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Coupled series–parallel resistance model for transport of solvent through inorganic nanofiltration membranes
Separation and Purification Technology 70 (2009) 46–52
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Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
Coupled series–parallel resistance model for transport of solvent through inorganic nanofiltration membranes Siavash Darvishmanesh a,∗ , Anita Buekenhoudt b , Jan Degrève a , Bart Van der Bruggen a a
Department of Chemical Engineering, Laboratory for Applied Physical Chemistry and Environmental Technology, Katholieke Universiteit Leuven, W. de Croylaan 46, B-3001 Leuven, Belgium Process Technology, Flemish Institute for Technological Research, Boeretang 200, 2400 Mol, Belgium
b
a r t i c l e
i n f o
Article history: Received 6 May 2009 Received in revised form 14 August 2009 Accepted 19 August 2009 Keywords: Nanofiltration Organic solvent Ceramic membrane Modeling Viscosity Surface tension Dielectric constant
a b s t r a c t In this work, permeation of a number of different classes of solvents through commercial TiO2 and ZrO2 ceramic nanofiltration membranes was measured. A wide variety in permeate flux levels were observed. Solvent permeation was found to be a function of solvent characteristics (viscosity, surface tension, effective molecular diameter and dielectric constant) along with membrane characteristics (surface tension, average pore size diameter and dielectric constant). This paper also presents a new mathematical model based on parallel convection–diffusion theory which relates permeation of solvent molecules to three different resistances in the surface and the main body of the membrane. Transport resistances are defined by easily measurable solvent and membrane properties as indicated above. The model was tested on a series of permeability experiments of water, acetonitrile, methanol, methyl ethyl ketone, ethylacetate, ethanol, tetrahydrofuran, 1-propanol, 1-butanol, toluene, cyclohexane and n-hexane, carried out with HITK275 and HITK2750 membranes (Inoceramic, Germany). Compared to the existing models, which are able to make predictions only for a given class of solvents (polar or apolar), the new model can surprisingly fit the results of the permeation study for all solvent classes, and even for water. The maximum deviation from experimental results was calculated as 4.8%. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Nanofiltration (NF) of organic liquids appears a promising separation tool in chemical industry. Different membrane manufactures produce their own solvent resistant polymeric membranes but none of these membranes can cover all the potential applications, due to the lack of chemical resistance of these membranes, although good result were obtained for specific application [1]. Experimental observations [2], physico-chemical characterization [3–5] as well as semi-empirical models [6–8] have shown that permeation of organic solvents through polymeric nanofiltration is not based solely on viscous-flow or simple molecular diffusion but depends on additional parameters due to interaction phenomena between the solvent and the membrane (surface tension, polarity, solubility of penetrants in membrane, resistance to swelling, hydrophilicity or hydrophobicity of interfaces). Compared to polymeric NF membranes, inorganic membranes have excellent chemical and mechanical stability toward solvents.
∗ Corresponding author. Tel.: +32 16 33 49 49; fax: +32 16 32 29 91. E-mail address: [email protected] (S. Darvishmanesh). 1383-5866/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.seppur.2009.08.011
In addition, their stability at high temperatures make them specific for membrane separations [9]. Until now, ceramic membranes have been manufactured successfully for aqueous and non-aqueous system application. At the side of membrane manufacturing, a performance study of NF membrane is essential for the design and optimization of filtration processes. This knowledge will be applied to generate a mathematical model, which reduces the number of experiments necessary to assess an application and consequently save time and money. In literature, different mathematical models have been used to predict transport of solvents through polymeric NF membranes. In most cases, solution-diffusion and pore flow models have been used to fit the experimental data [1,2,8,10–14]. A literature study shows that permeation of organic solvents through membranes does not simply follow the traditional models generally used in aqueous media. The origin of this deviation can be found in physicochemical interaction parameters occurring between solvent and membrane material. As pioneer in solvent resistant nanofiltration (SRNF) modeling, Machado et al. [7] developed the semi-empirical resistance-in series model based on resistance-in series to describe transport of solvents through thin film composite NF membranes. Resistances were defined as viscous-flow in both the NF-layer and the UF-support-layer, and a hydrophilic/hydrophobic resis-
S. Darvishmanesh et al. / Separation and Purification Technology 70 (2009) 46–52
tance at the membrane surface. Bhanushali et al. [8] introduced a model based on solution-diffusion theory. The sorption behavior of solvent in membrane plus solvent viscosity and the difference in surface tension of membrane and solvent were defined as key transport parameters. Cuperus and Ebert [15] and Geens [16] have identified the shortcomings of these models. Geens et al. [17] introduced another semi-empirical model, stating that solvent flux is dependent on viscosity, molecular size and the difference in surface tension between the membrane and the solvent. Guizard et al. [18] studied the permeability of pure organic solvents (ethanol, heptane and toluene) through composite ceramic oxide NF membranes (3Al2 O3 –2ZrO2 , SiO2 –ZrO2 , SiO2 –TiO2 ). Ethanol fluxes through membranes were higher than heptane and toluene fluxes. By comparison of fluxes for the different investigated solvent and NF membranes, they concluded that the (Si–Ti)-based membrane was best adapted for paraffinic solvents, the (Al–Zr) for polar and the (Si–Zr) for aromatic solvents. What can be concluded from the literature study is that the membrane performance is determined by its solvent through their solvent affinity. As mentioned previously, several variables were assumed to have effect on permeability. These variables can be generally classified into three categories, namely: solvent properties (polarity of the solvent, viscosity of the solvent, surface tension of solvent, solvent molar volume (size),. . .), membrane properties (surface energy of the membrane, swelling of membrane, pore size, MWCO,. . .) and process variables (feed temperature, feed concentration,. . .). It should be noted that the majority of research efforts in description and modeling of solvent transport through NF was conducted in polymeric membranes. However, there are some attempts in literature for ceramic membranes as well. Tsuru et al. [19] applied the Spiegler–Kedem equation to distinguish the contribution of diffusion and convection in filtration of aqueous feed solution containing a different solvent. Their study was performed on (Si–Zr) membranes with different MWCO values. They also state that the solvent permeation mechanism through silica–zirconia (Si–Zr) membranes is different from the viscous-flow mechanism [20] due to reduction of the membrane’s pore size through solvent adsorption [21]. Later they reported that experimental results of alcohol permeation through hydrophobic trimethylchlorosilane-modified (Si–Zr) membranes could be successfully fitted by the use of Darcy’s law, corresponding to viscous-flow mechanism holds for these membranes [22]. In a previous study [23], a general model for prediction of organic solvents permeation through tight nanoporous polymeric and ceramic nanofiltration membranes was developed. However, this model does not include a description of transport through loose nanoporous membranes. Furthermore, there is a large difference between the experimental water flux and the calculated one. It is evident that this cannot be described by a two-parameter model, in spite of the model’s proven predictive power for transport of organic solvent through tight nanoporous NF membranes. One way to extend the existing model is to attempt to include an additional parameter that describes size effects in filtration (pore size of membrane, effective diameter of solvent, etc.). In this paper, permeation of wide range organic solvents and water through both dense and
47
Fig. 1. Nanofiltration equipment for use with organic solvents.
