Citation

Eyring H, Caldwell D. Math. Model. 1980; 1(1): 33-40.

Copyright

(Copyright © 1980, Elsevier Publishing)

DOI

10.1016/0270-0255(80)90005-6

PMID

unavailable

Abstract

An important unfinished problem is the theory of transition from deflagration to detonation DDT. The understanding of this problem is critical for the safe handling of explosives. Some of the successes of deflagration and detonation theory are outlined. For detonation to occur in a cylindrical explosive, for example, one must remember that as a shock wave moves into cold explosive the shock loses energy and is dying out. Behind a developed wave front there is a succession of increasingly exothermic reaction surfaces rising to a maximum at the Chapman-Jouguet surface where rarefaction begins. A sufficiently sharp blow or an intense beam of laser light falling on unreacted explosive generates this type of structure which travels through the material as a self supporting shock wave. How to avoid forming such structures which will grow into travelling self supporting waves has many aspects. Here we consider: 1. Starvation kinetics which arise from a change of reaction mechanism due to the sudden introduction of unburned material into a hot environment. As the gradient from unburned to burned material rises a situation develops where the fastest way to get energy into the bond that breaks is not directly from translation to this bond but through a reservoir which readily communicates energy. This shifts the developing bottle neck of energizing the molecule (starvation kinetics) to a new pathway with interesting consequences; 2. Turbulence promotes initiation of detonation by sharpening the concentration and temperature gradients between unburned and burned materials; 3. The dependence of shock wave velocity, due to momentum loss out the side is related to the diameter of the explosive; and 4. The curvature of the wave front is related to drag of telescoping cylinders on the central axis of the cylindrical explosive.