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dextran binary suspension
Journal of Membrane Science 347 (2010) 75–82
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Filtration characteristics and membrane fouling in cross-flow microfiltration of BSA/dextran binary suspension Kuo-Jen Hwang ∗ , Pan-Yu Sz Department of Chemical and Materials Engineering, Tamkang University, Tamsui, Taipei Hsien 25137, Taiwan
a r t i c l e
i n f o
Article history: Received 22 August 2009 Received in revised form 4 October 2009 Accepted 6 October 2009 Available online 13 October 2009 Keywords: Cross-flow microfiltration Rejection coefficient Membrane fouling Membrane filtration Bio-separation
a b s t r a c t Filtration characteristics and membrane fouling in BSA/dextran binary suspension cross-flow microfiltration is studied. An increase in cross-flow velocity or transmembrane pressure leads to higher pseudo-steady filtration flux due to less membrane fouling or higher driving force. The fouled membrane pore size and fouled layer thickness under various conditions are estimated using a theoretical model based on the Hagen–Poiseuille law. The fouled membrane pore size decreases with increasing transmembrane pressure due to ever increasing fouling. The fouled layer thickness becomes thicker and invariant with operating conditions under a lower pressure drop through the fouled membrane. Molecular adsorption occurs on the pore walls until a specific wall shear stress is reached in the membrane pores. However, the fouled layer becomes thinner when the pressure drop exceeds a critical value. An increase in cross-flow velocity results in a larger fouled membrane pore size and a thicker fouled layer in such condition. The dextran molecular deformation under higher transmembrane pressure causes a thinner fouled layer and an ultimate equilibrium adsorption in the membrane pores. Furthermore, an increase in cross-flow velocity leads to higher BSA and dextran rejection due to the sweeping effect on the membrane surface. The BSA rejection increases with transmembrane pressure due to the reduction in membrane pore size, while the decrease in dextran rejection under higher transmembrane pressure is attributed to the molecular deformation. The “coil-stretched” deformation of dextran molecules can be indicated using the Deborah number. The fouled membrane pore size and dextran rejection decrease with increasing Deborah number and remain constant as the Deborah number exceeds a critical value. Taking the filtration flux and solute rejection into consideration, operating a cross-flow microfiltration system under lower cross-flow velocity and higher transmembrane pressure is more efficient from the selectivity and mean dextran mass flux view points. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Membrane filtration has been used increasingly in the separation or purification of bio-products in the biochemical and pharmaceutical industries in recent years. This is because of its economical, efficient and energy-saving advantages. However, unexpected membrane fouling is an obstacle to the continued development of this kind of separation technology. The components in a bio-process are varying and complex. Many components, such as polysaccharides, proteins, humic acid and microbial cells coexist in a general product stream. This causes membrane fouling to be rather complicated and difficult to manage. Therefore, realizing membrane fouling characteristics for specific bio-mixtures becomes an essential step in improving the separation efficiency.
∗ Corresponding author. Fax: +886 2 26209887. E-mail address: [email protected] (K.-J. Hwang). 0376-7388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2009.10.008
In most membrane filtration processes, membrane fouling occurs due to solute adsorption, particle interception or membrane blocking. The most important factors affecting membrane fouling are the membrane characteristics, particle or solute properties and operating conditions. In previous studies on single-component membrane filtration, Huisman et al. [1] carried out BSA crossflow ultrafiltration using polysulfone membranes with different pore sizes. They claimed that membrane fouling in the early filtration period was determined by the interaction between the protein and membrane, while the filtration performance in the later periods depended on the interaction among the proteins. These statements were similar to those in the study by Güell and Davis on the ultrafiltration of protein mixtures [2]. However, Ouammou et al. [3] concluded that the protein zeta potential was the most important parameter in membrane fouling. In those studies using a different approach, the modified gel-polarization model was proposed involving a gel layer formation on the membrane surface [4]. Cheng et al. [5] claimed that the filtration resistance in dextran ultrafiltration could be accurately predicted using this
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model. The concentration polarization or gel layer resistance was markedly reduced by increasing the cross-flow velocity. GarciaMolina et al. [6] indicated that a fouling layer was formed in dextran ultrafiltration, which was independent of the used membranes. Their experimental data showed that an increase in transmembrane pressure resulted in higher filtration flux and higher dextran rejection. These trends were the same as those in most previous researches [4]. Blatt et al. [7] concluded that the concentration polarization in protein ultrafiltration could be divided into two pressure-dependent regimes. The protein rejection decreased with increasing pressure in the low pressure region. This was attributed to the increase in polarization concentration. Conversely, gel layer formation or a reduction in membrane pore size under higher pressures increased the protein rejection. However, the protein rejection may be observed to decrease monotonously with increasing transmembrane pressure. This was attributed to the deformation of macromolecules with long and flexible chains [8]. Recently, Hwang and Huang [9] carried out the cross-flow microfiltration of blue dextran with a molecular weight of 2000 kDa. The membrane pore size was reduced by dextran adsorption during filtration. The dextran rejection increased with increasing crossflow velocity or decreasing transmembrane pressure under lower cross-flow velocity. They claimed that the contrary trend obtained under higher filtration flux was attributed to dextran molecular deformation. Several researchers have paid attention to the membrane filtration of bio-mixtures. Iritani et al. [10] performed the ultrafiltration of protein mixtures including BSA and egg white lysozyme. They concluded that the protein electrostatic interactions played major roles in determining the filtration flux and protein rejection. Hwang and co-workers [11,12] studied the cross-flow microfiltration of fine particle/dextran binary suspensions. The secondary membrane formed by the fine particles reduced the membrane fouling causing by dextran. The filtration flux and dextran rejection could be theoretically predicted using their derived models. The dextran rejection was significantly dependent on the tangential sweeping effect on the membrane surface and the capturing effect of the formed cake [12]. Vernhet and Moutounet [13] studied membrane fouling in the cross-flow microfiltration of red wine. They indicated that membrane fouling frequently occurred at the membrane pore entrances or on the membrane surface. The polysaccharides in red wind were the major foulants. Ye et al. [14,15] used a sodium alginate and BSA mixture to model the extracellular polymeric sub-
stances existing in a bioreactor. They found that the existence of BSA resulted in a more compact filter cake and reduced the sodium alginate transmission. Susanto et al. [16] studied the membrane fouling caused by protein/polysaccharide mixtures which were the major products in a fermentation tank. The fouled layer morphology was markedly dependent on the polysaccharide characteristics. Similar to the results of Ye et al. [14], they found that the fouled layer was more rigid and the flux was lower, relative to the filtration performance of a single component. These phenomena were attributed to the synergistic effects between protein and polysaccharide. In this study, BSA and dextran are used as the typical protein and polysaccharide samples, respectively, in bio-products. Cross-flow microfiltration was carried out to separate the binary suspension. The operating condition effects, e.g., the cross-flow velocity and transmembrane pressure, on the filtration flux and solute rejections at pseudo-steady state are discussed. The fouled membrane pore size and fouled layer thickness are theoretically estimated using a derived membrane fouling model. The Deborah number is introduced to indicate molecular deformation, and the operating condition effects on the dextran selectivity and mean dextran mass flux are also discussed. 2. Materials and experiments Bovine serum albumin (BSA) manufactured by United State Biochemical Co. and dextran (T2000) purchased from Sigma Chemical Co. were used as the protein and polysaccharide samples in this study. BSA and dextran, with molecular weights of 67 and 2000 kDa, respectively, were dissolved in a phosphate buffer solution to prepare the suspensions used in experiments. The BSA and dextran concentrations were set as 1.0 and 0.5 kg/m3 , respectively, to simulate the condition in fermentation products. The suspension pH and temperature were kept at 7.0 and 20 ◦ C during filtration. The BSA and dextran molecular sizes in the suspension were measured using Malvern MRK528-01 Zetasizer Nano System. The BSA molecules had a mean size of 8 nm. However, BSA coagulations as large as 300 nm were frequently found in the suspension. The dextran size distribution ranged from 21 to 300 nm with a mean value of 90 nm. A hydrophilic flat-sheet membrane made of mixed cellulose acetate was used in these experiments as the filter medium. A fresh membrane was used only for each experiment. The membrane was manufactured by Millipore Co. in USA and possessed a better BSA rejection property. Its porosity and thickness were 0.75 and 105 m, respectively. The mean nominal pore diameter of the
Fig. 1. A schematic diagram of the cross-flow microfiltration system.
