On the instability of a gradient explosion

Nonsteady-state phase transformation during bulk heat release in a material leads to a gradient explosion, characterized by a Pi-shaped temperature distribution evoked by finite superheating in the bulk of the material and to a high temperature gradient at the phase interface. A fast increase in heat flux at the phase transformation surface and the presence of internal superheating leads to explosive development of thermal instability of the phase interface. This paper presents a theoretical investigation of the stability of the spherical front of phase transformation in a special system of coordinates accompanying the surface in question. The study is relevant to the physics of exploding wires.