The modeling of weak shock waves in highly porous powder beds and comments on its relevance to exploding bridgewire (EBW) detonators

Abstract

A computer modeling study is reported about the constant-piston-velocity compaction response of a 50% porous fine particle and air mixture. It is established that for the 10- $$\upmu \hbox {m}$$ average particle diameter powder chosen (sugar), over the piston velocity range 100–1000 $$\hbox {m}\,\hbox {s}^{-1}$$ , a self-similar shock is formed in 12–14 particle diameters of motion ( $${\approx }\,140~\upmu \hbox {m}$$ ). The shock is found to be statistically bounded, but temporally and spatially variable. At the resulting shock velocities identified for this powder, this results in self-similar behavior if the shock is supported for approximately 100 ns. Therefore, the use of the shock jump equations to estimate the post-shock state is valid after this duration. Further, it is found that a linear shock- and particle-velocity relation works well to model the low-pressure compaction of the powder. The intercept of this relation (commonly called the bulk sound speed in solid materials) is very low (50–100 $$\hbox {m}\,\hbox {s}^{-1}$$ ), but positive. The implications of this powder response on the functioning of exploding bridgewire detonators and the porous pentaerythritol-tetranitrate fill commonly used in them are discussed and compared with other literature on the topic.