Page 60 - Advances in Textile Biotechnology

Developments in enzymatic textile treatments 39

2.4 The squeezing model
As previously stated, the mechanical energy in textile treatment equipment
is aimed at deforming the porous fabric to create velocities in the pores of
the textile. Figure 2.2 shows the yarn model with the stagnant core and a
convective shell. In the stagnant core, the mass transfer is fully controlled
by diffusion whereas in the convective shell this is based on convection, i.e.

the flow of liquid. Here, we derive a model that describes this system. In
this model, a squeezing factor α expresses the ratio between the stagnant
and the convective regions. To make the model less complicated, the fabric
is modelled as a porous slab with a stagnant centre layer and two convective
outer layers as indicated in Fig. 2.4.
In Fig. 2.4, d f,S is the thickness of the stagnant middle layer and d f is the
thickness of the fabric. Thus, the thickness of the convective layers d f,C is:

[2.4]
d f,C = d f − d f,S
The squeezing factor α is now defi ned as:

D = volume of the convective layers in the fabric = V f,C [2.5]
total volumee of the fabric f V
2
If the surface area of the textile is A (m ):

1
α = Ad f,C = d f,C = − d f,S [2.6]
Ad f d f d f
If α equals zero, d f,S equals d f , which is the case when there is no fl ow at all,
so the liquid in the total volume of the fabric is stagnant. If α equals 1, d f,S
equals zero, which is the case if the water flows in all the pores of the fabric.

If we relate the flow within the fabric to deformation we can also say that
if α = 1, all the pores are deformed, i.e. maximum deformation effect of the

mechanical energy and flow in all the pores. If α = 0, no pores are deformed,
i.e. no deformation effect of the mechanical energy and no flow in the pores.

It should be noted here that the value of the squeezing parameter α is a
mean value. So when the fabric is going through a padding bath, the squeez-
ing factor of this system is a mean value taken from the point where the

d f

d
f,S

2.4 Model of a textile slab with a stagnant centre layer and two
convective outer layers.

© Woodhead Publishing Limited, 2010