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Homoporous and heteroporous membrane models in describing key separative parameters of semipermeable membranes
Desalination 184 (2005) 89–97
Homoporous and heteroporous membrane models in describing key separative parameters of semipermeable membranes Eugene Tsapiuk, Ludmyla Melnyk* A.V. Dumansky Institute of Colloid and Water Chemistry, Ukrainian National Academy of Sciences, 42 Vernadsky Avenue., 03680 Kyiv, Ukraine, Tel. þ38 044 423 8227; Fax þ38 044 423 8224; email: [email protected] Received 21 February 2005; accepted 22 March 2005
Abstract A heteroporous membrane model consisting of two membranes (actually suitable to any number of membranes) differing in their separative parameters is advanced. This model has been verified using a number of industrial reverse osmosis and ultrafiltration membranes made of cellulose acetate as well as two nanofiltration ones. The experimental and computed results are in reasonable agreement, particularly taking into account the oversimplified and somewhat mechanistic character of the approach. The results reached clearly and convincingly illustrate the detrimental role which can be played by the presence of even a minor fraction of highly permeable and slightly retentive sections in the membrane structure, that is, the presence of imperfect sites as these often called. Keywords: Heteroporous membrane model; Hydrodynamic permeability; Retention; Semipermeable membranes; Volume flux
1. Introduction At present, the so-called ‘homoporous’ approach to membrane structure is generally used in modeling separative parameters of the semipermeable membranes (i.e. those used in
*Corresponding author.
pressure-driven membrane methods) [1]. According to this approach, pores in membranes are supposed to be of uniform size. The smaller the size, the higher the retentivity and the lower the transmembrane flux of the membrane. Numerous experimental data illustrate however, that most of semipermeable membranes (including track-etched ones)
Presented at the Conference on Desalination and the Environment, Santa Margherita, Italy, 22–26 May 2005. European Desalination Society. 0011-9164/05/$– See front matter Ó 2005 Elsevier B.V. All rights reserved doi:10.1016/j.desal.2005.03.066
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E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97
are characterized by a certain (most often, normal-logarithmic) pore distribution in their size [2,3]. Therefore, acceptance of that approach and accordingly any models based on it seem to be still open to discussion For that reason, we make an effort in this paper to develop the so called heteroporous membrane model and then to consider and to compare use of two alternative models (homoporous and heteroporous membrane) in describing key separative parameters of actual semipermeable membranes greatly differing in those parameters.
2. Theoretical elements First, as only the top (active) membrane layer determines retentivity as such of the whole membrane structure [1,4], only the retentive properties inherent to these layers are referred to in this paper when dealing with any actual data. Next, the authors are aware as well that the concept as pore size is currently not popular in all pressure-driven membrane methods and, in particular in reverse osmosis. Indeed, there are a number of serious reasons for this. However, that discussion is beyond the scope of this work. Sometimes however this approach not only may be, but also is indeed very helpful in understanding some important facts governing the above-mentioned retentivity phenomenon in spite of its somewhat ambiguous character. Next, we need to briefly explain the terms ‘homoporous’ and ‘heteroporous’ which relate to membrane structure and which do not occur in fact in the membrane literature. When the structure of any membrane layer, but primarily the top, retaining one, may be characterized by ‘single-shape’ pore-like elements, we call it ‘homoporous.’ In such a structure, these elements have the same size,
shape, etc. It is very similar to the so-called homogeneous membrane model [1,2] but, in a strict sense, is not identical to that. The point is that the latter model is more far-reaching. It concerns the whole membrane with its inherent properties, rather than those of its separate layers/constituents. We can state the same with respect to the heteroporous membrane model where the pore-like elements are more or less variable both in their form and size, i.e. are not uniform and not like each other, above all in their size. As opposed to the above case, it considerably differs from the well-known heterogeneous membrane model [2,4] but is very like the so-called ‘mosaic’ model [1,5]. Despite them somewhat uncertain character of the above terms, it is not difficult to detail them as it concerns the key separative parameters in pressure-driven membrane methods: retention coefficient and volume flux (or hydrodynamic permeability) of a membrane In this paper, their definitions do not differ from the generally accepted ones [4,6]. Let us assume a membrane model in which the membranes consists of one with high specific hydrodynamic permeability but low retention coefficient and, vice versa, low permeability but high retentivity, and ratio of their areas can be purposefully varied. Then, it is not difficult to determine, first, the retention coefficient and volume flux versus working pressure dependencies and, next, based on the previous calculations, the retention coefficient versus volume flux dependence if needed. The volume flux vs. working pressure drop [Jv (P)]2 curves can be calculated according to Jv ¼
P 0 0 lp A þ lp 00 A00 A
ð1Þ
where A is the total membrane area. It is more convenient to assume that the area is
E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97
one unit, but this does not mean of course that actual membrane area must be one unit. A0 and A00 are area fractions corresponding to highly and slightly permeable membranes (A0 þ A00 = A), and lp0 and lp00 are the hydrodynamic permeabilities of these membranes, respectively. It is also easy to show that the retention coefficient of that membrane at any working pressure is expressed as R¼1
