Times to ignition in systems initiated by light

Abstract

An infinite slab of an exothermic reactant has one face kept at ambient temperature whilst the other is subjected to a continuous flux of radiant energy. When reactant consumption can be ignored, a stationary temperature distribution is approached that can persist as long as conditions for criticality are not surpassed (δ≦δ_cr). When conditions are marginally supercritical, the temperature distribution eventually peels away. Times-to-ignition t_ign are shown to obey the rule t_ign∝(δ–δ_cr)^–1/2 where δ_cr depends on the intensity of the illumination, and values for the proportionality constant are calculated.