Examination of the Shrinking-Core Model of Sub-Micron Aluminum Combustion.

摘要

There has been significant interest in recent years in the combustion of sub-micron aluminum particles, and the standard theoretical framework is the shrinking-core model. This model, in the context of any fuel, has roots that go back 60 years. A common reference is a chapter in (2), although the discussion there, within a framework of global statements, is reminiscent of well stirred reactor discussions, familiar in the chemical engineering literature, so that certain details are obscured. However, the model is simply described: A spherical core of liquid aluminum is surrounded by a shell of alumina and the aluminum core shrinks as aluminum is converted to alumina at the metal/oxide interface. The conversion occurs because of the inward transport of O atoms (we assume that the surrounding atmosphere is air) from the outer boundary of the oxide shell. It is commonly assumed that this transport is solely diffusive in nature, and quasi-steady, at best an approximation; and that apart from the aluminum/oxide transformation, the geometry is fixed. Provided these approximations only lead to modest error it might be reasonably argued that it is acceptable in view of two significant uncertainties: the value of the diffusion coefficient of the O atoms; and the value of the O concentration within the oxide at the oxide boundary. However, as we shall see, one of the neglected ingredients has significant mechanical consequences in the context of the spherical geometry, and therefore it is important to consider it. Because of the mechanical consequences, an analytical treatment in the spherical geometry is not possible, and yet analytical treatments are of great value in revealing fundamental physics. And so we shall start our discussion with a planar model, purely because of the insights thereby achieved, not because it corresponds to a configuration to be found in the physical world.