# REPRESENTING THE CHARACTERISTICS OF PARTICLE ASSEMBLIES

## Measures of dispersity: fineness parameters

The nature of the disperse phase of a discretely disperse system has to be represented. It consists of an assembly of particles and is a population of elements (particles), which has to be described in terms of a distribution function [82]. To do this it is necessary to classify the particles according to some property, which must be a measurable physical magnitude specified by a numerical value and a unit. We call these measures of dispersity, which are directly or indirectly linked to the particle size, fineness parameters.

Fundamentally, any property by means of which the particles can be definitely classified is suitable as a measure of dispersity. Some measures of this type are preferentially used for describing particle assemblies.

### (a) Geometrical measures of dispersity

Geometrical measures of dispersity are based on a geometrical quantity - a length, an area or the particle volume. With particles of irregular shape it is necessary to stipulate which particle length or area is being measured. The main dimensions *а*, *b* and *c* which are used are those which can be defined by either circumscribed or inscribed regular bodies, such as ellipsoids or cuboids, or by comparison with the largest dimension of the particle.

Statistical lengths (Fig. 2.2) are determined by an automatic scanning of pictures of the particles in which they have taken up a random position relative to the measurement. As a consequence of this variable orientation in relation to the direction of measurement there is a distribution of the statistical length for each identical non-spherical particle.

Other geometrical measures are the volume, the surface area and a projected area of the particle either lying in its stable position or oriented in an average random direction.

If the particles are geometrically similar, these geometric parameters are related to each other by formulae which are the same for all such particles, but in practice this is seldom the case.

Figure 2.2 Statistical lengths, (a) Summary of the commonly used lengths: the Feret diameter jc_{Fe} is the projection of the particle’s outline onto a line perpendicular to the direction of measurement; the Martin diameter Jc_{Ma} is the chord parallel to the direction of measurement which bisects the projected area; the Nassenstein diameter x_{Na} is the chord perpendicular at the point of contact to a tangent parallel to the direction of measurement; the diameter jt_{c>max} is the longest chord parallel to the direction of measurement, (b) Distribution of a statistical length for a narrow range of particle size.