Membrane and Desalination Technologies - TCE Moodle Website

84 J. Ren and R. Wang
Dynamic viscosity (pa.s)
1.000
100
10
η'
η''
η*
approaching ratio also strongly influences the relaxation time and molecular orientation. With
the increase of the approaching ratio, the dope formulation is approached to the cloud point
curve and close to the thermodynamic instability limit, which speeds up the phase separation
process and the relaxation effects on the membrane orientation will be reduce.
ELONGATION FLOW IN THE AIR GAP
1
0.1 1.0 10.0
frequency (w)
100.0 1000.0
Fig. 2.31 Influence of dynamic frequency on the dynamic viscosity (polymer solution: 24 wt% 6FDA-
ODA/NDA; 3 wt% EtOH; 22 C; strain = 20%) [adapted from ref. (99)].
Because of the viscoelasticity of the dope solution, the nascent hollow fiber at the exit of
the spinneret would exhibit die-swell, where the outside diameter of the nascent fibers in the
air gap is in the maximum and the velocity is the smallest. The nascent hollow fiber
membranes accelerate from the velocity at the die-swell to the take up velocity by freefalling
or drawing process. The drawing ratio (DR) is defined as (85):
DR ¼ VF
¼
VD
VFpðD2 0 ; ð35Þ
4QP
where VF and VD are the drawing velocity and average extrusion rate at the spinneret exit (dieswell),
respectively. Qp is the volumetric flux of the dope solution. D0 and d0 define the dope
annular cross-section leaving the spinneret. If there is no die swell, then the velocity at the
spinneret exit is equal to the average extrusion velocity in the annular hollow channel.
However, for a viscoelastical dope solution, the rheology of the dope solution inside the
spinneret influences the die-swell of the nascent membranes in the air gap. At the higher shear
rate of the dope solution inside the spinneret, the dope solution also change from viscosity to
elasticity, which causes a bigger outer diameter of the nascent hollow fiber membranes,
shown in Fig. 2.27.
d 2 0 Þ
η 0