Asymptotic theory for ignition and extinction in droplet burning

The quasi-steady diffusion flame structure in droplet burning is analysed, in the limit of large activation energy, for a one-step Arrhenius reaction in the gas phase. The characteristic ignition-extinction S-shaped curve is produced with segments of it corresponding to a nearly frozen flow regime, a partial burning regime, a premixed flame regime, and a nearly equilibrium regime. Critical Damköhler numbers for ignition and extinction, as well as correction factors to the mass evaporation rate due to finite activation energy, are obtained. Close mathematical and physical analogies exist between the present problem and the counterflow problem recently analysed by Liñán such that through appropriate transformations most of his numerical results can be readily utilized.