Physical Chemistry of Foods

9.3.3 Complications

Many particles encountered in practice are not true homogeneous spheres,
although emulsion drops and small gas bubbles may be virtually so.
Deviations can be of two types.
The particles may beinhomogeneous. They may be hollow or have a
more intricate internal structure. If the inhomogeneity varies among
particles, a particle size distribution is insufficient to characterize the
dispersion. For instance, the mass average diameter and the volume average
diameter may be markedly different; this is illustrated by several spray-dried
powders, where some of the particles have large vacuoles, while others have
not. If the oil droplets in an emulsion are coated with a thick layer of
protein, the smallest droplets contain far more protein per unit amount of
oil than the largest ones, as illustrated in Table 9.3.
The particles may be anisometric, i.e., deviate from the spherical
form. Moreover, the particles may have a rough surface. The two cases
cannot be fully separated because intermediates occur, but a sphere can
have a rough surface and a platelet can be smooth. One parameter now is
insufficient to characterize a particle. If all particles have approximately
congruent shapes (think of a collection of screws of various sizes), it may
be possible to use just one size parameter, e.g., length. For irregularly
shaped but not very anisometric particles, as found in several powders, one
often defines anequivalent sphere diameter. This can be defined in various
ways, such as

dv¼diameter of a sphere of the same volume

ds¼diameter of a sphere of the same surface area

df¼diameter of a sphere that sediments at the same rate

de¼the edge of the smallest square through which the particle can

pass, or sieve diameter

dp¼diameter of a circle of the same surface area as the perpendicular

projection of the particle on the plane of greatest stability (explained

in Section 9.3.4)

To characterize the shape, various parameters are used. The deviation
from spherical is often expressed by the followingshape factor

c¼

dv

ds

 2

¼ 4 : 836

ðvolumeÞ^2 =^3

surface area

ð 9 : 8 Þ

The smaller the value ofc, the more anisometric the particle. Table 9.5 gives
examples. Surface roughness further decreases the value ofc. Often, the