shape factor varies considerably among individual particles. However, if
average and range ofcdo not significantly vary among size classes, a graph
of frequency versus a suitable equivalent sphere diameter, supplemented by
an average shape factor, may be sufficient to characterize the dispersion.
Another example of irregularly shaped particles is given byaggregates
of emulsion droplets or of small solid particles in a suspension. The
aggregates enclose a variable amount of solvent (Fig. 9.2, G), and it is
difficult to classify them according to size, and especially according to mass
of primary particles. For a powder of true spheres or other particles having
a fixed shape, the specific surface areaA, e.g., in m^2 ?kg^1 , is proportional to
d^1. For aggregates, however,Amay be (almost) independent ofd,ifdis the
aggregate diameter, since the primary particles determine the value ofA.In
practice, several powders show a proportionality ofAwithdto a power
between1 and zero. For very porous particles, the exponent can also be
close to zero.
9.3.4 Determination
Numerous methods exist for the determination of average particle size or
size distribution. They will not be treated here. Nevertheless, it may be
useful to discuss briefly some general aspects and examples, to warn the
reader against some of the pitfalls that may be encountered. Reliable
determination of particle size distribution is notoriously difficult, and all
methods employed have limitations and are prone to error. When
TABLE9.5 Shape Factorc[Eq. (9.8)] for Various
Particles, Either Calculated or Determined
Calculated sphere 1
cube 0.81
brick (1 : 2 : 4) 0.69
tetrahedron 0.67
cylinder, length/diameter¼ 1 0.87
same 5 0.70
same 20 0.47
postcard, e.g. 0.05
Determined sand: somewhat rounded grains 0.8
ground lime: irregular shapes 0.65
gypsum: flaky crystals 0.5
mica: very thin flakes 0.2