Modelling bubble growth in a burning metal droplet

Abstract

Numerous applications such as explosives, propellants, pyrotechnics, and bio-agent defeat employ combusting metal powders to augment performance and optimising this combustion is of great interest to many fields. Some metallic powders have been observed to explode during combustion, yielding new surface areas and potentially enhancing their burn rates. Enhancing our understanding of these microexplosion events opens the door to powder optimisation and superior performance. This paper investigates bubble growth within combusting metal droplets that leads to these microexplosions and compares experimental data from X-ray phase contrast images of bubble growth with solutions of a mathematical model. The model is developed from the Navier–Stokes equations in spherical coordinates while applying assumptions and substituting expressions of mass continuity for simplification to coupled first order ordinary differential equations. These simplifications allow the equations to be solved using ode45 in MATLAB to obtain a plot of the bubble radius over time. A number of candidate functions for expressing the molar flow of gas into the bubble are generated for use in the model. The graphs for different functions for molar flow rate are compared to radius-time data measured from images of bubble growth events in combusting aluminium-zirconium alloy powders. The model and data agree within limits of uncertainty when the flow of nitrogen into the bubble is linearly proportional to the bubble radius. These results offer more insights towards the rate at which molecules of gas are adsorbed onto an interface and the mechanisms of mass transfer in high temperature liquid metal solutions.