Approach

The development of the equations governing combustion involves derivation of the equations of motion of a chemically reacting gaseous mixture and judicious simplification to render them tractable while retaining their essential characteristics. A rigorous derivation requires a long apprenticeship in either kinetic theory or continuum mechanics. (Indeed, the general continuum theory of reacting mixtures is only now being perfected.) We choose instead a plausible, but potentially rigorous, derivation based on the continuum theory of a mixture of fluids, guided by experience with a single fluid. Ad hoc arguments, in particular the inconsistent assumption that the mixture itself is a fluid for the purpose of introducing certain constitutive relations, will not be used.

Treating the flow of a reacting mixture as an essentially isobaric process, the so-called combustion approximation, is a safe simplification under a wide range of circumstances if detonations are excluded. But the remaining simplifications, designed as they are solely to make the equations tractable, should be accepted tentatively. They are always revocable should faulty predictions result; for that reason they are explained carefully. Nevertheless, whosoever is primarily interested in solving nontrivial combustion problems, as we are, can have the same confidence in the final equations as is normally placed in the equations of a non-Newtonian fluid, for example.