i.e., about particle size—andt0.5¼time needed to halve a difference in
concentration over a distancex^0 ), we obtain for water transport
D¼ 10 ^15 ; x^0 ¼ 0 :1mm! t 0 : 5 ¼ 107 s&4 months
D¼ 10 ^15 ; x^0 ¼ 1 mm! t 0 : 5 ¼ 103 s&15 minutes
D¼ 10 ^18 ; x^0 ¼ 1 mm! t 0 : 5 ¼ 106 s&12 daysActually, zero water content will never be reached. The sample should be
very finely divided to obtain even reasonable sorption curves at low water
content. For instance, a curve for a boiled sweet as in Figure 8.3b can only
be obtained if the material is finely ground.
It is seen in Figure 8.4a that both curves converge at highaw,asisto
be expected, and they also seem to do so at lowaw. However, the latter is not
really the case. In Figure 8.4b the same relation is shown on a log–log scale
for low water contents, and it is seen that the relative difference does not
decrease with decreasingaw. One often sees desorption isotherms drawn
through the origin, but this is in fact misleading. That point is never reached
on dehydration at room temperature, and the lowest water content reached
may be a few percent (see, e.g., Figure 8.6b, below).
How then is the point of zero water content obtained? This can be
done by drying at high temperature, often at about 100 8 C, where the
diffusion coefficient generally is some orders of magnitude higher than at
room temperature (see also Figure 8.9b, later on). Moreover, the driving
force for water removal (the difference in chemical potential of water
between sample and air) then is greater, the more so when drying under
vacuum. On the other hand, prolonged keeping at high temperature, mostly
for several hours, may cause chemical reactions (e.g., involving uptake of
oxygen) or vaporization of other substances than water, making determina-
tion of the water content somewhat unreliable. Consequently, it may be
preferable to dry the sample under vacuum at a somewhat lower
temperature.
Sorption Enthalpy. When removing water from a product, heat is
consumed. This is because a lower water content goes along with a lower
water activity, and the water has to be removed against a water activity
gradient or, in other words, against an increasing osmotic pressure. The
sorption heat or enthalpyDHsgenerally increases asawdecreases (see Figure
8.5a), which would imply that removal of water becomes ever more difficult
in the course of drying. However,DHsmostly is small: it is rarely over 20 kJ
per mole of water, and its average (integrated) value over the whole drying
range is 0: 2 2kJ?mol^1. This is far smaller than the enthalpy of