Evaporation and combustion of thin films of liquid fuels

Abstract

We consider the evaporation and subsequent burning of thin films of liquid fuels. Previous studies on liquid films, with and without evaporation, have primarily considered the gas phase to be passive. The new element in this study is the introduction of combustion and the examination of both the liquid and gas phases and their effect on the film's behaviour. For the case of a liquid film burning in quiescent air we show that the problem can be simplified to a single nonlinear evolution equation for the film thickness. All remaining variables, which are simply expressed in terms of the function describing the instantaneous position of the liquid–vapour interface, are subsequently determined. This equation is then solved in order to understand the dynamics of the film in the presence of evaporation and combustion.

The planar configuration is discussed first. Predictions for the total evaporation time are obtained, along with the time history of the film thickness, the interfacial surface temperature, the flame standoff distance and its temperature, and the mass burning rate. The dependence of the burning characteristics on the fuel and oxidizer Lewis numbers, which measure the relative importance of thermal and molecular diffusivities, is also determined. Second, we analyse the case of a non-planar interface, where temperature variations along the film's surface cause fluid motion in the liquid that could either dampen or amplify spatial non-uniformities. We show that, while thermocapillarity has the tendency to destabilize the planar interface, combustion acts to reduce this effect. In particular, when the heat release by combustion is substantial, all disturbances are obliterated, the film remains nearly planar and the burning occurs along nearly horizontal surfaces.