Page 285 - Dust Explosions in the Process Industries

254 Dust Explosions in the Process Industries

particle is therefore governed by the rate of oxygen diffusion toward the reaction zone.
In the initial stage of combustion, the site of reaction is close to the outer surface of the
oxide layer. However, owing to depletion of oxygen, this zone is detached from the
oxide surface and shifted to a distance,L, from the particle shell. The rate of oxygen dif-
fusion and the rate of combustion are determinedby the gradient of oxygen partial pres-
sure at ro + L. This gradient remains approximately constant over the lifetime of the
burning particle, except for the final stage,when the reaction zone withdraws to the oxide
shell.
Cassel(l964) also suggested a theoretical model for the combustion of a magnesium
particle. On the assumption that the location of the liquid drop inside the oxide shell is
unimportant and the rate of oxygen diffusionis always slower than the rate of the chem-
ical reaction, the burning rate of a magnesium particle is given by the quasistationary
balance of the oxygen diffusion rate,

- DP P-PL
Wo2= 4;rd(r0+ L)-ln-
RT P-P,

and the rate of metal vaporization,

- 4;rdpr2 dr
w =---
Mg ME dt
Here D is the average oxygen diffusion coefficient at average temperature T,M is the
mole weight of magnesium, p is density of magnesium, E is oxygen equivalent (=2 for
oxidation of magnesium),p is the absolute total pressure at distance ro(just outside of
the oxide shell), and pL and p, are the partial pressures of oxygen at distances L and
infinity.
The time z required for complete combustion of a particle is obtained by combining
equations (4.1) and (4.2) and integrating from the initial drop radius roto 0. The result-
ing equation is

TI- (4.3)
MEDp 3(ro + L) P-P,

Equation (4.3) was used to derive values of (DIT)from observed Tvalues. Note that p,
p,, and D refer to different temperatures; namely, the boiling point of the metal, the ambi-
ent gas temperature, and the temperaturein the diffusionzone near the reaction front, T.
The estimates of D,assuming molecular diffusion, gave an unrealistically high T value
of 4860 K for a magnesium particle burning in air. Cassel suggested, therefore, that the
combustion of magnesium particles is governed predominantly by diffusion of atomic
oxygen. He also suggested that the same must be true in any dust flame burning at 3000 K
or more.
Liebman, Cony, and Perlee (1972) studied experimentally the ignition of individual
28-120 pm diameter magnesium particles suspended in cold air, by an approximately
square laser light pulse of 1.06 or 0.69 pm wavelength and 0.9 ms duration. The results
suggest that, during the heating of a magnesium particle by a short flash of thermal radi-
ation,the particle temperature first rises rapidly to the boiling point. Vaporized metal then