We study the nucleation and growth of flame fronts in slow combustion. This is modeled by a set of reaction-diffusion equations for the temperature field, coupled to a background of reactants and augmented by a term describing random temperature fluctuations for ignition. We establish connections between this model and the classical theories of nucleation and growth of droplets from a metastable phase. Our results are in good agreement with theoretical predictions.
Karttunen, M. E. J., Provatas, N., Ala-Nissila, T., & Grant, M. (1998). Nucleation, growth, and scaling in slow combustion. Journal of Statistical Physics, 90(5-6), 1401-1411. https://doi.org/10.1023/A:1023243831128