A0 lp 0 ð1 R0 Þ þ A00 lp 00 ð1 R00 Þ A0 lp 0 þ A00 lp 00
ð2Þ
where R0 and R00 are corresponding retention coefficients of the constituting membranes at a given pressure (volume flux). Because the trial runs have been performed over a comparatively wide range of working pressure variation (see Experimental section), it is necessary to take into account the concentration polarization effect. The reason is that this phenomenon can play a considerable role in determining actual retentive properties of membranes, especially those characterized by a high hydrodynamic permeability [1,2,4]. To examine its effect (i.e. to find out the intrinsic retention coefficient), Colton’s relationships have been used [7]. 3. Experimental Experimental runs have been performed in a crossflow unit equipped with a stirred batch cell modified to work in a continuous mode. The membrane area in this cell was 30.18 cm2. To reduce the concentration polarization effect, the cell was equipped with a magnetic stirrer. Its rotation rate was set at 500(5) rpm over all the trial runs and controlled by tachometry (TCt100). Sucrose of pharmaceutical grade was chosen as a testing solute. The reasons for this choice were as follows. First, sucrose is easily definable
91
analytically (interferometry carried out with the ITR-2 interferometer was used for this purpose). Next, this solute is quite perceptibly retained by the ultrafiltration membrane (the most finely porous ones of them) [1,8], and its retention coefficient gradually alters in the series of membranes we selected. We also tried to apply glucose, the molecular weight (180 Da, monosaccharide) of which is about half that of sucrose (342.3 Da, disaccharide) for this purpose, but its retention by the ultrafiltration membrane is too small to be acceptable in this paper (computation results were somewhat unreliable). Finally, because we have also used nanofiltration membranes, and these contain certain fixed-charge sites in their structure, it was desirable to keep any coulomb interactions out of the retention mechanism. The model advanced does not take into consideration these interactions, though they can play very important role in determining retentivity of ionic solutes, particularly at low concentrations [1,4,6]. To keep its concentration in the feed (10 g/l) virtually constant (i.e. to facilitate the corresponding calculations), the retentate stream was returned back to the feed tank. Its volume (10 l) was considerably greater than that of the sum of the permeate samples. The latter did not surpass 150 ml in any single trial we carried out. A number of reverse osmosis and ultrafiltration membranes made of cellulose acetate (Vladipor series, Russia) as well as two nanofiltration ones (the same vendor, but their composition was not given except that they consist of polymers with a weak ion-exchange capacity) have been tested for their separative characteristics. Some of the structural and semipermeable characteristics of these membranes are listed in the Table below. Retention coefficient and volume flux (or hydrodynamic permeability) of membranes
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under study have been determined by a conventional method [6]. The following should also be emphasized. On the one hand, we needed to study and to compare membranes greatly differing in their separative characteristics and designed to function over quite different working pressure ranges. On the other hand, it was very important to carry out the comparison over the same pressure range. Certainly, to rule out of membrane destruction, the upper limit cannot be too high. Further, excessive working pressures result in a high compaction of membranes. This is quite evident from the data represented in Table 1. As a result, their structure and retentive performance dramatically change, particularly those of ultrafiltration membranes. Taking into account these facts and foreseeable consequences from them, we selected a compromise range in varying working pressure: 1–25 bar. The upper pressure greatly surpasses that typically used in ultrafiltration (as a rule, 5 bar) [1,2]. Nonetheless, in our quite great
and long-term investigation ultrafiltration membranes of precisely this series under elevated pressure (even up to 100 bar), we actually did not meet failures at such pressures. All the membranes under test needed adequate pretreatment under heightened pressure. For that reason, the membranes have been pressurized with distilled water under a pressure of 30 bar until their hydrodynamic permeability did not vary with time. Most of their characteristics indeed altered to great extent after such their pretreatment (compare data in numerator and denominator in Table 1). 4. Results and discussion Fig. 1 shows the variation of the observed and intrinsic sucrose retention coefficient (a) and volume flux (b) versus working pressure for all the membranes under study. The trends in variation of these key separative parameters are quite ordinary: both increase with working pressure. The extreme variation in the observed retention coefficient found
Table 1 Some characteristics of semipermeable membranes under test Membrane Reverse osmosis membranes MGA-100 MGA-95 MGA-90 MGA-80 MGA-70 Ultrafiltration membranes UAM-50 UAM-100 UAM-150 Nanofiltration membranes OFMN-P OPMN-K
Total thickness, mm1
Total voidage
Hydrodynamic permeability, lp 107, m/(s bar)
Retention plateau coefficient of sucrose
101/60 102/59 115/58 102/47 95/50
0.79/0.55 0.79/0.51 0.80/0.49 0.81/0.48 0.80/0.50
0.66/0.62 0.83/0.79 1.45/1.20 3.05/2.45 4.33/2.82
0.994 0.989 0.975 0.942 0.915
110/54 105/79 105/50
0.79/0.50 0.80/0.51 0.80/0.52
11.91/6.72 24.15/12.03 55.31/28.24
0.422 0.230 0.081
97/61 96/62
0.81/0.53 0.82/0.51
4.88/4.01 5.01/4.93
0.821 0.771
1 The numerator and denominator give respectively the characteristics inherent to the initial membrane samples and those after their compression under a working pressure of 30 bar.
