The basic theory of thermal ignition is largely based on the heat conduction equation with an Arrhenius exothermic reaction term [1][2][3]. If one assumes that reactant concentration is uniform, depletion can be ignored, and conduction is the only heat transport mechanism, then criticality behavior can be discussed in terms of the steadystate solutions that can be obtained by analytical approximations [1,[4][5][6] as well as by essentially exact numerical methods [7,8]. It is difficult to realize these conditions in laboratory measurements; consequently the general validity of the continuum model results is not known.
In this note we describe a study of thermal instability of a self-heating slab using the technique of computer molecular dynamics simulation. This method has proved to be invaluable in probing the local structure and atomic motions in liquids [9]; it has been applied also to shock wave propagation [10] and chemical reactions [11]. The present application demonstrates the feasibility of atomic simulation of critical behavior in self-heating. Not only does one obtain data to check continuum theory, but also one can generate results on fluctuations which are not considered in the macroscopic description.
The model we have studied is a two-dimensional fluid having the symmetry of an infinite slab system. The slab is composed of particles, each of diameter a, which undergo hard-core collisions with or without chemical reactions. During each collision the relative kinetic energy at contact Trel is calculated. If Trel/> EO, where E o is a prescribed activation energy for exothermic reaction,