The fast-time instability of the Liñán's diffusion-flame regime is investigated asymptotically and numerically by employing the fast inner-zone time and length scales, as a model problem for the cellular instability in diffusion flames with Lewis numbers far from unity
by an amount of order unity. The stability analysis revealed the full spectral nature, particularly near the saddle-node bifurcation condition corresponding to the minimum reduced Damköhler number Δ. Contrary to the conventional belief, the minimum Δ condition, commonly known
as the Liñán's diffusion-flame extinction condition, is not necessarily an extinction condition for flames with Lewis numbers less than unity which can survive beyond the saddle-node bifurcation condition. The cellular instability could emerge upon passing the saddle-node bifurcation
condition. The cellular instability is thus observable for near-extinction diffusion flames with Lewis numbers less than unity, as predicted by the previous experimental studies and the linear stability analysis employing the NEF limit. The stable parametric regions of small wave number and
Lewis number just below unity were not predicted by the fast-time instability. But these parametric regions lie in the inner parametric layer of the distinguished limit employed in this analysis, so that the leading-order behavior is not contradictory with the previous experimental and analytical
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