Finite-rate evaporation and droplet drag effects in spherical flame front propagation through a liquid fuel mist

An evolution equation for a laminar flame front propagating into an air and liquid fuel mist cloud is derived for the first time, accounting for both the finite-rate evaporation of the fuel droplets and the slip velocity between them and their host environment. The asymptotic analysis employed in developing the equation exploits the usual inverse large activation energy parameter associated with chemical reaction in the flame and a small drag parameter. It is demonstrated that, in the no-slip velocity case, increasing the vaporization Damköhler number can produce flame extinction, presumably due to the more intense heat loss incurred due to droplet heat absorption necessary for vaporization. Droplet drag can also induce extinction due to the longer residence time of the droplets in any locale (than if there was no slip), leading to more vaporization with greater attendant heat loss. The predicted results for droplet velocity are compared to independent experimental data from the literature with good qualitative agreement.