Particle Size Distribution Plot

[Monica Okane]

Theparticle size distribution of a given material is an important analysis parameter in quality control processes and research applications, because many other product properties are directly related to it. Particle size distribution influences material properties like flow and conveying behavior (for bulk materials), reactivity, abrasiveness, solubility, extraction and reaction behavior, taste, compressibility, and many more.

The analysis of particle size distribution is an established procedure in many laboratories. Depending on the sample material and the scope of the examination, various methods are used for this purpose. These include Laser Diffraction (LD), Dynamic Light Scattering (DLS), Dynamic Image Analysis (DIA) or Sieve Analysis. Typically, suspensions, emulsions, and bulk materials are analyzed, in exceptional cases also aerosols (sprays).

With an extensive understanding of the strengths and weaknesses of each method, Microtrac offers an unrivalled product range of technologies for particle size distribution analysis. Our experts will be happy to assist finding the right solution for your application.

Most samples are so-called polydisperse systems, which means that the particles are not of the same size, but of different sizes. A particle size distribution indicates the percentage of particles of a certain size (or in a certain size interval). These intervals are also called size classes or fractions.

A simple example is shown below. Here, a mixture of grinding balls has been separated by size: 5 mm, 10 mm, 15 mm and 40 mm:

Thus, depending on the type of evaluation (number or mass/volume), one obtains a very different particle size distribution for the same sample.

Some particle size analyzers provide number-based distributions (Dynamic Image Analysis), others mass-based (Sieve Analysis) or volume-based particle size distributions (Laser Diffraction). With a suitable model, the distributions can be converted into each other. One special case is Dynamic Light Scattering, in which very often intensity-based particle size distributions are reported. This means that the different sizes are represented according to their contribution to the overall scattering intensity. This leads to a strong representation of large particles since the scattering intensity is decreasing with size by a factor of 106.

Particle size distribution can be represented either in tabular or in graphical form. The table below shows this for the grinding balls. The quantity in each fraction is represented by the letter p, index 0 means "number-based", index 3 means "mass- or volume-based".

Mean values (or mean particle size) can also be calculated from the tabulated values. This is done by multiplying the quantity in each measurement class by the mean size measurement class and summing the individual values. Various methods exist to calculate a mean, some are described in ISO 9276-2. To also characterize the distribution width, the standard deviation around the mean value can be used, or the span value. This is calculated as (d90 - d10) / d50. The wider the distribution, the larger the standard deviation and span.

The x-value at which the density distribution reaches a maximum (or the most frequently occupied measurement class) is called the mode size. Particle size distributions with multiple maximum values in the density distribution are referred to as multimodal (or bimodal, trimodal, etc.).

A special issue in the analysis of particle size distributions is the determination of oversize and undersize particles. These are small portions of particles that are significantly larger or significantly smaller than the bulk of the sample. In the cumulative curve, the presence of oversize or undersize is manifested by a step, in the density distribution by a small second peak (second maximum) outside the actual distribution. This oversize or undersize is best characterized by Q or 1-Q values at a suitable size x.

The example below shows a particle size distribution with 5% oversize. Here, 95 % of the particles are below 1 mm, the oversize has a size of 1 - 1.25 mm. This can be quantified by Q3(1 mm) = 95% or 1-Q3(1 mm) = 5%. This example also shows that the addition of oversize increases the mean particle size, while the median remains unchanged. Alternatively, the presence of oversize can also be described by the increased d95.

The Particle Size Distribution of a powder, granulate, suspension or emulsion indicates the frequency of particles of a certain size in a sample. It is therefore a statistical concept. In practice, percentages are specified per size interval (fraction) or cumulative values are used, in which the fractions are added up in ascending or descending order of size.

There are many methods to determine the particle size distribution of a sample. Which one is suitable for a particular sample depends on the size range of the particles and the material properties. Commonly used methods are sieve analysis, laser diffraction, dynamic light scattering and image analysis.

Particle Size Distribution is an important quality criterion for many products, but also for raw materials. Many material properties are influenced by the particle size distribution. These include, for example, flowability, surface area, conveying properties, extraction and dissolution behavior, reactivity, abrasiveness and even taste.

d10, d50 and d90 are so-called percentile values. These are statistical parameters that can be read directly from the cumulative particle size distribution. They indicate the size below which 10%, 50% or 90% of all particles are found.

The mode size found where the frequency distribution reaches a maximum. If the frequency distribution has only one maximum, this is called monomodal, if it has two maxima, it is called a bimodal distribution. A Particle Size Distribution with more maxima is called multimodal.

The width of the Particle Size Distribution is an important statistical property. If all particles are of the same size, the distribution is called monodisperse. Mostly, however, we are dealing with polydisperse systems. The width of the distribution can be given, for example, by the standard deviation around the mean value (mean particle size) or by the value (d90-d10)/d50.

Particle analysis, whether is test sieve analysis, air jet sieve analysis, or dynamic image analysis, is an essential aspect of a wide range of quality control programs across dozens of industries. The method you implement ultimately falls on your industry standards and the needs of your operation.

The end result of any particle analysis process is an accurate look into the individual particles that make up your production line. This is where a reliable particle size distribution curve comes into play.

Particle size distribution is the process in which a sample of material that is typically taken from a production line is examined to identify the average size of the individual particles. The particle size distribution curve is a graph that is generated to illustrate the average particle size, the smallest particle size, and the largest particle size.

The curve illustrates either the amount of material that passes through or is retained on each sieve. A good sample should, in general, follow the same particle size distribution curve every time you run it.

When conducting a particle size analysis, particularly test sieve analysis, you have a set stack of test sieves, some falling on the coarse end of the spectrum and some falling on the fine. Some material will be retained on the coarser sieves, and some will be retained on the finer sieves; however, a majority of your sample will be retained in the mid-range sieves.

That said, to calculate your distribution curve, you take the total mass of your sample material and divide it by either the weight retained or weight that passed through each sieve, plotting each sieve percentage on the graph. To make this process easy, it is recommended that a 100g sample is used to conduct a particle size analysis when possible.

Thinking back to math class, a distribution curve is really the mean, mode, and average of your particle sizes. A properly generated curve should show you what your average particle size is, what the minimum size is, and what the maximum size is.

If you begin to see any weird spike or anomalies in your distribution curve, this is an indication that you want to look to ensure everything surrounding your operation is in order. Now, depending on the anomaly or operation, there are several things that you may want to consider.

If you determine that your test sieves are in working order, you should turn to your production line and check to see if there are signs of wear and tear preventing you from obtaining the right size material in your quality control lab. This can come in the form of tears in media used for pre-screening, worn equipment used for grinding, etc.

The common mistakes that are seen when lab operators generate a particle size distribution curve ultimately come down to two factors: inconsistency and human error. In fact, if you go back and discover nothing was hindering the results at the begging of the process, by the time you make your way back to the lab, you most likely trace it back to inconsistency and human error.

Things like forgetting to tier the scale when weighing the material and test sieves, recording the data wrong, failure to record the correct starting weight, and failure to properly clean each sieve between testing are all common mistakes that can skew a distribution curve.

A particle size distribution curve is a graph that gives lab operators an inside look into the size of the individual particles that make up their production line. As it details the average particle size, smallest particle size, and largest particle size, it is easiest to compare it to the mean, median, and mode lesson we received in school.

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