Just as a reminder, for a weighted distribution, the Sauter mean = 1/ sum(xi/di).
I am looking for a formula that is like the D32 = median*exp(7/2 * std deviation2) (obtained by cumputing the higher moment of the number distribution); for a size distribution of n particles, D32 = sum (ni di3) / sum(ni di2)
If one has the full weighted distribution, there is no issue to get the Sauter mean, but I am trying to convert data of median/mean and std deviation (for which there is no published full PSD) into a Sauter mean diameter.
Thank you for the feedback and help.
E.
Hatch-Choate transformations: T Hatch, S P Choate. J. Franklin Inst., 207(3), 369 - 387 (March 1929) and ISO 9276-2:2014 Representation of results of particle size analysis -- Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions
You may also refer to: Riyad R. Irani and Clayton F. Callis; “Particle Size: Measurement, Interpretation, and Application”, John Wiley & Sons, 1963, pp. 42-45.
the answer in phi=-log2(d in mm) units: Sauter mean(phi) = geometric mean(phi) + 0.5 ln(2) * std_dev(phi)^2
Ask me for the derivation if needed.
E.
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