Effects of differential diffusion on thin and thick flames propagating in channels

Flame propagation in channels and cracks is a problem of considerable interest with applications in many combustion devices and in fire hazard scenarios. In this paper, the propagation of premixed flames in two-dimensional channels of variable width with a prescribed Poiseuille flow is discussed. The main objective is to assess the effects of differential diffusion on the burning process. For both thick (narrow channels) and thin (wide channels) flames, explicit asymptotic results are obtained for the burning rate and flame shape. These are complemented with numerical calculations spanning the remaining range of moderate flame thicknesses. The results show that unlike thin flames, known to be affected by the effective Lewis number of the mixture, in narrow channels Lewis number effects are negligible. Furthermore, in wide channels, not only does the burning rate strongly depend on the Lewis number, but flame tip-opening or dead-space near the wall may result in mixtures with a Lewis number sufficiently less than one.