Abstract
Recent experiments in microgravity suggest the possibility of stationary spherical premixed flames (flame balls) in which the only fluxes are diffusional. We construct stationary solutions of this nature, starting with simple model equations and using activation energy asymptotics. Sufficiently large volumetric heat losses quench the flame, and for heat losses less than the quenching value there are two possible solutions, a small flame, and a large flame. For vanishing heat loss the small solution is identical to one constructed by Zeldovich, and is known to be unstable, whereas the large solution is characterized by a flame of infinite radius. We examine the linear stability of these stationary solutions, and show that all small flames are unstable to one-dimensional (radial) perturbations. Large flames are unstable to three-dimensional perturbations, but only if they have a radius greater than some critical value. Thus there is a band of large flames, lying between the quenching point and unstable flames, that are stable.
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