Extinction of burning particles due to unstable combustion modes

Abstract

The objective of this paper is to derive analytically the conditions under which burning particles extinguish. Experiments indicate that the extinction may occur with a rapid drop in particle temperature, thus causing an insufficient burn-out. Both qualitative and quantitative description of this phenomenon is presented in this study. Based on Semenov's theory of thermal explosion, global heat release and loss balance determines the critical particle size, at which a rapid change of particle temperature occurs while the particle is burning. Under more general conditions, particles experience a temperature and oxidizer distribution, which is described by the conservation equations of mass and energy. By applying a linear stability analysis to these equations, regions are identified, for which the combustion mode becomes unstable, e.g. for which the hot solution changes rapidly to the cold solution and, thus leads to the extinction of the particle. The analysis shows that the regions of stable and unstable combustion are separated by critical heat and mass transfer conditions. These results enable engineers to assess the size of particles due to incomplete combustion, to apply appropriate filters or to change conditions favourable to further burn-out.