A general asymptotic formulation is presented for diffusion flames of large-activation-energy chemical reactions. In this limit chemical reaction is confined to a thin zone
which, when viewed from the much larger diffusion scale, is a moving two-dimensional
sheet. The formulation is not restricted to any particular configuration, and applies to
conditions extending from complete combustion to extinction. The detailed structure
of the reaction zone yields jump conditions that permit full determination of the
combustion field on both sides of the reaction zone, as well as the instantaneous shape
of the reaction sheet itself. The simplified system is subsequently used to study the
intrinsic stability properties of diffusion flames and, in particular, the onset of cellular
flames. We show that cellular diffusion flames form under near-extinction conditions
when the reactant in the feed stream is the more completely consumed reactant,
and the corresponding reactant Lewis number is below some critical value. Cell sizes
at the onset of instability are on the order of the diffusion length. Predicted cell
sizes and conditions for instability are therefore both comparable with experimental
observations. Finally, we provide stability curves in the fuel and oxidant Lewis number
parameter plane, showing where instability is expected for different values of both
the initial mixture strength and the Damköhler number.