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The Effect of Operating Conditions on Critical Flux in Membrane Filtration of Latexes
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THE EFFECT OF OPERATING CONDITIONS ON CRITICAL FLUX IN MEMBRANE FILTRATION OF LATEXES S. S. MADAENI Chemical Engineering Department, Razi University, Kermanshah, Iran
I
n microporous membrane ® ltration, formation of a cake of solids results in ¯ ux decline. Pumping the permeate can remove the deposited layer and improve the ¯ ux. This technique allows operation at low transmembrane pressure and provides stable ¯ ux if a `critical ¯ ux’ is not exceeded. Slow fouling can occur in time if the initial ¯ ux is beyond the critical value. Critical ¯ ux is dependent on the factors that in¯ uence concentration polarization, such as nature and concentration of the feed and shear rate, being higher for higher cross¯ ow velocity and lower concentration. These effects have been observed for activated sludge biomass. However, the complexity of the biomass can affect the dependency of critical ¯ ux on operating conditions. Wellcharacterized polystyrene latex particles were used to explain the factors in¯ uencing critical ¯ ux in a colloidal suspension without taking into account the complex nature of the feed. The main difference between these feeds was that the pumped permeate ¯ ux was signi® cantly lower in the activated sludge than in the pure water ¯ ux. In the latex suspension the same ¯ ux was obtained for the feed and for the pure water. However, the same trend for factors affecting critical ¯ ux was observed in the activated sludge biomass and latex suspension. Keywords: critical ¯ ux; micro® ltration; fouling; latex; activated sludge.
INTRODUCTION
EXPERIMENTAL
Membrane ® ltration of biomass is usually accompanied by signi® cant ¯ ux decline due to cake layer formation and fouling. Cross¯ ow ® ltration with ¯ ux controlled by pumping the permeate can produce stable ¯ uxes if a `critical ¯ ux’ is not exceeded1 ,2 ,3 . Pumping the permeate produces very low transmembrane pressure4 . At these low transmembrane pressures fouling can be avoided or minimized. In a previous work5 an activated sludge mixed liquor was used to illustrate the factors in¯ uencing critical ¯ ux. The results showed that the critical ¯ ux depends on feed concentration and cross¯ ow velocity being higher for higher cross¯ ow velocity or lower feed concentration. For operation below the critical ¯ ux it was observed that the ¯ ux was signi® cantly lower than the pure water ¯ ux, signifying interaction between the feed and the membrane even though cake formation was not evident. This behaviour could be due to particle-pore interactions or to an initial fouling of the membrane by ® ne debris or macromolecules. It was not clear that the effect of operating conditions observed in that work was due to interactions between the species in the complex feed and the membrane or due to the real effect of these factors. In this work a simple feed (latex suspension) was used to eliminate the effect of complexity of activated sludge and to explain the effect of operating conditions on critical ¯ ux in more detail.
Polystyrene latex beads (Cat. No. LB-1 and LB-11) were obtained from Sigma Chemical Company. The particle diameter reported by the manufacturer is 0.1 l m (std. dev. <0.024 l m) and 1.0 l m (std. dev. <0.004 l m) respectively. The latex suspensions (density = 1 g/cm- 3 , viscosity = 1 cp) were made using puri® ed water from a Milli-Q Water Puri® cation System with a quality of 18 MX .cm. Tests were performed in a cross¯ ow cell using Millipore hydrophilic 0.22 l m (GVWP) micro® ltration membranes. The membrane module was constructed of perspex and had a channel height of 2 mm, a channel width of 27 mm and a channel length of 80 mm. The effective membrane area was 19 cm2 . The membranes were supported by an aluminium plate punched with 3 mm holes. A peristaltic pump was used to supply the operating pressure and the feed circulation. The equipment set-up for pumped permeate tests is shown in Figure 1. Pressure transducers from the Labom Company supplied by Tempress Controls (E1301 for Pin , Pout and E2313 for Ppermeate ) were used for precise measurement of transmembrane pressure. Cross¯ ow rate was controlled by the recirculation pump, while ¯ ux was ® xed by the permeate pump. Transmembrane pressure was monitored as the independent variable. All pressure elements, as well as the permeate pump and balance, were monitored automatically. A special program was prepared to run the experiments. To determine critical ¯ ux, the feed was ® ltered at different ¯ ow rates by the permeate pump. Flux was 266
EFFECT OF OPERATING CONDITIONS ON CRITICAL FLUX IN MEMBRANE FILTRATION
267
Figure 3. Flux and transmembrane pressure versus time for a mixture of colloidal latex particles.
