  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 Damkohler number and Lewis number is treated in detail.
It is found that, below a critical Damkohler number Da(crit), 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 Da(crit)
increases monotonically with the Lewis number. Properties of the solutions are
studied analytically in the limit of large Damkohler number and for small and
large Lewis number.
