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Modelling of dead-end microfiltration with pore blocking and cake formation
Journal of Membrane Science 208 (2002) 181–192
Modelling of dead-end microfiltration with pore blocking and cake formation S. Kosvintsev, R.G. Holdich∗ , I.W. Cumming, V.M. Starov Department of Chemical Engineering, Loughborough University, Leicestershire, LE11 3TU, UK Received 16 November 2001; received in revised form 14 May 2002; accepted 15 May 2002
Abstract A series of dead-end filtration experiments are compared with a recently proposed pore blocking model that contains only one experimentally fitted parameter. This parameter has physical meaning and it can be verified by an independent check of the experimental data. The challenge suspension used was near monosized latex particles of ∼0.45 m filtered on a track-etched membrane with similar sized pores of ∼0.4 m. The filtered suspension concentration ranged from 0.00006 to 0.01% (w/w) and the transmembrane pressures varied from 1000 to 20,000 Pa. During the experiments three stages of microfiltration were observed. There was an initial stage that fitted a sieving (or pore blocking) model until the mass of latex deposited per unit membrane area (specific mass) reached 2 × 10−3 kg m−2 . The model required a single parameter that was found to fit all the data under different experimental operating conditions. The second stage of pore blocking could also be fitted using a second parameter and the predicted flux at the end of the first stage of pore blocking. When the deposited particles had reached a depth of approximately 12 particle layers, or specific mass of 4.8×10−3 kg m−2 , the flux then showed normal cake filtration behaviour. © 2002 Published by Elsevier Science B.V. Keywords: Sieve model; Resistance; Deposit; Prediction
1. Introduction Recent work [1] on the modelling of dead-end microfiltration employing a mechanism founded on treating membrane filtration as a type of sieving process has resulted in the following equation to describe the permeate volume (V) as a function of filtration time (t): 4S 1 πβnd¯ 2 dV V = ln 1 + t (1) 4S dt 0 π nd¯ 2 β
β is the ratio between the area of influence above a pore and the pore area itself. For a given filter, and suspension, several of the terms may be combined to provide a simplified equation: 1 dV V = ln 1 + γ nβ t (2) γ nβ dt 0 where γ is a single dimensionless constant for all values of suspension concentration and operating pressure. In physical terms, it is the area ratio of the pore to the filter area: π d¯ 2 4S
where S is the area of the filter, d the mean pore diameter, n the number of particles per unit volume and
γ =
∗ Corresponding author. E-mail address: [email protected] (R.G. Holdich).
Finally, the influence of different operating pressures and suspension concentrations can be removed from
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Eq. (2) by defining the following dimensionless variables: dV ∗ ∗ V = γ nV and t = γ n t dt 0 Hence, the filtration equation for the pore blocking mechanism is reduced to: 1 V ∗ = ln(1 + βt ∗ ) (3) β Eqs. (1) and (3) contrast with the conventional cake filtration description of membrane filtration, where the permeate volume would be expected to vary with the square root of filtration time, hence, the gradient on a log plot would be 0.5 during cake filtration conditions. According to Eq. (3), all operating data for microfilter pore blocking should reduce to a single plot of dimensionless volume and time, irrespective of suspension concentration and operating pressure. The latter term is an intrinsic part of the initial permeate flux rate. In the earlier model, there is only a single parameter that must be identified from experimental measurement, β, which should be a constant for a given membrane. Furthermore, the parameter has physical meaning, it is the ratio of the area of influence within the particle suspension per open area of the pore. Hence, values should be slightly greater than unity. The model was formulated for very low feed concentrations only and was experimentally tested on Texas tap water of indeterminate solids concentration. A sieving mechanism should be applicable to microfilters of regular pore shape, such as track-etched and other true surface filters. At the end of the ‘sieving’ (or pore blocking) period of filtration one would expect the conventional cake filtration mechanism to start. This period of filtration should be adequately described by the conventional equation based on Darcy’s law. Alternative approaches to a coupled sieving–cake filtration model have been based on the well-known filtration equations of Hermia [2]. A number of workers have published models based on the ‘standard law filtration’ and ‘blocking’ filtration analyses. For example, the microfiltration of proteins has been studied extensively [3–7], the filtration of oil emulsion has been modelled [8] as well as that of very dilute latex suspension [9]. These approaches have been adequate
for the prediction of the systems under investigation, but are limited in their scope for further elucidation of the mechanism of microfiltration and more general predictive modelling. The coupled sieving–cake filtration model should not be so limited as it is better able to predict the change from one mechanism to another.
