RADIATION-AFFECTED HYDRODYNAMIC INSTABILITY OF PARTICLE-LADEN FLAMES

We extend the classical stability analyses of Landau Darrieus and Mark stein to flames propagating in gases that are seeded with fine inert p articles, and account for the resulting radiative exchanges. Our main assumptions are that: i) the Zel'dovich number based upon the flame-sp eed sensitivity to reaction temperature can be considered large; ii) t he two-phase mixture is a one-velocity, one-temperature continuous med ium; iii) radiation follows the Eddington equation; iv) radiant exchan ges are weak, yet non negligible; v) the flame front is optically very thin but local curvature effects can be accounted for via a Markstein length that is proportional to the actual front thickness. Using asym ptotic techniques and the normal-mode method we show that radiative ex changes modify the classical dispersion relation in several, possibly antagonistic, ways: 1) radiation-enhanced propagation speed tends to s trengthen the Landau-Darrieus mechanism and to weaken the (stabilizing or destabilizing) influence of gravity and that of curvature. 2) tran sverse radiant exchanges bring about a stabilizing nonlocal curvature effect which is akin to Markstein's for long wavelengths of wrinkling but saturates for short waves (transverse optically-thin limit). The c ombined effects may result, e.g., in two disjoint ranges of unstable w avelengths. As the evolution equation equivalent to the dispersion rel ation is of fourth-order in time, the parametric destabilization/stabi lization of particle-laden flames might possibly differ from the class ical case.