Modeling the Combustion of a Sub-micron Aluminum Particle (PREPRINT)

摘要

We examine the shrinking-core model of aluminum combustion, one that has been proposed for sub-micron drop diameters. In this model a core of liquid aluminum is surrounded by alumina through which O atoms diffuse to the aluminum surface. It is shown that the volume changes intrinsic to this model necessarily lead to fracturing of the alumina and the creation of cracks and voids. A simple mathematical model is described which, because of the length and time scales, is quasi-steady, permitting analytical solutions. When the drop is sufficiently small this leads to a simple formula for the burn time as a function of the atmospheric pressure, temperature, and oxygen concentration, which is tested against experimental data. By introducing a fractal ingredient into the description, motivated by the fracturing, it is possible to generate agreement with experimental data on the variations of burn time with drop diameter, a d0.25-t law in contrast with the familiar d sq-t law of classical fuel-drop combustion. For larger drop diameters a non-linear differential equation for the burn rate is derived whose integration yields the burn time as a function of drop diameter and shows a transition from the d0.25 law to a d sq law.