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E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97 (a) 1 1 2 0.8
Retention coefficient
3
0.6 4
5 0.4
9
0.2
6 7
10
8 0 0
5
10
15
20
25
5
10
15
20
25
(b)
Volume flux × 106, m/s
30
20
10
0 0
Working pressure, bar
Fig. 1. Experimentally established dependencies of the observed (solid lines) and true (dotted lines) retention coefficients of sucrose (a) and the volume flux (b) versus working pressure on the MGA-100 (1), MGA-95 (2), MGA-90 (3), MGA-80 (4), MGA-70 (5), UAM-50 (6), UAM-100 (7), UAM-150 (8), OFMN-P (9), and OPMNK (10) membranes.
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with more permeable ultrafiltration membranes is due to the concentration polarization effect [1,9]. Regarding the intrinsic retention coefficient, it reaches a plateau with all the membranes, as is predicted by any mass transport theory of pressure-driven membrane methods [1,2,4]. As we expected, separative parameters of nanofiltration membranes, occupy an intermediate range between reverse osmosis and ultrafiltration membranes. It should be emphasized that this range is relatively wide. Apart from this remark, there are no other distinctions in principle between reverse osmosis membranes, on the one hand, and ultrafiltration ones, on the other hand. Taking into account the data represented in Table 1, it is quite evident that separative parameters showed by nanofiltration membranes should fall just between those of reverse osmosis and ultrafiltration membranes, and those indeed fall there (Fig. 1). As there are not any essential differences between all the membranes under study, we can thus select any of them to use as the constituents of an imaginary heteroporous structure such as the one described above. The number of foreseeable variants is high, actually it is infinitely large, but we limit ourselves to two membranes which are situated almost at the two opposite sides of the series investigated: MGA-95 and UAM-100. Again, there may be any number of variants as concerns the position occupied by each of them in that imaginary structure, (bearing in mind that their sum cannot differ from unity). However, it is not difficult to be convinced that these ‘partners’ are not equivalent in the contribution of each over all the variation range, and it is more interesting to have a closer look at the role played by the more permeable and less retentive constituent. Computation results shown in Fig. 2 clearly testify to the above. Varying the
relative fraction of any of two membranes (their relative parts are firmly interrelated themselves), we reach trends in changing volume flux and observed and intrinsic retention coefficients versus working pressure which are like much to those portrayed in Fig. 1. Some differences are observed at low working pressures: the retention coefficient versus working pressure dependences in Fig. 1(a) vary more sharply as compared with those in Fig. 2(a). That is to be expected nonetheless if we take into account the considerable oversimplification of the approach we advanced. It is too ‘mechanistic’ for the simple reason that it is too simple. If the latter may be considered as its advantage, the former naturally is its deficiency. The above difference, for example, might be caused by a number of reasons, the most important among them is likely the fact that we have neglected the role of the Peclet number of the internal membrane [3,10]. At any rate, the above model does not claim to provide a general approach to pressure-driven membrane transport answering all the questions open to discussion at present. Its role is quite limited, but some consequences of it appear to be of interest. Therefore, let us pay attention to these interesting facets of this approach. Above all, it clearly illustrates that minor imperfections in the membrane structure can dramatically impair its semipermeable characteristics. It seems there is no sense in analyzing in detail any of variants depicted in Fig. 2, because these are sufficiently convincing. However, a few inferences that follow from results are worth noting. First, the increase in the retentivity of a membrane may not be due to decreasing its pore size but rather to excluding several defective sites and zones (micro and macro defects). In each particular case, their origin may differ: ranging from problems associated
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E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97 (a) 1 1 2
Retention coefficient
0.8
3 4
0.6 5 0.4 6
0.2 7 8 9
0 0
5
10
15
20
25
10
15
20
25
(b)
Volume flux × 106, m/s
30
20
10
0 0
5
Working pressure, bar
Fig. 2. Dependencies of the observed (solid lines) and true (dotted lines) retention coefficients of sucrose (a) and the volume flux (b) versus working pressure on the MGA-95 (1) and UAM-100 (7) membranes as well as these dependencies calculated according to the heteroporous membrane model consisting of the membranes (1) and (2) at their ratio of 199/1 (3), 99/1 (4), 98 (5), 95/5 (6), 90/10 (7), 75/25 (8), and 50/50 (9), respectively.
