Intelligent Optimisation

The most important physical property of particulate samples is particle size. Particle size measurement is routinely carried out across a wide range of industries and is often a critical parameter in the manufacture of many products.

In the quest to optimise our cement production processes, we must understand the process itself, in terms of what we are producing and what we are producing it from.

Why measure particle properties?
There are two main reasons why many industries routinely employ particle characterisation techniques:

Better control of product quality
In an increasingly competitive global economy, better control of product quality delivers real economic benefits such as:

• ability to charge a higher premium for your product;
• reduce customer rejection rates and lost orders;
• demonstrate compliance in regulated markets.

Better understanding of products, ingredients and processes
In addition to controlling product quality, a better understanding of how particle properties affect your products, ingredients and processes will allow you to:

• improve product performance;
• troubleshoot manufacturing and supply issues;
• optimise the efficiency of manufacturing processes;
• increase output or improve yield;
• stay ahead of the competition;

Particle Properties
Particle size
By far the most important physical property of particulate samples is particle size. Particle size measurement is routinely carried out across a wide range of industries and is often a critical parameter in the manufacture of many products. Particle size has a direct influence on material properties such as:

• reactivity or dissolution rate;
• stability in suspension;
• efficacy of application;
• texture and feel;
• appearance;
• flowability and handling;
• packing density and porosity.

Measuring particle size and understanding how it affects your products and processes can be critical to the success of many manufacturing businesses.

What to do with particle size data
In order to simplify the interpretation of particle size distribution data, a range of statistical parameters can be calculated and reported. The choice of the most appropriate statistical parameter for any given sample will depend upon how that data will be used and with what it will be compared. For example, if you wanted to report the most common particle size in your sample, you could choose between the following parameters:

• Mean – ?average, size of a population;
• Median – size in the middle of a frequency distribution;
• Mode – size with highest frequency.

If the shape of the particle size distribution is asymmetric, as is often the case for many samples, you would not expect these three parameters to be exactly equivalent, as illustrated in Figure 1.

Means
There are many different means that can be defined, depending upon how the distribution data is collected and analysed. The three most commonly used for particle sizing are described below.

Number length mean D[1,0] or Xnl
The number length mean, often referred to as the arithmetic mean, is most important when the number of particles is of interest, e.g., in particle counting applications. It can only be calculated if we know the total number of particles in the sample, and is therefore limited to particle counting applications.

Surface area moment mean D[3, 2] or Xsv
The surface area mean (Sauter Mean Diameter) is most relevant when the specific surface area is important e.g., bioavailability, reactivity, dissolution. It is most sensitive to the presence of fine particulates in the size distribution.

Volume moment mean D[4, 3] or Xvm
The volume moment mean (De Brouckere Mean Diameter) is relevant for many samples as it reflects the size of those particles which constitute the bulk of the sample volume. It is most sensitive to the presence of large particulates in the size distribution.

An example of the surface area and volume moment means is shown in the particle size distribution below. If the aim is to monitor the size of the coarse particulates that make up the bulk of this sample, then the D[4,3] would be most appropriate. If, on the other hand, it is actually more important to monitor the proportion of fines present, then it might be more appropriate to use the D[3,2].

Percentiles
For volume-weighted particle size distributions, such as those measured by laser diffraction, it is often convenient to report parameters based upon the maximum particle size for a given percentage volume of the sample.

Percentiles are defined as XaB where:

• X= parameter, usually D for diameter
• a = distribution weighting, e.g., n for number, v for volume, i for intensity
• B = percentage of sample below this particle size e.g. 50 per cent, sometimes written as a decimal fraction i.e., 0.5

For example, the Dv50 would be the maximum particle diameter below which 50 per cent of the sample volume exists – also known as the median particle size by volume. The most common percentiles reported are the Dv10, Dv50 and Dv90, as illustrated in the frequency and cumulative plots in Figure 2.

By monitoring these three parameters, it is possible to see if there are significant changes in the main particle size, as well as changes at the extremes of the distribution, which could be due to the presence of fines, as shown in the particle size distribution in Figure 3, or oversized particles/agglomerates.

Particle shape
As well as particle size, the shape of constituent particles can also have a significant impact upon the performance or processing of particulate materials. Many industries are now also making particle shape measurements in addition to particle size measurements in order to gain a better understanding of their products and processes.

How do we define particle shape?
Particles are complex three-dimensional objects and, as with particle size measurement, some simplification of the description of the particle is required in order to make measurement and data analysis feasible. Particle shape is most commonly measured using imaging techniques, where the data collected is a two-dimensional projection of the particle profile. Particle shape parameters can be calculated from this two-dimensional projection using simple geometrical calculations.

Particle form
Aspect ratio can be used to distinguish between particles that have regular symmetry, such as spheres or cubes, and particles with different dimensions along each axis, such as needle shapes or ovoid particles. Other shape parameters that can be used to characterise particle form include elongation and roundness.

Particle outline
As well as enabling the detection of agglomerated particles, the outline of a particle can provide information about properties such as surface roughness. Particles with very smooth outlines will have a convexity/solidity value close to 1, whereas particles with rough outlines, or agglomerated primary particles, will have consequently lower convexity/solidity values.

Universal shape parameters
Some shape parameters capture changes in both particle form and outline. Monitoring these can be useful where both form and outline may influence the behaviour of the material being measured. The most commonly used parameter is circularity. Circularity is often used to measure how close a particle is to a perfect sphere, and can be applied in monitoring properties such as abrasive particle wear. However, care should be exercised in interpreting the data, since any deviations could be due to either changes in surface roughness or physical form, or both.

While circularity can be very useful for some applications, it is not suitable for all situations. To date, there is no definition of a universal shape parameter that will work in every case. In reality, careful consideration is necessary to determine the most suitable parameter for each specific application.

Summary
This article touches the surface of the different means we have at our disposal to analyse particle properties. Such information can be used to optimise and refine our cement production processes, increasing the efficiency and product quality.

(This article has been authored by Dr Michael Caves, Malvern Aimil Instruments Pvt Ltd, New Delhi).