In membrane ® ltration, if there is little or no accumulation of the deposited material on the membrane surface, ¯ ux is directly proportional to D P. If applied pressure is increased or materials are deposited, fouling occurs and ¯ ux no longer increases linearly with D P. Changes in transmembrane pressure indicate changes in conditions on the membrane surface. Figure 2 shows a typical variation of D P versus ¯ ux for the pumped permeate regime. An increase of D P at constant ¯ ux indicates deposition of solids and the formation of a cake layer. To determine critical ¯ ux, a step by step technique was used. As can be seen from Figure 3, D P is stable initially but at some point it starts to
increase with time. The highest value for which D P is stable is the critical ¯ ux. If ¯ ux is set above the critical ¯ ux, there is an increase in D P and a decline in ¯ ux (Figure 4). Stable ¯ uxes with stable transmembrane pressures can be achieved if the ¯ ux is lower than the critical value (Figure 5). Figures 2 to 5 are typical curves and the same trend was observed for different size latex particles and their mixture under all conditions (not shown). The pure water ¯ ux was higher than the activated sludge ¯ ux in pumped permeate. However the same ¯ ux was observed while using latex suspensions as the feed (Figure 6). This is the key difference between the two feeds, which can be explained due to the difference in the complexity of the feeds. Activated sludge consists of suspended solids, ® ne colloids, macromolecules, debris and dissolved matter in different sizes and shapes with a high tendency to accumulate on the membrane surface or in the membrane matrix. Latex is a spherical particle which produces a simple feed when mixed with water. The measured critical ¯ uxes for colloidal latexes of 1.0 and 0.1 l m and their mixtures in different conditions are shown in Tables 1, 2 and 3 respectively. The data are plotted in Figures 7 to 12. The critical ¯ ux is assumed to occur when convection towards the membrane is balanced by back transport. Higher back transport means higher critical ¯ ux. The mechanisms of back transport, such as lateral migration
Figure 2. Transmembrane pressure versus ¯ ux for a mixture of colloidal latex particles.
Figure 4. Flux and transmembrane pressure versus time for a mixture of colloidal latex particles (initial ¯ ux above the critical ¯ ux).
Figure 1. Equipment set-up for pumped permeate tests.
increased step by step and held for half an hour for each ¯ ux. Initially D P is stable but at some point it starts to increase with time. The highest ¯ ux for which D P is stable is the critical ¯ ux. Critical ¯ uxes for different sizes of latex particles and for different mixtures (1:1 by volume) were measured in a range of concentrations (0.1-0.3 g l- 1 ) and cross¯ ow velocities (0.25-0.75 m s- 1 ). RESULTS AND DISCUSSION
Trans IChemE, Vol 75, Part B, November 1997
268
MADAENI
Figure 5. Flux and transmembrane pressure versus time for a mixture of colloidal latex particles (initial ¯ ux below the critical ¯ ux).
Figure 8. Critical ¯ ux versus cross¯ ow velocity for 1.0 l m colloidal latex particles. Table 1. Critical ¯ ux (l m- 2 h- 1 ) for colloidal latex (1.0 l m) with 0.2 l m, hydrophilic (GVWP) membrane at different cross¯ ow velocities and concentrations. Cross¯ ow velocity, (m s- 1 ) Concentration (g l- 1 ) 0.0* 0.1 0.2 0.3
0.25 100 88 75 63
0.50 163 140 120 95
0.75 198 170 145 115
*Extrapolation Table 2. Critical ¯ ux (l m- 2 h- 1 ) for colloidal latex (0.1 l m) with 0.2 l m, hydrophilic (GVWP) membrane at different cross¯ ow velocities and concentrations.
Figure 6. Flux versus transmembrane pressure for activated sludge, 1.0 l m colloidal latex particles and pure water.
Cross¯ ow velocity, (m s- 1 ) Concentration (g l- 1 ) 0.0* 0.1 0.2 0.3
0.25 93 81 70 58
0.50 152 130 105 85
0.75 179 155 130 106
*Extrapolation
Table 3. Critical ¯ ux (l m- 2 h- 1 ) for a mixture of colloidal latex (1.0 l m + 0.1 l m) with 0.2 l m, hydrophilic (GVWP) membrane at different cross¯ ow velocities and concentrations. Cross¯ ow velocity, (m s- 1 ) Concentration (g l- 1 )
Figure 7. Critical ¯ ux versus concentration for 1.0 l m colloidal latex particles.