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Fig. 2. Time courses of filtration flux during cross-flow microfiltration under various transmembrane pressures.
fresh membrane was measured using a Power Image Analysis System as 0.13 m. Experiments were carried out using a two-parallel-plate crossflow microfilter. The clearance, width and length of the filter channel were 1.0 × 10−3 , 2.0 × 10−2 and 5.5 × 10−2 m, respectively. The filter membrane was laid on the permeable bottom plate which had an effective filtration area of 1.1 × 10−3 m2 . Fig. 1 shows a schematic diagram of the microfiltration system. The suspension was well mixed using a magnetic mixer and kept isothermal using a thermostat during filtration. The cross-flow velocity and transmembrane pressure were adjusted using a rotameter and a needle valve, respectively. The filtrate was collected into a filtrate receiver that was placed on a load cell. Therefore, the filtrate weight was detected and recorded on a personal computer at each time increment. The solute concentrations were measured using a HPLC (Thermal Co., Spectra series P-100) installed a chromatographic column (Waters Co., BioSuite 450, 8 m HR SEC). The BSA and dextran concentrations were therefore analyzed separately due to their different flow rates through the column. When an experiment was terminated, the fouled membrane was measured its filtration resistance using clean water permeation or sent out to have its morphology analyzed by a Leo-1530 SEM.
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Fig. 3. Effects of transmembrane pressure and cross-flow velocity on the pseudosteady filtration flux.
from 0.1 to 0.5 m/s, the flux increases 50% under lower transmembrane pressure and increases 30% under higher transmembrane pressure. Although more serious membrane fouling occurs under higher transmembrane pressure, a higher flux is obtained due to the higher resulting filtration driving force. The filtration flux increases ca 50% when the transmembrane pressure increases from 20 to 100 kPa for the bio-mixture used in this study. The flux attenuation during a cross-flow microfiltration is mainly due to the membrane fouling. The macromolecules in the suspension may adsorb onto the membrane surface or in the membrane pores to form a fouled layer. According to the basic filtration equation, the total filtration resistance can be calculated using Rt =
P q
(1)
where P is the transmembrane pressure, q is the filtration flux, and is the fluid viscosity. The fouled layer resistance is much higher than the resistance caused by the concentration polarization layer and fresh membrane in most microfiltration. The Rt values at the pseudo-steady state under various conditions are calculated using Eq. (1) and shown in Fig. 4. The Rt value linearly increases with increasing transmembrane pressure. When transmembrane pressure increases from 20 to 100 kPa, a 4-fold increase in Rt value is
3. Results and discussion Fig. 2 shows the time courses of filtration flux during crossflow microfiltration of BSA–dextran binary suspension under three different transmembrane pressures. The BSA and dextran concentrations in the suspension were kept at 1.0 and 0.5 kg/m3 , respectively. The cross-flow velocity was fixed at 0.5 m/s in these experiments. The filtration fluxes attenuated very quickly at the beginning of filtration and gradually approached pseudo-steady values after 300 s. This implies that most membrane fouling occurred in the early filtration period. Comparing the data shown in Fig. 2, the filtration flux increases with increasing transmembrane pressure. This result can be expected because a higher filtration driving force is caused by increasing transmembrane pressure. The cross-flow velocity and transmembrane pressure effects on the pseudo-steady filtration flux are shown in Fig. 3. The filtration flux increases with increasing cross-flow velocity and transmembrane pressure. An increase in cross-flow velocity leads to higher shear stress acting on the membrane surface, as a result, less membrane fouling. However, this impact becomes less significant under higher cross-flow velocity. When the cross-flow velocity increases
Fig. 4. Effects of transmembrane pressure and cross-flow velocity on the filtration resistance.
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scopic analysis indicates that the filtration resistance is mainly due to the membrane pore size reduction near the pore entrances. This result is far different from that in the microfiltration of fine particles, in which a filter cake is formed caused by particle bridging and accumulation. The flow of fluids through a porous media was simplified for analysis since a half century ago. A common model was used by considering the actual flow system as parallel capillary tubes. Because the solute adsorbed layer reduces the membrane pore size and results in major filtration resistance, as shown in Fig. 5, the relationship between the fluid flow rate and pressure drop through a fouled membrane layer can be modeled using the Hagen–Poiseuille law and expressed as [17]: 2 dm,b Pm,b qs = · εm 32 Lm,b
(2)
where qs is the pseudo-steady filtration flux, εm is the membrane surface porosity, dm,b is the mean pore size of the fouled membrane. Because the true fluid velocity becomes higher in the membrane pores, the velocity gradient or the pore tortuosity occurring at the membrane surface may cause molecular adsorption on the membrane pore walls near the pore entrances and results in a fouled layer with a thickness (depth) of Lm,b . Therefore, the increase in filtration resistance during filtration is attributed to the reduction in membrane pore size or the increase in fouled layer thickness. The variables in Eq. (2) should be estimated prior to understanding the membrane fouling under various conditions. The fouled layer resistance, Rf , can be measured in experiments using clean water permeation through the fouled membrane [9,11,12]. The Pm,b value is then calculated using the fraction of fouled layer to the total filtration resistances, that is, Pm,b =
Rf Rt
· P
(3)
According to the analyses in previous studies [9,18], the fouled membrane resistance is assumed to be inversely proportional to the open pore surface cross-sectional area. Therefore, the dm,b value can be estimated using experimental resistance data and expressed as
dm,b =
Fig. 5. SEM photos for (a) fresh membrane, (b) top-view of the fouled membrane, and (c) side-view of the fouled membrane under us = 0.5 m/s and P = 100 kPa (×100 kX).
found. On the other hand, an increase in cross-flow velocity leads to a lower Rt value. However, this impact becomes insignificant as us > 0.3 m/s. This implies that the reduction in membrane fouling by increasing cross-flow velocity has an ultimate limit. The flux cannot be enhanced anymore by increasing cross-flow velocity when us exceeds the limiting value. This trend can also be seen in Fig. 3. Fig. 5(a) shows a SEM photo of the fresh membrane surface. Although the mixed cellulose acetate membrane is sponge-like and isotropic, it has a relatively flat surface with round pore entrances. Fig. 5(b) and (c) show the top and side-views, respectively, of the fouled membrane under us = 0.5 m/s and P = 100 kPa. Comparing Fig. 5(a) and (b), the membrane is fouled by solute adsorption onto the membrane surface and pore walls, leading to a reduction in the pore size. The mean membrane pore size becomes only 30–60% of the original value due to the fouling in the conditions of this study. A thin fouled layer is formed near the membrane pore entrances instead of complete pore blocking, as shown in Fig. 5(c). This micro-
2 dm,o
Rm · Rf
0.5
(4)
where dm,o and Rm are the mean pore size and resistance of the fresh membrane. Since the membrane surface porosity is considered to be proportional to the open pore surface cross-sectional area [9], the value of εm can be evaluated once the membrane pore size variation is known by Eq. (4). Fig. 6 shows a plot of qs /(εm ·dm,b 2 ) vs. Pm,b under various operating conditions. When Pm,b < Pm,b,c (a critical Pm,b ), all data can be regressed into a unique straight line in spite of transmembrane pressure and cross-flow velocity. This indicates that the fouled layer thickness is constant (=25.34 m from the regressed line slope) whatever the operating condition is. However, when Pm,b exceeds the critical value, the data for a fixed cross-flow velocity are located on the same straight line. This means the transmembrane pressure effect on the fouled layer thickness Lm,b is negligible small. The Lm,b value depends solely on cross-flow velocity and can be determined by the regressed line slope. In other words, when Pm,b exceeds the critical value, the fouled layer thickness becomes thinner than those under low pressure and increases with increasing cross-flow velocity. Since higher flux is obtained under higher cross-flow velocity, the fouling (molecular adsorption) may occur at a deeper location in the membrane pores as the flux increases. The fouled layer thickness is therefore thicker under higher cross-flow velocity. The Lm,b values under
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Fig. 6. A plot of qs /(εm ·dm,b 2 ) versus Pm,b under various operating conditions.
