Particle Size Analysis and Screening, by Gordon Young

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-- 1: Selecting a Method and Sampling --

Selecting the method for determining particle size (or size distribution)

(i) Select a definition of particle size that is appropriate for the application

Some alternative definitions of particle size are

• Diameter of a sphere which has the same property as the particle itself -- that is, the same volume, same settling velocity, etc.

• Diameter of a circle which has the same property as the projected outline of the particle -- that is, the same projected area or same perimeter

• Linear dimension measured parallel to a particular direction

(ii) Select a method of measurement that is appropriate to the definition; for example

• for pneumatic conveying -- where the appropriate definition is the diameter of a sphere with the same settling velocity -- use a sedimentation method (Stoke’s diameter)

• for flow though packed or fluidised beds -- where the appropriate definition is the diameter of a sphere having the same surface to volume ratio as the particle -- measure the specific surface area (see below)

Sampling

The Golden Rules of Sampling are
        -- A powder should be sampled when in motion
        -- The whole stream of powder should be taken for many short increments of time rather than part of the stream taken for the whole of the time

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-- 2: Laboratory sieving --

Commonly used for size analysis, using sieves up to 16 mm aperture, though usually in the range of 50 m to 3 mm. The size of coarser particles is determined by direct measurement.

Based on a linear dimension, generally assuming spherical particles

Mean particle diameter retained by a screen is the sum of the aperture of the screen on which the material is retained, plus the aperture of the next largest screen, divided by 2.

Mean particle diameter of a sample is the sum of the mass fractions retained on each screen multiplied by the mean diameter of particles retained by that screen.

For a example see Toledo pp 539 - 540.

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-- 3: Particle Size Distribution --

Osmonics provides a pictorial representation of the size spectrum of materials at http://www.osmonics.com/library/zoom-sp.htm

The results of a sieve analysis (using the example below) may be presented as a plot of:

• cumulative percent undersize (falling through) vs aperture size

• cumulative percent oversize (retained on screen) vs aperture size
  

• weight or percent retained on each screen used in sequence versus aperture size (or average diameter)
  

The horizontal axes (aperture size or average diameter) may be on an arithmetic or on a logarithmic scale.

Calculation of specific surface

Total surface area of a sample may be estimated from the results of sieve analysis.

          A_s,i = (K_s / ) (m_i / D_p,i)

where
      A_s,i = surface area of the ith fraction (m²)
      K_s = shape factor for the particles
            = 6 for a sphere
            = 10.5 for particles from a hammermill
      m_i = mass of the ith fraction(kg)
      = density of the particles (kg / m³)
      D_p,i = average particle size of the ith fraction

Specific surface is the surface area per kg of material.

      S = (K_s / ) [(m_i / D_p,i)] / [m] = A_s,i / m_i