12 PARTICLE CHARACTERISATION 121 Single particles
The simplest shape of a particle is the sphere in that, because of its symmetry, any question of orientation does not have to be considered, since the particle looks exactly the same from whatever direction it is viewed and behaves in the same manner in a fluid, irrespective of its orientation. No other particle has this characteristic. Frequently, the size of a particle of irregular shape is defined in terms of the size of an equivalent sphere although the particle is represented by a sphere of different size according to the property selected. Some of the important sizes of equivalent spheres are:
(a) The sphere of the same volume as the particle.
(b) The sphere of the same surface area as the particle.
(c) The sphere of the same surface area per unit volume as the particle.
(d) The sphere of the same area as the particle when projected on to a plane perpendicular to its direction of motion.
(e) The sphere of the same projected area as the particle, as viewed from above, when lying in its position of maximum stability such as on a microscope slide for example.
(f) The sphere which will just pass through the same size of square aperture as the particle, such as on a screen for example.
(g) The sphere with the same settling velocity as the particle in a specified fluid.
Several definitions depend on the measurement of a particle in a particular orientation. Thus Feret's statistical diameter is the mean distance apart of two parallel lines which are tangential to the particle in an arbitrarily fixed direction, irrespective of the orientation of each particle coming up for inspection. This is shown in Figure 1.1. A measure of particle shape which is frequently used is the sphericity, f, defined as:
surface area of sphere of same volume as particle
surface area of particle
Another method of indicating shape is to use the factor by which the cube of the size of the particle must be multiplied to give the volume. In this case the particle size is usually defined by method (e).
Other properties of the particle which may be of importance are whether it is crystalline or amorphous, whether it is porous, and the properties of its surface, including roughness and presence of adsorbed films.
Feret's diameter
Figure 1.1. Feret's diameter
Feret's diameter
Figure 1.1. Feret's diameter
Hardness may also be important if the particle is subjected to heavy loading. 1.2.2. Measurement of particle size
Measurement of particle size and of particle size distribution is a highly specialised topic, and considerable skill is needed in the making of accurate measurements and in their interpretation. For details of the experimental techniques, reference should be made to a specialised text, and that of Allen(1) is highly recommended.
No attempt is made to give a detailed account or critical assessment of the various methods of measuring particle size, which may be seen from Figure 1.2 to cover a range of 107 in linear dimension, or 1021 in volume! Only a brief account is given of some of the principal methods of measurement and, for further details, it is necessary to refer to one of the specialist texts on particle size measurement, the outstanding example of which is the two-volume monograph by Allen1^, with Herdan1^ providing additional information. It may be noted that both the size range in the sample and the particle shape may be as important, or even more so, than a single characteristic linear dimension which at best can represent only one single property of an individual particle or of an assembly of particles. The ability to make accurate and reliable measurements of particle size is acquired only after many years of practical experimental experience. For a comprehensive review of methods and experimental details it is recommended that the work of Allen be consulted and also Wardle's work on Instrumentation and Control discussed in Volume 3.
Before a size analysis can be carried out, it is necessary to collect a representative sample of the solids, and then to reduce this to the quantity which is required for the chosen method of analysis. Again, the work of Allen gives information on how this is best carried out. Samples will generally need to be taken from the bulk of the powder, whether this is in a static heap, in the form of an airborne dust, in a flowing or falling stream, or on a conveyor belt, and in each case the precautions which need to be taken to obtain a representative sample are different.
A wide range of measuring techniques is available both for single particles and for systems of particles. In practice, each method is applicable to a finite range of sizes and gives a particular equivalent size, dependent on the nature of the method. The principles
|
Particle size (|im) |
Pelleted products Crystalline industrial chemicals |
|
104 |
— Granular fertilisers, herbicides, fungicides |
|
103 |
Detergents Granulated sugars Spray dried products |
|
102 |
Powdered chemicals Powdered sugar Flour |
|
Powder metals Ceramics | |
|
100 |
Electronic materials Photographic emulsions Magnetic and other pigments |
|
10-1 |
Organic pigments |
|
10-2 |
Fumed silica Metal catalysts Carbon blacks |
Figure 1.2. Sizes of typical powder products'1^
Figure 1.2. Sizes of typical powder products'1^
of some of the chief methods are now considered together with an indication of the size range to which they are applicable.
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