Thermal explosion in a thin-film composition

Abstract

We have studied the problem of thermal explosion in thin-film compositions consisting of alternating layers of two reagents. The density of the initial mixture and product were taken to be equal. We assumed that the concentrations of the initial reagents were linearly distributed in a thin layer of product. The formation of the reaction product was considered in the diffusion approximation with the final rates of the reaction at the interphase boundaries. The temperature gradients were not taken into account in the volume of the substance, since we assumed that the characteristic time of thermal relaxation was shorter than the characteristic time of heating. The problem was solved numerically by the Euler's method with a variable time step. We considered two ways of heating a thin-film composition: a constant-temperature oven and external energy source with a constant density. We received the analytical evaluations that determine the processes of ignition in the diffusion mode and the mode limited by boundary kinetics. Numerical calculations for thermal images of a ther-mal explosion in the layered composition were carried out depending on the thickness of the elementary layer. We have constructed the dependences of the critical Semenov number (heating in the oven) and the ignition temperature (linear heating) versus the thickness of the layer, which show a regime change of the chemical interaction in thin-film composition. The analytical dependences were shown to be in good agreement with numerical calculations in the limiting cases of chemical interaction. We found that the thin layers of reagents increased the areas of explosive modes of chemical transformations and softened the conditions of synthesis. We have proposed a method for estimating the parameters of diffusion and boundary kinetics: activation energy and pre-exponential factor using the experimental data in the coordinates of "elementary layer thickness - ignition temperature of the layered composition" for the case of heating by an external heat source with a constant density.