Of the two-phase mixture models used to study deflagration-to-detonation transition in granular explosives, the Baer–Nunziato model is the most highly developed. It allows for unequal phase velocities and phase pressures, and includes source terms for drag and compaction that strive to erase velocity and pressure disequilibria. Since typical time scales associated with the equilibrating processes are small, source terms are stiff. This stiffness motivates the present work where we derive two reduced models in sequence, one with a single velocity and the other with both a single velocity and a single pressure. These reductions constitute outer solutions in the sense of matched asymptotic expansions, with the corresponding inner layers being just the partly dispersed shocks of the full model. The reduced models are hyperbolic and are mechanically as well as thermodynamically consistent with the parent model. However, they cannot be expressed in conservation form and hence require a regularization in order to fully specify the jump conditions across shock waves. Analysis of the inner layers of the full model provides one such regularization [Kapila et al., Phys. Fluids 9, 3885 (1997)], although other choices are also possible. Dissipation associated with degrees of freedom that have been eliminated is restricted to the thin layers and is accounted for by the jump conditions.

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An unexpected mechanism for fast reaction of Al nanoparticles covered by a thin oxide shell during fast heating is proposed and justified theoretically and experimentally. For nanoparticles, the melting of Al occurs before the oxide fracture. The volume change due to melting induces pressures of 1–2 GPa and causes dynamic spallation of the shell. The unbalanced pressure between the Al core and the exposed surface creates an unloading wave with high tensile pressures resulting in dispersion of atomic scale liquid Al clusters. These clusters fly at high velocity and their reaction is not limited by diffusion (this is the opposite of traditional mechanisms for micron particles and for nanoparticles at slow heating). Physical parameters controlling the melt dispersion mechanism are found by our analysis. In addition to an explanation of the extremely short reaction time, the following correspondence between our theory and experiments are obtained: (a) For the particle radius below some critical value, the flame propagation rate and the ignition time delay are independent of the radius; (b) damage of the oxide shell suppresses the melt dispersion mechanism and promotes the traditional diffusive oxidation mechanism; (c) nanoflakes react more like micron size (rather than nanosize) spherical particles. The reasons why the melt dispersion mechanism cannot operate for the micron particles or slow heating of nanoparticles are determined. Methods to promote the melt dispersion mechanism, to expand it to micron particles, and to improve efficiency of energetic metastable intermolecular composites are formulated. In particular, the following could promote the melt dispersion mechanism in micron particles: (a) Increasing the temperature at which the initial oxide shell is formed; (b) creating initial porosity in the Al; (c) mixing of the Al with a material with a low (even negative) thermal expansion coefficient or with a phase transformation accompanied by a volume reduction; (d) alloying the Al to decrease the cavitation pressure; (e) mixing nano- and micron particles; and (f) introducing gasifying or explosive inclusions in any fuel and oxidizer. A similar mechanism is expected for nitridation and fluorination of Al and may also be tailored for Ti and Mg fuel.

Combustion velocities were experimentally determined for nanocomposite thermite powders composed of aluminum (Al) fuel and molybdenum trioxide (MoO3) oxidizer under well-confined conditions. Pressures were also measured to provide detailed information about the reaction mechanism. Samples of three different fuel particle sizes (44, 80, and 121nm) were analyzed to determine the influence of particle size on combustion velocity. Bulk powder density was varied from approximately 5% to 10% of the theoretical maximum density (TMD). The combustion velocities ranged from approximately 600 to 1000m∕s. Results indicate that combustion velocities increase with decreasing particle size. Pressure measurements indicate that strong convective mechanisms are integral in flame propagation.

An unexpected mechanism for fast oxidation of Al nanoparticles covered by a thin oxide shell (OS) is proposed. The volume change due to melting of Al induces pressures of 0.1–4GPa and causes spallation of the OS. A subsequent unloading wave creates high tensile pressures resulting in dispersion of liquid Al clusters, oxidation of which is not limited by diffusion (in contrast to traditional mechanisms). Physical parameters controlling this process are determined. Methods to promote this melt dispersion mechanism, and consequently, improve efficiency of energetic nanothermites are discussed.