Numerous applications are interested in the use of combusting metal powders such as explosives, propellants, pyrotechnics, and bio-agent defeat. Optimising the performance of these reactions is of great interest to many of these fields. Particles of such powders have been observed to explode during combustion, yielding new surface areas and potentially enhancing the burn rate of the powder. It is thought that better understanding this process will help to design more optimised powders with greater benefits. Following the work in Wainwright et al. (2019), this thesis investigates the bubble growth within combusting metal droplets and compares the data from experimental recordings with solutions of a mathematical model. This model is developed from the Navier-Stokes equations in spherical coordinates and by ap- plying assumptions and substituting expressions of mass continuity is simplified 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 data measured from images of bubble growth events from experiments done by Wainwright et al. of a combusting aluminium and zirconium alloy powder. Within the limits of uncertainty there is most agreement between the model solution and experimental data when the flow of nitrogen into the bubble is linearly proportional to the bubble radius. This finding should help shed light on the mass transfer process during bubble growth.

Modelling of the bubble expansion was also completed using COMSOL Multiphysics for a two-dimensional axisymmetric case. This approach enables the influence of nucleation position to be evaluated. When concentric, the solution has a similar profile to that obtained from the ODE which gives confidence in the validity of the off-centre bubble simulations. It was found that as the location of the bubble nucleation site gets closer to the surface of the droplet, there is no large change in the growth rate of the bubble. The closer the nucleation is to the droplet surface does impact the rate at which the liquid phase thins as there does not appear to be flow in the liquid phase around the bubble, and then results in longer calculation times due to the warping mesh. As the liquid phase thins, the likelihood of the surface rupturing for some instability increases and so off-centre nucleations would then result in surface bursting at a smaller bubble size than concentric nucleation, however without the entire droplet breaking apart.

Further investigation towards understanding the different transport mechanisms was made by modelling chemical transport from diffusion and adsorption. To this end, the diffusion equation was applied to the domain with a coordinate trans form and coupled with the bubble growth ODE. This PDE was then solved with the Crank-Nicolson method and flux was input to the ODE to calculate the growth of the bubble. Different boundary conditions were applied to the domain with Dirchlet, Neumann, and Robin conditions solved and compared with data from the event analysis. Flux into the bubble for the Dirichlet and Robin conditions was calculated from the concentration profile at the given time step. The resulting bubble radius profile did not agree with the experimental data for these conditions. The Neumann condition showed the concentration plots for molar flow that matches the data. The required initial concentration for the simulation leads to an estimated initial amount of 3.5332×10-12 mol of nitrogen in the liquid phase. Compared with the amount of metal atoms in solution, this makes up roughly 0.3% of the atomic matter which suggests that the required initial concentration is attainable for most particles to undergo bubble growth.