Critical behavior in small particle combustion

Small particles combusting under free molecular conditions are shown to exhibit critical behavior under conditions of high collision efficiency. At a particular collision efficiency, the particle behavior transitions from noncritical to critical (or runaway) behavior. Noncritical behavior is defined as a finite particle temperature at burnout, whereas critical behavior implies an infinitely increasing particle temperature at burnout. The critical collision efficiency is derived from the governing equations for free molecular combustion of small particles. The critical collision efficiency is shown to be a function of the specific heats of the gas and the particle and is independent of the particle size. Analytic and numerical results are compared. Particle radiation is included in the numerical results. The inclusion of radiation does not effect the critical collision efficiency, although radiation does decrease the rate of particle temperature increase.