Physical Chemistry of Foods

In the next part, we will for sake of simplicity consider spherical
particles. The following parameters can be defined:

d¼sphere diameter, dimension [L]; in other wordsx¼d

Sn¼

Z?

0

dnfðdÞdd&

X

i¼ 1

Nidin ð 9 : 4 Þ

Snis thenth moment of the distribution, dimension [Ln
^3 ]. It has no

physical meaning, but it is useful as an auxiliary parameter.

S 0 ¼N¼total number of particles, dimension [L
^3 ].

dab¼

Sa

Sb

 1 =ða
bÞ

ð 9 : 5 Þ

This is a general equation for an average diameter, and the kind of

average depends on the values foraandb; dimension [L].

cn¼

SnSnþ 2

S^2 nþ 1

1

! 1 = 2

ð 9 : 6 Þ

cnis the relative standard deviation or the variation coefficient of the

distribution weighted with the nth power of d; it is thus

dimensionless.

9.3.2 Characteristics

Figure 9.10 gives an example of a size frequency distribution of considerable
width. It would be a reasonable example for a homogenized emulsion,
assuming thedscale to be in 10
^7 m. It is seen that the number frequency
can give a quite misleading picture: more than half of the volume of the
particles is not even shown in the number distribution. We will use this
figure to illustrate some characteristic numbers.

Average. The most important one is usually an average value, often
anaverage diameter. As indicated by Eq. (9.5), several types of diameter can
be calculated, by choosing values foraandb. Examples are

d 10 ¼

S 1

S 0

¼number averageor mean diameter