0.0* 0.1 0.2 0.3
0.25 89 78 66 55
0.50 113 100 88 75
0.75 127 115 102 90
*Extrapolation
and shear-enhanced diffusivity, are greater at higher cross¯ ow velocity. Therefore a higher critical ¯ ux is expected with higher cross¯ ow. The critical ¯ ux was lower at higher concentrations due to the potential for more deposition when the feed is concentrated. The critical ¯ ux was higher for larger particles (compare Tables 1 and 2). This effect can be explained due to
diffusivity. Shear-enhanced diffusivity is proportional to size, being higher for larger particles. Back transport of larger latex particles is greater than small particles, resulting in higher critical ¯ ux. For a mixture of colloidal latex particles, the critical ¯ ux was lower than the critical ¯ ux for Trans IChemE, Vol 75, Part B, November 1997
EFFECT OF OPERATING CONDITIONS ON CRITICAL FLUX IN MEMBRANE FILTRATION
269
Figure 9. Critical ¯ ux versus concentration for 0.1 l m colloidal latex particles.
Figure 11. Critical ¯ ux versus concentration for a mixture of colloidal latex particles.
Figure 10. Critical ¯ ux versus cross¯ ow velocity for 0.1 l m colloidal latex particles.
Figure 12. Critical ¯ ux versus cross¯ ow velocity for a mixture of colloidal latex particles.
each of the particles (compare Table 3 with Tables 1 and 2). This is probably due to the packing density of the ¯ owing cake layer resulting from the concentration polarization close to the membrane surface. Evidence of the ¯ owing cake layer in pumping permeate regimes has been shown in a paper presented by Fane6 . A videotape clearly showed that a cake is formed and removed. A feature of the mechanism of critical ¯ ux is intermittent obstruction of the pores by a ¯ owing cake layer. The nature of this cake depends on the particle size and packing density. A mixture of particles causes denser cake and results in lower critical ¯ ux.
CONCLUSIONS In micro® ltration, formation of a cake of solids results in ¯ ux decline. Pumping of permeate helps to remove the cake and to improve the ¯ ux. Pumped permeate allows operation at low transmembrane pressure with stable ¯ uxes below the critical ¯ ux. Flux decline can occur in time if the initial ¯ ux is even marginally beyond the critical value. Simple and well-characterized polystyrene latex particles were used to show the factors in¯ uencing critical ¯ ux. Critical ¯ ux is dependent on the nature and concentration of the feed and shear rate, being higher for higher cross¯ ow velocity, lower concentration and larger particles. Trans IChemE, Vol 75, Part B, November 1997
REFERENCES 1. Madaeni, S. S., 1995, Membrane ® ltration of biological and nonbiological colloids, PhD Thesis (University of New South Wales, Sydney, Australia). 2. Field, R. W., Wu, D., Howell, J. A. and Gupta, B. B., 1995, Critical ¯ ux concept in micro® ltration fouling, Journal of Membrane Science, 100: 259±272. 3. Howell, J. A., 1994, Is cleaner production the future?, Plenary presentation, Proceedings of Engineering of Membrane Processes II Conference, Environmental Applications, Il Ciocco, Italy. 4. Madaeni, S. S., Shu, Q. L., Wiley, D. E. and Fane, A. G., 1994, The effect of transmembrane pressure regimes on ¯ ux for the cross¯ ow micro® ltration of activated sludge, Chemical Engineering Conference (CHEMECA’ 94), Perth, Australia. 5. Madaeni, S. S., Fane, A. G. and Wiley, D. E., 1996, Factors in¯ uencing critical ¯ ux in membrane ® ltration of biomass, International Membrane Science and Technology Conference (IMSTEC’ 96), Sydney, Australia. 6. Fane, A. G., 1997, Control of concentration polarisation in membrane process by process operation strategies and module design, Proceedings of the Symposium on Characterization of Polymers with Surface, Lappeenranta, Finland.
ADDRESS Correspondence concerning this paper should be addressed to Dr S. S. Madaeni, Chemical Engineering Department, Razi University, Daneshgah Road, Tagh Bostan 67149, Kermanshah, Iran. The manuscript was received 7 January 1997 and accepted for publication after revision 28 July 1997.