2. Experimental Isopore track-etched membrane filters with a nominal pore size of 0.4 m and filtering diameter of 0.04 m, supplied by Millipore, were used. The surface of a typical Isopore filter is illustrated in Fig. 1(a) and the uniform pore geometry expected from a track-etched membrane filter can be clearly seen. However, there are some double and multiple pores visible. Generally, direct analysis from the image shows that the pore distribution on the membrane surface is: 79% single pores, 16% double pores and 3.5% triple, and more, pores present. Also included in Fig. 1 is a scanning electron microscope picture of the reverse side (not usually filtering side) of an Isopore filter. Comparison of Fig. 1(a) and (b) show that the filter is asymmetric, with pores 0.44 m ± 0.04 m in diameter on the filtering side and coarser ones on the reverse side. The difference in surface structure between the two sides is also evident in Fig. 1. According to Eq. (1), this should give rise to different filtration performance between the two different filter orientations. To investigate the model, a suspension of a nearly monosized polystyrene latex particles was used. The particles were formed by the emulsion polymerisation of styrene using a conventional preparation technique [10]. The mean particle diameter was measured as 0.46 m by a Malvern Mastersizer with 80% of the particles between 0.4 and 0.51 mm. Many different feed suspension concentrations were investigated, from 0.000063 to 0.01% by mass. The particles were first suspended in filtered water from a MilliQ purification device, to form two stock suspensions 3.5 and 0.01% by mass. A diagram of the test apparatus is shown in Fig. 2. The filtration cell was made from clear acrylic and consisted of two cylinders, with the membrane placed between them. The top and bottom of each cylinder had tube connections to reservoir and receiving vessels, respectively. The feed reservoir
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Fig. 1. (a) Filtering surface of Isopore track-etched membrane. (b) Reverse side of Isopore track-etched membrane.
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Fig. 2. Experimental apparatus.
could be raised, or lowered, as a means to control the pressure head effecting the filtration. For experiments at different transmembrane pressures, the difference in height between the feed and receiver free surfaces varied from 0.1 to 2 m. The permeate weight was measured at time intervals of between 1 and 5 s. Before each experiment, a preliminary run to determine the membrane permeability was performed by measuring the clean water flux at the same pressure drop to be used in the filtration. At the end of this preliminary experiment, some water was left in the rig to ensure that air did not enter the filtration circuit. The volume of water left to cover the membrane surface was 6 ml, when the latex suspension was added to this, the suspension concentration reduced by less than 0.5%. Then the vessel with the challenge suspension was connected to the filter cell and permeate mass was measured for between 2000 and 8000 s.
3. Results and discussion The primary aim of this work was to investigate the pore blocking model at different challenge concentrations to those reported in the original paper with the
aim of investigating the concentration dependency of the blocking mechanism. A concentration of 0.01% (w/w) represented the realistic maximum value for this study. Even with this apparently low feed concentration the blocking period was short and the cake filtration period soon established itself. The experiments showed that there are apparently three identifiable stages of microfiltration. The first stage corresponds to the blocking of the pores themselves. This stage is observed best at very small concentrations (lower then 0.001%) and relatively low pressures. Fig. 3(a) shows an example of a volume–time plot where the two pore blocking stages of filtration are identifiable. In the first blocking phase, the initial filtrate rate is correctly predicted by Eq. (1) using the clean water permeation test value for dV/dt at time zero, together with a value of 3 for β. It can be seen that the model fits the data well until about 800 s, when the transition to second stage blocking takes place. The two stages of pore blocking are shown perhaps more clearly in Fig. 3(b) where the data is plotted on a log–log plot. Eq. (2) can be represented by a power law fit when the values of the time term, in the logarithm expression, are small. All the experiments at low solids concentration showed
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Fig. 3. (a) Cumulative permeate volume with time for filtration at feed concentration 0.000063% by mass and transmembrane pressure of 3020 Pa. (b) The same data from Fig. 3(a) plotted on a log scale.
the same behaviour and the transition only depended on the permeate volume passed through membrane or, more exactly, on the quantity of particles deposited and blocking the membrane pores. In the second
blocking stage, the value of (dV/dt|0 ) needs to be changed to 0.25 cm3 s−1 , instead of 0.86 cm3 s−1 for water flux, whilst the value of β was found to be lower at 1.1.
