Flame instability in a Hele-Shaw cell: thickness effect

International audienceAn Hele-Shaw burner is a convenient device for studying the development of premixed flame instabilities in a quasi-two dimensional configuration. It is possible to ignite a plane flame at the top of the cell, and to measure quantitatively the growth rates of the instability by some simple image analysis. Starting from this linear growth rate, it is also possible to forecast the non-linear evolution of the flame for short times using a Sivashinsky equation. We study here the effect of the thickness of the Hele-Shaw cell on the growth rate and compare the results to theoretical predictions and numerical simulations. In addition to the usual Darrieus Landau instability of flames propagating in tubes, it has been predicted in the literature that in a Hele-Shaw geometry, two further effects come into play, Saffman Taylor instability and the effect of heat losses. We discuss here the relevance of these two effects