Page 67 - Advances in Textile Biotechnology

46 Advances in textile biotechnology

Thus, equation [2.24] can also be written in a dimensionless form:
− )
−
C E,B e ) − kt k S −α k C − kt k S (1 α − kt
1
=−(1 α S − e C + e S [2.26]
C E,B,∞ k S − k C k S − k C
The dimensionless bulk concentration C E,B / C E,B,∞ has a value between 0
(for t = 0) and 1 (for t = ∞). Two limiting cases are also α = 0 and α = 1. If
α = 0, there is no convection zone and the mass transfer is fully controlled
by diffusion. From equation [2.26], it follows that:
⎛ C E,B ⎞
1
⎜ ⎝ C E,B,∞ ⎟ ⎠ α =0 =− e − kt [2.27]
S
If α = 1, the mass transfer is fully controlled by convection and equation
[2.26] becomes:
⎛ C E,B ⎞
⎜ ⎟ =− e − kt [2.28]
C
1
⎝ C E,B,∞ ⎠ D =1
Equation [2.26] can be applied to find the values for α, k S and k C . This

can be done by measuring the enzyme concentration in the bath during a
release experiment in time. Applying non-linear curve fitting then delivers

the required values.
We have also done some model calculations to show the effect of the
squeezing factor α on the transfer of enzymes into the fabric. The values
used for this example are:
−11
2 −1
• diffusion coeffi cient, D = 10 m s
• fabric thickness, d f = 0.5 mm
• liquid to cloth ratio, LCR = 5
• liquid density, ρ B = 1000 kg m −3
• fabric density, ρ f = 1200 kg m −3
Figure 2.11 shows the results of the calculations.
In this case we used equation [2.26] to calculate the transport of enzymes

from a bath to the fabric. For the mass transfer coefficient in the stagnant
region, we have taken:

k S = D [2.29]
2
d S
or by substituting the defi nition for α:

k S = D [2.30]
− )]
[ d f (1 α 2

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