The determination of explosion limits from a unified thermal and chain theory

A general equation for explosion limits (P-T relation) is derived from a unified thermal and chain theory. From this general equation, the criteria of explosion limits for either the pure chain or pure thermal theory can be deduced. For a purely thermal system (no chain reactions involved), the limits are shown to depend upon knowledge of the kinetics instead of the gross heat release rate alone. The result of the classical theory is obtained from the unified theory again when a single step reaction is assumed. It is also shown that explosions in a system which contains a branching chain in its kinetic scheme always go through a path of both energy and chain-carrier concentration divergence. In some cases, it may even go through a pure thermal mechanism without involving the divergence of the chain carrier at all (such as the third limit of the H₂ and O₂ system). In application of the theory to the H₂ and O₂ system, the general equation of explosion limits is shown to prescribe all three limits, lower, upper, and third. The discussion is extended to the CO and O₂ system. It shows that the unified theory may be used to explain the previously unaccountably high activation energy deduced from the upper limit.