Analytical Model for Size Effect of Activation Energy of Zirconium and Aluminum Particles

Abstract:

A theoretical model of calculating activation energy by ignition temperature of metal particles is proposed. The critical condition of ignition temperature is that the heat generation rate of combustion reaction and the heat loss rate to the surrounding reach a heat balance. The heat loss rate is controlled by Knudsen number. The heat generation rate of aluminum particle combustion is calculated using the simplest Arrhenius-type model. The heat generation rate of zirconium particle combustion is calculated by diffusion model. And the activation energy corresponding to the ignition temperature of metal particle is obtained by iterative calculation. The results show that the activation energy of aluminum particles and zirconium particles increases with the increase of particle size, which is linear with the logarithm of particle size. In the larger size range of nanometer to micron, a single theoretical model is not enough to describe the size effect of activation energy of metal particles. The polynomial model based on data fitting is more universal.

Key words:activation energy; ignition temperature; zirconium; aluminum; nanoparticles; micron particles