mean particle diameter

A mean particle diameter is a single average size that stands in for a whole distribution, much like quoting the average height of a class instead of listing everyone. It is convenient, but as with any average it can hide a lot, and there is more than one way to take it.

Several means exist, each emphasising different particles. The number-length mean weights every particle equally. The volume-surface mean, written d[3,2] and often called the Sauter mean diameter, is weighted toward surface area and is the natural choice when dissolution or reactivity matters. The volume-weighted mean, d[4,3] or De Brouckere mean, is dominated by the largest particles. The median, or d50, is simply the middle of the distribution and is robust to extreme values.

Which mean you should use depends on the question. For surface-controlled processes like dissolution, the Sauter mean is most relevant because dissolution scales with surface area. For describing the bulk of the material, a volume mean or the d50 is often more meaningful.

The honest caveat is that no single mean fully captures a real powder, especially a broad or bimodal one. Reporting a mean alongside the spread, or quoting d10, d50 and d90 together, gives a far truer picture than any one average alone.