Linear stability of the activation-energy-asymptotics reactive-layer structure: II. Liñán’s diffusion flame regime

The present study examines the linear stability characteristics of the reaction zone in Liñán’s diffusion flame regime. By utilizing characteristic temporal and length scales of the thin reactive layer, an explicit dispersion relation is derived through an asymptotic analysis near the critical Damköhler number Δ_c under the limit of 1–L = O(β⁻¹). Each term in the dispersion relation captures the contributions of three key physical mechanisms driving the instability: sensitivity to reactant leakage, excess enthalpy effects associated with the Lewis number, and diffusion relaxation due to outer perturbations. The analysis reveals three primary instability modes—planar, cellular, and pulsating—similar to those found in conventional diffusive-thermal instabilities. It is confirmed that these modes emerge with changes in the key parameters, Damköhler number (Δ) and Lewis number (L). The onset conditions for each mode were derived analytically and showed excellent agreement with previously reported numerical results. Based on these results, a stability map was constructed in the Δ–L parameter space. Furthermore, by incorporating outer-layer disturbances associated with complex flame configurations, this framework offers a promising extension to the conventional analysis of diffusive-thermal instability.