Page 233 - Dust Explosions in the Process Industries

Generation of Explosible Dust Clouds 205

Figure 3,2 Liquid bridge between two identical spherical particles (From Schubert, 1973).

Here E is the porosity of the bed, F(E)the mean interparticleforce (dependent on E), and
x is the particle diameter. Equation (3.8) is derived from equation (3.10) via the rela-
tionship E x k( E) = 3.1 = x,found experimentally for spherical particles.
Schubert’s equation for the tensile strength of a powder due to interparticle liquid
bridges is as follows:

(r =-Y.1-E-OF,(€, S, 6, ;)U
T (3.9)
X E
Here y is the surfacetension of the liquid. FF(e,S, 6, dx) is the dimensionlessliquid-bridge
interparticle attraction force, where S is the fraction of the total pore volume between
the particles that is filled with liquid, and uand 6are as shown in Figure 3.2. Equation
(3.9) cannot be solved analytically, but Schubert (1973) arrived at a graphical solution.
The liquid bridge regime extends up to about S = 0.25 (Schubert’s experiments with
70 pm limestone particles). This regime is the most relevant one with a view to trans-
formation of dust deposits into explosible dust clouds. For a powder of specific density
of 1g/cm3packed to a porosity E of 0.4, S = 0.25 represents a moisture content of 14%
(neglecting moisture absorbed by the interior of the particles). The transition regime in
which the liquid partly forrns bridges between particles and partly fills the voids com-
pletely spans from S=0.25 to S=0.8. When the voids between the particles arejust filled
with liquid, the tensile strength of the bulk powder is determined solely by the internal
underpressurecaused by capillary forces. In practice, this is the case for 0.8 < S < 1.0.
Figure 3.3 summarizessome of Schubert’s (1973) experimentaland theoreticalresults.
He found that equation (3.9), using alx =0.05,yielded excellent agreementwith the exper-
iments in the liquid bridge regime, for which there is a strong increase of o,as S increases
from 0 to 0.1.
For particles of density 1g/cm3packed to a porosity of 0.4, S =0.1 correspondsto a mois-
ture content of 6.25%. It is therefore to be expected that the influence of the moisture con-
tent on the dispersibilityof the powder is particularly strong in the range of a few percent
of moisture. However, this does not apply if a significant fraction of the moisture is
absorbed by the interior of the particles rather than adhering to the particle surfaces.
As S increases and moves into the capillary pressure region, the tensile strength of the
powder bed increases further. As Figure 3.3 shows, the tensile strength of the powder