De Brouckere mean diameter
{{Short description|Average particle size weighted by volume}}
File:The_De_Brouckere_Mean.jpg
The De Brouckere mean diameter is the mean of a particle size distribution weighted by the volume (also called volume-weighted mean diameter, volume moment mean diameter.{{Cite book|last=Allen|first=Terence|title=Particle size measurement|publisher=Springer|year=2013|pages=128}} or volume-weighted mean size). It is the mean diameter, which is directly obtained in particle size measurements, where the measured signal is proportional to the volume of the particles. The most prominent examples are laser diffraction{{Cite web|url=https://www.iso.org/standard/69111.html|title=ISO 13320:2020 Particle size analysis - Laser diffraction methods|last=|first=|date=|website=|access-date=}} and acoustic spectroscopy (Coulter counter).
The De Brouckere mean is defined in terms of the moment-ratio system as,
Where ni is the frequency of occurrence of particles in size class i, having a mean Di diameter.{{Cite web|url=https://www.iso.org/standard/57641.html|title=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|last=|first=|date=|website=ISO|language=en|access-date=}} Usually in logarithmic spaced classes, the geometric mean size of the size class is taken.{{Cite book|url=https://books.google.com/books?id=lLx4GzA-7AUC&dq=Merkus%2C+Particle+Size+Measurements+-+Fundamentals&pg=PP5|title=Particle Size Measurements: Fundamentals, Practice, Quality|last=Merkus|first=Henk G.|date=2009-01-07|publisher=Springer Science & Business Media|isbn=9781402090165|language=en}}
Applications
The De Brouckere mean has the advantage of being more sensitive to the larger particles, which take up the largest volume of the sample, therefore giving crucial information about the product in the mining and milling industries. It was also used in combustion analysis, as the D[4,3] is less affected by the presence of very small particulate residuals, which enabled the evaluation of the primary diesel spray.[https://web.archive.org/web/20190307164437/http://pdfs.semanticscholar.org/d99c/395a1b76c4c5f4b3bb88a65f7af4c2744f50.pdf]Risi, Arturo & Colangelo, Gianpiero. (2004). Optical Characterization of a Diesel Spray at High Temperature and Pressure.
Further reading
{{Cite book|last=|first=|title=Standardization and Quality Assurance in Fluorescence Measurements II|publisher=Springer-Verlag|year=2008|isbn=978-3-540-70570-3|editor-last=Resch-Genger|editor-first=Ute|location=|pages=456–457|lccn=2008934168}}