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It is possible to define an overall system permeability based on Darcy’s law: µ dV 1 − P = L k dt A
(4)
where P is the pressure drop, L the porous media depth, µ the liquid dynamic viscosity, k the actual hydraulic permeability and A is the filter area. The system permeability (k ) is: k =
kA µL
hence, Darcy’s law becomes − P =
1 dV k dt
(5)
During the blocking stages, any variation in porous media depth (L) is negligible. However, this will not be the case during the cake filtration period. So, during the blocking period, reduction in system permeability must be due to the progressive plugging of the membrane, until the cake filtration period starts. The overall system permeability reduces during both stages of pore blocking. However, the change in
system permeability is greatest during the first blocking stage, this is illustrated for several filtrations in Fig. 4. The sharp break between first and second stage pore blocking is readily observed. The break occurs after a consistent mass of solids has been deposited, suggesting that first and second stage blocking filtration are commonly encountered and that the change from one form to another is a property of the filter, but not of the operating conditions. For this filter and particle type, the threshold occurs when 0.0025 g of solids are deposited. During this time, the system permeability has decreased from an initial value of 2.0 × 10−5 s cm4 g−1 , corresponding to the pure water value, to 0.4 × 10−5 s cm4 g−1 . The originally presented theory [1] does not explain the occurrence of two pore blocking stages, it suggested that blocking should continue until the permeate flow decreases to a negligible amount. A possible explanation for the change in behaviour is that the mechanism has changed from a particle/membrane interaction to a particle/deposit interaction. The deposited particles are now behaving as a new membrane. Fig. 5 is a picture taken under a scanning electron microscope of the filter surface at the threshold point
Fig. 4. System permeability with mass of particles deposited for various concentrations at a transmembrane pressure of 3920 Pa.
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Fig. 5. Surface of membrane at the end of the first blocking filtration stage.
between the two pore blocking periods. A manual count of the particles and number of pores resulted in the ratio of three particles to one pore, corresponding to the point of change between the stages. Considering the two possible orientations of the membrane filter, with the wider or narrower pore openings to the flow, provides the results illustrated in Fig. 6. For the narrower pore side opening facing the feed, the data are successfully represented by Eq. (3): V∗ =
1 Ln(1 + βt ∗ ) β
where β has the value of 3. However, for the reverse orientation this value is 1.1. Hence, the area ratio of the region of influence within the suspension compared to the pore area is 3 and 1.1 depending upon the orientation of the membrane filter, i.e. the pore size open to the flow. Examination of Fig. 1 shows that the morphology of the membrane appears to be significantly different so this may also have an important
impact on the area of influence of a pore. Only a restricted range of experiments could be plotted this way because, at the higher feed concentrations, second stage blocking and cake filtration rapidly became established. The orientation of the membrane had no effect on the value of β for the second stage of blocking and β was found to have a value of 1.1 for both orientations. This result is consistent with the belief that the filtration is now controlled by the interaction between the suspended particles and the a membrane formed by deposited particles. The second pore blocking stage of filtration is more obvious at the higher concentrations and pressure, or as reported earlier, when the mass of deposit on the surface is bigger than 0.0025 g. Again, this stage is better described by the blocking model rather than cake filtration. However, for comparison purposes, Fig. 7 provides the experimental data for second stage pore blocking for the same experiments reported in Fig. 6, together with the first stage model relations extrapolated into the second stage region. It can be
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Fig. 6. Dimensionless permeate volume with time for various concentrations at transmembrane pressure of 3290 Pa and two different orientations over limited filtration time (open symbols: reverse membrane orientation; closed symbols: normal membrane orientation).
Fig. 7. Dimensionless permeate volume with time for various concentrations at transmembrane pressure of 3290 Pa and two different orientations over the full filtration time (open symbols: reverse membrane orientation; closed symbols: normal membrane orientation).
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clearly seen that the first pore blocking stage model does not adequately represent the data during the second stage. Hence, in order to apply Eq. (1), the value for the ‘initial flux rate’ has to be reduced for the second pore blocking stage. It is possible to predict the required value for ‘initial flux rate’ for the second stage knowing the true membrane resistance (hence, real initial flux rate at time zero), together with a knowledge of the mass of particles that must be deposited before the second stage starts. Hence, the ‘initial flux rate’ corresponding to the start of the second stage can be calculated, as it is the same as the flux rate at the end of the first stage of pore blocking when the specific mass of deposited latex reached 2×10−3 kg m−3 . Thus, this is an independently verifiable value and the complete filtration model still only requires two empirically determined values for β, one for each stage of blocking. Fig. 8 illustrates the variation of initial flux rate at the start of the first and second blocking stages of filtration, at one of the tested challenge concentrations over a range of filtration pressures. The transition between second stage blocking and cake filtration is evident for the filtration at 0.01% by mass and transmembrane pressure of 1568 Pa in Fig. 9.
