Heterogeneous removal of one or more chain-carrying species at first explosion limit of hydrogen + oxygen mixtures. Part 2.—An analytical solution of the diffusion equations

Abstract

A mathematical analysis of the simultaneous diffusion and heterogeneous removal of any number of chain centres in competition with linear branching is presented. The theory is applied in particular to the derivation of an exact expression for the first explosion limit of hydrogen + oxygen mixtures in a cylindrical vessel. Expressions for the apparent rate constants k^e_{i (app)} for the heterogeneous removal of each chain centre at the explosion limit have been derived that are analogous to the well-known formulations for the removal of one species. However, the values of such expressions differ markedly in magnitude from the values of the expressions that are obtained if the equations for the one-species case are assumed to hold in the multi-species case. Also, such expressions are not independent parameters of the system, and, in general, an interaction between the diffusion processes occurs.

The consequences of this interaction are examined; although the interaction does not markedly affect the variation of explosion pressure with mixture composition, it always causes an increase in the explosion pressure. For some combinations of efficiencies for the surface removal of H, O and OH, this increase is as large as 50 % in a 3.3 cm diam. vessel at 540°C.