bentonite suspension after four settlings
Number of particles (%)
14
12
10
8
6
4
2
0
0.1
1
10
Particle size (µm)
Figure 1. Particle size distribution of a bentonite suspension after four settlings
11
2
2
-6
d t/dV (s.m )
10
t = 10 s
t = 20 s
10
10
106
107
-3
dt/dV (s.m )
Figure 2. Influence of the time step t on the k-value
determination by using the representation for the experiment
using a 0.2 µm membrane (C = 10-2 g/L and P = 0.3 bar)
12
10
Step III
11
Step II
-6
d t/dV (s.m )
10
10
10
2
Step I
9
2
10
8
n>2
n=2
n=0
10
7
10
105
106
107
108
-3
dt/dV (s.m )
Figure 3. Example of the determination of the slope n in the representation
for the fouling mechanisms identification ( experimental data for 5 µm
membrane; C = 10-2 g/L and P = 0.3 bar)
-6
4 10
-6
(A)
QB,0
3
-1
dV/dt (m .s )
3 10
-6
2 10
-6
1 10
0
0 10
0
0 10
-4
1 10
(B) n =2
VB,0
-4
2 10
-4
3 10
-4
4 10
-4
5 10
-4
6 10
3
V (m )
7
-3
dt/dV (s.m )
2 10
7
1 10
(C) n = 0
0
0 10
0
0 10
-4
1 10
-4
2 10
-4
3 10
3
V (m )
-4
4 10
-4
5 10
-4
6 10
VC,0
Figure 4. Split of the curves into successive mechanisms: (A) very
low fouling mechanism , ( B) blocking , (C) cake filtration.
0.8 µm (exp.)
0.8 µm (calc.)
0.2 µm (exp.)
0.2 µm (calc.)
-4
3 10
-4
3.5 10
-4
-4
3 10
2.5 10
-4
-4
2 10
V (m )
-4
2 10
3
3
V (m )
2.5 10
-4
1.5 10
-4
1.5 10
-4
1 10
-4
1 10
-5
5 10
5 10-5
0
0
0 10
0 10
0
500
0
1000 1500 2000 2500 3000 3500 4000
500
1000
1500
2000
2500
3000
3500
t (s)
t (s)
5 µm (exp.)
5µm (calc.)
8 µm (exp.)
8 µm (calc.)
-3
1.4 10
-3
2 10
-3
1.2 10
-3
1.5 10
8 10-4
3
V (m )
3
V (m )
1 10-3
6 10-4
-3
1 10
-4
4 10
-4
5 10
-4
2 10
0
0 10
0
500
1000 1500 2000 2500 3000 3500 4000
t (s)
0
0 10
0
1000
2000
3000
4000
t (s)
Figure 5. Plot of cumulative permeate volume V versus time t - comparison between
experimental and calculated curves for four experiments (C = 10-2 g/L and P = 0.3
bar): ( 0.2 µm;  0.8 µm;  5 µm;  8 µm)
5000
0.2 µm (exp.)
0.2 µm (calc.)
8 µm (exp.)
8 µm (calc.)
1.2
1
B,f
0.8
0.6
0.4
0.2
0
-2
10
-1
0
10
10
1
10
P (bar)
Figure 6. Effect of the transmembrane pressure P on the final surface
coverage ratio, B,f for two different membranes (0.2 µm and 8 µm)
B,f = 25%
0,2 µm
= 50%
0,8 µm
= 75%
5 µm

10-2

B,f
B,f
B,f = 100%
8 µm
10-4
V
B,f
-V
B,0
3
(m )
10-3
10-5
10-6
0
10
1
2
10

*
B
10
-1
(m )
Figure 7. Symbols are the values of VB,f – VB,0 versus B, for a series of data (dpore = 0.2;
0.8; 5; 8 µm). Operating conditions were kept the same for all these experiments: C = 10-2
g.L-1, P = 0.3 bar. Lines are the calculated data of VB,f – VB,0 versus B, for different
values of B,f
R
R
m,0
mB,f
12
-1
Rm (m )
10
11
10
10
10
0
2
4
d
pore
6
8
10
(µm)
Figure 8. Evolution of a clean and fouled filter media resistance (respectively, Rm,0
and RmB,f) with its initial mean pore diameter, dpore
C *  7.15 1014  C1.1
0.2 µm
0.8 µm
5 µm
8 µm
r 2  1.0
16
10
15
C

*
-2
(m )
10
1014
13
10
1012
11
10
-3
10
-2
10
0
-1
10
10
1
10
-1
C (g.L )
Figure 9. Effect of feed suspension concentration C on the specific parameter, C,
for cake formation at constant pressure 0.3 bar
0.2 µm
0.8 µm
5 µm
8µm
4
10
3
B

*
-1
(m )
10
102
1
10
100
-1
10
-4
10
-3
10
-2
10
-1
10
0
10
-1
C (g.L )
Figure 10. Effect of feed suspension concentration C on the specific
parameter, B , for pore blocking at constant pressure 0.3 bar
1
10
4
10
0.2 µm
0.8 µm
5 µm
8 µm
3
2
B
10

*
-1
(m )
10
1
10
0
10
10-5
10-4
10-3
Cx
10-2
10-1
100
-1
p/pore
(g.L )
Figure 11. Plot of B versus the product of feed concentration, C times the number of
blocked pores per unit of blocking particle, p/pore (C  p/pore) at constant pressure
0.3 bar
0.2 µm; C = 0.1 g.L
8 µm; C = 1 g.L
-1
-1
15
-1.1
)
2 10
15
15
1 10
C
*
 /C
1.1
(m
1.3
kg
1.5 10
14
5 10
0
0 10
-2
10
-1
0
10
10
1
10
P (bar)
Figure 12. Effect of transmembrane pressure on cake formation: comparison between
two membranes (0.2 µm and 8 µm) by considering the plot of C /C1.1 versus P
8 µm; C = 1 g.L
-1
2000
B
1000

*
-1
(m )
1500
500
0
-2
10
-1
10
0
10
0
10
10
1
P (bar)
0.2 µm; C = 0.1 g.L
-1
150
*

B
-1
(m )
100
50
0
-2
10
-1
10
10
1
P (bar)
Figure 13. Effect of transmembrane pressure on pore blocking for two different membranes (0.2
µm and 8 µm) by considering the plot of B versus P
0.2 µm; C = 0.1 g.L
8 µm; C = 1 g.L
-1
-1
1600
1400
1000
800

*
B
-1
(m )
1200
600
400
200
0
-2
10
-1
0
10
10
1
10
2
10
 (Pa)
w
Figure 14. Effect of the wall shear stress, w on pore blocking mechanism for two
different membranes (0.2 µm and 8 µm)
80
70
50
40

*
B
-1
(m )
60
30
20
10
0
0.1
1
10
dpore (µm)
Figure 15. Effect of the mean pore diameter of the filter media on the specific
parameter, B, for pore blocking (C = 10-2 g/L and P = 0.3 bar)