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The transition from first to second stage blocking occurred at a very low time (i.e. 0.0025 g of solids were deposited within 20 s). Transition into cake filtration occurs after about 400 s and the gradient of the linear fit to the experimental data from this time onwards is 0.5 on the log plot. This is consistent with cake filtration as the predominant filtration mechanism after 400 s. A scanning electron microscope picture of the membrane surface, at this threshold time, is shown in Fig. 10 and a filter cake is apparent. The mass of particles deposited at this time was 0.006 g, the total filtering area was 12.6 cm2 hence, the number of layers of particles deposited at the start of the cake filtration period was approximately 12, using an estimated cake porosity of approximately 30%. In Fig. 11, all the data with appreciable second stage pore blocking and cake filtration stages are plotted, for a given concentration. It is apparent that the pore blocking data does reduce to a single curve represented by ln(1 + 1.1t ∗ ) and that this relation no longer holds when cake filtration starts, for t∗ greater than 4. Hence, it appears that the start of the cake filtration period is also a unique function of the mass of particles deposited, or number of layers of particles formed on the filter.
Fig. 8. Initial filtration fluxes for both first and second blocking filtration stages at a suspension concentration of 0.01% by mass.
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Fig. 9. Permeate volume with time for filtration at 1568 Pa and a suspension concentration of 0.01% by mass.
Fig. 10. Image of cake at point of transition between blocking and cake filtration.
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Fig. 11. Dimensionless permeate volume with time for various pressures at a concentration of 0.01% by mass and two different orientations.
4. Conclusions Three separate periods of filtration were identified during the microfiltration of near monosized latex particles on track-etched filters. The first two stages involved a pore blocking (sieving) mechanism and the final stage is one that can be described as cake filtration. A sieving model for microfiltration, requiring a single experimentally determined parameter for each stage of pore blocking, was used to accurately describe the pore blocking filtration stages. In the model, the initial permeate flux is also required, but this can be obtained by independent means. For the first pore blocking stage, this flux is the same as the clean water permeation flux. For the second pore blocking stage, the new effective “initial permeate flux” was obtained from the calculated flux at the end of the first stage. This is independently predictable, given a knowledge of β because the volume–time graph during the first stage is predictable and the end of the first stage occurred when the number of particles deposited per pore is also equal to the value of β. The term β has physical meaning, it is the area ratio between the region of influence inside the suspension and the pore opening area. It should, therefore, be equal to or greater than unity.
The track-etched filters tested were significantly asymmetric and the pore blocking behaviour significantly differed depending on the orientation of the membrane. The value of β was 3 when filtering in the conventional direction, but using the alternative orientation (larger diameter pores facing the feed suspension), the β ratio reduced to 1.1. However, for the second stage of pore blocking β had a value of 1.1 for either filter orientation which suggests that the blocking mechanism was no longer dependant on the filter properties, but on the thin layer of deposited particles. The transition from pore blocking filtration into cake filtration also occurred consistently when 12 layers of particles were deposited on the filters. This is observed for all the filtrations, regardless of feed starting concentrations, operating pressures and flux rates.
Acknowledgements The authors wish to acknowledge the provision of a research grant from The Engineering and Physical Research Council, UK to support this work, reference GR/N05697. The authors also wish to thank
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Mr. Frank Page for taking the scanning electron microscope pictures. References [1] A. Flippov, V.M. Starov, D.R. Lloyd, S. Chakravarti, S. Glaser, Sieve mechanism of microfiltration, J. Membr. Sci. 89 (1994) 199–213. [2] J. Hermia, Constant pressure blocking filtration laws— application to power law non-Newtonian flows, Trans. Inst. Chem. Eng. 60 (1982) 183–187. [3] C.-C. Ho, A.L. Zydney, A combined pore blockage and cake filtration model for protein fouling during microfiltration, J. Colloid Interface Sci. 232 (2000) 389–399. [4] C.-C. Ho, A.L. Zydney, Effect of membrane morphology on the initial rate of protein fouling during microfiltration, J. Membr. Sci. 155 (1999) 261–275.
[5] M. Hlavacek, F. Bouchet, Constant flowrate blocking laws and an example of their application to dead-end microfiltration of protein solutions, J. Membr. Sci. 82 (1993) 285–295. [6] E.M. Tracey, R.H. Davis, Protein fouling of track-etched polycarbonate microfiltration membranes, J. Colloid Interface Sci. 167 (1994) 104–106. [7] C. Guell, R.H. Davis, Membrane fouling during microfiltration of protein mixtures, J. Membr. Sci. 82 (1996) 269– 284. [8] T.C. Arnot, R.W. Field, A.B. Koltuniewicz, Cross-flow and dead-end microfiltration of oily-water emulsions. Part II. Mechanisms and modelling of flux decline, J. Membr. Sci. 169 (2000) 1–15. [9] J. Granger, J. Dodds, D. Leclerc, Filtration of low concentrations of latex particles on membrane filters, Filtration and Separation (January/February) (1985) 58–60. [10] J.W. Goodwin, J. Hearn, C.C. Ho, R. Ottewill, J. Colloid Polym. Sci. 252 (1974) 464–471.