us = 0.1, 0.3 and 0.5 m/s are calculated as 9.38, 10.71 and 11.54 m, respectively. The fouled layer thickness is very thin, relative to the whole membrane. In comparison to the authors’ previous study on the cross-flow microfiltration of blue dextran [9], the existence of BSA causes the fouling layer to be thicker. The occurrence of the critical Pm,b is attributed to the variation of molecular adsorption mechanism. The mechanism depends significantly on the molecular morphology and will be discussed as follows. In order to understand the operating condition effects on the fouled membrane pore size, the dm,b values under various shear stresses on the pore walls, m,b , are plotted in Fig. 7. If the fouled membrane pore can be modeled as a circular tube, the m,b value can be estimated by making a momentum balance around the membrane pore, that is [17], m,b =
dm,b 4
Pm,b Lm,b
(5)
In low Pm,b region, dm,b value varies in the range from 6.65 × 10−8 to 1.05 × 10−7 m. An increase in Pm,b leads to a smaller dm,b but a constant Lm,b , as shown in Fig. 6. As a result, the m,b values are constant within the operating conditions. This is because the suspended molecules exhibit “round” or “coil” morphology under low
Fig. 7. A plot of dm,b versus w,b under various operating conditions.
Fig. 8. SEM photos for top-view of the fouled membrane (a) us = 0.1 m/s and P = 20 kPa, (b) us = 0.1 m/s and P = 100 kPa (×100 kX).
pressure (low flow rate). The molecules adsorb onto the membrane pore walls until the wall shear stress reaches a critical value. The molecules cannot stably “stick” onto the membrane pore wall under a shear stress higher than the critical value. This fact is similar to the selective deposition of fine particles in cross-flow filtration [11,12]. On the other hand, in the high Pm,b region, the m,b value increases with Pm,b because the fouled layer becomes thinner compared to that in the low Pm,b region. The deformation causes the molecules to more easily adsorb onto the membrane pore walls. The dm,b values are therefore smaller than those in low Pm,b region. It is inferred that the stretched molecular bonds cause the adsorption to approach the ultimate equilibrium value. This results in little differences among the dm,b values in the high Pm,b region. However, the higher pore shear stress under higher cross-flow velocity leads to a slightly larger dm,b value although the fouled layer is thicker (as shown in Fig. 6). The transmembrane pressure effect on membrane fouling is illustrated in Fig. 8. The transmembrane pressures were 20 and 100 kPa in Fig. 8(a) and (b), respectively, while the cross-flow velocity was fixed at 0.1 m/s. Comparing the SEM photos shown in Fig. 8(a) and (b), the pore sizes under higher pressure are smaller at a given cross-flow velocity. This reveals that more solute molecules adsorb onto the membrane pore walls in such condition. However, it can be found by comparing Figs. 5(b) and 8(b) that the mean pore sizes of the fouled membrane under a fixed transmembrane pressure increase slightly with cross-flow velocity. These trends in the SEM results agree with the calculated dm,b results using Eq. (4).
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Fig. 9. A plot of dm,b versus De under various operating conditions.
Because dextran molecules have long and flexible chains, their flow and adsorption behaviors are significantly affected by the molecular configuration. According to the dumbbell model for macromolecules [19], the Deborah number, De, is an important parameter for indicating molecular deformation and flow behaviors, which is defined as: De ≡ ˙
(6)
where and ˙ are the characteristic relaxation time and macromolecular elongation rate, respectively. A long-chain macromolecule may be in a “coil” configuration under a low Deborah number and stretches its chains as De increases. The elongation rate of macromolecules flowing through a fouled membrane can be evaluated using [20] qs (1 − εm ) ˙ = k1 dm,b
(7)
where k1 is a molecular characteristic constant. Substituting Eq. (7) into Eq. (6) yields De = k1
qs (1 − εm ) = k2 De dm,b
where Cb and Cp are the solute concentrations in the bulk suspension and in the filtrate, respectively. Thus, the rejection can be used to evaluate the solute fraction which is retained by the membrane. Fig. 10 depicts the cross-flow velocity and transmembrane pressure effects on the pseudo-steady solute rejection. Although the monomolecular size of BSA is only 8 nm, which is far smaller than the membrane pore size, the BSA rejection exceeds 0.6 in all operating conditions. This is due to the existence of BSA coagulations in the suspension. The BSA rejection increases with increasing transmembrane pressure and cross-flow velocity. This reveals that the BSA rejection becomes higher under more series membrane fouling. The BSA rejection increases 30% when transmembrane pressure increases from 20 to 100 kPa. However, an increase in transmembrane pressure leads to a lower dextran rejection. The rejection is contrarily lower for a membrane with smaller effective pore size. This is because the molecular deformation causes dextran to penetrate through the membrane pores more easily into the filtrate. Therefore, the data shown in Fig. 10 infers that the BSA rejection is determined directly by the membrane pore size, while the dextran rejection is significantly affected by the molecular deformation. A larger rejection difference between BSA and dextran can be seen under higher transmembrane pressure, although their values are close to each other under a pressure of 20 kPa. The thicker fouled layer and higher sweeping effect on the membrane surface under higher cross-flow velocity result in higher BSA and dextran rejections although the dm,b value is larger. However, the cross-flow velocity effect on BSA rejection is relatively small. A parameter, selectivity, can be used in place of the dextran fractional yield in the filtrate, which is defined as the ratio of the amount of dextran to the amount of BSA collected in filtrate. The selectivity values under various conditions are calculated using the data shown in Fig. 10 for comparison. The dextran selectivity is enhanced by increasing transmembrane pressure. For instance, under a given cross-flow velocity of 0.5 m/s, the dextran selectivity increases from 0.5 to 1.8 as the pressure increases from 20 to 100 kPa. The dextran selectivity becomes higher under lower cross-flow velocity. The highest selectivity is 2.5 under us = 0.1 m/s and P = 100 kPa. The rejection and selectivity data reveal that BSA and dextran are separated more efficiently under lower cross-flow velocity and higher transmembrane pressure.
(8)
where k2 is a coefficient combining two constants, k1 and . Therefore, the De value can be used for indicating the molecular deformation if the dumbbell model is valid. The dm,b values are plotted against De under various operating conditions in Fig. 9. The data reveals that dm,b can be expressed as a unique function of De , and a critical Deborah number, De c = 1.56 × 102 , exists. When De is smaller than the critical value, the dm,b value linearly decreases with De . In this region, the dm,b value decreases with the increase in filtration flux (by increasing cross-flow velocity or transmembrane pressure). The pseudo-steady pore size is therefore determined by the fixed pore wall shear stress, as shown in Fig. 7. However, the dm,b value remains constant when De exceeds the critical value. The dm,b value is invariant with De once the macromolecular chains are fully stretched. Therefore, the Deborah number and macromolecular deformation can be used to explain the membrane pore reduction in this study. Excepting the filtration flux, another important factor affecting separation efficiency is the solute rejection (or transmission). The observed rejection coefficient, Rrej , is defined as: Rrej ≡ 1 −
Cp Cb
(9)
Fig. 10. Effects of operating conditions on the BSA and dextran rejection.
