Chemistry Reference
In-Depth Information
food products and materials, as most important data for technological appli-
cations. A variety of mathematical models have been proposed to describe
these curves, the most popular of which being the BET and GAB isotherms.
According to the adsorption BET model, the vapour molecules are first
adsorbed on the solid as a monolayer, with a constant energy; further layers
are then deposited with the liquefaction heat. The following expression is
derived:
m
m
1
ð
c
1
Þ
a
w
1
þð
c
1
Þ
a
w
a
w
1
a
w
¼
þ
(11)
m being the water content, m
1
the water content corresponding to the mono-
layer and c a constant related to the adsorption energy of the first layer. This
model correctly describes the sorption isotherms of food materials for 0.2
<
a
w
<
0.5. Many other expressions can be found in the literature: Van den Berg
and Bruin (1981) counted 75 expressions, comprising one to seven para-
meters. The GAB expression, which is currently the most often used, can be
satisfactorily fitted
to experimental data up to a
w
0.90,
with three
parameters:
m
m
1
ð
c
1
Þ
ka
w
1
þð
c
1
Þ
ka
w
ka
w
1
ka
w
¼
þ
(12)
It must be noted that the parameters m
1
and c do not necessarily have
the same values in the BET and GAB expressions for the same product
(Timmermann et al., 2001). A better fitting, however, can be obtained with
a four-parameter expression, even for non-sigmoid curves, which cannot be
fitted to GAB (Peleg, 1993):
m
¼
k
1
a
w
n1
þ
k
2
a
w
n2
(13)
In the end, a two-parameter expression was claimed to have the advan-
tage over GAB of allowing water content to infinitely rise for a
w
approaching
1 (Lewicki, 2000):
1
b
1
1
a
w
m
¼
A
(14)
The mathematical description of sorption isotherms is extremely useful
in many circumstances of food technology: It provides the necessary informa-
tion for food formulation, i.e. the water content of the different ingredients,
