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Research and Development 589

oxide cap is gradually built up around the liquid particle core. This model deviates sorne-
what from the classic Cassel model (see Section 4.1.2 in Chapter 4).
Fedorov and Gosteev (1996) combined the classic thermal explosion theory and the ca-
tastrophe theory in their mathematical analysis of ignition of single magnesiumparticles.
In their basic study, Rosenband, Gany, and Timnat (1998) investigatedthe combustion of
magnesium and boron particles in a hot steam flow, whereas Foelsche, Burton, and Krier
(1999) and Zhou et al. (1999) studiedthe ignitionand combustion of singleboron particles.
Zevenbergen (2002) conducted a series of experimentsin which he ignited single mag-
nesium particles by a continuous light beam from a carbon dioxide laser. The single par-
ticle was kept suspended in airin a fixed position by means of an acoustic levitator.This
made it possible to heat the particle in a controlled manner by the laser beam and moni-
tor the particle temperature continuously during the heating process, using an optical
multiwavelength thermometer, right up to the sudden very steep temperature rise at the
point of ignition.For this particular setup, Zevenbergenfound that the criticalparticle tem-
perature for ignition was independent of the particle diameter over the diameter range
150-750 pm investigated.This means that the minimum radiated energy that had to be
absorbed by a particle for the particle to ignite, assuming negligible heat loss from the
particle during the heating period, was proportional to the particle volume. This, in turn,
means that a constant minimum radiated energyper unit particle volume had to be absorbed
y a particle for the particle to ignite,irrespectiveof particle size. As discussed in Section
1.3.2 of Chapter I and illustrated in Figure 1.30, previous experimental and theoretical
work indicate that the minimum ignition energies of clouds of some dusts in air are also
proportional to the particle volume. However, the absence of any observed influence of
particle size on the criticalparticle temperature for ignition cannot be expected to hold as
the particle size increases far beyond the maximum size investigated by Zevenbergen.
Banagiotou, Levendis, and Delichatsios (1996) used a three-color near-infrared opti-
cal pyrometer for monitoring the combustionof single sphericalpolystyrene particles of
diameters in the range 47-355 pm, whereas Joutsenoja et al. (1999) applied a two-color
optical pyrometer for nonintrusive in situ measurement of the dependencebetween the
temperature and size of burning coal particles.
Experimentsunder close-to-zero gravity conditions have been used to study the detailed
mechanisms of Combustion of single particles for quite some time (see Figures 4.4 and
4.5 in Chapter 4). More recently Yang, Hamins, and Donnelly (2000) used this method
to study zero-gravity combustion of supported thermoplastic particles of BMMA,
pokypropylene, and polystyrene. Although the particle sizes used, 2-6.5 111111,were corn-
paratively large from the point of view of dust explosions, the basic combustion mech-
anisms found are probably also qualitatively valid for smaller particles.
Zhang and Bar-Ziv (1997) presented a new method for determining thermal conduc-
tivities of single pm-sized particles. This parameter is important when modeling the
microscopic mechanisms of flame propagation in dust clouds.

9.2.3.3
initiation and Propagation of Fires in Dust Layers and Deposits

Work on this problem up to 1990is discussed in Section 5.2 in Chapter 5 and Section 7.7
in Chapter 7. An overview of research on self-heating and self-ignitionin dust deposits
was given by Crowhurst(1993a). Hensel and John (1992, 1993)provided further insight