Physical Chemistry of Foods

d 30 ¼

S 3

S 0

 1 = 3

¼volume averagediameter

d 32 ¼

S 3

S 2

¼volume/surfaceaverage;or Sauter mean, diameter

d 63 ¼

S 6

S 3

 1 = 3

¼volume-weighted average volumediameter

Other characteristic diameters are

The modal diameter, corresponding to the peak of the number
frequency distribution, and the modal volume diameter
Themediandiameterdm, which divides the distribution into halves of
equal number, i.e., FðdmÞ¼ð 1 = 2 ÞFð?Þ. One can also use the
median volume diameter.
Figure 9.10 shows that the various averages can differ widely. The sum
aþbis called the order of the average, and the higher it is, the larger the
average. The common mean,d 10 , is a poor measure of the center of the

FIGURE9.10 Example of a log-normal size distribution. Number frequency and

volume frequency versus diameter (d) are given, and the various types of

characteristic diameters are indicated, as well as the distribution width.