Modeling aluminum combustion in oxidizing environment with the Gibbs formulation

Abstract

We have developed a continuum modeling approach, grounded in classical physical chemistry, based on the following assumptions: (1) That the states in the material can be represented by local stationary averages of the pressure (stress), temperature, and mass fractions computed from atomistic simulation, (2) and that the mixture has well-defined molecular components, each with a complete equation of state. The continuum model, “Gibbs formulation”, applies to near-atomic length and time scales, which we identify as the scales where the high frequency, high energy phonons equilibrate in molecular mixtures, (about six atomic radii and six to ten vibrational periods). Phase changes and chemical changes due to reaction are not in (asymptotically, long-time) equilibrium, and changes are assumed to occur on much longer time scales than those required for stress and temperature equilibration. The Gibbs formulation can be thought of as a generalization of the classical non-equilibrium formulations used in gaseous, multicomponent combustion theory, but expanded to mixtures with simultaneously present concentrations of solids, liquids and gases. We present an example of this approach applied to the ignition and burning of a nano-sized aluminum flake, modeled as a slab of aluminum coated with a thin alumina layer. The model considers up to six components: solid, liquid and gaseous aluminum, solid and liquid aluminum oxide (alumina), and oxygen. We discuss the many different behaviors and possible regimes of combustion, that depend on what is assumed for the thermal and mass transport and reaction rates.