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with the proper/improper synthesis of a membrane structure to problems associated with its particular application. In the former case, it is necessary to follow manufacturing protocol thoroughly and, in the latter, there are a great number of foreseeable problems. Many of them can be averted to a great extent by adequate pretreatment of solutions to be treated by the pressure-driven membrane methods. Continuing with this approach, that is, considering problems associated with damaging membrane structure during its operation, the positive role of the dynamically formed structures [1,8,11] becomes clearer. If the membrane contains such imperfect sites in its structure, or these have been generated during its functioning, the local transmembrane fluxes essentially increase here. As a result, transport of dispersed matter (i.e. properly the dynamic membrane forming additive) to such imperfect sites becomes more intense and, finally, there takes place their overlapping/plugging/healing, etc. One more inference is the important role of pressure-driven membrane technology such as membrane fractionation [1,8]. A minor inconsistency in size ratios of dispersed matter and membrane pores results in total failure of the method. Further, the operating conditions are of great importance. Therefore, to succeed in solving such problems, it is necessary either to use a semipermeable membrane without any defects/imperfections (i.e. that characterized by a highly regular/homogeneous structure) or to modify it in a purposeful way [8]. In the latter case, there are a great number of as yet unanswered problems. Nevertheless, the above results may held in reexamining this problem. One can reach likely some other fairly important conclusions and inferences from the above model, despite its oversimplified character. We again use the term
‘oversimplified’ to emphasize that this model may be expanded. It is not difficult to provide that the number of constituents in the heteroporous membrane model may be any number: two, three, four, etc. and to modify Eqs. (1) and (2) accordingly. The single fact that cannot be overlooked is that the sum of membrane area fractions cannot differ from unity. In so doing, one can reach better agreement with actual data but, before doing that, it should be kept in mind that the above approach is far from that covering all the theoretical arguments. 5. Conclusions (1) The so-called heteroporous membrane model consisting of two membranes differing in their separative parameters is advanced. This model may consist of any reasonable number of constituents. (2) Verification of that model using a number of industrial reverse osmosis and ultrafiltration membranes made of cellulose acetate as well as nanofiltration ones shows a reasonable agreement between experimental results and theoretical premises despite the somewhat mechanistic character of the approach advanced. (3) The model provides a means to reexamine the role played by minor imperfections in the membrane structure. (4) Proper understanding of that role provides a means to find and to fix similar problems.>
References [1] M.T. Bryk, E.A. Tsapiuk, Ultrafiltration, Kyiv, Naukova Dumka, 1989. [2] M. Mulder, An introduction into membrane technology, Moscow, Mir, 1999 (Russian translation). [3] E.A, Tsapiuk M.T, Bryk, An interpretation of the seperation of low and high molecular weight solutes by ultrafiltration, J. Membrane Sci., 79 (1993), 227–240.
E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97 [4] R.W. Baker, Membrane Technology and Application, New York, McGraw-Hill, 2000. [5] A.G. Fane, C.J.D. Fell, A.J. Waters, The relationship between membrane surface pore characteristics and flux of ultrafiltration membranes, J. Membrane Sci., 9 (1981) 245–263. [6] W. Pusch, Measurements techniques of transport through membranes, Desalination, 59 (1986) 105–198. [7] D.D. Do, A.A. Elhassadi, A theory of limiting flux in a stirred bath cell, J. Membrane Sci., 25 (1985) 113–132. [8] E. Tsapiuk, V. Kochkodan, V. Badekha, Change in molecular weight retetion curves of
97
ultrafiltration membranes with respect to lignosulfonates under gel formation conditions, Ibid, 210 (2002) 183–196. [9] E.A. Tsapiuk, Ibid., Ultrafiltration separation of aqueous solutions of poly (ethylene glycol)s on the dynamic membrane formed by gelatin, 116 (1996) 17–29. [10] B.V. Deryaguin, N.V. Churaev, G.A. Martunov, V.M. Starov, Solution sepration theory by means of reverse osmosis, Khim. Tekhnol. Vody. 3 (1981) 99–104. [11] G.B. Tanny, Dynamic membranes in ultrafiltration and reverse osmosis, Sep. Purif. Methods, 7 (1978) 183–220.
