Marangoni instability at a contaminated liquid–vapor interface of a burning thin film

Abstract

We consider the evaporation and subsequent burning of thin films of liquid fuels on which a nonsoluble surface active agent (surfactant) is present. This work complements a previous study where we have considered the same problem but in the absence of surfactant. Surfactant may result from impurities of the liquid fuel or from backward diffusion of unoxidized combustion intermediaries and heavy soot precursors. When burning occurs in a quiescent ambient, the mathematical problem can be systematically reduced to a pair of nonlinear evolution equations for the film’s thickness and surfactant’s concentration. These equations contain, in particular, the temperature and mass flux at the liquid–vapor interface as additional parameters, determined from full consideration of the gas-phase processes. We show that in the absence of combustion or, when the heat released by the chemical reactions is relatively small, thermo-capillary effects tend to destabilize a nominally planar interface. The presence of surfactant brings about a slower growth and can possibly stabilize the film. Combustion generally acts to reverse these trends: When the heat release is large, thermo-capillary effects stabilize the liquid–vapor interface while the presence of surfactant leads to destabilization.