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Fig. 11. Effect of Deborah number on the BSA and dextran rejection.
Fig. 11 shows the relationships between solute rejection and De under various conditions. The BSA rejections under various crossflow velocities and transmembrane pressures can be regressed to a unique empirical equation of De . The BSA rejection increases with increasing De value, but the impact becomes smaller under higher De . This is because more BSA coagulations are retained by the membrane with a smaller effective pore size. In contrast, the dextran rejection decreases with increasing De and remains constant when De exceeds the critical value, which is the same as that shown in Fig. 9. The decrease in dextran rejection is attributed to the molecular deformation. A stretched molecule more easily penetrates through the membrane pores. However, this effect becomes trivial when the molecular chains are fully stretched at the critical condition. A higher cross-flow velocity results in a higher dextran rejection because of the sweeping effect on the membrane surface [12]. The dextran molecules may be swept away from the mem-
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brane surface by the tangential suspension flow before they have an opportunity to touch the membrane surface. This effect is more significant under higher cross-flow velocity. Taking the filtration flux and solute rejection into consideration, the mean solute mass flux can be used to evaluate the recovery or production in a microfiltration system. Fig. 12 shows the mean mass fluxes of BSA and dextran under various operating conditions. Because both filtration flux and BSA rejection increase with increasing transmembrane pressure and cross-flow velocity, a lower mean BSA mass flux is obtained under a higher transmembrane pressure. However, the cross-flow velocity effect on the BSA mass flux is trivial due to less effect on BSA rejection. On the other hand, the mean dextran mass flux is significantly enhanced by increasing the transmembrane pressure because of the increase in filtration flux and the decrease in dextran rejection. The dextran mass flux increases more than three times when the transmembrane pressure increases from 20 to 100 kPa. However, the higher dextran rejection under higher cross-flow velocity leads to a lower mean dextran mass flux. This impact is more obvious under higher transmembrane pressure. Comparing the data shown in Fig. 12, the operating condition effects on the BSA mass flux are relatively small. Although the dextran concentration in the suspension is only a half that of BSA, the dextran mass flux is 2-fold higher than that for BSA flux under high transmembrane pressure. Therefore, operating a cross-flow microfiltration system under low cross-flow velocity and high transmembrane pressure is more efficient from the selectivity and mean mass flux viewpoint. 4. Conclusions The operating condition effects on the filtration flux, solute rejection and membrane fouling in BSA/dextran binary suspension cross-flow microfiltration were studied. The filtration flux was increased 30–50% by increasing the cross-flow velocity or transmembrane pressure. A membrane fouling model based on the Hagen–Poiseuille law was derived. The molecular adsorption onto the membrane pore walls reduced the pore size and resulted in a significant filtration resistance. The fouled membrane pore size decreased with increasing transmembrane pressure, but increased slightly with increasing cross-flow velocity. When the pressure drop through the fouled membrane was lower than a critical value, the fouled layer thickness becomes thicker and independent of the operating conditions. Molecular adsorption occurred until reaching a specific wall shear stress in the membrane pores. When the pressure drop exceeds the critical value, the fouled layer became thinner, relative to those under low pressure. An increase in crossflow velocity led to a slightly larger fouled membrane pore size and thicker fouled layer. The BSA rejection increased with increasing transmembrane pressure and cross-flow velocity. The dextran rejection significantly decreased with increasing transmembrane pressure or decreasing cross-flow velocity. This was attributed to the sweeping effect on the membrane surface and the molecular deformation. The fouled membrane pore size and dextran rejection decreased with increasing Deborah number and remained constant as the Deborah number exceeded a critical value. To operate a cross-flow microfiltration system under low cross-flow velocity and high transmembrane pressure would be more efficient from the selectivity and mean dextran mass flux viewpoint. The highest selectivity was as high as 2.5 under such condition. Acknowledgement
Fig. 12. Effect of operating conditions on the mean mass fluxes of BSA and dextran.
The authors wish to express their sincere gratitude to the National Science Council of the Republic of China for its financial support.
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Nomenclature Cb Cp De De dm,o dm,b k1 k2 Lm,b m q qs Rf Rm Rrej Rt t us
solute concentration in the bulk suspension [kg/m3 ] solute concentration in the filtrate [kg/m3 ] Deborah number defined in Eq. (6) modified Deborah number defined in Eq. (8) [s−1 ] clean membrane pore diameter [m] fouled membrane pore diameter [m] a coefficient defined in Eq. (7) a coefficient defined in Eq. (8) fouled layer thickness [m] mean solute mass flux [kg/m2 s] filtration flux [m3 /m2 s] pseudo-steady filtration flux [m3 /m2 s] filtration resistance due to membrane fouling [m−1 ] filtration resistance of clean membrane [m−1 ] observed solute rejection coefficient at pseudosteady state total filtration resistance [m−1 ] filtration time [s] cross-flow velocity [m/s]
Greek letters P transmembrane pressure [Pa] Pm,b pressure drop through the fouled membrane [Pa] εm membrane surface porosity relaxation time of macromolecules [s] ˙ elongation rate of macromolecules [s−1 ] fluid viscosity [kg/s m] w,b shear stress on the membrane pore wall [N/m2 ] Subscript c the critical value
References [1] I.H. Huisman, P. Prádanos, A. Hernández, The effect of protein–protein and protein–membrane interactions on membrane fouling in ultrafiltration, J. Membr. Sci. 179 (1–2) (2000) 79–90.
