The structure of flame filaments in chaotic flows

The structure of flame filaments resulting from chaotic mixing within a combustion reaction is considered. The transverse profile of the filaments is investigated numerically and analytically based on a one-dimensional model that represents the effect of stirring as a convergent flow. The dependence of the steady solutions on the Damkِhler number and Lewis number is treated in detail. It is found that, below a critical Damkِhler number Dacrit, the flame is quenched by the flow. The quenching transition appears as a result of a saddle-node bifurcation where the stable steady filament solution collides with an unstable one. The shape of the steady solutions for the concentration and temperature profiles changes with the Lewis number and the value of Dacrit increases monotonically with the Lewis number. Properties of the solutions are studied analytically in the limit of large Damkِhler number and for small and large Lewis number.