A Nonlinear Theory of Cellular Flames

Experiments with laminar flames in gaseous combustible mixtures show that for certain mixtures a flame front will often break up into numerous cells. Cellular flames are periodic structures with pointed crests, pointing in the direction of the burned gas. The smoother sections (troughs) of the front are convex toward the fresh mixture. The flame appears darker at its crests than at its troughs, which indicates that the temperature at the crests is lower than in other parts of the cell. Sometimes the flame in the vicinity of the crests disappears entirely. We employ a model derived by Matkowsky and Sivashinsky to consider the stability of a uniformly curved propagating flame front. We show that the uniform front becomes unstable if the Lewis number L of the limiting reaction component is less than some critical number $L_c $, and if the radius of the front is greater than a critical value $R_c $. When the critical values are exceeded, perturbations of the uniform front evolve to a cellular front which bifurcates supercritically from the uniform front.