Lynne Wong's PhD thesis

6.8 CALCULATION OF BOUND WATER AND DISSOLVED WATER FROM
THE HAILWOOD-HORROBIN MODEL
The Hailwood-Horrobin sorption model is based on the assumption that the subject of
study forms an ideal solid solution with three species present in the solid phase: dissolved
water, hydrated molecules and unhydrated molecules. Hence the adsorbed water is either
in simple solution or combined with a fibre molecule to form a hydrate. When the sorption
equation of the model (Hailwood and Horrobin, 1946) is expressed as:
W K a K K
m
1800 +
2 w
1 2 w
= +
(5)
1 − K2aw
1 K1K2aw
a
The first term on the right hand side refers to dissolved water (m s ) and the second term
refers to the hydrated water (m h ). In equation (5), m is the equilibrium moisture content
(%), W is the molecular mass of the adsorbate substance necessary to bond one molecular
mass of water (mol/mol), K is the equilibrium constant between the free dissolved water
and the hydrated water, K 2 is the equilibrium constant between the dissolved water and the
external vapour pressure and a w is the water activity.
The amount of dissolved water can be calculated by:
m
s
=
K2aw
− K a
1
2
w
1800
×
W
and the amount of hydrated water by:
m
h
K1K2aw
1800
= × ,
+ K K a W
1 1 2
w
hence the total adsorbed water, m is given by:
m = m s + m h
In this work the experimental EMC data at various values of a w were fitted to the following
form of Hailwood-Horrobin sorption model:
aw
m
=
b +
c a
w
+
d
( a ) 2
w
and the ‘best fit’ values for the parameters b, c and d determined.
Equation (5) can be rearranged to be in the above form as written in Table 5.1.
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