Clavin–Garcia equation or Clavin–Garcia dispersion relation provides the relation between the growth rate and the wave number of the perturbation superposed on a planar premixed flame, named after Paul Clavin and Pedro Luis Garcia Ybarra, who derived the dispersion relation in 1983.
[1] The dispersion relation accounts for Darrieus–Landau instability, Rayleigh–Taylor instability and diffusive–thermal instability and also accounts for the temperature dependence of transport coefficients.
be the wavenumber (measured in units of planar laminar flame thickness
) and the growth rate (measured in units of the residence time
of the planar laminar flame) of the perturbations to the planar premixed flame.
Then the Clavin–Garcia dispersion relation is given by[2][3][4][5][6] where and Here The function
, In the constant transport coefficient assumption,