A Model for the Reduction of Specific Surface Area of Powders with Age

Abstract

PETN is a high explosive, sometimes stored for periods of up to many years, in powdered form. In storage, the explosive particles change size and shape owing to sublimation, condensation and surface di usion. AWE measurements are available on the changing particle size distri- bution (PSD), and the speci c surface area (SSA) of the powder, taken from experiments on accelerated ageing. But a mathematical model of the ageing process is wanted in order to interpret the processes at work. Various modelling issues and unusual features of the measure- ment data were discussed. Four models of important processes were developed, and are reported here. Model (i) addresses the fundamental physics associated with the transport of mass by sublimation, di usion and condensation. Model (ii) uses chemical kinetics to develop a system of ordinary di erential equations (ODEs) for the time-evolution of the frequencies of particle sizes. Model (iii) extends Model (ii) to a contin- uum particle size distribution. Lastly, Model (iv) considers the growth of particles as described by Cahn-Hilliard equations for the inter-particle transport of matter in Ostwald Ripening. Models (i) and (iv) include the complex geometry and thermodynamics of the problem. By con- trast, Models (ii) and (iii) focus on the time evolution of the PSD, but they are more di cult to associate with controllable variables, such as ambient temperature. Our discussions of models (ii) and (iii) suggest we can choose mass-transfer rate constants that reproduce the kind of ob- served evolution to a bimodal PSD. But more investigation is needed to determine how the rate constants may be associated with the particles' geometry and the thermodynamics of the mass transport processes.