Basic Principles of Particle Size Analysis-3

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Measurement Methods 

From the previous explanation, measuring different dimensions of particles results in different outputs for each measurement technique. We shall now discuss some relative advantages and disadvantages of the main different methods.

  Sieves

This is a very old technique but it is inexpensive and easily useful for larger particles found in mining.

Terence Allen discusses the difficulty of regenerative sieving but many users’ main disadvantages are as follows:

 –Droplet or emulsion measurement is not possible.

– Measurement of dry powder below 400#(38u) is very difficult. Wet sieving claims to solve this problem, but the results from this technology offer very low production feasibility and are very difficult to perform.

– Cohesive and lumpy materials like clay are difficult to measure.

– Substances like 0.3u TiO2 cannot be measured and resolved by sieves. This method is originally not a good solution.

– The longer the measurement, aligned particles falling through the sieve become smaller. This indicates that measurement time and given methods (e.g. tapping) need to be accurately standardized.

– Mass distribution is not actually generated. Instead, it relies on measuring the second smallest dimension of particles. This can yield some odd results in certain rod materials such as paracetamol (an antipyretic analgesic) in the pharmaceutical industry.

– Resistance is good for measuring tables of ASTM or BS sieve size. And looks at the permitted tolerance above the average and maximum deviation.

  Sedimentation

It has been traditionally used in the paint and ceramic industries and offers attractively low answers.

 

Despite being required by the manufacturer, the range of application is 2~50 microns (Ref.1&2).

The principle of measurement is based on the Stokes’ Law equation. 

 

  

The equipment can be as simple as an Andreason pipette, or more sophisticated including the use of centrifuges or X-rays.

Examining this equation shall reveal one or two potential pitfalls.

The density of the material is required. Thus, this method is not good for emulsions that do not settle or quickly settle emulsions of high density materials.

The final result is the Stokes diameter (Dst), which is different from the mass diameter D[4,3], and it’s simply a comparison of particle settling rates according to settling at the same speed as a sphere.

The viscosity term within the common element indicates that temperature needs to be controlled very precisely so that a ‘1 degree change in temperature changes viscosity by 2%.’ Calculating settling times using the equation is relatively easy. It takes 3.5 hours for a single SiO2 (density = 2.5) micron particle to settle 1cm under gravity in water at 20 degrees.

Therefore, measurements lead to repeated slow and tedious measurements.

Therefore, attempts are made to move to increase g, to remedy the situation. The disadvantages of increasing g were discussed in (Ref.3). More pronounced criticisms of the sedimentation technique can be found in (Ref.2). 

 

Stoke’s law is effective only in spheres which have the peculiar property of being the densest shape for the volume and surface area they possess.

Thus, the more irregularly shaped ‘ordinary’ particles possess a greater surface area than spheres.

And these particles will fall more slowly due to the increased hindrance over their equivalent spherical diameters.

In materials like kaolin that are disk-shaped, these results are more pronounced, and we expect significant deviations in reality.
Furthermore, with small particles, there are two competitive forces (gravitational sedimentation, Brownian motion). Stokes’ law only applies to gravitational sedimentation.

The table above shows a comparison between the two competing forces.

If sedimentation occurs in particles below the size of 2μm, very large errors (about 20%) are expected. Errors shall occur in excess of 100% in particles with a size of 0.5μm.

Sedimentation techniques presented smaller values than actual, which is also a reason some manufacturers misunderstand.

In summary, the main issues of the technique for pigment users are as follows:

– Speed of Measurements

The average time taken to make measurements makes repeated analyses difficult and raises opportunities for re-agglomeration, taking about 25 minutes to 1 hour.

– Accurate Temperature Control

It is necessary to prevent changes in temperature and viscosity.

– Incapability to Handle Mixtures with Different Densities

Many pigments are a mixture of colorants and extenders/injectors.

– Usage of X-ray

Some systems use X-rays, and theoretically, all staff should be monitored.

– Limited Range 

Below 2μm, Brownian motion is dominant, and the system is inaccurate. Above 50μm, sedimentation occurs roughly, and Stokes’ law revisitation is inappropriate.

Exhibit 6 shows the anticipated differences between sedimentation and laser diffraction results.

  Electrozone Sensing (Coulter Counter)
 

The technique was developed in the mid-1950s to arrange blood cells present as a monomodal suspension in a dilute electrolyte.

The operative principle is very simple.

A glass vessel contains a hole or aperture within it.

The dilute suspension flows through this hole, and voltage is applied across it.

As particles flow through this hole, the capacitance changes, manifesting as a voltage pulse or peak.

The height of the peak inside the machine is measured and it relates to the peak height of a standard latex.

Therefore, this method is not complete but relatively natural.
 

Issues of particle alignment in the beam can be corrected by measuring the area under the peak instead of the peak height.
 

In blood cells, this technique is very excellent, and the method is very useful for both counting and volume distribution.
 

In fact, industries dealing with substances like pigments have many fundamental shortcomings.
 

– Difficult to Measure Emulsions. (Sprays are impossible!) 

Dry powder must be floating in a pigment (medium) and cannot be measured directly.
 

– Must be Measured in Electrolyte.  

In cases like organic substances, measurement in electrolyte is difficult as measurement in xylene, butanol, or other low conductivity solutions is impossible.
 

– This method is expensive and requires calibration standards that change size in distilled water and electrolyte. (Ref.2)
 

– For materials with relatively wide particle size distribution, it’s slow as changes must be made, and there is a risk of smaller apertures being blocked.

– The most fundamental limitation of this method is the issue of measuring very small apertures, making it difficult to measure below 2μm. Naturally, 0.2μm of TiO2 is immeasurable.
 

– Porous particles have huge issues as the surface area or apparent diameter of the particles is measured.
 

– High density or large-sized materials are difficult to drive through the aperture as they settle before being measured.
 

So in summary, this technique is excellent for blood cell measurements and ambiguous characterizations in many industrial materials.