Homoporous and heteroporous membrane models in describing key separative parameters of semipermeable membranes Eugene Tsapiuk, Ludmyla Melnyk* A.V. Dumansky Institute of Colloid and Water Chemistry, Ukrainian National Academy of Sciences, 42 Vernadsky Avenue., 03680 Kyiv, Ukraine, Tel. þ38 044 423 8227; Fax þ38 044 423 8224; email: [email protected] Received 21 February 2005; accepted 22 March 2005
Abstract A heteroporous membrane model consisting of two membranes (actually suitable to any number of membranes) differing in their separative parameters is advanced. This model has been verified using a number of industrial reverse osmosis and ultrafiltration membranes made of cellulose acetate as well as two nanofiltration ones. The experimental and computed results are in reasonable agreement, particularly taking into account the oversimplified and somewhat mechanistic character of the approach. The results reached clearly and convincingly illustrate the detrimental role which can be played by the presence of even a minor fraction of highly permeable and slightly retentive sections in the membrane structure, that is, the presence of imperfect sites as these often called. Keywords: Heteroporous membrane model; Hydrodynamic permeability; Retention; Semipermeable membranes; Volume flux
1. Introduction At present, the so-called ‘homoporous’ approach to membrane structure is generally used in modeling separative parameters of the semipermeable membranes (i.e. those used in
*Corresponding author.
pressure-driven membrane methods) [1]. According to this approach, pores in membranes are supposed to be of uniform size. The smaller the size, the higher the retentivity and the lower the transmembrane flux of the membrane. Numerous experimental data illustrate however, that most of semipermeable membranes (including track-etched ones)
Presented at the Conference on Desalination and the Environment, Santa Margherita, Italy, 22–26 May 2005. European Desalination Society. 0011-9164/05/$– See front matter Ó 2005 Elsevier B.V. All rights reserved doi:10.1016/j.desal.2005.03.066
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E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97
are characterized by a certain (most often, normal-logarithmic) pore distribution in their size [2,3]. Therefore, acceptance of that approach and accordingly any models based on it seem to be still open to discussion For that reason, we make an effort in this paper to develop the so called heteroporous membrane model and then to consider and to compare use of two alternative models (homoporous and heteroporous membrane) in describing key separative parameters of actual semipermeable membranes greatly differing in those parameters.
2. Theoretical elements First, as only the top (active) membrane layer determines retentivity as such of the whole membrane structure [1,4], only the retentive properties inherent to these layers are referred to in this paper when dealing with any actual data. Next, the authors are aware as well that the concept as pore size is currently not popular in all pressure-driven membrane methods and, in particular in reverse osmosis. Indeed, there are a number of serious reasons for this. However, that discussion is beyond the scope of this work. Sometimes however this approach not only may be, but also is indeed very helpful in understanding some important facts governing the above-mentioned retentivity phenomenon in spite of its somewhat ambiguous character. Next, we need to briefly explain the terms ‘homoporous’ and ‘heteroporous’ which relate to membrane structure and which do not occur in fact in the membrane literature. When the structure of any membrane layer, but primarily the top, retaining one, may be characterized by ‘single-shape’ pore-like elements, we call it ‘homoporous.’ In such a structure, these elements have the same size,
shape, etc. It is very similar to the so-called homogeneous membrane model [1,2] but, in a strict sense, is not identical to that. The point is that the latter model is more far-reaching. It concerns the whole membrane with its inherent properties, rather than those of its separate layers/constituents. We can state the same with respect to the heteroporous membrane model where the pore-like elements are more or less variable both in their form and size, i.e. are not uniform and not like each other, above all in their size. As opposed to the above case, it considerably differs from the well-known heterogeneous membrane model [2,4] but is very like the so-called ‘mosaic’ model [1,5]. Despite them somewhat uncertain character of the above terms, it is not difficult to detail them as it concerns the key separative parameters in pressure-driven membrane methods: retention coefficient and volume flux (or hydrodynamic permeability) of a membrane In this paper, their definitions do not differ from the generally accepted ones [4,6]. Let us assume a membrane model in which the membranes consists of one with high specific hydrodynamic permeability but low retention coefficient and, vice versa, low permeability but high retentivity, and ratio of their areas can be purposefully varied. Then, it is not difficult to determine, first, the retention coefficient and volume flux versus working pressure dependencies and, next, based on the previous calculations, the retention coefficient versus volume flux dependence if needed. The volume flux vs. working pressure drop [Jv (P)]2 curves can be calculated according to Jv ¼
P 0 0 lp A þ lp 00 A00 A
ð1Þ
where A is the total membrane area. It is more convenient to assume that the area is
E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97
one unit, but this does not mean of course that actual membrane area must be one unit. A0 and A00 are area fractions corresponding to highly and slightly permeable membranes (A0 þ A00 = A), and lp0 and lp00 are the hydrodynamic permeabilities of these membranes, respectively. It is also easy to show that the retention coefficient of that membrane at any working pressure is expressed as R¼1
