may develop within the reaction zone of a flame, where the chemical kinetic time scales are very brief. Premixed flames with order one heat losses and diffusion flames with order one reactant leakage are known to possess this instability when the Lewis number is one (Peters, 1978). Work by Stewart (1986) indicates that the instability should also arise for adiabatic flames with Lewis numbers exceeding one. Recent work in reverse smouldering combustion (Lozinski and Buckmaster, 1994) requires an examination of the combined effect of heat losses and Lewis numbers well below unity. Because of the general nature of the results, they are presented here. The numerical computations reveal that while heat losses tend to destabilize the flame, small Lewis numbers have a countervailing stabilizing effect, suppressing the instability for an order one range of heat losses. This plays a key role in selecting the physically significant solution to the reverse smouldering combustion model (Lozinski and Buckmaster, 1994). The instability is one-dimensional; an examination of higher dimensions reveals no new instabilities arising for reasonable parameter values.
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