Modelling of dead-end microfiltration with pore blocking and cake formation S. Kosvintsev, R.G. Holdich∗ , I.W. Cumming, V.M. Starov Department of Chemical Engineering, Loughborough University, Leicestershire, LE11 3TU, UK Received 16 November 2001; received in revised form 14 May 2002; accepted 15 May 2002
Abstract A series of dead-end filtration experiments are compared with a recently proposed pore blocking model that contains only one experimentally fitted parameter. This parameter has physical meaning and it can be verified by an independent check of the experimental data. The challenge suspension used was near monosized latex particles of ∼0.45 m filtered on a track-etched membrane with similar sized pores of ∼0.4 m. The filtered suspension concentration ranged from 0.00006 to 0.01% (w/w) and the transmembrane pressures varied from 1000 to 20,000 Pa. During the experiments three stages of microfiltration were observed. There was an initial stage that fitted a sieving (or pore blocking) model until the mass of latex deposited per unit membrane area (specific mass) reached 2 × 10−3 kg m−2 . The model required a single parameter that was found to fit all the data under different experimental operating conditions. The second stage of pore blocking could also be fitted using a second parameter and the predicted flux at the end of the first stage of pore blocking. When the deposited particles had reached a depth of approximately 12 particle layers, or specific mass of 4.8×10−3 kg m−2 , the flux then showed normal cake filtration behaviour. © 2002 Published by Elsevier Science B.V. Keywords: Sieve model; Resistance; Deposit; Prediction
1. Introduction Recent work [1] on the modelling of dead-end microfiltration employing a mechanism founded on treating membrane filtration as a type of sieving process has resulted in the following equation to describe the permeate volume (V) as a function of filtration time (t): 4S 1 πβnd¯ 2 dV V = ln 1 + t (1) 4S dt 0 π nd¯ 2 β
β is the ratio between the area of influence above a pore and the pore area itself. For a given filter, and suspension, several of the terms may be combined to provide a simplified equation: 1 dV V = ln 1 + γ nβ t (2) γ nβ dt 0 where γ is a single dimensionless constant for all values of suspension concentration and operating pressure. In physical terms, it is the area ratio of the pore to the filter area: π d¯ 2 4S
where S is the area of the filter, d the mean pore diameter, n the number of particles per unit volume and
γ =
∗ Corresponding author. E-mail address: [email protected] (R.G. Holdich).
Finally, the influence of different operating pressures and suspension concentrations can be removed from
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Eq. (2) by defining the following dimensionless variables: dV ∗ ∗ V = γ nV and t = γ n t dt 0 Hence, the filtration equation for the pore blocking mechanism is reduced to: 1 V ∗ = ln(1 + βt ∗ ) (3) β Eqs. (1) and (3) contrast with the conventional cake filtration description of membrane filtration, where the permeate volume would be expected to vary with the square root of filtration time, hence, the gradient on a log plot would be 0.5 during cake filtration conditions. According to Eq. (3), all operating data for microfilter pore blocking should reduce to a single plot of dimensionless volume and time, irrespective of suspension concentration and operating pressure. The latter term is an intrinsic part of the initial permeate flux rate. In the earlier model, there is only a single parameter that must be identified from experimental measurement, β, which should be a constant for a given membrane. Furthermore, the parameter has physical meaning, it is the ratio of the area of influence within the particle suspension per open area of the pore. Hence, values should be slightly greater than unity. The model was formulated for very low feed concentrations only and was experimentally tested on Texas tap water of indeterminate solids concentration. A sieving mechanism should be applicable to microfilters of regular pore shape, such as track-etched and other true surface filters. At the end of the ‘sieving’ (or pore blocking) period of filtration one would expect the conventional cake filtration mechanism to start. This period of filtration should be adequately described by the conventional equation based on Darcy’s law. Alternative approaches to a coupled sieving–cake filtration model have been based on the well-known filtration equations of Hermia [2]. A number of workers have published models based on the ‘standard law filtration’ and ‘blocking’ filtration analyses. For example, the microfiltration of proteins has been studied extensively [3–7], the filtration of oil emulsion has been modelled [8] as well as that of very dilute latex suspension [9]. These approaches have been adequate
for the prediction of the systems under investigation, but are limited in their scope for further elucidation of the mechanism of microfiltration and more general predictive modelling. The coupled sieving–cake filtration model should not be so limited as it is better able to predict the change from one mechanism to another.
