Page 64 - Advances in Textile Biotechnology

Developments in enzymatic textile treatments 43

1
a
3

a
2
E

a
1
= Pe = Pe
Pe 1 2 3
0
0 Time
2.10 Three curves representing the transport of enzymes into a fabric
as a function of time for different values of α and identical values of
Pe.

all for a constant value of α and three different values of Pe. Because dif-
fusion is identical for all three cases, the slow parts of the curves coincide
at longer times. However, for high Pe numbers the diffusion regime starts
earlier because the convective transport is completed faster. Figure 2.10
shows three curves for three different values of α and a constant value of
the Pe number. The rate of convective transport is the same for all cases
because the deformation rate is constant. However, for high values of α,
the extent of deformation is higher, leading to a higher value of E at which
the diffusion regime starts.

2.5 A mass transfer model
The mass transfer in a fabric can be modelled using the squeezing factor α.
The model derived here is for rinsing mass from the fabrics to a rinsing
bath. Because the impregnation of fabrics by enzymes from an enzymatic
solution is just the other way around, the equations of the model can easily
been applied for rinsing as well as for impregnation. The model is based on
the squeezing principles leading to a stagnant core and a convective region.
The release of enzymes is modelled by the principles of chemical reaction
kinetics. The release ‘reaction’ can be written as:
⎯
⎯
k C
C E,f,S ⎯→ C E,f,C ⎯ → C E,B [2.9]
k S
The enzymes in the stagnant region of the fabrics C E,f,S become enzymes
in the convective region in the fabric C E,f,C by diffusion. The enzymes in the
convective region become enzymes in the bath C E,B by convective transport

from the convective regions to the bath. The transfer coefficient for trans-
−1
port from the stagnant to the convective region is k S (s ) and the transfer

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