THERMOHYDRODYNAMICS OF THIN SURFACE-FILMS IN HETEROGENEOUS COMBUSTION

Heterogenous reactions under transport control can be modelled in term s of a film of reaction products covering the reaction surface. Such a surface defines a unique direction in space which may be used to clas sify transport processes as transverse or longitudinal. Since crossed- gradient transport occurs, a Peclet number Pe is introduced, represent ing the ratio of the velocities characterizing transverse and longitud inal transport, with transverse transport being by film diffusion of s ome 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 approxima tion for the evolution of thin films on reaction surfaces is shown to be equivalent to a distinguished limit Pe-->0, Sc-->infinity, while ke eping 1/(ScPe(2))=O(1). The long-wave approximation is derived by an a pplication of the method of strained variables which leads to a film e quation for the spatio-temporal evolution of the film thickness h whic h represents the crucial element for a complete solution of the thermo -hydrodynamics of the layer. Since film generation due to chemical rea ction and film removal due to evaporation may compensate for certain t hicknesses h, surface phases are found to occur which correspond to st ationary layers of uniform thickness. The evolution of the surface lay er is shown to be a generalized reaction-diffusion process, with surfa ce waves representing dynamical transitions between surface phases.