loose nanoporous ceramic NF membranes will be measured, which leads to a new and generalized model for SRNF. 2. Materials and methods 2.1. Solvents The solvents used for this study were water, acetonitrile, methanol, methyl ethyl ketone, ethylacetate, ethanol, tetrahydrofuran, 1-propanol, 1-butanol, toluene, cyclohexane, n-hexane. All solvents were analytical grade and were supplied by Chem-Lab NV (Belgium). Distilled water was used in the experiments. 2.2. Membranes The commercial membranes used in the experiments were HITK275 and HITK2750 (Inoceramic, Germany), which are hydrophilic ceramic membranes consisting of a TiO2 and ZrO2 top layer, respectively. The HITK ceramic tubes had an inner diameter of 6.8 mm, and an effective membrane length of 12 cm. The surface tension of the membrane was measured by contact angle measurements, performed with a Drop Shape Analysis System DSA 10 Mk2 (Krüss). The sessile drop method was chosen and the contact angle was measured in equilibrium mode: a droplet of water and diiodomethane (CH2 I2 ) is placed on the membrane surface, after which the contact angle between the droplet and the membrane surface is calculated. Table 1 gives an overview on membranes and their common properties. 2.3. Membrane filtration cell Filtration experiments were carried out with a solvent compatible nanofiltration laboratory unit (Fig. 1). A cross flow filtration cell containing tubular module was used. The active surface of the ceramic membranes applicable for this module was 0.00194 m2 . Membrane module and the ceramic membrane are shown in Fig. 2. The applied pressure was 8 bar for the tight nanoporous ceramic membrane (HITK275) and 3 bar for the loose one (HITK2750). The permeate was collected in glass and weighted by a PC-connected balance, continuously. The retentate can be recycled to the tank.
Table 1 Membranes used in this study and membrane characteristic. Membrane
Material
MWCO (Da)
Pore diameter (nm)
Dielectric constanta
Surface tension
HITK275 HITK2750
TiO2 ZrO2
275 2750
0.9 3
86 12.5
54.7 30.9
a
Dielectric constant value taken from [18].
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Fig. 2. Membrane module used in experiments and membrane used inside the module.
Fig. 3. Ethanol flux as function of time.
Membranes were soaked for 24 h in a measuring solvent before measurement. Through interactions with the different organic solvent, it is possible that the structure of the membrane changes. Polymeric membranes may swell. Ceramic membranes do not swell, but adsorption of solvent molecules within the membrane may occur. To evaluate the stability of the permeability, the ethanol flux has been measured in the beginning, in the middle and in the end of solvent series. Ethanol was used as reference because it is miscible with all solvent used. After this, the procedure for solvent exchange was repeated with the next solvent in series. In this way the minimum of solvent remained in the membrane structure and in the filtration equipment. When the second ethanol flux in deviated from the previous one by more than 10%, all measurement were repeated until a reproducible flux obtained. The reproducibility of the obtain flux is shown in Fig. 3. The first ethanol flux was prior to series of solvents, the second ethanol flux was measured at the end. The temperature in all experiments was 25 ◦ C. The flux was calculated automatically by PC through the following equation:
Table 2 lists permeability values of solvents having different physical properties used in this study for two ceramic membranes with a different pore size, i.e. HITK275 and HITK2750. Physical properties were taken from the literature [25]. Table 2 shows that there are very significant variations in the solvent permeability from the differences in physical properties.
J (l/h m2 ) =
m (g) (1/) (cm3 /g) × 10−3 (l/cm3 ) t (h) A (m2 )
(1)
The experiment for each solvent was repeated with five different membranes. The experimental errors were up to 5%. 3. Results and discussion Solvent permeability can be expected to vary with changes in solvent properties such as surface tension, dielectric constant, molecular size, molar volume and viscosity parameter [6,14,23,24].
