Sufficiently large flame-balls are subject to a three:dimensional instability which defines a maximum mixture strength for which steady flame-balls can exist. We study the dynamics of flame-balls in the neighborhood of the neutral stability point and show that there is a transcritical bifurcation and the dynamics is governed by a fifth-order system of nonlinear ordinary differential equations. The late time behavior of the solution of these equations corresponds either to a stationary sphere (stable solution) or a growing oblate spheroid. Oblate spheroids are observed experimentally, and the relationship between the experimental observations and the theoretical predictions is discussed.
Buckmaster, J., Gessman, R., Ronney, P.D., The Three-Dimensional Dynamics of Flame-Balls, 24th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA,pp. 53-59,July 05,1992.