![]() ![]() Thus there is an infinite number of ‘right answers’. So each technique is liable to generate a different mean diameter as well as measuring different properties of the particles. Laser diffraction can generate the D or equivalent volume mean, which is identical to the weight equivalent mean if density is constant. Image analysis measures the area of each particle and divides by the number of particles to generate the D.Ī technique like electrozone sensing will measure the volume of each particle and divide by the number of particles to give the D. Using an electron microscope, it is likely that diameters will be measured with a graticule, then summed and divided by the number of particles to give a mean. catalysis or combustion).ĭ = (1 3+2 3+3 3)/(1 2+2 2+3 2) = 2.57 = S d 3/ S d 2ĭifferent techniques give different means The surface area moment mean D or Sauter Mean Diameter (SMD), is often of use in applications where the active surface or surface area is important (eg. This would be inconvenient for any measurable size of fine powder (1g of powder of density 2.5 would contain around 7.6 X 10 11 particles if all were 1 m m).ĭ = (1 4+2 4+3 4)/(1 3+2 3+3 3) = 2.72 = S d 4/ S d 3 This is what is usually understood as the Volume Mean Diameter (VMD).Īcademics normally prefer the D – the volume moment mean of the particle, because the number of particles is not required. This again is a number mean (number-volume or number weight mean) which in mathematical terms is expressed as D. The surface area of a sphere is 4p r 2, so to compare on the basis of surface area, the diameters must be squared, divided by the number of particles, and the square root taken to get back to mean diameter: However, a catalyst engineer will want to compare these spheres on the basis of surface area because the higher the surface area the higher the activity of the catalyst. In mathematical terms, this is called D because the diameter terms on the top of the equation are to the power (d1), and there are no diameter terms (d 0) on the bottom of the equation. This is the mean number, or more accurately the number length mean because the number of particles appears in the equation: If you sum all the diameters ( S d=1+2+3) then divide by the number of particles (n=3), the answer is 2. Imagine three spheres of diameters 1,2 and 3 units. However, it is possible to have a particle size standard for a particular technique, permitting comparisons between instruments that use that technique. Standards must be spherical for comparison between techniques. This also means that there cannot be anything like a particle size standard for grains of sands. The answers become meaningless if two different measuring procedures are used to compare values at different points in the processing chain or if different departments use different measurement methods. It follows, therefore, that the only sensible comparison of measurements is by using the same technique. Using minimum diameter or some other quantity such as Feret’s diameter, minimum length, volume, or surface area, will produce a different particle size result.Įach answer will be correct, giving a true result for the property being measured. If you take maximum particle length as the diameter, you actually say that the particle is a sphere (equivalent) of this maximum dimension. There are a number of diameters that can be measured in order to characterize it. The examination of a particle under a microscope provides a two-dimensional image. Different Measurement Techniques, Different Answers Using Equivalent Sphere theory, it is at least possible to say that a particle has got bigger or smaller, according to changes in volume or weight properties. This removes the need to describe three-dimensional particles with more than one number. This measurement of some one-dimensional property of a particle, and referring it to a sphere to derive one unique number, is known as the Equivalent Sphere theory. r ), enabling the calculation of one unique number (2r) for the diameter of a sphere that has the same weight as the matchbox. So, the weight of the matchbox can be converted into the weight of a sphere (using the formula: Weight = (4/3) p r 3. Returning to the matchbox, this has a number of properties that can be described by a single number – weight, volume, and surface area for example. It is impossible to do the same even for a cube, where 50 m m may refer to an edge or a diagonal. ![]() ![]() If you say that you have a 50 m m sphere, this describes it exactly. ![]() A sphere is the only shape that can be described by a single number. ![]()
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