A0 lp 0 ð1 R0 Þ þ A00 lp 00 ð1 R00 Þ A0 lp 0 þ A00 lp 00
ð2Þ
where R0 and R00 are corresponding retention coefficients of the constituting membranes at a given pressure (volume flux). Because the trial runs have been performed over a comparatively wide range of working pressure variation (see Experimental section), it is necessary to take into account the concentration polarization effect. The reason is that this phenomenon can play a considerable role in determining actual retentive properties of membranes, especially those characterized by a high hydrodynamic permeability [1,2,4]. To examine its effect (i.e. to find out the intrinsic retention coefficient), Colton’s relationships have been used [7]. 3. Experimental Experimental runs have been performed in a crossflow unit equipped with a stirred batch cell modified to work in a continuous mode. The membrane area in this cell was 30.18 cm2. To reduce the concentration polarization effect, the cell was equipped with a magnetic stirrer. Its rotation rate was set at 500(5) rpm over all the trial runs and controlled by tachometry (TCt100). Sucrose of pharmaceutical grade was chosen as a testing solute. The reasons for this choice were as follows. First, sucrose is easily definable
91
analytically (interferometry carried out with the ITR-2 interferometer was used for this purpose). Next, this solute is quite perceptibly retained by the ultrafiltration membrane (the most finely porous ones of them) [1,8], and its retention coefficient gradually alters in the series of membranes we selected. We also tried to apply glucose, the molecular weight (180 Da, monosaccharide) of which is about half that of sucrose (342.3 Da, disaccharide) for this purpose, but its retention by the ultrafiltration membrane is too small to be acceptable in this paper (computation results were somewhat unreliable). Finally, because we have also used nanofiltration membranes, and these contain certain fixed-charge sites in their structure, it was desirable to keep any coulomb interactions out of the retention mechanism. The model advanced does not take into consideration these interactions, though they can play very important role in determining retentivity of ionic solutes, particularly at low concentrations [1,4,6]. To keep its concentration in the feed (10 g/l) virtually constant (i.e. to facilitate the corresponding calculations), the retentate stream was returned back to the feed tank. Its volume (10 l) was considerably greater than that of the sum of the permeate samples. The latter did not surpass 150 ml in any single trial we carried out. A number of reverse osmosis and ultrafiltration membranes made of cellulose acetate (Vladipor series, Russia) as well as two nanofiltration ones (the same vendor, but their composition was not given except that they consist of polymers with a weak ion-exchange capacity) have been tested for their separative characteristics. Some of the structural and semipermeable characteristics of these membranes are listed in the Table below. Retention coefficient and volume flux (or hydrodynamic permeability) of membranes
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E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97
under study have been determined by a conventional method [6]. The following should also be emphasized. On the one hand, we needed to study and to compare membranes greatly differing in their separative characteristics and designed to function over quite different working pressure ranges. On the other hand, it was very important to carry out the comparison over the same pressure range. Certainly, to rule out of membrane destruction, the upper limit cannot be too high. Further, excessive working pressures result in a high compaction of membranes. This is quite evident from the data represented in Table 1. As a result, their structure and retentive performance dramatically change, particularly those of ultrafiltration membranes. Taking into account these facts and foreseeable consequences from them, we selected a compromise range in varying working pressure: 1–25 bar. The upper pressure greatly surpasses that typically used in ultrafiltration (as a rule, 5 bar) [1,2]. Nonetheless, in our quite great
and long-term investigation ultrafiltration membranes of precisely this series under elevated pressure (even up to 100 bar), we actually did not meet failures at such pressures. All the membranes under test needed adequate pretreatment under heightened pressure. For that reason, the membranes have been pressurized with distilled water under a pressure of 30 bar until their hydrodynamic permeability did not vary with time. Most of their characteristics indeed altered to great extent after such their pretreatment (compare data in numerator and denominator in Table 1). 4. Results and discussion Fig. 1 shows the variation of the observed and intrinsic sucrose retention coefficient (a) and volume flux (b) versus working pressure for all the membranes under study. The trends in variation of these key separative parameters are quite ordinary: both increase with working pressure. The extreme variation in the observed retention coefficient found
Table 1 Some characteristics of semipermeable membranes under test Membrane Reverse osmosis membranes MGA-100 MGA-95 MGA-90 MGA-80 MGA-70 Ultrafiltration membranes UAM-50 UAM-100 UAM-150 Nanofiltration membranes OFMN-P OPMN-K
Total thickness, mm1
Total voidage
Hydrodynamic permeability, lp 107, m/(s bar)
Retention plateau coefficient of sucrose
101/60 102/59 115/58 102/47 95/50
0.79/0.55 0.79/0.51 0.80/0.49 0.81/0.48 0.80/0.50
0.66/0.62 0.83/0.79 1.45/1.20 3.05/2.45 4.33/2.82
0.994 0.989 0.975 0.942 0.915
110/54 105/79 105/50
0.79/0.50 0.80/0.51 0.80/0.52
11.91/6.72 24.15/12.03 55.31/28.24
0.422 0.230 0.081
97/61 96/62
0.81/0.53 0.82/0.51
4.88/4.01 5.01/4.93
0.821 0.771
1 The numerator and denominator give respectively the characteristics inherent to the initial membrane samples and those after their compression under a working pressure of 30 bar.
