Page 70 - Advances in Textile Biotechnology

Developments in enzymatic textile treatments 49

enzyme concentration in the capillary liquid decreases immediately as a
result of the adsorption process, leading to a lower equilibrium concentra-
tion at the surface. If the capillary liquid is not refreshed this results in a
surface concentration that is lower than can be expected for particular
enzyme concentrations in the liquid. There will be some transfer of enzymes
from the inter-yarn liquid to the intra yarn liquid by diffusion. However,
this is a relatively slow process as shown above and therefore it is expected
that the adsorption process becomes controlled by diffusion.
In most models describing the adsorption of enzymes at a surface, it is
assumed that the enzyme concentration in the liquid bulk does not change
as a result of adsorption. However, this assumption is only valid if the bulk
liquid volume is much larger than the available surface. In capillary systems
it is the other way around, the bulk liquid volume is much smaller than the
available surface, and, therefore, the assumption of a constant enzyme con-
centration in the liquid can not be made. This phenomenon leads to a more
complex model.

2.6.1 Modelling the adsorption limitation in textile pores
The adsorption of enzymes at a substrate surface is shown schematically in
Fig. 2.12. The rate equation for the enzyme concentration at the surface Γ ES
follows from the adsorption–desorption equilibrium, equation [2.31]:
d*
A C ES = kV C A C * C E S k A C * − des ES [2.37]
ads
t d
where A C is the surface area of the capillary wall and V C is the volume of
the capillary. It is assumed that this volume is totally filled with the enzy-

matic solution, so V C is also the volume of the enzymatic solution in the

Enzymatic solution

E E
E
E
C E E
E E
E k ads E k des
G ES
G S S S S S S S S S S S S S S S S S S S S S
Substrate surface
2.12 A schematic view of the adsorption of enzymes at a substrate
surface.

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