Physical Chemistry of Foods

9.2.1 Geometric Aspects

Thenumberof particles present per unit volume (N) is, for a given volume
fraction (j), inversely proportional to particle diameter (d) cubed. For
monodisperse spherical particles,j¼Npd^3 =6. Examples are in Table 9.3.
Thespecific surface area(A), i.e., the surface area per unit volume of
dispersion, is proportional to jand inversely proportional to d. For
monodisperse spherical particles,A¼ 6 j=d. The amount of material needed
to cover particles is proportional toA, and this amount can be appreciable if
the particles are small. Examples are in Table 9.3.

Question

Which of the values given in the table is in fact impossible?

Thedistancebetween particles (x) can be defined in various ways.
Assuming a regular cubic arrangement of particles, the smallest distance
between adjacent ones is given by

x¼N
^1 =^3 
d¼d

0 : 81

j^1 =^3

1



ð 9 :1aÞ

where the second part is valid for spheres only. The average free distance
over which a sphere can be moved before it touches another one is, assuming
the distribution of the spheres throughout the volume to be random, given

TABLE9.3 Number and Surface Area of Spherical

Particles of Various Diameters in a Dispersion at a

Volume Fraction of 0.5 (the volume occupied by surface

layers around the spheres is also given)

Diameter of spheres,mm 0.1 1 10

Number per ml 1015 1012 109

Surface area, m^2 per ml 30 3 0.3

Surface layer of 2 nm,%v/v 6.2 0.6 0.06

Same, of 10 nm thickness 36 3.1 0.30