2. Experimental Isopore track-etched membrane filters with a nominal pore size of 0.4 m and filtering diameter of 0.04 m, supplied by Millipore, were used. The surface of a typical Isopore filter is illustrated in Fig. 1(a) and the uniform pore geometry expected from a track-etched membrane filter can be clearly seen. However, there are some double and multiple pores visible. Generally, direct analysis from the image shows that the pore distribution on the membrane surface is: 79% single pores, 16% double pores and 3.5% triple, and more, pores present. Also included in Fig. 1 is a scanning electron microscope picture of the reverse side (not usually filtering side) of an Isopore filter. Comparison of Fig. 1(a) and (b) show that the filter is asymmetric, with pores 0.44 m ± 0.04 m in diameter on the filtering side and coarser ones on the reverse side. The difference in surface structure between the two sides is also evident in Fig. 1. According to Eq. (1), this should give rise to different filtration performance between the two different filter orientations. To investigate the model, a suspension of a nearly monosized polystyrene latex particles was used. The particles were formed by the emulsion polymerisation of styrene using a conventional preparation technique [10]. The mean particle diameter was measured as 0.46 m by a Malvern Mastersizer with 80% of the particles between 0.4 and 0.51 mm. Many different feed suspension concentrations were investigated, from 0.000063 to 0.01% by mass. The particles were first suspended in filtered water from a MilliQ purification device, to form two stock suspensions 3.5 and 0.01% by mass. A diagram of the test apparatus is shown in Fig. 2. The filtration cell was made from clear acrylic and consisted of two cylinders, with the membrane placed between them. The top and bottom of each cylinder had tube connections to reservoir and receiving vessels, respectively. The feed reservoir
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Fig. 1. (a) Filtering surface of Isopore track-etched membrane. (b) Reverse side of Isopore track-etched membrane.
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Fig. 2. Experimental apparatus.
could be raised, or lowered, as a means to control the pressure head effecting the filtration. For experiments at different transmembrane pressures, the difference in height between the feed and receiver free surfaces varied from 0.1 to 2 m. The permeate weight was measured at time intervals of between 1 and 5 s. Before each experiment, a preliminary run to determine the membrane permeability was performed by measuring the clean water flux at the same pressure drop to be used in the filtration. At the end of this preliminary experiment, some water was left in the rig to ensure that air did not enter the filtration circuit. The volume of water left to cover the membrane surface was 6 ml, when the latex suspension was added to this, the suspension concentration reduced by less than 0.5%. Then the vessel with the challenge suspension was connected to the filter cell and permeate mass was measured for between 2000 and 8000 s.
3. Results and discussion The primary aim of this work was to investigate the pore blocking model at different challenge concentrations to those reported in the original paper with the
aim of investigating the concentration dependency of the blocking mechanism. A concentration of 0.01% (w/w) represented the realistic maximum value for this study. Even with this apparently low feed concentration the blocking period was short and the cake filtration period soon established itself. The experiments showed that there are apparently three identifiable stages of microfiltration. The first stage corresponds to the blocking of the pores themselves. This stage is observed best at very small concentrations (lower then 0.001%) and relatively low pressures. Fig. 3(a) shows an example of a volume–time plot where the two pore blocking stages of filtration are identifiable. In the first blocking phase, the initial filtrate rate is correctly predicted by Eq. (1) using the clean water permeation test value for dV/dt at time zero, together with a value of 3 for β. It can be seen that the model fits the data well until about 800 s, when the transition to second stage blocking takes place. The two stages of pore blocking are shown perhaps more clearly in Fig. 3(b) where the data is plotted on a log–log plot. Eq. (2) can be represented by a power law fit when the values of the time term, in the logarithm expression, are small. All the experiments at low solids concentration showed
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Fig. 3. (a) Cumulative permeate volume with time for filtration at feed concentration 0.000063% by mass and transmembrane pressure of 3020 Pa. (b) The same data from Fig. 3(a) plotted on a log scale.
the same behaviour and the transition only depended on the permeate volume passed through membrane or, more exactly, on the quantity of particles deposited and blocking the membrane pores. In the second
blocking stage, the value of (dV/dt|0 ) needs to be changed to 0.25 cm3 s−1 , instead of 0.86 cm3 s−1 for water flux, whilst the value of β was found to be lower at 1.1.
