Page 65 - Advances in Textile Biotechnology

44 Advances in textile biotechnology

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coefficient for transport from the convective regions to the bulk is k C (s ).
During the release process, the enyme concentration in the bulk liquid C E,B
increases. For an impregnation process, this bulk concentration decreases.
The model describes the change of the bulk concentration as a function of
time. The starting equation is a mass balance for the enzymes present in the
total system. This balance is valid for all times.

VC E,f,0 = V C E,S + V C E,C + V C E,B [2.10]
f,C
B
f,S
f
This balance assumes that there is initially a homogeneous enzyme concen-
tration in the fabric C E,f,0 . V f , V f,S and V f,C are, respectively, the total fabric
volume, the volume of the stagnant region and the volume of the convective
region. C E,S , C E,C , and C E,B are, respectively, the enzyme concentration in the
liquid bath, in the stagnant region and in the convective region as a function
of time.
Thus, from the mass balance an expression for C E,B can be derived:
VC E,f,0 − V C E,S − V C E,C
C E,B = f f,S f,C [2.11]
V B
The volumes V f , V f,S , V f,C and V B can be expressed in α as defi ned earlier
and the liquid to cloth ratio LCR:

V f,C = α
[2.12]
V f
V f,S
1
=−α [2.13]
V f
LCR = ρ B V B [2.14]
ρ f V f
−3
in which ρ B is the density of the liquid in the bath (kg m ) and ρ f is the
−3
density of the fabric (kg m ). Substitution of equations [2.12], [2.13] and
[2.14] into equation [2.11] gives:
ρ 1
α
C E,B = B [ C E,f,0 −(1 − ) C E,S −α C E,C ] [2.15]
f ρ LCR
Expressions for the enzyme concentration in the stagnant and convective
regions C E,S and C E,C can be found with the following rate equations result-
ing from the release ‘reaction’ equation above.

d C E,S
V f,S =− Vk C E,S [2.16]
f,S S
t d
d C E,C
V f,C = Vk C E,S − V k C E,C [2.17]
C
f,S S
f,C
t d
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