0

2

4

6

8

10

12

14

0.1 1 10

bentonite suspension after four settlingsN

um

ber

of

par

tic

les

(%

)

Particle size (µm)

Figure 1. Particle size distribution of a bentonite suspension after four settlings

1010

1011

106 107

t = 10 st = 20 s

d2t/

dV

2 (s.

m-6

)

dt/dV (s.m-3)

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)

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)

107

108

109

1010

1011

1012

105 106 107 108

d2 t/

dV

2 (s

.m-6

)

dt/dV (s.m-3)

n = 2 n = 0n > 2

Step I

Step II

Step III

0 100

1 107

2 107

0 100 1 10-4 2 10-4 3 10-4 4 10-4 5 10-4 6 10-4

dt/

dV

(s

.m-3

)

V (m3)

0 100

1 10-6

2 10-6

3 10-6

4 10-6

0 100 1 10-4 2 10-4 3 10-4 4 10-4 5 10-4 6 10-4

dV

/dt

(m3 .s

-1)

V (m3)

Figure 4. Split of the curves into successive mechanisms: (A) very low fouling mechanism , ( B) blocking , (C) cake filtration.

(C) n = 0

(B) n =2

QB,0

VB,0

VC,0

(A)

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)

0 100

5 10-5

1 10-4

1.5 10-4

2 10-4

2.5 10-4

3 10-4

3.5 10-4

0 500 1000 1500 2000 2500 3000 3500 4000

0.2 µm (exp.)0.2 µm (calc.)

V (

m3 )

t (s)

0 100

5 10-5

1 10-4

1.5 10-4

2 10-4

2.5 10-4

3 10-4

0 500 1000 1500 2000 2500 3000 3500

0.8 µm (exp.)0.8 µm (calc.)

V (

m3 )

t (s)

0 100

2 10-4

4 10-4

6 10-4

8 10-4

1 10-3

1.2 10-3

1.4 10-3

0 500 1000 1500 2000 2500 3000 3500 4000

5 µm (exp.)5µm (calc.)

V (

m3 )

t (s)

0 100

5 10-4

1 10-3

1.5 10-3

2 10-3

0 1000 2000 3000 4000 5000

8 µm (exp.)8 µm (calc.)

V (

m3 )

t (s)

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)

0

0.2

0.4

0.6

0.8

1

1.2

10-2 10-1 100 101

0.2 µm (exp.)0.2 µm (calc.)8 µm (exp.)8 µm (calc.)

B,f

P (bar)

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

10-6

10-5

10-4

10-3

10-2

100 101 102

B,f

= 25%

B,f

= 50%

B,f

= 75%

B,f

= 100%

0,2 µm

0,8 µm

5 µm

8 µm

VB

,f -

VB

,0 (

m3 )

B

* (m-1)

Figure 8. Evolution of a clean and fouled filter media resistance (respectively, Rm,0 and RmB,f) with its initial mean pore diameter, dpore

1010

1011

1012

0 2 4 6 8 10

Rm,0

RmB,f

Rm

(m

-1)

dpore

(µm)

Figure 9. Effect of feed suspension concentration C on the specific parameter, C, for cake formation at constant pressure 0.3 bar

1011

1012

1013

1014

1015

1016

10-3 10-2 10-1 100 101

0.2 µm0.8 µm5 µm8 µm

C

* (m

-2)

C (g.L-1)

* 14 1.1

2

7.15 10

1.0

C C

r

10-1

100

101

102

103

104

10-4 10-3 10-2 10-1 100 101

0.2 µm0.8 µm5 µm8µm

B

* (m

-1)

C (g.L-1)

Figure 10. Effect of feed suspension concentration C on the specific parameter, B , for pore blocking at constant pressure 0.3 bar

100

101

102

103

104

10-5 10-4 10-3 10-2 10-1 100

0.2 µm0.8 µm5 µm8 µm

B

* (m

-1)

C x p/pore

(g.L-1)

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

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

0 100

5 1014

1 1015

1.5 1015

2 1015

10-2 10-1 100 101

0.2 µm; C = 0.1 g.L-1

8 µm; C = 1 g.L-1

C

* / C

1.1 (

m1.

3 kg

-1.1

)

P (bar)

0

500

1000

1500

2000

10-2 10-1 100 101

8 µm; C = 1 g.L-1

B

* (m

-1)

P (bar)

0

50

100

150

10-2 10-1 100 101

0.2 µm; C = 0.1 g.L-1

B

* (m

-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

Figure 14. Effect of the wall shear stress, w on pore blocking mechanism for two different membranes (0.2 µm and 8 µm)

0

200

400

600

800

1000

1200

1400

1600

10-2 10-1 100 101 102

0.2 µm; C = 0.1 g.L-1

8 µm; C = 1 g.L-1

B

* (m

-1)

w

(Pa)

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)

0

10

20

30

40

50

60

70

80

0.1 1 10

B

* (m

-1)

dpore

(µm)