THE EFFECT OF OPERATING CONDITIONS ON CRITICAL FLUX IN MEMBRANE FILTRATION OF LATEXES S. S. MADAENI Chemical Engineering Department, Razi University, Kermanshah, Iran
I
n microporous membrane ® ltration, formation of a cake of solids results in ¯ ux decline. Pumping the permeate can remove the deposited layer and improve the ¯ ux. This technique allows operation at low transmembrane pressure and provides stable ¯ ux if a `critical ¯ ux’ is not exceeded. Slow fouling can occur in time if the initial ¯ ux is beyond the critical value. Critical ¯ ux is dependent on the factors that in¯ uence concentration polarization, such as nature and concentration of the feed and shear rate, being higher for higher cross¯ ow velocity and lower concentration. These effects have been observed for activated sludge biomass. However, the complexity of the biomass can affect the dependency of critical ¯ ux on operating conditions. Wellcharacterized polystyrene latex particles were used to explain the factors in¯ uencing critical ¯ ux in a colloidal suspension without taking into account the complex nature of the feed. The main difference between these feeds was that the pumped permeate ¯ ux was signi® cantly lower in the activated sludge than in the pure water ¯ ux. In the latex suspension the same ¯ ux was obtained for the feed and for the pure water. However, the same trend for factors affecting critical ¯ ux was observed in the activated sludge biomass and latex suspension. Keywords: critical ¯ ux; micro® ltration; fouling; latex; activated sludge.
INTRODUCTION
EXPERIMENTAL
Membrane ® ltration of biomass is usually accompanied by signi® cant ¯ ux decline due to cake layer formation and fouling. Cross¯ ow ® ltration with ¯ ux controlled by pumping the permeate can produce stable ¯ uxes if a `critical ¯ ux’ is not exceeded1 ,2 ,3 . Pumping the permeate produces very low transmembrane pressure4 . At these low transmembrane pressures fouling can be avoided or minimized. In a previous work5 an activated sludge mixed liquor was used to illustrate the factors in¯ uencing critical ¯ ux. The results showed that the critical ¯ ux depends on feed concentration and cross¯ ow velocity being higher for higher cross¯ ow velocity or lower feed concentration. For operation below the critical ¯ ux it was observed that the ¯ ux was signi® cantly lower than the pure water ¯ ux, signifying interaction between the feed and the membrane even though cake formation was not evident. This behaviour could be due to particle-pore interactions or to an initial fouling of the membrane by ® ne debris or macromolecules. It was not clear that the effect of operating conditions observed in that work was due to interactions between the species in the complex feed and the membrane or due to the real effect of these factors. In this work a simple feed (latex suspension) was used to eliminate the effect of complexity of activated sludge and to explain the effect of operating conditions on critical ¯ ux in more detail.
Polystyrene latex beads (Cat. No. LB-1 and LB-11) were obtained from Sigma Chemical Company. The particle diameter reported by the manufacturer is 0.1 l m (std. dev. <0.024 l m) and 1.0 l m (std. dev. <0.004 l m) respectively. The latex suspensions (density = 1 g/cm- 3 , viscosity = 1 cp) were made using puri® ed water from a Milli-Q Water Puri® cation System with a quality of 18 MX .cm. Tests were performed in a cross¯ ow cell using Millipore hydrophilic 0.22 l m (GVWP) micro® ltration membranes. The membrane module was constructed of perspex and had a channel height of 2 mm, a channel width of 27 mm and a channel length of 80 mm. The effective membrane area was 19 cm2 . The membranes were supported by an aluminium plate punched with 3 mm holes. A peristaltic pump was used to supply the operating pressure and the feed circulation. The equipment set-up for pumped permeate tests is shown in Figure 1. Pressure transducers from the Labom Company supplied by Tempress Controls (E1301 for Pin , Pout and E2313 for Ppermeate ) were used for precise measurement of transmembrane pressure. Cross¯ ow rate was controlled by the recirculation pump, while ¯ ux was ® xed by the permeate pump. Transmembrane pressure was monitored as the independent variable. All pressure elements, as well as the permeate pump and balance, were monitored automatically. A special program was prepared to run the experiments. To determine critical ¯ ux, the feed was ® ltered at different ¯ ow rates by the permeate pump. Flux was 266
EFFECT OF OPERATING CONDITIONS ON CRITICAL FLUX IN MEMBRANE FILTRATION
267
Figure 3. Flux and transmembrane pressure versus time for a mixture of colloidal latex particles.