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It is possible to define an overall system permeability based on Darcy’s law: µ dV 1 − P = L k dt A
(4)
where P is the pressure drop, L the porous media depth, µ the liquid dynamic viscosity, k the actual hydraulic permeability and A is the filter area. The system permeability (k ) is: k =
kA µL
hence, Darcy’s law becomes − P =
1 dV k dt
(5)
During the blocking stages, any variation in porous media depth (L) is negligible. However, this will not be the case during the cake filtration period. So, during the blocking period, reduction in system permeability must be due to the progressive plugging of the membrane, until the cake filtration period starts. The overall system permeability reduces during both stages of pore blocking. However, the change in
system permeability is greatest during the first blocking stage, this is illustrated for several filtrations in Fig. 4. The sharp break between first and second stage pore blocking is readily observed. The break occurs after a consistent mass of solids has been deposited, suggesting that first and second stage blocking filtration are commonly encountered and that the change from one form to another is a property of the filter, but not of the operating conditions. For this filter and particle type, the threshold occurs when 0.0025 g of solids are deposited. During this time, the system permeability has decreased from an initial value of 2.0 × 10−5 s cm4 g−1 , corresponding to the pure water value, to 0.4 × 10−5 s cm4 g−1 . The originally presented theory [1] does not explain the occurrence of two pore blocking stages, it suggested that blocking should continue until the permeate flow decreases to a negligible amount. A possible explanation for the change in behaviour is that the mechanism has changed from a particle/membrane interaction to a particle/deposit interaction. The deposited particles are now behaving as a new membrane. Fig. 5 is a picture taken under a scanning electron microscope of the filter surface at the threshold point
Fig. 4. System permeability with mass of particles deposited for various concentrations at a transmembrane pressure of 3920 Pa.
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Fig. 5. Surface of membrane at the end of the first blocking filtration stage.
between the two pore blocking periods. A manual count of the particles and number of pores resulted in the ratio of three particles to one pore, corresponding to the point of change between the stages. Considering the two possible orientations of the membrane filter, with the wider or narrower pore openings to the flow, provides the results illustrated in Fig. 6. For the narrower pore side opening facing the feed, the data are successfully represented by Eq. (3): V∗ =
1 Ln(1 + βt ∗ ) β
where β has the value of 3. However, for the reverse orientation this value is 1.1. Hence, the area ratio of the region of influence within the suspension compared to the pore area is 3 and 1.1 depending upon the orientation of the membrane filter, i.e. the pore size open to the flow. Examination of Fig. 1 shows that the morphology of the membrane appears to be significantly different so this may also have an important
impact on the area of influence of a pore. Only a restricted range of experiments could be plotted this way because, at the higher feed concentrations, second stage blocking and cake filtration rapidly became established. The orientation of the membrane had no effect on the value of β for the second stage of blocking and β was found to have a value of 1.1 for both orientations. This result is consistent with the belief that the filtration is now controlled by the interaction between the suspended particles and the a membrane formed by deposited particles. The second pore blocking stage of filtration is more obvious at the higher concentrations and pressure, or as reported earlier, when the mass of deposit on the surface is bigger than 0.0025 g. Again, this stage is better described by the blocking model rather than cake filtration. However, for comparison purposes, Fig. 7 provides the experimental data for second stage pore blocking for the same experiments reported in Fig. 6, together with the first stage model relations extrapolated into the second stage region. It can be
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Fig. 6. Dimensionless permeate volume with time for various concentrations at transmembrane pressure of 3290 Pa and two different orientations over limited filtration time (open symbols: reverse membrane orientation; closed symbols: normal membrane orientation).
Fig. 7. Dimensionless permeate volume with time for various concentrations at transmembrane pressure of 3290 Pa and two different orientations over the full filtration time (open symbols: reverse membrane orientation; closed symbols: normal membrane orientation).
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clearly seen that the first pore blocking stage model does not adequately represent the data during the second stage. Hence, in order to apply Eq. (1), the value for the ‘initial flux rate’ has to be reduced for the second pore blocking stage. It is possible to predict the required value for ‘initial flux rate’ for the second stage knowing the true membrane resistance (hence, real initial flux rate at time zero), together with a knowledge of the mass of particles that must be deposited before the second stage starts. Hence, the ‘initial flux rate’ corresponding to the start of the second stage can be calculated, as it is the same as the flux rate at the end of the first stage of pore blocking when the specific mass of deposited latex reached 2×10−3 kg m−3 . Thus, this is an independently verifiable value and the complete filtration model still only requires two empirically determined values for β, one for each stage of blocking. Fig. 8 illustrates the variation of initial flux rate at the start of the first and second blocking stages of filtration, at one of the tested challenge concentrations over a range of filtration pressures. The transition between second stage blocking and cake filtration is evident for the filtration at 0.01% by mass and transmembrane pressure of 1568 Pa in Fig. 9.