3.1. HITK275 As can be seen in Table 2, acetonitrile has the highest permeability compared to the other solvents; even water when 1-butanol with the highest viscosity has a lower permeability. HITK275 is a highly hydrophilic tight nanoporous membrane ( = 54.7), which is expected to show the highest permeability for water and the lowest permeability for n-hexane among the solvents used [26]. Higher fluxes are evident in the case of relatively polar solvents, such as water and acetonitrile, while lower fluxes are indicated in the case of non-polar solvents, such as toluene and cyclohexane. Surprisingly, n-hexane permeates faster than ethanol, which is a polar alcohol with a higher surface tension than n-hexane. Presumably, the lower viscosity value of n-hexane counterbalances the effect of surface tension. In case of solvents with similar viscosity (water and ethanol or methyl ethyl ketone and n-hexane), surface tension and dielectric constant as polarity value of solvent become more important. For solvents with similar surface tension and dielectric constant value (methyl ethyl ketone and 1-butanol) permeability depends on viscosity. The effect of the dielectric constant on solvent permeability appears to be important. The dielectric constant plays an important role for solvents with close amount of viscosity and surface tension (methyl ethyl ketone and ethylacetate). This
Table 2 Permeability of different solvent through HITK275 and HITK2750. Solvent
HITK275 permeability (l/h m2 bar)
HITK2750 permeability (l/h m2 bar)
Molecular weight (g/mol)
Effect diameter (nm)
Viscosity (mPa s)
Surface tension (mN/m)
Dielectric constant
Water Acetonitrile Methanol Methyl ethyl ketone Ethylacetate Ethanol Tetrahydrofuran 1-Propanol 1-Butanol Toluene Cyclohexane n-Hexane
23.1 29.50 13.50 12.10 7.70 3.20 5.90 0.90 0.50 2.30 1.90 8.20
93.00 109.90 86.70 114.60 88.60 28.70 67.50 9.50 7.60 5.80 14.30 12.90
18.00 41.10 32.00 72.10 88.10 46.10 72.10 60.10 74.10 92.10 84.20 86.20
0.21 0.37 0.27 0.63 0.71 0.34 0.59 0.39 0.69 0.50 0.66 0.46
1.00 0.34 0.54 0.39 0.42 1.08 0.46 2.06 2.63 0.55 0.88 0.33
72.8 28.66 22.12 23.96 23.24 21.99 24.98 21.01 24.41 27.92 24.65 17.98
78.2 35.70 33.00 18.20 6.00 24.90 7.50 19.30 17.30 2.40 2.00 1.90
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is possibly due to the relatively high values of the dielectric constant of ceramic material (TiO2 ). However, for solvents having a low dielectric constant, such as toluene and cyclohexane, this parameter could have a barely noticeable effect on permeate flux due to their low values of the dielectric constant compare to ceramic material. No clear correlation could be observed between permeability values and solvent molecular size. However, within the homologous series of alcohols it was found that permeability decreases with increasing the solvent molecular size. This is like what is observed in aqueous systems, of a decreasing solute permeation with an increasing solute molecular volume. As given in Table 2, in the case of HITK275, the permeability among solvent depends on viscosity, surface tension, dielectric constant and solvent molecular size. 3.2. HITK2750 Table 2 provides the permeability value Lp of HITK2750 for the same series of solvents as used for HITK275. As in seen at Table 2, for the loose nanoporous semi-hydrophilic HITK2750 ( = 30.9), the permeabilities of methyl ethyl ketone and acetonitrile are higher than for the other solvent. Methyl ethyl ketone and acetonitrile have very low viscosity values with surface tension and dielectric constant value close to surface tension and dielectric constant of the HITK2750 membrane. So the membrane shows more affinity toward these solvents. Here again the permeability of alcohols decrease by increasing the viscosity. Similar permeabilities were expected for solvent with the same viscosity since the membrane is loose nanoporous, and viscosity is the key transport parameter. However, a large difference between water and ethanol permeabilities or methyl ethyl ketone and n-hexane permeabilities with the same viscosity has been observed. It confirms that for loose nanoporous ceramic NF membranes, polarity still plays an important role in solvent permeation. Molecules with high affinity toward the membrane material would tend to stick and slip at the pore walls. So solvent permeation mechanism through loose nanoporous ceramic membranes is different from the viscous-flow mechanism due to reduction of the membrane’s pore size [21]. From the above discussion for solvent permeation through tight nanoporous and loose nanoporous ceramic membranes, it seems reasonable to assume that combined viscous, polarity and solvent molecular size, represented by solvent viscosity, surface tension, dielectric constant and solvent effective molecular diameter determine solvent permeation through the tight nanoporous ceramic NF membranes. 4. Model development In the literature, it is often found that in SRNF transport through the membrane cannot be described solely by diffusion approach [27]. Bhanushali et al. [28] determined the percentage of diffusive and convective transport of the solvents through hydrophobic NF membranes by using the Spiegler–Kedem model. They found that viscous transport is higher for low retention solutes. Robinson
49
Fig. 4. Representation of a NF active layer.
et al. [13] found that the permeability of pure alkanes and aromatics through a laboratory made PDMS membrane follows the Hagen–Poiseuille law. The convective transport has been taken into account in diffusive transport through the solution-diffusion with imperfections model. This model is an extension of the solutiondiffusion model taking into account the occurring convective flow through imperfections in the membrane by adding an extra term for the convective flow to the solution-diffusion model [29]. Typically, a solution-diffusion with imperfection based model use the following approach: Permeability ˛ Solubility · Diffusivity + Convectivity
(2)
NF membranes combine a high selectivity of a dense top layer with high permeation rate of a very thin support layer. So permeability mainly depends on NF top layer properties. As illustrated in Fig. 4, the active layer of NF composite membrane may also be assumed to consist of two different parts: (I) membrane matrix, and (II) nanoporous. Transport occurs through the ceramic material and through pores simultaneously. So the proportion of diffusivity and convectivity depends directly on the membrane structure. On the one hand, as the pore size of the membrane decreases, the membrane becomes tighter. Consequently, solubility, diffusivity and molecular forces at the interface become important [6]. On the other hand, for porous structures with large pore size the viscosity of solvent has a significant influence [30]. As indicated schematically in Fig. 5 the permeation of solvent molecules through a membrane consist of three main steps: (1) transfer of solvent molecules to the top active layer, which is characterized by a surface resistance Rs , (2) viscous-flow through NF nanopores, which is characterized as pore resistant (viscous resistance), Rp and (3) diffusive flow through the membrane ceramic material, Rm , which is characterized by a matrix resistance. A surface resistance is the difference between molecular forces at the interface. The overall resistance of the active layer is represented at left side of Fig. 5, which consists of an outer surface resistance Rs in series, followed by two resistances in parallel inside the membrane. To find the total amount of parallel resistance, the reciprocals of the Rp and Rm should be added together. The reciprocal of the sum is the total resistance which should be added to Rs
Fig. 5. Representation of the resistant encountered by a solvent molecule through the NF ceramic membrane.
