Chemistry Reference
In-Depth Information
converging dies - 3D
converging dies - 2D
converging flow fields -
open syphon
Figure 6.24
Flow through contracting geometries and converging flow fields.
converging flow fields -
through two nozzles
problem is centred on residence time. As an example of this, consider a simple
Couette geometry that we fill with a polymer solution. We can apply a constant
shear stress with time and follow the increase in rate until a steady-state
response is achieved. It may take several hours or days to achieve but none-
theless for many systems a steady response is practically achievable. However,
extension presents a more formidable challenge. One way in which an elonga-
tional field can be created is to force the fluid through a contracting geometry
such as that shown in Figure 6.24.
Suppose we have designed our geometry such that the radius r is propor-
tional to the length l via a constant k:
Þ
2
¼
k
=
l
ð
R
ðÞ
ð
6
:
109
Þ
In our thought experiment we can force fluid to flow through this die at a
certain volume per unit time or volumetric flow rate Q and allow no drag with
the walls. This is a total-slip condition so no shear will be applied to the fluid.
The fluid will travel faster as the geometry contracts so the velocity V(l)ina
plane across the geometry simply depends upon the area at any length l:
Q
p R
ðÞ
Þ
2
¼
Ql
V
ð
l
Þ¼
ð
6
:
110
Þ
pk
ð
