Particle size distribution

Particle size distribution describes how the particles in a particle population are distributed across different size classes. It is a key parameter for dispersed systems – whether powders, suspensions or emulsions – and is sometimes also referred to as grain size distribution.

A narrow particle size distribution occurs when most particles are of a similar size. Such powders usually exhibit low dust generation and offer excellent flow and conveying properties – for instance, in high-speed filling processes (e.g. tea bag, sachet or capsule production) or in adaptive manufacturing processes. Instant products are also typically agglomerated and exhibit a narrow distribution to ensure rapid settling, dispersion and dissolution behaviour.

A broad particle size distribution, on the other hand, describes a bulk material with widely varying grain sizes. This heterogeneity is advantageous when materials are to be compacted or agglomerated – for example, in powder metallurgy, in high-performance ceramics or in processes requiring high bulk density and compressibility.

The particle size distribution influences many processing properties: flow and conveying behaviour, specific surface area, reactivity, abrasiveness, drying and sedimentation behaviour, solubility, taste perception, suitability for agglomeration and much more.

Measurement methods:

The classic method for determination is sieve residue analysis. Modern techniques such as laser diffraction, image analysis, dynamic light scattering or sedimentation analysis provide detailed information on number, volume or mass distributions.

Advanced in-situ sensor technology now enables real-time measurements directly within the process space – in the moving bulk material bed of a mixer, in continuous grinding processes or in agglomerators. This allows the target distribution to be precisely set and monitored.

Forms of representation:

Particle size distributions are frequently represented graphically, with the equivalent diameter on the x-axis and a measure of quantity (mass, volume or number fraction) on the y-axis.

• Histograms (q-distributions) show the relative proportions of individual size classes.
• Cumulative curves (Q-distributions) are suitable for determining percentiles.
• Logarithmic scales facilitate the representation of large size ranges.

In cement and grinding technology, the Rosin–Rammler or Rosin–Rammler–Sperling–Bennett (RRSB) representation is widely used. Its linearised form allows for a quick comparison of different crushing processes.

Many natural or process-generated powders exhibit a statistical similarity in particle size to the Gaussian bell curve. The probability density of a normal distribution is described by:

f(x) = (1 / (x σ √(2π))) exp(- ((ln x - μ)² / (2σ²)))

• f(x): probability density (frequency) at particle size x
• x: particle diameter [µm, mm]
• μ: Mean of the logarithm of the diameter (location parameter)
• σ: Standard deviation of the logarithm of the diameter (dispersion parameter)
• ln: Natural logarithm
• e: Euler’s number (≈ 2.718)
• π: Pi (≈ 3.14159)

Practical example:

In the manufacture of baby food, the porosity and strength of the particles play a role alongside the particle size distribution. Spray-drying processes produce porous agglomerates that are wetted with suitable emulsifiers. A low-dust product quality is crucial here to ensure packaging integrity and consumer-friendliness.

The spray-drying process facilitates the attachment of suitable emulsifiers to the particles. During handling, it is important to note that dust is undesirable. Dust not only disrupts the preparation process for the end consumer; it also poses a problem for packaging closures. High-performance closure seals are only permanently airtight if they are applied dust-free. For high-quality bulk materials, particle size distributions are generally specified and are therefore important quality parameters.

The higher the quality of a bulk material, the more important its formulation becomes – and particle size distribution plays a central role in this.