When an explosive burns, gaseous products are formed as a result. The interaction of the burning solid and gas is not well understood. More specifically, the process of the gaseous product heating the explosive is yet to be explored in detail. The present work sets out to fill some of that gap using mathematical modelling: this aims to track the temperature profile in the explosive. The work begins by modelling single-step reactions using a simple Arrhenius model. The model is then extended to include three-step reaction. An alternative asymptotic approach is also employed. There is close agreement between results from the full reaction-diffusion problem and the asymptotic problem.

We show that an enslaved phase-separation front moving with diffusive speeds can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. To our knowledge this is the first fully analytical derivation of the Liesegang laws. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.