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S. Darvishmanesh et al. / Separation and Purification Technology 70 (2009) 46–52 Table 3 Parameters necessary for the modeling.
to find the overall membrane resistance, Roveral Roveral = Routside the membrane + Rinside the membrane
(3)
Eq. (3) shows that the total resistance consists of the resistance on surface of membrane plus the resistance inside the membrane. Roveral = Rs +
Rm × Rp Rm + Rp
(4)
Total solvent flux through the membrane is given by: J=
P
(5)
Roveral
The surface resistance arises from differences in surface energy between the solvent molecules and the ceramic membrane surface [6–8,17,31] and also the porosity of membrane. It is assumed that the surface resistance increases with decreasing pore size and increasing solvent molecular size [6,32]. Machado et al. [7] and Geens et al. [17] related the solvent permeation in membrane matrix to the reciprocal of the surface energy difference (). The effect of surface tension should not lead to an infinite flux in case of identical surface tensions. The surface tension of solvent and polymer has been chosen as solvent–membrane interaction parameter. From the literature [7,17], it is clear that surface tension also has effect on both diffusive and viscous permeability parameters. However, the effect of surface tension should not lead to an infinite flux in case of identical surface tensions. Darvishmanesh et al. [33] considered the effect of surface tension in the view of the mathematical integrity as exp(1 − ˇ) instead of (). ˇ is the ratio of the surface tension of the membrane and solvent. ˇ is calculated as: ˇhydrophilic membrane =
L (surface tension of solvent) M (surface tension of membrane)
ˇhydrophobic hydrophobic =
M (surface tension of the membrane) L (surface tension of solvent)
(exp(1 − ˇ))
Surface resistance constant, Ks (Eq. (8)) Matrix resistance constant, Km (Eq. (12)) Pore resistance constant, Kp (Eq. (13)) Viscosity of solvents Solvent size Membrane pore size Dielectric constant of solvent Dielectric constant of membranes Surface tension of solvent Surface tension of membrane
Estimated during modeling Estimated during modeling Estimated during modeling Literature data Calculated from [34] Manufacture data sheet Literature data from [25] Literature data from [18] Literature data from [25] Determined with DSA 10 Mk2 (Krüss)
for the solubility parameter, which shows solvent affinity to the membrane. Polarity could be expressed as dielectric constant, which is an easy measurable physical property. Non-dimensional polarity coefficients (˛) for hydrophilic and hydrophobic SRNF membrane have been already presented elsewhere [33]. In case of ceramic membranes, this coefficient can be improved, since dielectric constant of ceramic membrane materials are available. The modified polarity coefficient for the hydrophilic and hydrophobic membrane is assumed as: Dielectric constant of solvent Dielectric constant of membrane
˛hydrophilic =
Dielectric constant of membrane Dielectric constant of solvent
(9)
˛hydrophobic =
(7)
Solvent diffusivity in the membrane matrix can be related to viscosity of solvent through the following approximation [8,36]:
2 rs rp
Obtained by
(6)
When the effect of surface tension, is combined with the effect of pore size (rp ) and solvent molecular size (rs ), one can obtain the following equation: Rs = ks
Parameter
(8)
where ks is a constant determined during the fitting. Rm presents the solubility and diffusivity resistance together. For the calculation of the molecular size, and energetic optimization procedure was used base on approach indicated elsewhere [34]. Reddy et al. [35] showed that the solubility parameter cannot correlate their experimental data. Polarity can be a relevant replacement
Diffusivity ˛
1
(10)
(11)
From the above approach, the ceramic matrix resistance, Rm is given by Rm = km
˛
(12)
is the viscosity of the solvent and km is a constant depends on porosity and tortuosity of the ceramic membrane. The value of Rm for tight pores membranes is lower than loose pores ones.
Fig. 6. Comparison of experimental and fitting value of the permeability of series solvent through a HITK275 ceramic membrane, using the new model.
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51
Fig. 7. Comparison of experimental and fitting value of the permeability of series solvent through a HITK2750 ceramic membrane, using the new model.
Finally, the pores resistance Rp is given base on the capillary flow approach:
2
Rp = kp
rs rp
(13)
kp is also a geometric membrane constant. The value of Rp for tight nanoporous membranes is higher than for loose nanoporous ones. The overall resistance Rm can be evaluated by substituting Eqs. (8), (12) and (13) in Eq. (4). The flux of solvent through membrane calculated by substituting, Rm in Eq. (5). Ks , Km and Kp are experimentally determined parameter. These results from permeation study were used to obtain the transport model coefficient. Therefore, the suggested transport model was implemented in mathematical computing software (Matlab R2006b) and a least square fit was used to obtain the values of the unknown parameters (Ks , Km and Kp ). In Table 3 the parameters necessary for the modeling are summarized. In attempts to correlate the extensive data obtained with Eq. (5), it was found that the constant parameters Ks , Km and Kp were constant for all solvents and each membrane type, and therefore, they characterize intrinsic membrane properties. The best regression values of Ks , Km and Kp were obtained for HITK275 and for HITK2750. Fig. 6 shows plot of permeability data measured for HTIK275. It can be seen that proposed model gives a very good fit to the experimental data. The model provides a reasonable approximation for the permeation data for different class of solvent through tight nanoporous ceramic membrane. Fig. 7 compares the calculated permeability data with the experimental data for HITK2750. HITK275 is made of TiO2 , which is a hydrophilic material. In contrast, HITK2750 is made of ZrO2 , a more hydrophobic material (as confirmed by contact angle measurement). In this context, it was appropriate to use the equation for hydrophobic membranes. The new model shows a very high correlation over the entire range of solvents. The new model did not show any problem when dealing with all different solvent, different number of varying solvent properties. The error variances were found to be between 0.5 and 4.2% for the new model. This confirms that the proposed model is able to predict the pure solvent flux for tight nanoporous and ceramic membrane rightly. 5. Conclusions The main objective of the current paper was to develop a model for predicting the flux of organic solvents permeating through ceramic NF membranes from membrane and solvent parameters.
