Mean particle diameters.Part III:an empirical evaluation of integration and summation methods for estimating mean particle diameters from histogram data

摘要

Mean particle diameters of histograms of size distributions were estimated by integration and by summation over the histogram intervals using several,partly model,size distributions.The summation method,used in the Moment-Ratio(M-R) method,tends to be more accurate than the Integration method and is less sensitive to low values of the lower limit of size distributions.The mathematical equations for the Integration method appear to be didficult to apply indaily practice and their complexity may easily hide the physical background of a meanparticle diameter.The Integration approach leads to peculiar saw-tooth shaped histograms,which makes the calculation of (histograms of)density distriubtions of other particle quantities irreversible and the calcualtion of mean diameters ambiguous.The Summation method equations are straightforward and generally applicable.Owing to the use of midpoints of particle size classes,the method is both unambiguous and reversible.The order of a mean diameter appears to be a useful quantity for the visualization of properties of methods to estimate meanparticle diameters.The Summation method is therefore proposed as the method of choice for standardization.