Preparation and Characterization of Ceramic Membranes
2.2 Results and discussion
2.2.3 Permeation characterization of membranes .1 Membrane compaction
The compaction profiles for different membranes prepared in this work are shown in Fig.
2.10. From the figure, it can be observed that the PWF was initially high and declined gradually to reach a steady state value after 60 - 90 minutes for all fabricated membranes. The reduction in PWF was due to the fact that the walls of the pores become closer, denser and uniform during compaction [3]. For the A3 membrane, the observed pure water flux at the beginning of compaction was 6.4×10-4 m3/m2.s which subsequently reached to a steady state value of 5.0 ×10-4 m3/m2.s.
0 40 80 120 160 200 0
5 10 15 20 25 30
Pressure: 310 kPa Membrane:
A1 A2 A3 A4
Composition A (a)
Pure water flux X 104 (m3 /m2 .s)
Time (minute)
0 40 80 120 160 200
0 2 4 6 8
10 (b) Compsotiton B
Pressure: 414 kPa Membrane:
B1 B2 B3 B4
Pure water flux X 104 (m3 /m2 .s)
Time (minute)
Figure 2.10: Variation of pure water flux with time during compaction study for (a) composition A and (b) composition B membranes.
2.2.3.2 Hydraulic pore diameter, permeability and effective permeable area factor The variation of hydraulic pore diameter and hydraulic permeability of the membranes with sintering temperatures are summarized in Table 2.5. As shown, for composition A membranes, the hydraulic pore diameter increased from 0.77 - 1.54 µm with an increase in the sintering temperature from 850 - 1000 oC. Therefore, εmdl2 (from 249.02×10-3 - 783.63 × 10-3µm2) as well as Pm (19.44×10-10 - 61.36×10-10 m3/m2.s.Pa) also increased. Similarly for composition B membranes, the hydraulic pore diameter increased from 0.237 - 0.645 µm with an increase in the sintering temperature from 800 - 950 oC and hence εmdl2 (from 19.32×10-3 - 81.12 ×10-3 µm2) as well as Pm (1.51×10-10 - 6.33×10-10 m3/m2.s.Pa) also increased. The enhancement in hydraulic pore diameter with increasing sintering temperature was due to the growth of grains at higher sintering temperatures that lead to the formation of larger pores and elimination of smaller pores from the porous structure (as discussed in section 2.2.2.3).
Table 2.5: Characteristic parameters obtained from water permeation experiments for membranes prepared at various sintering temperatures.
Composition type
Membrane εm dl(µm) 2
l md
ε ×103 (µm2)
Pm×1010 (m3/m2.s.Pa)
A1 0.42 0.77 249.02 19.44
A2 0.395 0.863 294.19 22.93
A3 0.38 1.08 443.23 34.75
A
A4 0.33 1.54 783.63 61.36
B1 0.344 0.237 19.32 1.51
B2 0.273 0.359 35.18 2.75
B
B3 0.236 0.511 61.62 4.83
B4 0.195 0.645 81.12 6.33
Similar trends were reported in literature for other types of clay based inorganic membranes [29, 31].
2.2.3.3 Gas transport
Figures 2.11a and 2.11b presents the variation of effective permeability factor (K) with average pressure ( ) for composition A and composition B membranes, respectively. For composition A membranes, the measured gas permeance for the membranes were 2.08
P
×103, 3.34×103, 3.59×103 and 4.53×103 m3m-2 h-1 MPa-1 at a ∆P of 0.206 MPa for A1, A2, A3 and A4 membranes, respectively. Similarly for composition B, the measured gas permeance for the membranes were 1.26×10-4, 1.544×10-4, 1.63×10-4 and 1.93×10-4 m3/m2.s.kPa at a ∆P of 206.84 kPa for B1, B2, B3 and B4 membranes, respectively. Table 2.6 summarizes parameters evaluated from graphical analysis of trans-membrane flux data. As shown in the table, the average pore diameter obtained from theoretical analysis of permeation data for composition A membranes (A1, A2, A3 and A4) varied from 0.31 - 0.56 µm. In this regard,
measured pore radius from SEM analysis could be observed to vary from 0.55 - 0.81 µm which was close to the values evaluated from liquid permeation data. Similarly, for composition B membranes, the average pore diameter obtained from theoretical analysis of permeation data varied from 0.162 - 285 µm. This was also close to the evaluated pore diameter from SEM analysis (from 0.185 - 0.332 µm). The table also summarized effective porosity factor values ranging from 0.477 - 0.368 for membrane prepared using composition A and 0.315 - 0.198 for membrane prepared using composition B, which truly represent and contribute to the membrane transport. In this regard, it can be observed that the constant average porosity of the membrane was about 0.42 - 0.33 for membrane prepared using composition A and 0.344 - 0.195 for composition B membranes, which were close to the predicted value of the effective porosity. Henceforth, the assumption of cylindrical pores in the calculation procedure was justified with the fact that tortuosity is close to one.