A semi-empirical correlation is presented which describes solvent transport properties through a ceramic NF membrane, governed by surface, pore and membrane matrix resistances. The model embodies three fitting parameters, Ks , Km and Kp . The model have been evaluated for ceramic NF membranes. Two different ceramic membranes (tight and loose nanoporous) have been tested. A good fit for a large number of different solvent, was obtained. In conclusion, the semi-empirical model presented in this paper provides an appropriate framework for practical as well as theoretical research interest. Acknowledgment The Research Council of the K.U. Leuven is gratefully acknowledged for their financial support to this work (OT/2006/37). References [1] L.S. White, Transport properties of a polyimide solvent resistant nanofiltration membrane, Journal of Membrane Science 205 (1–2) (2002) 191–202. [2] X.J. Yang, A.G. Livingston, L. Freitas dos Santos, Experimental observations of nanofiltration with organic solvents, Journal of Membrane Science 190 (1) (2001) 45–55. [3] I.F.J. Vankelecom, et al., Physico-chemical interpretation of the SRNF transport mechanism for solvents through dense silicone membranes, Journal of Membrane Science 231 (1–2) (2004) 99–108. [4] J.D.B. Katleen Boussu, D. Charles, W. Marc, G.L. Kelvin, D. Diederik, A. Steliana, I.F.J. Vankelecom, C. Vandecasteele, B. Van der Bruggen, Physico-chemical characterization of nanofiltration membranes, ChemPhysChem 8 (3) (2007) 370–379. [5] L.E.M. Gevers, et al., Physico-chemical interpretation of the SRNF transport mechanism for solutes through dense silicone membranes, Journal of Membrane Science 274 (1–2) (2006) 173–182. [6] J. Geens, et al., Polymeric nanofiltration of binary water–alcohol mixtures: influence of feed composition and membrane properties on permeability and rejection, Journal of Membrane Science 255 (1–2) (2005) 255–264. [7] D.R. Machado, D. Hasson, R. Semiat, Effect of solvent properties on permeate flow through nanofiltration membranes: Part II. Transport model, Journal of Membrane Science 166 (1) (2000) 63–69. [8] D. Bhanushali, et al., Performance of solvent-resistant membranes for nonaqueous systems: solvent permeation results and modeling, Journal of Membrane Science 189 (1) (2001) 1–21. [9] K. Li, Ceramic Membranes for Separation and Reaction, John Wiley, Chichester, England; Hoboken, NJ, 2007, x, 306 p. [10] N. Stafie, D.F. Stamatialis, M. Wessling, Effect of PDMS cross-linking degree on the permeation performance of PAN/PDMS composite nanofiltration membranes, Separation and Purification Technology 45 (3) (2005) 220–231. [11] L.G. Peeva, et al., Effect of concentration polarisation and osmotic pressure on flux in organic solvent nanofiltration, Journal of Membrane Science 236 (1–2) (2004) 121–136. [12] E. Gibbins, et al., Observations on solvent flux and solute rejection across solvent resistant nanofiltration membranes, Desalination 147 (1–3) (2002) 307–313. [13] J.P. Robinson, et al., Solvent flux through dense polymeric nanofiltration membranes, Journal of Membrane Science 230 (1–2) (2004) 29–37.
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[26] B. Van der Bruggen, J. Geens, C. Vandecasteele, Fluxes and rejections for nanofiltration with solvent stable polymeric membranes in water, ethanol and n-hexane, Chemical Engineering Science 57 (13) (2002) 2511–2518. [27] M.F.J. Dijkstra, S. Bach, K. Ebert, A transport model for organophilic nanofiltration, Journal of Membrane Science 286 (1–2) (2006) 60–68. [28] D. Bhanushali, S. Kloos, D. Bhattacharyya, Solute transport in solvent-resistant nanofiltration membranes for non-aqueous systems: experimental results and the role of solute–solvent coupling, Journal of Membrane Science 208 (1–2) (2002) 343–359. [29] E.A. Mason, H.K. Lonsdale, Statistical–mechanical theory of membrane transport, Journal of Membrane Science 51 (1–2) (1990) 1–81. [30] R.W. Lencki, S. Williams, Effect of nonaqueous solvents on the flux behavior of ultrafiltration membranes, Journal of Membrane Science 101 (1–2) (1995) 43–51. [31] B. Van der Bruggen, et al., Determination of parameters affecting transport in polymeric membranes: parallels between pervaporation and nanofiltration, The Journal of Physical Chemistry B 108 (35) (2004) 13273–13279. [32] J.N. Israelachvili, Intermolecular and Surface Forces: with Applications to Colloidal and Biological Systems, 2nd ed., Academic Press, London, 1992, 450 p. [33] S. Darvishmanesh, et al., General model for prediction of solvent permeation through organic and inorganic solvent resistant nanofiltration membranes, Journal of Membrane Science 334 (1–2) (2009) 43–49. [34] B. Van der Bruggen, et al., Influence of molecular size, polarity and charge on the retention of organic molecules by nanofiltration, Journal of Membrane Science 156 (1) (1999) 29–41. [35] K.K. Reddy, et al., Membrane concentration and separation of l-aspartic acid and l-phenylalanine derivatives in organic solvents, Separation Science and Technology 31 (8) (1996) 1161–1178. [36] J.A. Wesselingh, A.M. Bollen, Multicomponent diffusivities from the free volume theory, Chemical Engineering Research and Design 75 (6) (1997) 590–602.