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E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97 (a) 1 1 2 0.8
Retention coefficient
3
0.6 4
5 0.4
9
0.2
6 7
10
8 0 0
5
10
15
20
25
5
10
15
20
25
(b)
Volume flux × 106, m/s
30
20
10
0 0
Working pressure, bar
Fig. 1. Experimentally established dependencies of the observed (solid lines) and true (dotted lines) retention coefficients of sucrose (a) and the volume flux (b) versus working pressure on the MGA-100 (1), MGA-95 (2), MGA-90 (3), MGA-80 (4), MGA-70 (5), UAM-50 (6), UAM-100 (7), UAM-150 (8), OFMN-P (9), and OPMNK (10) membranes.
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with more permeable ultrafiltration membranes is due to the concentration polarization effect [1,9]. Regarding the intrinsic retention coefficient, it reaches a plateau with all the membranes, as is predicted by any mass transport theory of pressure-driven membrane methods [1,2,4]. As we expected, separative parameters of nanofiltration membranes, occupy an intermediate range between reverse osmosis and ultrafiltration membranes. It should be emphasized that this range is relatively wide. Apart from this remark, there are no other distinctions in principle between reverse osmosis membranes, on the one hand, and ultrafiltration ones, on the other hand. Taking into account the data represented in Table 1, it is quite evident that separative parameters showed by nanofiltration membranes should fall just between those of reverse osmosis and ultrafiltration membranes, and those indeed fall there (Fig. 1). As there are not any essential differences between all the membranes under study, we can thus select any of them to use as the constituents of an imaginary heteroporous structure such as the one described above. The number of foreseeable variants is high, actually it is infinitely large, but we limit ourselves to two membranes which are situated almost at the two opposite sides of the series investigated: MGA-95 and UAM-100. Again, there may be any number of variants as concerns the position occupied by each of them in that imaginary structure, (bearing in mind that their sum cannot differ from unity). However, it is not difficult to be convinced that these ‘partners’ are not equivalent in the contribution of each over all the variation range, and it is more interesting to have a closer look at the role played by the more permeable and less retentive constituent. Computation results shown in Fig. 2 clearly testify to the above. Varying the
relative fraction of any of two membranes (their relative parts are firmly interrelated themselves), we reach trends in changing volume flux and observed and intrinsic retention coefficients versus working pressure which are like much to those portrayed in Fig. 1. Some differences are observed at low working pressures: the retention coefficient versus working pressure dependences in Fig. 1(a) vary more sharply as compared with those in Fig. 2(a). That is to be expected nonetheless if we take into account the considerable oversimplification of the approach we advanced. It is too ‘mechanistic’ for the simple reason that it is too simple. If the latter may be considered as its advantage, the former naturally is its deficiency. The above difference, for example, might be caused by a number of reasons, the most important among them is likely the fact that we have neglected the role of the Peclet number of the internal membrane [3,10]. At any rate, the above model does not claim to provide a general approach to pressure-driven membrane transport answering all the questions open to discussion at present. Its role is quite limited, but some consequences of it appear to be of interest. Therefore, let us pay attention to these interesting facets of this approach. Above all, it clearly illustrates that minor imperfections in the membrane structure can dramatically impair its semipermeable characteristics. It seems there is no sense in analyzing in detail any of variants depicted in Fig. 2, because these are sufficiently convincing. However, a few inferences that follow from results are worth noting. First, the increase in the retentivity of a membrane may not be due to decreasing its pore size but rather to excluding several defective sites and zones (micro and macro defects). In each particular case, their origin may differ: ranging from problems associated
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Retention coefficient
0.8
3 4
0.6 5 0.4 6
0.2 7 8 9
0 0
5
10
15
20
25
10
15
20
25
(b)
Volume flux × 106, m/s
30
20
10
0 0
5
Working pressure, bar
Fig. 2. Dependencies of the observed (solid lines) and true (dotted lines) retention coefficients of sucrose (a) and the volume flux (b) versus working pressure on the MGA-95 (1) and UAM-100 (7) membranes as well as these dependencies calculated according to the heteroporous membrane model consisting of the membranes (1) and (2) at their ratio of 199/1 (3), 99/1 (4), 98 (5), 95/5 (6), 90/10 (7), 75/25 (8), and 50/50 (9), respectively.