In membrane ® ltration, if there is little or no accumulation of the deposited material on the membrane surface, ¯ ux is directly proportional to D P. If applied pressure is increased or materials are deposited, fouling occurs and ¯ ux no longer increases linearly with D P. Changes in transmembrane pressure indicate changes in conditions on the membrane surface. Figure 2 shows a typical variation of D P versus ¯ ux for the pumped permeate regime. An increase of D P at constant ¯ ux indicates deposition of solids and the formation of a cake layer. To determine critical ¯ ux, a step by step technique was used. As can be seen from Figure 3, D P is stable initially but at some point it starts to
increase with time. The highest value for which D P is stable is the critical ¯ ux. If ¯ ux is set above the critical ¯ ux, there is an increase in D P and a decline in ¯ ux (Figure 4). Stable ¯ uxes with stable transmembrane pressures can be achieved if the ¯ ux is lower than the critical value (Figure 5). Figures 2 to 5 are typical curves and the same trend was observed for different size latex particles and their mixture under all conditions (not shown). The pure water ¯ ux was higher than the activated sludge ¯ ux in pumped permeate. However the same ¯ ux was observed while using latex suspensions as the feed (Figure 6). This is the key difference between the two feeds, which can be explained due to the difference in the complexity of the feeds. Activated sludge consists of suspended solids, ® ne colloids, macromolecules, debris and dissolved matter in different sizes and shapes with a high tendency to accumulate on the membrane surface or in the membrane matrix. Latex is a spherical particle which produces a simple feed when mixed with water. The measured critical ¯ uxes for colloidal latexes of 1.0 and 0.1 l m and their mixtures in different conditions are shown in Tables 1, 2 and 3 respectively. The data are plotted in Figures 7 to 12. The critical ¯ ux is assumed to occur when convection towards the membrane is balanced by back transport. Higher back transport means higher critical ¯ ux. The mechanisms of back transport, such as lateral migration
Figure 2. Transmembrane pressure versus ¯ ux for a mixture of colloidal latex particles.
Figure 4. Flux and transmembrane pressure versus time for a mixture of colloidal latex particles (initial ¯ ux above the critical ¯ ux).
Figure 1. Equipment set-up for pumped permeate tests.
increased step by step and held for half an hour for each ¯ ux. Initially D P is stable but at some point it starts to increase with time. The highest ¯ ux for which D P is stable is the critical ¯ ux. Critical ¯ uxes for different sizes of latex particles and for different mixtures (1:1 by volume) were measured in a range of concentrations (0.1-0.3 g l- 1 ) and cross¯ ow velocities (0.25-0.75 m s- 1 ). RESULTS AND DISCUSSION
Trans IChemE, Vol 75, Part B, November 1997
268
MADAENI
Figure 5. Flux and transmembrane pressure versus time for a mixture of colloidal latex particles (initial ¯ ux below the critical ¯ ux).
Figure 8. Critical ¯ ux versus cross¯ ow velocity for 1.0 l m colloidal latex particles. Table 1. Critical ¯ ux (l m- 2 h- 1 ) for colloidal latex (1.0 l m) with 0.2 l m, hydrophilic (GVWP) membrane at different cross¯ ow velocities and concentrations. Cross¯ ow velocity, (m s- 1 ) Concentration (g l- 1 ) 0.0* 0.1 0.2 0.3
0.25 100 88 75 63
0.50 163 140 120 95
0.75 198 170 145 115
*Extrapolation Table 2. Critical ¯ ux (l m- 2 h- 1 ) for colloidal latex (0.1 l m) with 0.2 l m, hydrophilic (GVWP) membrane at different cross¯ ow velocities and concentrations.
Figure 6. Flux versus transmembrane pressure for activated sludge, 1.0 l m colloidal latex particles and pure water.
Cross¯ ow velocity, (m s- 1 ) Concentration (g l- 1 ) 0.0* 0.1 0.2 0.3
0.25 93 81 70 58
0.50 152 130 105 85
0.75 179 155 130 106
*Extrapolation
Table 3. Critical ¯ ux (l m- 2 h- 1 ) for a mixture of colloidal latex (1.0 l m + 0.1 l m) with 0.2 l m, hydrophilic (GVWP) membrane at different cross¯ ow velocities and concentrations. Cross¯ ow velocity, (m s- 1 ) Concentration (g l- 1 )
Figure 7. Critical ¯ ux versus concentration for 1.0 l m colloidal latex particles.