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Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
Coupled series–parallel resistance model for transport of solvent through inorganic nanofiltration membranes Siavash Darvishmanesh a,∗ , Anita Buekenhoudt b , Jan Degrève a , Bart Van der Bruggen a a
Department of Chemical Engineering, Laboratory for Applied Physical Chemistry and Environmental Technology, Katholieke Universiteit Leuven, W. de Croylaan 46, B-3001 Leuven, Belgium Process Technology, Flemish Institute for Technological Research, Boeretang 200, 2400 Mol, Belgium
b
a r t i c l e
i n f o
Article history: Received 6 May 2009 Received in revised form 14 August 2009 Accepted 19 August 2009 Keywords: Nanofiltration Organic solvent Ceramic membrane Modeling Viscosity Surface tension Dielectric constant
a b s t r a c t In this work, permeation of a number of different classes of solvents through commercial TiO2 and ZrO2 ceramic nanofiltration membranes was measured. A wide variety in permeate flux levels were observed. Solvent permeation was found to be a function of solvent characteristics (viscosity, surface tension, effective molecular diameter and dielectric constant) along with membrane characteristics (surface tension, average pore size diameter and dielectric constant). This paper also presents a new mathematical model based on parallel convection–diffusion theory which relates permeation of solvent molecules to three different resistances in the surface and the main body of the membrane. Transport resistances are defined by easily measurable solvent and membrane properties as indicated above. The model was tested on a series of permeability experiments of water, acetonitrile, methanol, methyl ethyl ketone, ethylacetate, ethanol, tetrahydrofuran, 1-propanol, 1-butanol, toluene, cyclohexane and n-hexane, carried out with HITK275 and HITK2750 membranes (Inoceramic, Germany). Compared to the existing models, which are able to make predictions only for a given class of solvents (polar or apolar), the new model can surprisingly fit the results of the permeation study for all solvent classes, and even for water. The maximum deviation from experimental results was calculated as 4.8%. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Nanofiltration (NF) of organic liquids appears a promising separation tool in chemical industry. Different membrane manufactures produce their own solvent resistant polymeric membranes but none of these membranes can cover all the potential applications, due to the lack of chemical resistance of these membranes, although good result were obtained for specific application [1]. Experimental observations [2], physico-chemical characterization [3–5] as well as semi-empirical models [6–8] have shown that permeation of organic solvents through polymeric nanofiltration is not based solely on viscous-flow or simple molecular diffusion but depends on additional parameters due to interaction phenomena between the solvent and the membrane (surface tension, polarity, solubility of penetrants in membrane, resistance to swelling, hydrophilicity or hydrophobicity of interfaces). Compared to polymeric NF membranes, inorganic membranes have excellent chemical and mechanical stability toward solvents.
∗ Corresponding author. Tel.: +32 16 33 49 49; fax: +32 16 32 29 91. E-mail address: [email protected] (S. Darvishmanesh). 1383-5866/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.seppur.2009.08.011
In addition, their stability at high temperatures make them specific for membrane separations [9]. Until now, ceramic membranes have been manufactured successfully for aqueous and non-aqueous system application. At the side of membrane manufacturing, a performance study of NF membrane is essential for the design and optimization of filtration processes. This knowledge will be applied to generate a mathematical model, which reduces the number of experiments necessary to assess an application and consequently save time and money. In literature, different mathematical models have been used to predict transport of solvents through polymeric NF membranes. In most cases, solution-diffusion and pore flow models have been used to fit the experimental data [1,2,8,10–14]. A literature study shows that permeation of organic solvents through membranes does not simply follow the traditional models generally used in aqueous media. The origin of this deviation can be found in physicochemical interaction parameters occurring between solvent and membrane material. As pioneer in solvent resistant nanofiltration (SRNF) modeling, Machado et al. [7] developed the semi-empirical resistance-in series model based on resistance-in series to describe transport of solvents through thin film composite NF membranes. Resistances were defined as viscous-flow in both the NF-layer and the UF-support-layer, and a hydrophilic/hydrophobic resis-
S. Darvishmanesh et al. / Separation and Purification Technology 70 (2009) 46–52
tance at the membrane surface. Bhanushali et al. [8] introduced a model based on solution-diffusion theory. The sorption behavior of solvent in membrane plus solvent viscosity and the difference in surface tension of membrane and solvent were defined as key transport parameters. Cuperus and Ebert [15] and Geens [16] have identified the shortcomings of these models. Geens et al. [17] introduced another semi-empirical model, stating that solvent flux is dependent on viscosity, molecular size and the difference in surface tension between the membrane and the solvent. Guizard et al. [18] studied the permeability of pure organic solvents (ethanol, heptane and toluene) through composite ceramic oxide NF membranes (3Al2 O3 –2ZrO2 , SiO2 –ZrO2 , SiO2 –TiO2 ). Ethanol fluxes through membranes were higher than heptane and toluene fluxes. By comparison of fluxes for the different investigated solvent and NF membranes, they concluded that the (Si–Ti)-based membrane was best adapted for paraffinic solvents, the (Al–Zr) for polar and the (Si–Zr) for aromatic solvents. What can be concluded from the literature study is that the membrane performance is determined by its solvent through their solvent affinity. As mentioned previously, several variables were assumed to have effect on permeability. These variables can be generally classified into three categories, namely: solvent properties (polarity of the solvent, viscosity of the solvent, surface tension of solvent, solvent molar volume (size),. . .), membrane properties (surface energy of the membrane, swelling of membrane, pore size, MWCO,. . .) and process variables (feed temperature, feed concentration,. . .). It should be noted that the majority of research efforts in description and modeling of solvent transport through NF was conducted in polymeric membranes. However, there are some attempts in literature for ceramic membranes as well. Tsuru et al. [19] applied the Spiegler–Kedem equation to distinguish the contribution of diffusion and convection in filtration of aqueous feed solution containing a different solvent. Their study was performed on (Si–Zr) membranes with different MWCO values. They also state that the solvent permeation mechanism through silica–zirconia (Si–Zr) membranes is different from the viscous-flow mechanism [20] due to reduction of the membrane’s pore size through solvent adsorption [21]. Later they reported that experimental results of alcohol permeation through hydrophobic trimethylchlorosilane-modified (Si–Zr) membranes could be successfully fitted by the use of Darcy’s law, corresponding to viscous-flow mechanism holds for these membranes [22]. In a previous study [23], a general model for prediction of organic solvents permeation through tight nanoporous polymeric and ceramic nanofiltration membranes was developed. However, this model does not include a description of transport through loose nanoporous membranes. Furthermore, there is a large difference between the experimental water flux and the calculated one. It is evident that this cannot be described by a two-parameter model, in spite of the model’s proven predictive power for transport of organic solvent through tight nanoporous NF membranes. One way to extend the existing model is to attempt to include an additional parameter that describes size effects in filtration (pore size of membrane, effective diameter of solvent, etc.). In this paper, permeation of wide range organic solvents and water through both dense and
47
Fig. 1. Nanofiltration equipment for use with organic solvents.