[2] C. Güell, R.H. Davis, Membrane fouling during microfiltration of protein mixtures, J. Membr. Sci. 119 (2) (1996) 269–284. [3] M. Ouammou, N. Tijani, J.I. Calvo, C. Velasco, A. Martín, F. Martínez, F. Tejerina, A. Hernández, Flux decay in protein microfiltration through charged membranes as a function of pH, Colloids Surf. A 298 (3) (2007) 267–273. [4] M. Cheryan, Ultrafiltration and Microfiltration Handbook, Technomic Publishing Co., Pennsylvania, USA, 1998, pp.113–130. [5] T.W. Cheng, H.M. Yeh, C.T. Gau, Resistance analyses for ultrafiltration in tubular membrane module, Sep. Sci. Technol. 32 (1997) 2623–2640. [6] V. Garcia-Molina, S. Esplugas, Th. Wintgens, Th. Melin, Ultrafiltration of aqueous solutions containing dextran, Desalination 188 (2006) 217–227. [7] W.F. Blatt, A. Dravid, A.S. Michaels, L.M. Nelsen, Solute polarization and cake formation in membrane ultrafiltration, causes, consequences, and control techniques, in: J.E. Flinn (Ed.), Membrane Science and Technology, Plenum Press, New York, USA, 1970, pp. 47–97. [8] A.E. Polotsky, A.N. Cherkasov, On the mechanism of flexible chain polymer ultrafiltration, Sep. Sci. Technol. 41 (2006) 1773–1787. [9] K.J. Hwang, P.S. Huang, Cross-flow microfiltration of dilute macromolecular suspension, Sep. Purif. Technol. 68 (2009) 328–334. [10] E. Iritani, Y. Mukai, T. Murase, Upward dead-end ultrafiltration of binary protein mixtures, Sep. Sci. Technol. 30 (3) (1995) 369–382. [11] K.J. Hwang, Y.H. Cheng, The role of dynamic membrane in cross-flow microfiltration of macromolecules, Sep. Sci. Technol. 38 (2003) 779–795. [12] K.J. Hwang, Y.H. Cheng, K.L. Tung, Modeling of cross-flow microfiltration of fine particle/macromolecule binary suspension, J. Chem. Eng. Jpn. 36 (2003) 1488–1497. [13] A. Vernhet, M. Moutounet, Fouling of organic microfiltration membranes by wine constituents: importance, relative impact of wine polysaccharides and polyphenols and incidence of membrane properties, J. Membr. Sci. 201 (1–2) (2002) 103–122. [14] Y. Ye, P.L. Clech, V. Chen, A.G. Fane, Evolution of fouling during crossflow filtration of model EPS solutions, J. Membr. Sci. 264 (1–2) (2005) 190–199. [15] Y. Ye, P. Le Clech, V. Chen, A.G. Fane, B. Jefferson, Fouling mechanisms of alginate solutions as model extracellular polymeric substances, Desalination 175 (2005) 7–20. [16] H. Susanto, H. Arafat, E.M.L. Janssen, M. Ulbricht, Ultrafiltration of polysaccharide–protein mixtures: elucidation of fouling mechanisms and fouling control by membrane surface modification, Sep. Purif. Technol. 63 (3) (2008) 558–565. [17] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd edition, Wiley & Sons, NY, USA, 2002, Chapter 2. [18] W.M. Lu, K.L. Tung, K.J. Hwang, Effect of woven structure on transient characteristics of cake filtration, Chem. Eng. Sci. 52 (11) (1997) 1743–1756. [19] R.G. Larson, Constitutive Equation for Polymer Melts and Solutions, Butteworth, Boston, USA, 1988, chapters 2–11. [20] S. Flew, R.H.J. Sellin, Non-Newtonian flow in porous media: a laboratory study of polyacrylamide solutions, J. Non-Newtonian Fluid Mech. 47 (1993) 169– 210.
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Filtration characteristics and membrane fouling in cross-flow microfiltration of BSA/dextran binary suspension Kuo-Jen Hwang ∗ , Pan-Yu Sz Department of Chemical and Materials Engineering, Tamkang University, Tamsui, Taipei Hsien 25137, Taiwan
a r t i c l e
i n f o
Article history: Received 22 August 2009 Received in revised form 4 October 2009 Accepted 6 October 2009 Available online 13 October 2009 Keywords: Cross-flow microfiltration Rejection coefficient Membrane fouling Membrane filtration Bio-separation
a b s t r a c t Filtration characteristics and membrane fouling in BSA/dextran binary suspension cross-flow microfiltration is studied. An increase in cross-flow velocity or transmembrane pressure leads to higher pseudo-steady filtration flux due to less membrane fouling or higher driving force. The fouled membrane pore size and fouled layer thickness under various conditions are estimated using a theoretical model based on the Hagen–Poiseuille law. The fouled membrane pore size decreases with increasing transmembrane pressure due to ever increasing fouling. The fouled layer thickness becomes thicker and invariant with operating conditions under a lower pressure drop through the fouled membrane. Molecular adsorption occurs on the pore walls until a specific wall shear stress is reached in the membrane pores. However, the fouled layer becomes thinner when the pressure drop exceeds a critical value. An increase in cross-flow velocity results in a larger fouled membrane pore size and a thicker fouled layer in such condition. The dextran molecular deformation under higher transmembrane pressure causes a thinner fouled layer and an ultimate equilibrium adsorption in the membrane pores. Furthermore, an increase in cross-flow velocity leads to higher BSA and dextran rejection due to the sweeping effect on the membrane surface. The BSA rejection increases with transmembrane pressure due to the reduction in membrane pore size, while the decrease in dextran rejection under higher transmembrane pressure is attributed to the molecular deformation. The “coil-stretched” deformation of dextran molecules can be indicated using the Deborah number. The fouled membrane pore size and dextran rejection decrease with increasing Deborah number and remain constant as the Deborah number exceeds a critical value. Taking the filtration flux and solute rejection into consideration, operating a cross-flow microfiltration system under lower cross-flow velocity and higher transmembrane pressure is more efficient from the selectivity and mean dextran mass flux view points. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Membrane filtration has been used increasingly in the separation or purification of bio-products in the biochemical and pharmaceutical industries in recent years. This is because of its economical, efficient and energy-saving advantages. However, unexpected membrane fouling is an obstacle to the continued development of this kind of separation technology. The components in a bio-process are varying and complex. Many components, such as polysaccharides, proteins, humic acid and microbial cells coexist in a general product stream. This causes membrane fouling to be rather complicated and difficult to manage. Therefore, realizing membrane fouling characteristics for specific bio-mixtures becomes an essential step in improving the separation efficiency.
∗ Corresponding author. Fax: +886 2 26209887. E-mail address: [email protected] (K.-J. Hwang). 0376-7388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2009.10.008
In most membrane filtration processes, membrane fouling occurs due to solute adsorption, particle interception or membrane blocking. The most important factors affecting membrane fouling are the membrane characteristics, particle or solute properties and operating conditions. In previous studies on single-component membrane filtration, Huisman et al. [1] carried out BSA crossflow ultrafiltration using polysulfone membranes with different pore sizes. They claimed that membrane fouling in the early filtration period was determined by the interaction between the protein and membrane, while the filtration performance in the later periods depended on the interaction among the proteins. These statements were similar to those in the study by Güell and Davis on the ultrafiltration of protein mixtures [2]. However, Ouammou et al. [3] concluded that the protein zeta potential was the most important parameter in membrane fouling. In those studies using a different approach, the modified gel-polarization model was proposed involving a gel layer formation on the membrane surface [4]. Cheng et al. [5] claimed that the filtration resistance in dextran ultrafiltration could be accurately predicted using this
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model. The concentration polarization or gel layer resistance was markedly reduced by increasing the cross-flow velocity. GarciaMolina et al. [6] indicated that a fouling layer was formed in dextran ultrafiltration, which was independent of the used membranes. Their experimental data showed that an increase in transmembrane pressure resulted in higher filtration flux and higher dextran rejection. These trends were the same as those in most previous researches [4]. Blatt et al. [7] concluded that the concentration polarization in protein ultrafiltration could be divided into two pressure-dependent regimes. The protein rejection decreased with increasing pressure in the low pressure region. This was attributed to the increase in polarization concentration. Conversely, gel layer formation or a reduction in membrane pore size under higher pressures increased the protein rejection. However, the protein rejection may be observed to decrease monotonously with increasing transmembrane pressure. This was attributed to the deformation of macromolecules with long and flexible chains [8]. Recently, Hwang and Huang [9] carried out the cross-flow microfiltration of blue dextran with a molecular weight of 2000 kDa. The membrane pore size was reduced by dextran adsorption during filtration. The dextran rejection increased with increasing crossflow velocity or decreasing transmembrane pressure under lower cross-flow velocity. They claimed that the contrary trend obtained under higher filtration flux was attributed to dextran molecular deformation. Several researchers have paid attention to the membrane filtration of bio-mixtures. Iritani et al. [10] performed the ultrafiltration of protein mixtures including BSA and egg white lysozyme. They concluded that the protein electrostatic interactions played major roles in determining the filtration flux and protein rejection. Hwang and co-workers [11,12] studied the cross-flow microfiltration of fine particle/dextran binary suspensions. The secondary membrane formed by the fine particles reduced the membrane fouling causing by dextran. The filtration flux and dextran rejection could be theoretically predicted using their derived models. The dextran rejection was significantly dependent on the tangential sweeping effect on the membrane surface and the capturing effect of the formed cake [12]. Vernhet and Moutounet [13] studied membrane fouling in the cross-flow microfiltration of red wine. They indicated that membrane fouling frequently occurred at the membrane pore entrances or on the membrane surface. The polysaccharides in red wind were the major foulants. Ye et al. [14,15] used a sodium alginate and BSA mixture to model the extracellular polymeric sub-
