Incipient group combustion particles

In assuming WF.p to be a constant, we anticipate a heat/mass compensation eflFect which tends to suppress particle temperature variation through a QS cloud. Specifically, the decreased oxidizer concentration found as one penetrates the cloud, which tends to decrease particle temperature, is offset by an increase in the local ambient temperature. (Such an effect has been observed recently for the case of evaporation of interacting particles of low volatility (II). Extension of these results follows, since for the conditions of incipient group combustion, the variable T + [Q/(vCp)](oo satisfies the Laplace equation both inside and outside the cloud. The condition for total heat/mass compensation follows provided that Q >> L),... 

Approach. The use of continuum models is defensible only when the particles are suflBciently far apart that suitable averaged oxidizer and fuel mass fraction can be defined. This implies not only the Rp/L < < 1 but also the Rf/L < < 1, where Rf is the individual envelope flame radius, and L is the interparticle distance. Indeed, the use of a continuum approach to establish the incipient group combustion criterion may be suspect since this last inequality is not met. Further, continuum models cannot be defended when the number of particles in the cloud is small... 

---