The calculation of the volume mean diameter is based on the definition of moments of a distribution. The kth moment of a distribution q of order r (r=0 Number, ... r=3 Volume) over the particle size x is defined as a weighted integral of that distribution as follows:
For finite size classes, the integration in the above formula is replaced by a sum over n elements:
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arithmetic mean value of particle size interval i |
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upper limit of particle size interval i |
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lower limit of particle size interval i |
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n |
number of particle size intervals |
In terms of the definitions above, the VMD is the first moment of a q3(x) (particle volume over particle size) distribution.
A comprehensive explanation of the calculation including an example is given in ISO/FDIS 9276-2: Representation of results of particle size analysis ? Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions
