Membrane and Desalination Technologies - TCE Moodle Website

Membrane Separation: Basics and Applications 297
Fig. 7.8. Calculating
void space between
spherical nodules.
1. Calculate the area of the triangular void space.
2. Calculate the radius of the circular pore whose cross-sectional area is equal to the triangular area
calculated above.
3. Subtract the thickness of the monolayer of water, 0.28 nm, which is adsorbed at the pore wall and
assumed to be immobile.
4. Calculate the water flux using the relevant data in Example 7.1 and the following numerical
values:
np=Am ¼ 6:5 10 15 m 2 ;
Dp ¼ 4:134 10 6 Pa;
Dx ¼ 10 7 m;
t ¼ 2:5;
m ¼ 0:035 Pa s ðviscosity of water that fills nano-sized poresÞ:
Answer
1. Area of the triangular void space is 9:42 pffiffiffi
ð 3 p=2Þ ¼14:25 nm2 2.
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
The radius is 14:30=p ¼ 2:13 nm.
.
3. The effective radius of the mobile water channel is r ¼ 2:13 0:28 ¼ 1:85 nm:
4. Water flux is
J ¼ ð6:5 1015 Þð3:1416Þð1:85 10 9 Þ 4 ð4:134 10 6 Þ
ð8Þð3:5 10 2 Þð2:5Þð10 7 Þ
¼ 141:26 10 7 m 3 =m 2 s:
Assuming water density of 10 3 kg/m 3 , the water flux is 141.26 10 -4 kg/m 2 s.
6. MEMBRANE MODULE AND PROCESS DESIGN
6.1. Introduction
d = 18.8 nm
Void
space
Spherical
nodules
As we know, large surface areas are required for industrial applications of membrane
processes. A practical solution for providing this large surface area is packing the membranes