stances existing in a bioreactor. They found that the existence of BSA resulted in a more compact filter cake and reduced the sodium alginate transmission. Susanto et al. [16] studied the membrane fouling caused by protein/polysaccharide mixtures which were the major products in a fermentation tank. The fouled layer morphology was markedly dependent on the polysaccharide characteristics. Similar to the results of Ye et al. [14], they found that the fouled layer was more rigid and the flux was lower, relative to the filtration performance of a single component. These phenomena were attributed to the synergistic effects between protein and polysaccharide. In this study, BSA and dextran are used as the typical protein and polysaccharide samples, respectively, in bio-products. Cross-flow microfiltration was carried out to separate the binary suspension. The operating condition effects, e.g., the cross-flow velocity and transmembrane pressure, on the filtration flux and solute rejections at pseudo-steady state are discussed. The fouled membrane pore size and fouled layer thickness are theoretically estimated using a derived membrane fouling model. The Deborah number is introduced to indicate molecular deformation, and the operating condition effects on the dextran selectivity and mean dextran mass flux are also discussed. 2. Materials and experiments Bovine serum albumin (BSA) manufactured by United State Biochemical Co. and dextran (T2000) purchased from Sigma Chemical Co. were used as the protein and polysaccharide samples in this study. BSA and dextran, with molecular weights of 67 and 2000 kDa, respectively, were dissolved in a phosphate buffer solution to prepare the suspensions used in experiments. The BSA and dextran concentrations were set as 1.0 and 0.5 kg/m3 , respectively, to simulate the condition in fermentation products. The suspension pH and temperature were kept at 7.0 and 20 ◦ C during filtration. The BSA and dextran molecular sizes in the suspension were measured using Malvern MRK528-01 Zetasizer Nano System. The BSA molecules had a mean size of 8 nm. However, BSA coagulations as large as 300 nm were frequently found in the suspension. The dextran size distribution ranged from 21 to 300 nm with a mean value of 90 nm. A hydrophilic flat-sheet membrane made of mixed cellulose acetate was used in these experiments as the filter medium. A fresh membrane was used only for each experiment. The membrane was manufactured by Millipore Co. in USA and possessed a better BSA rejection property. Its porosity and thickness were 0.75 and 105 m, respectively. The mean nominal pore diameter of the
Fig. 1. A schematic diagram of the cross-flow microfiltration system.
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Fig. 2. Time courses of filtration flux during cross-flow microfiltration under various transmembrane pressures.
fresh membrane was measured using a Power Image Analysis System as 0.13 m. Experiments were carried out using a two-parallel-plate crossflow microfilter. The clearance, width and length of the filter channel were 1.0 × 10−3 , 2.0 × 10−2 and 5.5 × 10−2 m, respectively. The filter membrane was laid on the permeable bottom plate which had an effective filtration area of 1.1 × 10−3 m2 . Fig. 1 shows a schematic diagram of the microfiltration system. The suspension was well mixed using a magnetic mixer and kept isothermal using a thermostat during filtration. The cross-flow velocity and transmembrane pressure were adjusted using a rotameter and a needle valve, respectively. The filtrate was collected into a filtrate receiver that was placed on a load cell. Therefore, the filtrate weight was detected and recorded on a personal computer at each time increment. The solute concentrations were measured using a HPLC (Thermal Co., Spectra series P-100) installed a chromatographic column (Waters Co., BioSuite 450, 8 m HR SEC). The BSA and dextran concentrations were therefore analyzed separately due to their different flow rates through the column. When an experiment was terminated, the fouled membrane was measured its filtration resistance using clean water permeation or sent out to have its morphology analyzed by a Leo-1530 SEM.
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Fig. 3. Effects of transmembrane pressure and cross-flow velocity on the pseudosteady filtration flux.
from 0.1 to 0.5 m/s, the flux increases 50% under lower transmembrane pressure and increases 30% under higher transmembrane pressure. Although more serious membrane fouling occurs under higher transmembrane pressure, a higher flux is obtained due to the higher resulting filtration driving force. The filtration flux increases ca 50% when the transmembrane pressure increases from 20 to 100 kPa for the bio-mixture used in this study. The flux attenuation during a cross-flow microfiltration is mainly due to the membrane fouling. The macromolecules in the suspension may adsorb onto the membrane surface or in the membrane pores to form a fouled layer. According to the basic filtration equation, the total filtration resistance can be calculated using Rt =
P q
(1)
where P is the transmembrane pressure, q is the filtration flux, and is the fluid viscosity. The fouled layer resistance is much higher than the resistance caused by the concentration polarization layer and fresh membrane in most microfiltration. The Rt values at the pseudo-steady state under various conditions are calculated using Eq. (1) and shown in Fig. 4. The Rt value linearly increases with increasing transmembrane pressure. When transmembrane pressure increases from 20 to 100 kPa, a 4-fold increase in Rt value is
3. Results and discussion Fig. 2 shows the time courses of filtration flux during crossflow microfiltration of BSA–dextran binary suspension under three different transmembrane pressures. The BSA and dextran concentrations in the suspension were kept at 1.0 and 0.5 kg/m3 , respectively. The cross-flow velocity was fixed at 0.5 m/s in these experiments. The filtration fluxes attenuated very quickly at the beginning of filtration and gradually approached pseudo-steady values after 300 s. This implies that most membrane fouling occurred in the early filtration period. Comparing the data shown in Fig. 2, the filtration flux increases with increasing transmembrane pressure. This result can be expected because a higher filtration driving force is caused by increasing transmembrane pressure. The cross-flow velocity and transmembrane pressure effects on the pseudo-steady filtration flux are shown in Fig. 3. The filtration flux increases with increasing cross-flow velocity and transmembrane pressure. An increase in cross-flow velocity leads to higher shear stress acting on the membrane surface, as a result, less membrane fouling. However, this impact becomes less significant under higher cross-flow velocity. When the cross-flow velocity increases
Fig. 4. Effects of transmembrane pressure and cross-flow velocity on the filtration resistance.
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scopic analysis indicates that the filtration resistance is mainly due to the membrane pore size reduction near the pore entrances. This result is far different from that in the microfiltration of fine particles, in which a filter cake is formed caused by particle bridging and accumulation. The flow of fluids through a porous media was simplified for analysis since a half century ago. A common model was used by considering the actual flow system as parallel capillary tubes. Because the solute adsorbed layer reduces the membrane pore size and results in major filtration resistance, as shown in Fig. 5, the relationship between the fluid flow rate and pressure drop through a fouled membrane layer can be modeled using the Hagen–Poiseuille law and expressed as [17]: 2 dm,b Pm,b qs = · εm 32 Lm,b
(2)
where qs is the pseudo-steady filtration flux, εm is the membrane surface porosity, dm,b is the mean pore size of the fouled membrane. Because the true fluid velocity becomes higher in the membrane pores, the velocity gradient or the pore tortuosity occurring at the membrane surface may cause molecular adsorption on the membrane pore walls near the pore entrances and results in a fouled layer with a thickness (depth) of Lm,b . Therefore, the increase in filtration resistance during filtration is attributed to the reduction in membrane pore size or the increase in fouled layer thickness. The variables in Eq. (2) should be estimated prior to understanding the membrane fouling under various conditions. The fouled layer resistance, Rf , can be measured in experiments using clean water permeation through the fouled membrane [9,11,12]. The Pm,b value is then calculated using the fraction of fouled layer to the total filtration resistances, that is, Pm,b =
Rf Rt
· P
(3)
According to the analyses in previous studies [9,18], the fouled membrane resistance is assumed to be inversely proportional to the open pore surface cross-sectional area. Therefore, the dm,b value can be estimated using experimental resistance data and expressed as
dm,b =
Fig. 5. SEM photos for (a) fresh membrane, (b) top-view of the fouled membrane, and (c) side-view of the fouled membrane under us = 0.5 m/s and P = 100 kPa (×100 kX).
