Page 235 - Dust Explosions in the Process Industries

Generation of Explosible Dust Clouds 207

following equation for the relationship between the bulk strength CT of a powder bed of
monosized particles and the mean interparticle force F( E),the coordinationnumber k(E)
(averagenumber of neighboring particles with which a given particle is in contact), par-
ticle diameter x,and porosity of the powder bed E:

l-E
0-= -k(€)7 E(€) (3.10)
7T X
Equation (3.10) shows that, for geometrically similarpowder beds, differing only in par-
ticle size x,and assuming that the mean attraction force per interparticle contact is inde-
pendent of particle size, the strength of the bulk powder is inversally proportional to x2;
that is, the powder strength increases strongly as the particle size decreases.
Rumpf (1970) was able to show that equation (3.10) is valid not only for spherical par-
ticles, but also for irregular ones provided certain statistical conditions concerning the
arrangement of the particles in the bed and the particle shape are fulfilled.By extending
his treatment to beds containing a variety of particle sizes, he arrived at the equation

(3.11)

Heref, is a particle shape factor and M30the “third moment” of the particle size distri-
bution (distribution of particle volume).
For integration of equation (3.11), the coordination number k(x) as a function of par-
ticle size and the interparticle force F(x, n(x))as a function of particle size and particle
size distributionmust be known. The practical usefulness of equation (3.11) is therefore
limited, but it establishes a formal logical link between the bulk strength of a powder
and the mean microscopic interparticle attraction force.
Molerus (1978) also studied the link between interparticle forces and bulk powder
strength. He used the following empirical relationship between the adhesive force F
between a limestoneparticle and a plane metal surface and the external force Nused ini-
tially for pressing the particle against the surface:

F=F,+KN (3.12)

F, is the attractionforce for particles that arejust touching the plate without having been
pressed against it by an external force. On the basis of theoretical considerationsof the
interparticle forces in a cohesive bulk powder, Molerus developed a relationship of the
same form as equation (3.12), where F, and Kwere expressed in terms of the Hamaker
constant, the plastic yield pressure of the particle material, a characteristic distance of
adhesion (about 0.9 nm), and the size of the spot where the particles touch. An encour-
aging agreement with experiment was obtained for limestone. Molerus then developed
a theoretical model for the connection between such interparticle forces and the cohe-
sive properties of the bulk material by assuming that
1. Van der Waals forces and deformation of the contact areas where the particles touch
each other are responsible for the interparticle adhesion.
2. The coordinationnumber k(~)is a unique function of the porosity of the particle bed.