On the Wind Generated by a Collapsing Diffusion Flame

We examine the stationary spherical diffusion flame attached to a fuel drop, and consider the consequences of an instantaneous reduction of the Damkohler number below the extinction threshold, so that steady vigorous burning is no longer possible. Extinction occurs in two stages that are described by a combination of analysis and numerical calculation, valid in the limit of infinite activation energy. The first stage is characterized by a small but very rapid drop in the flame temperature, and a corresponding small but rapid density increase within the reaction zone or flame sheet. The associated increase in mass within the sheet is fed by an unsteady 0(1) velocity field, induced beyond the sheet, and superimposed on the initial 0(1) velocity defined by the steady state. This induced velocity is responsible, in due course, for the drawing in of fluid from infinity towards the collapsing flame. The second stage takes over once reaction becomes negligible, and is characterized by the dispersion of the temperature field through diffusion and advection. This is a rather slow process.