100 125 150 175 200 225 250
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14
0.16 (a) Composition A
Effective permeability factor (K, m/s)
Average pressure (P, kPa) Sintering temperature (OC)
850 900 950 1000
160 180 200 220 240 260 280 300 320 0.010
0.013 0.016 0.019 0.022 0.025 0.028
Sintering temperature: OC 800 850 900 950
(b) Composition B
Effective permeability factor (K, m/s)
Average pressure (kPa)
Figure 2.11: Variation of effective permeability factor with mean pressure for the membranes prepared using (a) composition A and (b) composition B.
Table 2.6: Various membrane parameters evaluated from graphical analysis of gas permeation data.
Composition type
Membrane A ×102 (m/s)
B ×107 (m/s.Pa)
ds
(nm) q2
ε Viscous flux (%)
Knudsen flux (%)
A1 1.55 2.09 313 0.477 65-76 35-24
A2 1.89 3.66 449 0.405 70 – 81 30-19
A3 2.02 3.93 452 0.428 73-82 27-18
A
A4 2.14 5.17 560 0.368 77-84 23-16
B1 5.26 3.68 162 0.315 54-68 46-32
B2 5.35 4.89 211 0.259 61-74 39-26
B
B3 5.45 5.45 223 0.241 63-76 37-24
B4 5.51 6.75 285 0.198 67-79 33-21
However, the most important relevance of gas permeation data was the ability to judge upon the percentage contribution of Knudsen and viscous diffusion to the trans-membrane flux. As presented in Table 2.6, for A2 membrane, the viscous flux contributed to 70 to 81 percent to the total flux and 19 to 30 percent was contributed by Knudsen flux. This conveys that, about 70 to 81 percent of the pores in the membrane have pore sizes well above the regime where Knudsen diffusion dominates (1 - 20 nm). The reduction in the percent contribution of Knudsen flux to the total flux with increasing sintering temperatures is due to enhancement in pore sizes as well as the distributions at higher sintering temperatures (Figs. 2.6 and 2.7).
2.2.3.4 Comparative study of pore diameters from different methods
With respect to the trends in average pore diameters calculated from SEM ( presented in Table 2.4), air permeation ( presented in Table 2.6) and pure water permeation ( presented in Table 2.5), it was observed that average pore diameter calculated from air permeation ( ) provided the minimum pore diameter and pure water permeation ( )
ds
dg dl
dg dl
provided the highest pore diameter. The average pore diameters calculated from SEM analysis were in between and . As gas molecules are more likely to pass through small voids or interstices than water molecules, gas permeation experiments provided the smallest pore diameters. On the other hand, liquid permeation experiments not only detected actual pores but also other non-interconnected voids of the porous matrix. Hence, was higher than . For the calculation of using SEM images, only pores greater than 50 nm were considered on the membrane surface. Therefore, there was a possibility that this method may overestimate the mean pore size by considering the wider pores on the surface and ignoring the smaller pores. As a result, was higher than and may be higher or lower than (lower than in the present study). However, since hydraulic permeability involves the transport of liquid through pores accountable for MF process, the most appropriate average pore size of the membrane could be inferred from liquid flux data but not gaseous flux data or SEM images. Gaseous flux characterization enables one to evaluate the percentage distribution of micro-pores of varying sizes and their contribution to the overall transport behavior of the membrane. Pore diameters using SEM image provides an approximate estimate upon the possible pore diameters and their distributions. These trends are in agreement with the experimental data reported in the literature [81].
dg dl
dl dg
ds
ds dg dl
dl