Thermo-hydrodynamics of thin surface films in heterogeneous combustion

Heterogenous reactions under transport control can be modelled in terms of a film of reaction products covering the reaction surface. Such a surface defines a unique direction in space which may be used to classify transport processes as transverse or longitudinal. Since crossed-gradient transport occurs, a Peclet number Pe is introduced, representing the ratio of the velocities characterizing transverse and longitudinal transport, with transverse transport being by film diffusion of some reacting species and longitudinal transport corresponding to film flow as with wetting processes. If the influence of viscosity is taken into account in terms of a Schmidt number Sc, the long-wave approximation for the evolution of thin films on reaction surfaces is shown to be equivalent to a distinguished limit Pe-->0, Sc-->infinity, while keeping 1/(ScPe(2))=O(1). The long-wave approximation is derived by an application of the method of strained variables which leads to a film equation for the spatio-temporal evolution of the film thickness h which represents the crucial element for a complete solution of the thermo-hydrodynamics of the layer. Since film generation due to chemical reaction and film removal due to evaporation may compensate for certain thicknesses h, surface phases are found to occur which correspond to stationary layers of uniform thickness. The evolution of the surface layer is shown to be a generalized reaction-diffusion process, with surface waves representing dynamical transitions between surface phases.