Wrinkling of spherically expanding flames

The onset of instability and subsequent development of cells on spherically expanding flames is examined theoretically. The model used accounts for both hydrodynamic and diffusive-thermal effects and, in contrast to earlier theories, is valid for variable transport properties over a wide range of equivalence ratios. The analysis yields predictions for a number of flame properties, including growth rate of small disturbances, critical flame size for the instability onset, cell size beyond the threshold, and an estimate of the speed of the developing turbulent flame. It is shown that results using the more realistic temperature-dependent transport coefficients are more commensurate with experimental data concerning the critical conditions, that is, flame size or Peclet number, at the transition from one burning regime to another.