found. On the other hand, an increase in cross-flow velocity leads to a lower Rt value. However, this impact becomes insignificant as us > 0.3 m/s. This implies that the reduction in membrane fouling by increasing cross-flow velocity has an ultimate limit. The flux cannot be enhanced anymore by increasing cross-flow velocity when us exceeds the limiting value. This trend can also be seen in Fig. 3. Fig. 5(a) shows a SEM photo of the fresh membrane surface. Although the mixed cellulose acetate membrane is sponge-like and isotropic, it has a relatively flat surface with round pore entrances. Fig. 5(b) and (c) show the top and side-views, respectively, of the fouled membrane under us = 0.5 m/s and P = 100 kPa. Comparing Fig. 5(a) and (b), the membrane is fouled by solute adsorption onto the membrane surface and pore walls, leading to a reduction in the pore size. The mean membrane pore size becomes only 30–60% of the original value due to the fouling in the conditions of this study. A thin fouled layer is formed near the membrane pore entrances instead of complete pore blocking, as shown in Fig. 5(c). This micro-
2 dm,o
Rm · Rf
0.5
(4)
where dm,o and Rm are the mean pore size and resistance of the fresh membrane. Since the membrane surface porosity is considered to be proportional to the open pore surface cross-sectional area [9], the value of εm can be evaluated once the membrane pore size variation is known by Eq. (4). Fig. 6 shows a plot of qs /(εm ·dm,b 2 ) vs. Pm,b under various operating conditions. When Pm,b < Pm,b,c (a critical Pm,b ), all data can be regressed into a unique straight line in spite of transmembrane pressure and cross-flow velocity. This indicates that the fouled layer thickness is constant (=25.34 m from the regressed line slope) whatever the operating condition is. However, when Pm,b exceeds the critical value, the data for a fixed cross-flow velocity are located on the same straight line. This means the transmembrane pressure effect on the fouled layer thickness Lm,b is negligible small. The Lm,b value depends solely on cross-flow velocity and can be determined by the regressed line slope. In other words, when Pm,b exceeds the critical value, the fouled layer thickness becomes thinner than those under low pressure and increases with increasing cross-flow velocity. Since higher flux is obtained under higher cross-flow velocity, the fouling (molecular adsorption) may occur at a deeper location in the membrane pores as the flux increases. The fouled layer thickness is therefore thicker under higher cross-flow velocity. The Lm,b values under
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Fig. 6. A plot of qs /(εm ·dm,b 2 ) versus Pm,b under various operating conditions.
us = 0.1, 0.3 and 0.5 m/s are calculated as 9.38, 10.71 and 11.54 m, respectively. The fouled layer thickness is very thin, relative to the whole membrane. In comparison to the authors’ previous study on the cross-flow microfiltration of blue dextran [9], the existence of BSA causes the fouling layer to be thicker. The occurrence of the critical Pm,b is attributed to the variation of molecular adsorption mechanism. The mechanism depends significantly on the molecular morphology and will be discussed as follows. In order to understand the operating condition effects on the fouled membrane pore size, the dm,b values under various shear stresses on the pore walls, m,b , are plotted in Fig. 7. If the fouled membrane pore can be modeled as a circular tube, the m,b value can be estimated by making a momentum balance around the membrane pore, that is [17], m,b =
dm,b 4
Pm,b Lm,b
(5)
In low Pm,b region, dm,b value varies in the range from 6.65 × 10−8 to 1.05 × 10−7 m. An increase in Pm,b leads to a smaller dm,b but a constant Lm,b , as shown in Fig. 6. As a result, the m,b values are constant within the operating conditions. This is because the suspended molecules exhibit “round” or “coil” morphology under low
Fig. 7. A plot of dm,b versus w,b under various operating conditions.
Fig. 8. SEM photos for top-view of the fouled membrane (a) us = 0.1 m/s and P = 20 kPa, (b) us = 0.1 m/s and P = 100 kPa (×100 kX).
pressure (low flow rate). The molecules adsorb onto the membrane pore walls until the wall shear stress reaches a critical value. The molecules cannot stably “stick” onto the membrane pore wall under a shear stress higher than the critical value. This fact is similar to the selective deposition of fine particles in cross-flow filtration [11,12]. On the other hand, in the high Pm,b region, the m,b value increases with Pm,b because the fouled layer becomes thinner compared to that in the low Pm,b region. The deformation causes the molecules to more easily adsorb onto the membrane pore walls. The dm,b values are therefore smaller than those in low Pm,b region. It is inferred that the stretched molecular bonds cause the adsorption to approach the ultimate equilibrium value. This results in little differences among the dm,b values in the high Pm,b region. However, the higher pore shear stress under higher cross-flow velocity leads to a slightly larger dm,b value although the fouled layer is thicker (as shown in Fig. 6). The transmembrane pressure effect on membrane fouling is illustrated in Fig. 8. The transmembrane pressures were 20 and 100 kPa in Fig. 8(a) and (b), respectively, while the cross-flow velocity was fixed at 0.1 m/s. Comparing the SEM photos shown in Fig. 8(a) and (b), the pore sizes under higher pressure are smaller at a given cross-flow velocity. This reveals that more solute molecules adsorb onto the membrane pore walls in such condition. However, it can be found by comparing Figs. 5(b) and 8(b) that the mean pore sizes of the fouled membrane under a fixed transmembrane pressure increase slightly with cross-flow velocity. These trends in the SEM results agree with the calculated dm,b results using Eq. (4).
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Fig. 9. A plot of dm,b versus De under various operating conditions.
Because dextran molecules have long and flexible chains, their flow and adsorption behaviors are significantly affected by the molecular configuration. According to the dumbbell model for macromolecules [19], the Deborah number, De, is an important parameter for indicating molecular deformation and flow behaviors, which is defined as: De ≡ ˙
(6)
where and ˙ are the characteristic relaxation time and macromolecular elongation rate, respectively. A long-chain macromolecule may be in a “coil” configuration under a low Deborah number and stretches its chains as De increases. The elongation rate of macromolecules flowing through a fouled membrane can be evaluated using [20] qs (1 − εm ) ˙ = k1 dm,b
(7)
where k1 is a molecular characteristic constant. Substituting Eq. (7) into Eq. (6) yields De = k1
qs (1 − εm ) = k2 De dm,b
where Cb and Cp are the solute concentrations in the bulk suspension and in the filtrate, respectively. Thus, the rejection can be used to evaluate the solute fraction which is retained by the membrane. Fig. 10 depicts the cross-flow velocity and transmembrane pressure effects on the pseudo-steady solute rejection. Although the monomolecular size of BSA is only 8 nm, which is far smaller than the membrane pore size, the BSA rejection exceeds 0.6 in all operating conditions. This is due to the existence of BSA coagulations in the suspension. The BSA rejection increases with increasing transmembrane pressure and cross-flow velocity. This reveals that the BSA rejection becomes higher under more series membrane fouling. The BSA rejection increases 30% when transmembrane pressure increases from 20 to 100 kPa. However, an increase in transmembrane pressure leads to a lower dextran rejection. The rejection is contrarily lower for a membrane with smaller effective pore size. This is because the molecular deformation causes dextran to penetrate through the membrane pores more easily into the filtrate. Therefore, the data shown in Fig. 10 infers that the BSA rejection is determined directly by the membrane pore size, while the dextran rejection is significantly affected by the molecular deformation. A larger rejection difference between BSA and dextran can be seen under higher transmembrane pressure, although their values are close to each other under a pressure of 20 kPa. The thicker fouled layer and higher sweeping effect on the membrane surface under higher cross-flow velocity result in higher BSA and dextran rejections although the dm,b value is larger. However, the cross-flow velocity effect on BSA rejection is relatively small. A parameter, selectivity, can be used in place of the dextran fractional yield in the filtrate, which is defined as the ratio of the amount of dextran to the amount of BSA collected in filtrate. The selectivity values under various conditions are calculated using the data shown in Fig. 10 for comparison. The dextran selectivity is enhanced by increasing transmembrane pressure. For instance, under a given cross-flow velocity of 0.5 m/s, the dextran selectivity increases from 0.5 to 1.8 as the pressure increases from 20 to 100 kPa. The dextran selectivity becomes higher under lower cross-flow velocity. The highest selectivity is 2.5 under us = 0.1 m/s and P = 100 kPa. The rejection and selectivity data reveal that BSA and dextran are separated more efficiently under lower cross-flow velocity and higher transmembrane pressure.
