טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentFrumkin Valeri
SubjectReaction Front Propagation in a Thin Film Thermally Coupled
with a Thick Heat-Conducting Substrate
DepartmentDepartment of Applied Mathematics
Supervisors Professor Amy Novick-Cohen
Professor Emeritus Alexander Nepomniashchy


Abstract

We consider a thin film that can undergo exothermic conversion. The thin film is assumed to be resting on a thick substrate made of an inert material, although there is no exothermic (or any other) conversion in the substrate. The film and substrate can exchange heat, and, therefore, the presence of the substrate may affect combustion wave propagation along the film. Indeed, the substrate acts on the film as a heat sink when the temperature of the film is higher than that of the substrate but as a heat source when the relation between the temperatures is opposite. In our model, we assume the thin film to be of zero thickness, and the substrate to be infinitely thick.

The model can reflect a film containing, e.g., a mixture of a fuel and an oxidizer through which a combustion wave can propagate, or a mixture of a monomer and initiator, in which case propagation of a polymerization wave is possible in the film, or it can reflect an overcooled liquid that can undergo the process of explosive crystallization. In certain sense our model is similar to sandwich models studied both in combustion and polymerization contexts, in which two thin layered systems are considered. An important difference is that here we consider a chemically active layer which is thin, and which is modeled as a one-dimensional medium, and we consider the substrate layer to be thick, in fact infinitely thick; In the sandwich models both chemically inert and chemically active layers are considered thin. The results of heat exchange between the film and the substrate in our model can therefore be very different from those in the sandwich models. A set of equations governing the propagation of the reaction front in the film is derived, the solutions corresponding to a flat front propagation are found, and their stability is studied. Afterwards, a two dimensional generalization of the model is presented, and the stability of the front with respect to distortions is studied.