Granular Explosives and Initiation Sensitivity

Yet for numerical simulations of detonation waves in plastic binded explosives (PBX) empirical pressure dependent reaction rates, such as ``Forest fire'' or the ``Ignition and Growth'' model, are typically used. The underlying reason for this disparity between between fundamental chemical rate laws and empirical burn models is due to the fact that a PBX is a heterogeneous material consisting of small crystals of an explosive material held together with an inert binder material. Due to the strong temperature dependence, the overall reaction rate of a heterogeneous explosive is dominated physically by peaks in the temperature field, called hot spots. The hot spots occur on the length scale of the heterogeneities and are absent from continuum models based on homogenized constitutive properties. Consequently, the effective burn rate is not determined by the average temperature. Empirical burn rates represent ``sub-grid'' models which account for the short wavelength reaction phenomenon not resolved withina simulation.