Hydrodynamic and diffusion effects on the stability of spherically expanding flames

We examine the stability of an outwardly propagating spherical flame accounting for both hydrodynamic and thermodiffusive effects. For Lewis numbers less than a critical value Le^* < 1, disturbances of the flame front grow during the initial phase of propagation, i.e., when the radius is comparable to the flame thickness. However, for Le > Le^*, the flame, which is stable to thermodiffusive effects, becomes unstable only after a critical size is reached. This instability is hydrodynamic in nature and is caused by the thermal expansion of the gas. In this study we provide an expression for the determination of the critical size, or a critical Peclet number, which depends on the thermal expansion coefficient and on the Lewis number. The explicit dependence on all the relevant physicochemical parameters enables us to compare our results with experimental data.