A theory of ignition is presented to analyse the effect of porosity on the time to ignition of a semi-infinite porous energetic solid subjected to a constant energy flux. An asymptotic perturbation analysis, based on the smallness of the gas-to-solid density ratio and the largeness of the activation energy, is utilized to describe the inert and transition stages leading to thermal runaway. As in the classical study of a nonporous solid, the transition stage consists of three spatial regions in the limit of large activation energy: a thin reactive-diffusive layer adjacent to the exposed surface of the material where chemical effects are first felt, a somewhat thicker transient-diffusive zone and, finally, an inert region where the temperature field is still governed solely by conductive heat transfer. Solutions in each region are constructed at each order with respect to the density-ratio parameter and matched to one another using asymptotic matching principles. It is found that the effects of porosity provide a leading-order reduction in the time to ignition relative to that for the nonporous problem, arising from the reduced amount of solid material that must be heated and the difference in thermal conductivities of the solid and gaseous phases. A positive correction to the leading-order ignition-delay time, however, is provided by the convective flow of gas out of the solid, which stems from the effects of thermal expansion and removes energy from the system. The latter phenomenon is absent from the corresponding calculation for the nonporous problem and produces a number of modifications at the next order in the analysis arising from the relative transport effects associated with the gas flow.
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