loose nanoporous ceramic NF membranes will be measured, which leads to a new and generalized model for SRNF. 2. Materials and methods 2.1. Solvents The solvents used for this study were water, acetonitrile, methanol, methyl ethyl ketone, ethylacetate, ethanol, tetrahydrofuran, 1-propanol, 1-butanol, toluene, cyclohexane, n-hexane. All solvents were analytical grade and were supplied by Chem-Lab NV (Belgium). Distilled water was used in the experiments. 2.2. Membranes The commercial membranes used in the experiments were HITK275 and HITK2750 (Inoceramic, Germany), which are hydrophilic ceramic membranes consisting of a TiO2 and ZrO2 top layer, respectively. The HITK ceramic tubes had an inner diameter of 6.8 mm, and an effective membrane length of 12 cm. The surface tension of the membrane was measured by contact angle measurements, performed with a Drop Shape Analysis System DSA 10 Mk2 (Krüss). The sessile drop method was chosen and the contact angle was measured in equilibrium mode: a droplet of water and diiodomethane (CH2 I2 ) is placed on the membrane surface, after which the contact angle between the droplet and the membrane surface is calculated. Table 1 gives an overview on membranes and their common properties. 2.3. Membrane filtration cell Filtration experiments were carried out with a solvent compatible nanofiltration laboratory unit (Fig. 1). A cross flow filtration cell containing tubular module was used. The active surface of the ceramic membranes applicable for this module was 0.00194 m2 . Membrane module and the ceramic membrane are shown in Fig. 2. The applied pressure was 8 bar for the tight nanoporous ceramic membrane (HITK275) and 3 bar for the loose one (HITK2750). The permeate was collected in glass and weighted by a PC-connected balance, continuously. The retentate can be recycled to the tank.
Table 1 Membranes used in this study and membrane characteristic. Membrane
Material
MWCO (Da)
Pore diameter (nm)
Dielectric constanta
Surface tension
HITK275 HITK2750
TiO2 ZrO2
275 2750
0.9 3
86 12.5
54.7 30.9
a
Dielectric constant value taken from [18].
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Fig. 2. Membrane module used in experiments and membrane used inside the module.
Fig. 3. Ethanol flux as function of time.
Membranes were soaked for 24 h in a measuring solvent before measurement. Through interactions with the different organic solvent, it is possible that the structure of the membrane changes. Polymeric membranes may swell. Ceramic membranes do not swell, but adsorption of solvent molecules within the membrane may occur. To evaluate the stability of the permeability, the ethanol flux has been measured in the beginning, in the middle and in the end of solvent series. Ethanol was used as reference because it is miscible with all solvent used. After this, the procedure for solvent exchange was repeated with the next solvent in series. In this way the minimum of solvent remained in the membrane structure and in the filtration equipment. When the second ethanol flux in deviated from the previous one by more than 10%, all measurement were repeated until a reproducible flux obtained. The reproducibility of the obtain flux is shown in Fig. 3. The first ethanol flux was prior to series of solvents, the second ethanol flux was measured at the end. The temperature in all experiments was 25 ◦ C. The flux was calculated automatically by PC through the following equation:
Table 2 lists permeability values of solvents having different physical properties used in this study for two ceramic membranes with a different pore size, i.e. HITK275 and HITK2750. Physical properties were taken from the literature [25]. Table 2 shows that there are very significant variations in the solvent permeability from the differences in physical properties.
J (l/h m2 ) =
m (g) (1/) (cm3 /g) × 10−3 (l/cm3 ) t (h) A (m2 )
(1)
The experiment for each solvent was repeated with five different membranes. The experimental errors were up to 5%. 3. Results and discussion Solvent permeability can be expected to vary with changes in solvent properties such as surface tension, dielectric constant, molecular size, molar volume and viscosity parameter [6,14,23,24].
3.1. HITK275 As can be seen in Table 2, acetonitrile has the highest permeability compared to the other solvents; even water when 1-butanol with the highest viscosity has a lower permeability. HITK275 is a highly hydrophilic tight nanoporous membrane ( = 54.7), which is expected to show the highest permeability for water and the lowest permeability for n-hexane among the solvents used [26]. Higher fluxes are evident in the case of relatively polar solvents, such as water and acetonitrile, while lower fluxes are indicated in the case of non-polar solvents, such as toluene and cyclohexane. Surprisingly, n-hexane permeates faster than ethanol, which is a polar alcohol with a higher surface tension than n-hexane. Presumably, the lower viscosity value of n-hexane counterbalances the effect of surface tension. In case of solvents with similar viscosity (water and ethanol or methyl ethyl ketone and n-hexane), surface tension and dielectric constant as polarity value of solvent become more important. For solvents with similar surface tension and dielectric constant value (methyl ethyl ketone and 1-butanol) permeability depends on viscosity. The effect of the dielectric constant on solvent permeability appears to be important. The dielectric constant plays an important role for solvents with close amount of viscosity and surface tension (methyl ethyl ketone and ethylacetate). This
Table 2 Permeability of different solvent through HITK275 and HITK2750. Solvent
HITK275 permeability (l/h m2 bar)
HITK2750 permeability (l/h m2 bar)
Molecular weight (g/mol)
Effect diameter (nm)
Viscosity (mPa s)
Surface tension (mN/m)
Dielectric constant
Water Acetonitrile Methanol Methyl ethyl ketone Ethylacetate Ethanol Tetrahydrofuran 1-Propanol 1-Butanol Toluene Cyclohexane n-Hexane
23.1 29.50 13.50 12.10 7.70 3.20 5.90 0.90 0.50 2.30 1.90 8.20
93.00 109.90 86.70 114.60 88.60 28.70 67.50 9.50 7.60 5.80 14.30 12.90
18.00 41.10 32.00 72.10 88.10 46.10 72.10 60.10 74.10 92.10 84.20 86.20
0.21 0.37 0.27 0.63 0.71 0.34 0.59 0.39 0.69 0.50 0.66 0.46
1.00 0.34 0.54 0.39 0.42 1.08 0.46 2.06 2.63 0.55 0.88 0.33
72.8 28.66 22.12 23.96 23.24 21.99 24.98 21.01 24.41 27.92 24.65 17.98
78.2 35.70 33.00 18.20 6.00 24.90 7.50 19.30 17.30 2.40 2.00 1.90
S. Darvishmanesh et al. / Separation and Purification Technology 70 (2009) 46–52