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with the proper/improper synthesis of a membrane structure to problems associated with its particular application. In the former case, it is necessary to follow manufacturing protocol thoroughly and, in the latter, there are a great number of foreseeable problems. Many of them can be averted to a great extent by adequate pretreatment of solutions to be treated by the pressure-driven membrane methods. Continuing with this approach, that is, considering problems associated with damaging membrane structure during its operation, the positive role of the dynamically formed structures [1,8,11] becomes clearer. If the membrane contains such imperfect sites in its structure, or these have been generated during its functioning, the local transmembrane fluxes essentially increase here. As a result, transport of dispersed matter (i.e. properly the dynamic membrane forming additive) to such imperfect sites becomes more intense and, finally, there takes place their overlapping/plugging/healing, etc. One more inference is the important role of pressure-driven membrane technology such as membrane fractionation [1,8]. A minor inconsistency in size ratios of dispersed matter and membrane pores results in total failure of the method. Further, the operating conditions are of great importance. Therefore, to succeed in solving such problems, it is necessary either to use a semipermeable membrane without any defects/imperfections (i.e. that characterized by a highly regular/homogeneous structure) or to modify it in a purposeful way [8]. In the latter case, there are a great number of as yet unanswered problems. Nevertheless, the above results may held in reexamining this problem. One can reach likely some other fairly important conclusions and inferences from the above model, despite its oversimplified character. We again use the term
‘oversimplified’ to emphasize that this model may be expanded. It is not difficult to provide that the number of constituents in the heteroporous membrane model may be any number: two, three, four, etc. and to modify Eqs. (1) and (2) accordingly. The single fact that cannot be overlooked is that the sum of membrane area fractions cannot differ from unity. In so doing, one can reach better agreement with actual data but, before doing that, it should be kept in mind that the above approach is far from that covering all the theoretical arguments. 5. Conclusions (1) The so-called heteroporous membrane model consisting of two membranes differing in their separative parameters is advanced. This model may consist of any reasonable number of constituents. (2) Verification of that model using a number of industrial reverse osmosis and ultrafiltration membranes made of cellulose acetate as well as nanofiltration ones shows a reasonable agreement between experimental results and theoretical premises despite the somewhat mechanistic character of the approach advanced. (3) The model provides a means to reexamine the role played by minor imperfections in the membrane structure. (4) Proper understanding of that role provides a means to find and to fix similar problems.>
References [1] M.T. Bryk, E.A. Tsapiuk, Ultrafiltration, Kyiv, Naukova Dumka, 1989. [2] M. Mulder, An introduction into membrane technology, Moscow, Mir, 1999 (Russian translation). [3] E.A, Tsapiuk M.T, Bryk, An interpretation of the seperation of low and high molecular weight solutes by ultrafiltration, J. Membrane Sci., 79 (1993), 227–240.
E. Tsapiuk, L. Melnyk / Desalination 184 (2005) 89–97 [4] R.W. Baker, Membrane Technology and Application, New York, McGraw-Hill, 2000. [5] A.G. Fane, C.J.D. Fell, A.J. Waters, The relationship between membrane surface pore characteristics and flux of ultrafiltration membranes, J. Membrane Sci., 9 (1981) 245–263. [6] W. Pusch, Measurements techniques of transport through membranes, Desalination, 59 (1986) 105–198. [7] D.D. Do, A.A. Elhassadi, A theory of limiting flux in a stirred bath cell, J. Membrane Sci., 25 (1985) 113–132. [8] E. Tsapiuk, V. Kochkodan, V. Badekha, Change in molecular weight retetion curves of
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ultrafiltration membranes with respect to lignosulfonates under gel formation conditions, Ibid, 210 (2002) 183–196. [9] E.A. Tsapiuk, Ibid., Ultrafiltration separation of aqueous solutions of poly (ethylene glycol)s on the dynamic membrane formed by gelatin, 116 (1996) 17–29. [10] B.V. Deryaguin, N.V. Churaev, G.A. Martunov, V.M. Starov, Solution sepration theory by means of reverse osmosis, Khim. Tekhnol. Vody. 3 (1981) 99–104. [11] G.B. Tanny, Dynamic membranes in ultrafiltration and reverse osmosis, Sep. Purif. Methods, 7 (1978) 183–220.