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The transition from first to second stage blocking occurred at a very low time (i.e. 0.0025 g of solids were deposited within 20 s). Transition into cake filtration occurs after about 400 s and the gradient of the linear fit to the experimental data from this time onwards is 0.5 on the log plot. This is consistent with cake filtration as the predominant filtration mechanism after 400 s. A scanning electron microscope picture of the membrane surface, at this threshold time, is shown in Fig. 10 and a filter cake is apparent. The mass of particles deposited at this time was 0.006 g, the total filtering area was 12.6 cm2 hence, the number of layers of particles deposited at the start of the cake filtration period was approximately 12, using an estimated cake porosity of approximately 30%. In Fig. 11, all the data with appreciable second stage pore blocking and cake filtration stages are plotted, for a given concentration. It is apparent that the pore blocking data does reduce to a single curve represented by ln(1 + 1.1t ∗ ) and that this relation no longer holds when cake filtration starts, for t∗ greater than 4. Hence, it appears that the start of the cake filtration period is also a unique function of the mass of particles deposited, or number of layers of particles formed on the filter.
Fig. 8. Initial filtration fluxes for both first and second blocking filtration stages at a suspension concentration of 0.01% by mass.
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Fig. 9. Permeate volume with time for filtration at 1568 Pa and a suspension concentration of 0.01% by mass.
Fig. 10. Image of cake at point of transition between blocking and cake filtration.
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Fig. 11. Dimensionless permeate volume with time for various pressures at a concentration of 0.01% by mass and two different orientations.
4. Conclusions Three separate periods of filtration were identified during the microfiltration of near monosized latex particles on track-etched filters. The first two stages involved a pore blocking (sieving) mechanism and the final stage is one that can be described as cake filtration. A sieving model for microfiltration, requiring a single experimentally determined parameter for each stage of pore blocking, was used to accurately describe the pore blocking filtration stages. In the model, the initial permeate flux is also required, but this can be obtained by independent means. For the first pore blocking stage, this flux is the same as the clean water permeation flux. For the second pore blocking stage, the new effective “initial permeate flux” was obtained from the calculated flux at the end of the first stage. This is independently predictable, given a knowledge of β because the volume–time graph during the first stage is predictable and the end of the first stage occurred when the number of particles deposited per pore is also equal to the value of β. The term β has physical meaning, it is the area ratio between the region of influence inside the suspension and the pore opening area. It should, therefore, be equal to or greater than unity.
The track-etched filters tested were significantly asymmetric and the pore blocking behaviour significantly differed depending on the orientation of the membrane. The value of β was 3 when filtering in the conventional direction, but using the alternative orientation (larger diameter pores facing the feed suspension), the β ratio reduced to 1.1. However, for the second stage of pore blocking β had a value of 1.1 for either filter orientation which suggests that the blocking mechanism was no longer dependant on the filter properties, but on the thin layer of deposited particles. The transition from pore blocking filtration into cake filtration also occurred consistently when 12 layers of particles were deposited on the filters. This is observed for all the filtrations, regardless of feed starting concentrations, operating pressures and flux rates.
Acknowledgements The authors wish to acknowledge the provision of a research grant from The Engineering and Physical Research Council, UK to support this work, reference GR/N05697. The authors also wish to thank
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Mr. Frank Page for taking the scanning electron microscope pictures. References [1] A. Flippov, V.M. Starov, D.R. Lloyd, S. Chakravarti, S. Glaser, Sieve mechanism of microfiltration, J. Membr. Sci. 89 (1994) 199–213. [2] J. Hermia, Constant pressure blocking filtration laws— application to power law non-Newtonian flows, Trans. Inst. Chem. Eng. 60 (1982) 183–187. [3] C.-C. Ho, A.L. Zydney, A combined pore blockage and cake filtration model for protein fouling during microfiltration, J. Colloid Interface Sci. 232 (2000) 389–399. [4] C.-C. Ho, A.L. Zydney, Effect of membrane morphology on the initial rate of protein fouling during microfiltration, J. Membr. Sci. 155 (1999) 261–275.
[5] M. Hlavacek, F. Bouchet, Constant flowrate blocking laws and an example of their application to dead-end microfiltration of protein solutions, J. Membr. Sci. 82 (1993) 285–295. [6] E.M. Tracey, R.H. Davis, Protein fouling of track-etched polycarbonate microfiltration membranes, J. Colloid Interface Sci. 167 (1994) 104–106. [7] C. Guell, R.H. Davis, Membrane fouling during microfiltration of protein mixtures, J. Membr. Sci. 82 (1996) 269– 284. [8] T.C. Arnot, R.W. Field, A.B. Koltuniewicz, Cross-flow and dead-end microfiltration of oily-water emulsions. Part II. Mechanisms and modelling of flux decline, J. Membr. Sci. 169 (2000) 1–15. [9] J. Granger, J. Dodds, D. Leclerc, Filtration of low concentrations of latex particles on membrane filters, Filtration and Separation (January/February) (1985) 58–60. [10] J.W. Goodwin, J. Hearn, C.C. Ho, R. Ottewill, J. Colloid Polym. Sci. 252 (1974) 464–471.