INSTABILITIES IN SMOOTH 2D AND 3D ISOTHERMAL FLAMES

Chemical reactions exhibiting autocatalytic feedback support constant- form, constant-velocity reaction-diffusion wave fronts. The dimensionl ess velocity c of planar fronts depends on the ratio delta of the diff usion coefficients for the reactant A and autocatalytic species B and an approximate expression for c(delta) for delta > 1 (but 1 - delta(-1 ) much less than 1) is presented. The implications of this, along with previous results for c appropriate to other ranges of delta, in terms of the dependence of the actual wave velocity dx/dt as a function of the species diffusion coefficients D-A and D-B are discussed. An eikon al equation is then presented for the effect of curvature on the wave velocity for smooth circular or spherical waves. The coefficient that appears in the curvature term depends on delta: for delta less than so me 'critical' value delta approximate to 2.3, the coefficient is nega tive, indicating that the wave velocity increases towards the planar w ave velocity c(delta) as the curvature decreases; for delta > delta, however, the coefficient is positive, indicating that the wave velocit y decreases as the curvature decreases. This change in behaviour sugge sts that systems with delta > delta will not exhibit a 'critical radi us' below which wave propagation fails. The change in response to curv ature also underlies the loss of stability of smooth waves to spatial perturbation transverse to the direction of propagation. For planar wa ves, the requirement for instability is delta > delta with an additio nal condition on the wave number of the imposed perturbation (or, equi valently, on the width of the reaction zone). For spherical or circula r waves, this latter condition is translated as a requirement on the r adius of the smooth wave at the moment the perturbation is applied.