make quantitative predictions. At very smallw, the system may be in a
glassy state; this is further discussed in Section 16.1. Besides water content,
other factors play a part, for instance,
- Composition of the dry matter. Figure 5.16a suggests that for
several materials roughly one curve is found, but closer inspection shows
differences by about an order of magnitude inDefffor the samew. If the dry
matter contains a water soluble substance of fairly small molar mass,
diffusivity can be markedly greater than in its absence, at least at smallw.If
glycerol is added to an aqueous system of not too low water content, sayw
0.5, it will cause the diffusion coefficient to decrease, since glycerol has a
higher viscosity than water. In a very dry food, however, say forw<0.1, the
presence of glycerol will generally increase the diffusion coefficient, since its
presence means a greater proportion of liquid. The presence of sugars, like
glucose or sucrose, may also enhance diffusivity of water at very smallw.
These substances then act as ‘‘plasticizers’’ (see Section 16.1).
- Molecular size. Point 1 concerns the properties, including
molecular size, of the materials that form most of the mass of the system,
for convenience called the matrix. Here we consider the size of diffusing
molecules, which may be present in small quantities only. According to the
Stokes–Einstein relation [Eq. (5.16)], the diffusion coefficient of a molecule
is inversely proportional to its radius. At smallwthis dependence is much
stronger, since it now concerns diffusion through narrow pores in the matrix
(see Figure 5.15). Semiquantitative examples are given in Figure 8.9a, where
the upper curve relates to water. It is seen that at smallwthe differences
become very large. This phenomenon explains retention of volatiles during
drying of foods (e.g., coffee essence): most volatiles concerned have a
distinctly larger molar mass than water. Most gases, on the other hand, will
diffuse relatively fast.
To be sure, interaction forces between the diffusing molecules and the
material of the matrix would also play a part, but this has received little
study. - Temperature. Figure 8.9b gives some examples, and it seen that the
effect again is very strong at smallw, involving several orders of magnitude.
This temperature effect is all that allows reasonably fast drying of several
materials, or determination of dry matter content of most foods by oven
drying. - Physical inhomogeneityof the system. Some authors have reported
that diffusivities in systems of smallwwere markedly greater than expected
on the basis of some theory, or when extrapolating from higherwvalues.
Such a discrepancy may well be due to physical inhomogeneity of the
matrix. Especially at very smallw, tiny cracks may develop in the matrix,
allowing much faster transport of small molecules. This phenomenon