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The average particle size, i.e. the average equivalent diameter, is defined as the diameter where 50 mass-% (of the particles) of the powder have a larger equivalent diameter, and the other 50 mass-% have a smaller equivalent diameter. Hence the average particle size is denoted as equivalent d50. The d50 can be read from the cumulative (either oversize or undersize) PSD graph. From the point where the 50% horizontal line intersects the PSD curve, a line can be drawn perpendicular to the x-axis. The numerical value of d50 can be read (or interpolated) at the point of intersection of the perpendicular with the x-axis.
| Product |
D50 |
Lactochem Crystals
Lactochem Coarse powder
Lactochem Powder
Lactochem Fine powder
Lactochem Microfine |
158
96
62
39
5 |
Typical d50 values of some Friesland Foods Domo lactose products.
The d50 of a PSD does not necessarily coincide with the equivalent diameter corresponding to the top (maximum) of the differential PSD curve.
Asymmetrical fractional PSD curve, with d50=67µ and dmode=110µ
The equivalent diameter corresponding to the top of the PSD curve is called the dmode. Only in the theoretical case where the bell-shaped PSD curve is exactly symmetrical will d50 and dmode coincide. Real-world PSDs show asymmetrical curves, which are often very skew. The more asymmetrical the PSD curve, the larger the difference between d50 and dmode.
The preceding paragraph shows that d50 does not tell us anything about the shape of the PSD curve, and hence about the actual distribution of particle sizes around the average (d50). This can be seen from the next figure, where two PSDs with the same d50 but totally different shapes are overlayed (for reasons of simplicity, two almost symmetrical curves have been chosen, but the same applies to asymmetrical curves).
A wide and a narrow PSD with the same d50
The powders represented by both curves have the same average particle size (d50), but the particle size distributions around the average are very different. The powder represented by curve 1 contains a fairly large amount of very large particles as well as a considerable amount of very fine particles. The powder of curve 2, on the other hand, contains hardly any fine or coarse particles. Both powders would differ considerably with respect to flow properties, bulk density, tabletting properties, etc. Hence to characterise a PSD, d50 alone is absolutely insufficient. Other equivalent diameters can be used in addition to d50. Often used equivalent diameters in addition to d50 are d10 and d90. The definition of d10 is: that equivalent diameter where 10 mass-% (of the particles) of the powder has a smaller diameter (and hence the remaining 90% is coarser). The definition of d90 can be derived similarly. |