(8)
where k2 is a coefficient combining two constants, k1 and . Therefore, the De value can be used for indicating the molecular deformation if the dumbbell model is valid. The dm,b values are plotted against De under various operating conditions in Fig. 9. The data reveals that dm,b can be expressed as a unique function of De , and a critical Deborah number, De c = 1.56 × 102 , exists. When De is smaller than the critical value, the dm,b value linearly decreases with De . In this region, the dm,b value decreases with the increase in filtration flux (by increasing cross-flow velocity or transmembrane pressure). The pseudo-steady pore size is therefore determined by the fixed pore wall shear stress, as shown in Fig. 7. However, the dm,b value remains constant when De exceeds the critical value. The dm,b value is invariant with De once the macromolecular chains are fully stretched. Therefore, the Deborah number and macromolecular deformation can be used to explain the membrane pore reduction in this study. Excepting the filtration flux, another important factor affecting separation efficiency is the solute rejection (or transmission). The observed rejection coefficient, Rrej , is defined as: Rrej ≡ 1 −
Cp Cb
(9)
Fig. 10. Effects of operating conditions on the BSA and dextran rejection.
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Fig. 11. Effect of Deborah number on the BSA and dextran rejection.
Fig. 11 shows the relationships between solute rejection and De under various conditions. The BSA rejections under various crossflow velocities and transmembrane pressures can be regressed to a unique empirical equation of De . The BSA rejection increases with increasing De value, but the impact becomes smaller under higher De . This is because more BSA coagulations are retained by the membrane with a smaller effective pore size. In contrast, the dextran rejection decreases with increasing De and remains constant when De exceeds the critical value, which is the same as that shown in Fig. 9. The decrease in dextran rejection is attributed to the molecular deformation. A stretched molecule more easily penetrates through the membrane pores. However, this effect becomes trivial when the molecular chains are fully stretched at the critical condition. A higher cross-flow velocity results in a higher dextran rejection because of the sweeping effect on the membrane surface [12]. The dextran molecules may be swept away from the mem-
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brane surface by the tangential suspension flow before they have an opportunity to touch the membrane surface. This effect is more significant under higher cross-flow velocity. Taking the filtration flux and solute rejection into consideration, the mean solute mass flux can be used to evaluate the recovery or production in a microfiltration system. Fig. 12 shows the mean mass fluxes of BSA and dextran under various operating conditions. Because both filtration flux and BSA rejection increase with increasing transmembrane pressure and cross-flow velocity, a lower mean BSA mass flux is obtained under a higher transmembrane pressure. However, the cross-flow velocity effect on the BSA mass flux is trivial due to less effect on BSA rejection. On the other hand, the mean dextran mass flux is significantly enhanced by increasing the transmembrane pressure because of the increase in filtration flux and the decrease in dextran rejection. The dextran mass flux increases more than three times when the transmembrane pressure increases from 20 to 100 kPa. However, the higher dextran rejection under higher cross-flow velocity leads to a lower mean dextran mass flux. This impact is more obvious under higher transmembrane pressure. Comparing the data shown in Fig. 12, the operating condition effects on the BSA mass flux are relatively small. Although the dextran concentration in the suspension is only a half that of BSA, the dextran mass flux is 2-fold higher than that for BSA flux under high transmembrane pressure. Therefore, operating a cross-flow microfiltration system under low cross-flow velocity and high transmembrane pressure is more efficient from the selectivity and mean mass flux viewpoint. 4. Conclusions The operating condition effects on the filtration flux, solute rejection and membrane fouling in BSA/dextran binary suspension cross-flow microfiltration were studied. The filtration flux was increased 30–50% by increasing the cross-flow velocity or transmembrane pressure. A membrane fouling model based on the Hagen–Poiseuille law was derived. The molecular adsorption onto the membrane pore walls reduced the pore size and resulted in a significant filtration resistance. The fouled membrane pore size decreased with increasing transmembrane pressure, but increased slightly with increasing cross-flow velocity. When the pressure drop through the fouled membrane was lower than a critical value, the fouled layer thickness becomes thicker and independent of the operating conditions. Molecular adsorption occurred until reaching a specific wall shear stress in the membrane pores. When the pressure drop exceeds the critical value, the fouled layer became thinner, relative to those under low pressure. An increase in crossflow velocity led to a slightly larger fouled membrane pore size and thicker fouled layer. The BSA rejection increased with increasing transmembrane pressure and cross-flow velocity. The dextran rejection significantly decreased with increasing transmembrane pressure or decreasing cross-flow velocity. This was attributed to the sweeping effect on the membrane surface and the molecular deformation. The fouled membrane pore size and dextran rejection decreased with increasing Deborah number and remained constant as the Deborah number exceeded a critical value. To operate a cross-flow microfiltration system under low cross-flow velocity and high transmembrane pressure would be more efficient from the selectivity and mean dextran mass flux viewpoint. The highest selectivity was as high as 2.5 under such condition. Acknowledgement
Fig. 12. Effect of operating conditions on the mean mass fluxes of BSA and dextran.
The authors wish to express their sincere gratitude to the National Science Council of the Republic of China for its financial support.
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K.-J. Hwang, P.-Y. Sz / Journal of Membrane Science 347 (2010) 75–82
Nomenclature Cb Cp De De dm,o dm,b k1 k2 Lm,b m q qs Rf Rm Rrej Rt t us
solute concentration in the bulk suspension [kg/m3 ] solute concentration in the filtrate [kg/m3 ] Deborah number defined in Eq. (6) modified Deborah number defined in Eq. (8) [s−1 ] clean membrane pore diameter [m] fouled membrane pore diameter [m] a coefficient defined in Eq. (7) a coefficient defined in Eq. (8) fouled layer thickness [m] mean solute mass flux [kg/m2 s] filtration flux [m3 /m2 s] pseudo-steady filtration flux [m3 /m2 s] filtration resistance due to membrane fouling [m−1 ] filtration resistance of clean membrane [m−1 ] observed solute rejection coefficient at pseudosteady state total filtration resistance [m−1 ] filtration time [s] cross-flow velocity [m/s]
Greek letters P transmembrane pressure [Pa] Pm,b pressure drop through the fouled membrane [Pa] εm membrane surface porosity relaxation time of macromolecules [s] ˙ elongation rate of macromolecules [s−1 ] fluid viscosity [kg/s m] w,b shear stress on the membrane pore wall [N/m2 ] Subscript c the critical value
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