0.0* 0.1 0.2 0.3
0.25 89 78 66 55
0.50 113 100 88 75
0.75 127 115 102 90
*Extrapolation
and shear-enhanced diffusivity, are greater at higher cross¯ ow velocity. Therefore a higher critical ¯ ux is expected with higher cross¯ ow. The critical ¯ ux was lower at higher concentrations due to the potential for more deposition when the feed is concentrated. The critical ¯ ux was higher for larger particles (compare Tables 1 and 2). This effect can be explained due to
diffusivity. Shear-enhanced diffusivity is proportional to size, being higher for larger particles. Back transport of larger latex particles is greater than small particles, resulting in higher critical ¯ ux. For a mixture of colloidal latex particles, the critical ¯ ux was lower than the critical ¯ ux for Trans IChemE, Vol 75, Part B, November 1997
EFFECT OF OPERATING CONDITIONS ON CRITICAL FLUX IN MEMBRANE FILTRATION
269
Figure 9. Critical ¯ ux versus concentration for 0.1 l m colloidal latex particles.
Figure 11. Critical ¯ ux versus concentration for a mixture of colloidal latex particles.
Figure 10. Critical ¯ ux versus cross¯ ow velocity for 0.1 l m colloidal latex particles.
Figure 12. Critical ¯ ux versus cross¯ ow velocity for a mixture of colloidal latex particles.
each of the particles (compare Table 3 with Tables 1 and 2). This is probably due to the packing density of the ¯ owing cake layer resulting from the concentration polarization close to the membrane surface. Evidence of the ¯ owing cake layer in pumping permeate regimes has been shown in a paper presented by Fane6 . A videotape clearly showed that a cake is formed and removed. A feature of the mechanism of critical ¯ ux is intermittent obstruction of the pores by a ¯ owing cake layer. The nature of this cake depends on the particle size and packing density. A mixture of particles causes denser cake and results in lower critical ¯ ux.
CONCLUSIONS In micro® ltration, formation of a cake of solids results in ¯ ux decline. Pumping of permeate helps to remove the cake and to improve the ¯ ux. Pumped permeate allows operation at low transmembrane pressure with stable ¯ uxes below the critical ¯ ux. Flux decline can occur in time if the initial ¯ ux is even marginally beyond the critical value. Simple and well-characterized polystyrene latex particles were used to show the factors in¯ uencing critical ¯ ux. Critical ¯ ux is dependent on the nature and concentration of the feed and shear rate, being higher for higher cross¯ ow velocity, lower concentration and larger particles. Trans IChemE, Vol 75, Part B, November 1997
REFERENCES 1. Madaeni, S. S., 1995, Membrane ® ltration of biological and nonbiological colloids, PhD Thesis (University of New South Wales, Sydney, Australia). 2. Field, R. W., Wu, D., Howell, J. A. and Gupta, B. B., 1995, Critical ¯ ux concept in micro® ltration fouling, Journal of Membrane Science, 100: 259±272. 3. Howell, J. A., 1994, Is cleaner production the future?, Plenary presentation, Proceedings of Engineering of Membrane Processes II Conference, Environmental Applications, Il Ciocco, Italy. 4. Madaeni, S. S., Shu, Q. L., Wiley, D. E. and Fane, A. G., 1994, The effect of transmembrane pressure regimes on ¯ ux for the cross¯ ow micro® ltration of activated sludge, Chemical Engineering Conference (CHEMECA’ 94), Perth, Australia. 5. Madaeni, S. S., Fane, A. G. and Wiley, D. E., 1996, Factors in¯ uencing critical ¯ ux in membrane ® ltration of biomass, International Membrane Science and Technology Conference (IMSTEC’ 96), Sydney, Australia. 6. Fane, A. G., 1997, Control of concentration polarisation in membrane process by process operation strategies and module design, Proceedings of the Symposium on Characterization of Polymers with Surface, Lappeenranta, Finland.
ADDRESS Correspondence concerning this paper should be addressed to Dr S. S. Madaeni, Chemical Engineering Department, Razi University, Daneshgah Road, Tagh Bostan 67149, Kermanshah, Iran. The manuscript was received 7 January 1997 and accepted for publication after revision 28 July 1997.