Page 241 - Dust Explosions in the Process Industries

Generation of Explosible Dust Clouds 2 13

3.5
DYNAMICS OF PARTICLES SUSPENDED IN A GAS

3.5.1
TERMINAL SETTLING VELOCITY OF A PARTICLE
IN THE GRAVITATIONAL FIELD

Terminal settling velocities of particles in air have been determined experimentally in
numerous investigations.An early exampleis the work of Zeleny and McKeehan (1910),
who conducted careful measurements of the terminal velocities of spherical drops and
particles of paraffin, black wax, and mercury in air at atmospheric pressure and room
temperature.The measurementswere in excellent agreementwith Stokes’theory for the
laminar flow regime.
Some pollens and spores were also included in this investigation,but for these parti-
cles, the experimental terminal settling velocities were generally somewhat lower than
the theoretical Stokes’velocity. This also applied to lycopodium,the spore of club moss,
which has been widely used all over the world in dust explosion research (Eckhoff,
1970).Lycopodium particles are close to monosized, with an arithmetic mean diameter
of about 30 pm. The particle density is about 1.18g/cm3.According to Figure 3.10, this
corresponds to a Stokes’terminal velocity of 0.035 m/s, whereas the experimentalvalue
was only 0.017 ds. The difference by a factor of 2 was attributed to the formation of
eddies in the wake of the spore and rotational settling, due to assymetric particle shape
and a very rough surfacetexture (see Figures 3.11 and 3.12). If, on the other hand. a lower
particle density based on the hydrodynamic envelope volume is used, agreement with
Stokes’law might be found. Geldart (1986) gives a simple method for measurement of
appropriate particle densities of porous particles.
Figure 3.10 gives the terminal settling velocity in air in the gravitational field for
smooth spherical particles of various diameters and densities. The straight parts of the
lines in Figure 3.10 essentially represent the Stokes’law regime for the terminal settling
velocity, vt,of smooth spherical solid particles in a quiescent gas:

As smooth, spherical particles get smaller than a few pm diameter, they attain some-
what higher terminal settling velocities than predicted by Stokes’law (Cunningham slip
correction). For comparatively large particles, the viscous drag becomes greater than
assumed in Stokes’law and the terminal settlingvelocities are lower thanpredicted. This
is the reason for the curving of the lines in Figure 3.10 in the range of large particles.
The settling velocities indicated in Figure 3.10 apply even to particles in a dust cloud,
provided the particle concentrationis not too high and particle agglomerationcan be ne-
glected. For solids volume fractions below 0.001, the hindered settlingeffect causes less
than 1%reduction of the settlingvelocities given in Figure 3.10 (Perry and Chilton, 1973).
For a dust of particle density 1 g/cm3,a volume fraction of 0.001 corresponds to a dust
concentration of 1 kg/m3, which would be in the upper part of the explosible range.
Therefore, Figure 3.10 is also adequate for a rough evaluation of the gravitational set-
tling velocities of particles in explosible dust clouds.