Viewing measurement results Chapter 5
Mastersizer 3000 Page 5-17
in the size category 6.97-7.75 microns, this means that the volume of all particles
with diameters in this range represents 11% of the total volume of all particles.
It is useful to consider a numerical example to illustrate this point. Suppose, for
simplicity, that a sample consists of only two sizes of particle, 50% by number hav-
ing a diameter of 1 micron and 50% by number a diameter of 10 microns. Assum-
ing that the particles are spherical, the volume of each of the larger particles is 1000
times the volume of one of the smaller ones. Thus, as a volume distribution, the
larger particles represent 99.9% of the total volume.
The graph below illustrates this for a more realistic distribution:
ill 1874
Equivalent spheres
Mie theory presumes that the particles measured are perfect spheres. In practice
they are very rarely so. This causes a problem in the definition of the term “meas-
ure the particle’s size”: if the particle is an irregular shape, which particular dimen-
sion should be measured?
As an example, imagine that I give somebody a matchbox and a ruler and ask them
to tell me the size of it. They may reply by saying that the matchbox is 50mm x
25mm x 10mm. They cannot say that “the matchbox is 25mm” as this is only one
aspect of its size. It is not possible to describe the three dimensional matchbox with
one unique dimension. Obviously the situation is even more complex for irregular
shaped particles such as grains of sand or the pigment particles in paint.
Most people want a single measurement to describe their sample, for example, they
wish to say that their sample is made up of 50 micron particles. What is required is
a unique number that describes the particle. There is only one shape that can be
described by one unique number and that is a sphere. If we say we have a sphere of
%
Particle Diameter (µm.)
0
10
20
0.1 1.0 10.0 100.0 1000.0
10000.0
1
1
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