# How to Describe a Particle Using a Single Number — Understanding Equivalent Sphere Theory

## Why is laser diffraction one of the most used particle size analysis techniques?

Laser diffraction is one of the most popular methods for particle size analysis due to its dynamic nature and range. Laser diffraction can be used to determine a variety of particle sizes in a range of substances such as liquid suspensions, dry materials, and aerosols.

However, it is important to note that different particle size analysis technologies can quite often produce different results for the same sample. The logical reason for this is that each particle analysis measurement technique measures a different part or aspect of the same material.

For this reason, all particle size analysis results must be considered as the best indications possible — rather than definitive and exact measurements.

## What does it mean to describe a particle?

One unique number cannot be accurately given to describe the size of a three dimensional shape. Whilst this is true in many situations and circumstances, it’s particularly relevant when attempting to describe complex shapes, such as a grain of sand or even a particle within a can of paint.

Although it may be hard for many to understand the need for such minute measurements, many industries today rely on the ability to use a particle size analyser to measure the size of incredibly fine particles. Quality Assurance Managers within specific industries and organisations may need to know whether the average size of particles has increased or decreased since the last production run.

For all ground and milled materials (such as coffee, powders, minerals, etc), it is the particle size that is produced that typically determines the performance of the product which if not optimised can impact the manufacturing efficiency and increase overall costs. Particle size can affect a wide range of material properties including, reaction and dissolution rates, how easily ingredients flow and mix, or compressibility and abrasivity. In order to simplify the measurement process, it is often convenient to define the particle size using the concept of equivalent spheres.

## What is equivalent sphere theory and how is it used?

As with the example offered in the previous section, we very often seek to describe a shape by only one number.

However, this is problematic as a sphere is the only shape that can be accurately described by one number. Therefore, in order to arrive at a particular number to explain the size of a shape, equivalent sphere theory is frequently used.

Using the equivalent sphere theory, some property of the particle is measured and it is then assumed that this refers to the diameter of a sphere to describe the particle. This essentially mean that three or more numbers do not have to be used to describe a three dimensional particle. Although it is more accurate to describe three dimensional particles with three or more numbers, it is an inconvenient practice and can quickly become unmanageable.

Even the smallest particles are multidimensional and it is very hard, and problematic, to describe a multi-dimensional particle using only one dimension.

As there is only one shape that can be described by one dimension – a sphere – all techniques that measure particle size relate this to an ‘equivalent sphere’.

## Techniques for reporting particle size

Laser diffraction is a popular and preferred measurement technique when reporting on particle size and also has the advantage of being one of the most accurate ways of measuring the size of a particle.

However, laser diffraction is not the only particle size analyser available. There are many instruments that can be used and each one utilises different measuring techniques.

In order to understand more about the different results that are obtained through particle measurement and analysis, it is useful to be aware of some commonly used methods, such as:

• Sieves: This is one of the oldest and most traditional of all the methods of measuring particle size and is often used as it is cheap and reasonably effective when measuring larger particles.

However, the use of a sieve makes it impossible to measure very fine particles such as within sprays or emulsions. Reproducing results is also extremely difficult, especially when the ‘wet sieving’ technique is applied.

• Sedimentation: This is another technique that has been around for a very long time and has long been used to measure coarse grained soils (such as sand) and has been used in the ceramics industry. However, the calculation of size with the sedimentation technique is only valid for spherical particles.

If particles are not spherical, the reports will be different to the results. There are also difficulties with measuring emulsion particles, and it is also necessary to know the density of a material in order to easily produce accurate results.

• Electrozone Sensing:

Electrozone Sensing is particularly useful for measuring the size of blood cells but it poses some problems as a technique for measuring industrial materials. Samples must be suspended in a salt solution so it is not possible to measure emulsions and many dry powders.

In addition to these limitations, measuring the particle size within sprays cannot be done.

Despite these alternative methods,laser diffraction continues to remain the most accurate way of measuring particle size.

• Provides a great degree of flexibility for the analysis of different materials
• Results and answers can be provided quickly (in less than one minute)
• It is an absolute method of particle size distribution analysis
• There is no need to calibrate instruments against a standard
• It is possible to measure dry powders, suspensions, emulsions, sprays and many other materials
• The technique provides a wide and dynamic range of measurement
• The measurement of an entire sample is possible
• The technique can be repeated quickly and easily

While there are a range of ways to measure and analyse particle size, the most appropriate way of measuring any given material will, and should, depend on the type of material that is being measured.

## Making use of the Mastersizer 3000 system

The flexibility of the Mastersizer 3000 system allows the user to develop a robust method for every type of sample and, compared with other laser diffraction systems, the Mastersizer 3000 significantly broadens the range of materials and applications to which this measurement technique can be applied.

Contact the ATA Scientific team to receive a quote today.

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