is possibly due to the relatively high values of the dielectric constant of ceramic material (TiO2 ). However, for solvents having a low dielectric constant, such as toluene and cyclohexane, this parameter could have a barely noticeable effect on permeate flux due to their low values of the dielectric constant compare to ceramic material. No clear correlation could be observed between permeability values and solvent molecular size. However, within the homologous series of alcohols it was found that permeability decreases with increasing the solvent molecular size. This is like what is observed in aqueous systems, of a decreasing solute permeation with an increasing solute molecular volume. As given in Table 2, in the case of HITK275, the permeability among solvent depends on viscosity, surface tension, dielectric constant and solvent molecular size. 3.2. HITK2750 Table 2 provides the permeability value Lp of HITK2750 for the same series of solvents as used for HITK275. As in seen at Table 2, for the loose nanoporous semi-hydrophilic HITK2750 ( = 30.9), the permeabilities of methyl ethyl ketone and acetonitrile are higher than for the other solvent. Methyl ethyl ketone and acetonitrile have very low viscosity values with surface tension and dielectric constant value close to surface tension and dielectric constant of the HITK2750 membrane. So the membrane shows more affinity toward these solvents. Here again the permeability of alcohols decrease by increasing the viscosity. Similar permeabilities were expected for solvent with the same viscosity since the membrane is loose nanoporous, and viscosity is the key transport parameter. However, a large difference between water and ethanol permeabilities or methyl ethyl ketone and n-hexane permeabilities with the same viscosity has been observed. It confirms that for loose nanoporous ceramic NF membranes, polarity still plays an important role in solvent permeation. Molecules with high affinity toward the membrane material would tend to stick and slip at the pore walls. So solvent permeation mechanism through loose nanoporous ceramic membranes is different from the viscous-flow mechanism due to reduction of the membrane’s pore size [21]. From the above discussion for solvent permeation through tight nanoporous and loose nanoporous ceramic membranes, it seems reasonable to assume that combined viscous, polarity and solvent molecular size, represented by solvent viscosity, surface tension, dielectric constant and solvent effective molecular diameter determine solvent permeation through the tight nanoporous ceramic NF membranes. 4. Model development In the literature, it is often found that in SRNF transport through the membrane cannot be described solely by diffusion approach [27]. Bhanushali et al. [28] determined the percentage of diffusive and convective transport of the solvents through hydrophobic NF membranes by using the Spiegler–Kedem model. They found that viscous transport is higher for low retention solutes. Robinson
49
Fig. 4. Representation of a NF active layer.
et al. [13] found that the permeability of pure alkanes and aromatics through a laboratory made PDMS membrane follows the Hagen–Poiseuille law. The convective transport has been taken into account in diffusive transport through the solution-diffusion with imperfections model. This model is an extension of the solutiondiffusion model taking into account the occurring convective flow through imperfections in the membrane by adding an extra term for the convective flow to the solution-diffusion model [29]. Typically, a solution-diffusion with imperfection based model use the following approach: Permeability ˛ Solubility · Diffusivity + Convectivity
(2)
NF membranes combine a high selectivity of a dense top layer with high permeation rate of a very thin support layer. So permeability mainly depends on NF top layer properties. As illustrated in Fig. 4, the active layer of NF composite membrane may also be assumed to consist of two different parts: (I) membrane matrix, and (II) nanoporous. Transport occurs through the ceramic material and through pores simultaneously. So the proportion of diffusivity and convectivity depends directly on the membrane structure. On the one hand, as the pore size of the membrane decreases, the membrane becomes tighter. Consequently, solubility, diffusivity and molecular forces at the interface become important [6]. On the other hand, for porous structures with large pore size the viscosity of solvent has a significant influence [30]. As indicated schematically in Fig. 5 the permeation of solvent molecules through a membrane consist of three main steps: (1) transfer of solvent molecules to the top active layer, which is characterized by a surface resistance Rs , (2) viscous-flow through NF nanopores, which is characterized as pore resistant (viscous resistance), Rp and (3) diffusive flow through the membrane ceramic material, Rm , which is characterized by a matrix resistance. A surface resistance is the difference between molecular forces at the interface. The overall resistance of the active layer is represented at left side of Fig. 5, which consists of an outer surface resistance Rs in series, followed by two resistances in parallel inside the membrane. To find the total amount of parallel resistance, the reciprocals of the Rp and Rm should be added together. The reciprocal of the sum is the total resistance which should be added to Rs
Fig. 5. Representation of the resistant encountered by a solvent molecule through the NF ceramic membrane.
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S. Darvishmanesh et al. / Separation and Purification Technology 70 (2009) 46–52 Table 3 Parameters necessary for the modeling.
to find the overall membrane resistance, Roveral Roveral = Routside the membrane + Rinside the membrane
(3)
Eq. (3) shows that the total resistance consists of the resistance on surface of membrane plus the resistance inside the membrane. Roveral = Rs +
Rm × Rp Rm + Rp
(4)
Total solvent flux through the membrane is given by: J=
P
(5)
Roveral
The surface resistance arises from differences in surface energy between the solvent molecules and the ceramic membrane surface [6–8,17,31] and also the porosity of membrane. It is assumed that the surface resistance increases with decreasing pore size and increasing solvent molecular size [6,32]. Machado et al. [7] and Geens et al. [17] related the solvent permeation in membrane matrix to the reciprocal of the surface energy difference (). The effect of surface tension should not lead to an infinite flux in case of identical surface tensions. The surface tension of solvent and polymer has been chosen as solvent–membrane interaction parameter. From the literature [7,17], it is clear that surface tension also has effect on both diffusive and viscous permeability parameters. However, the effect of surface tension should not lead to an infinite flux in case of identical surface tensions. Darvishmanesh et al. [33] considered the effect of surface tension in the view of the mathematical integrity as exp(1 − ˇ) instead of (). ˇ is the ratio of the surface tension of the membrane and solvent. ˇ is calculated as: ˇhydrophilic membrane =
L (surface tension of solvent) M (surface tension of membrane)
ˇhydrophobic hydrophobic =
M (surface tension of the membrane) L (surface tension of solvent)
(exp(1 − ˇ))
Surface resistance constant, Ks (Eq. (8)) Matrix resistance constant, Km (Eq. (12)) Pore resistance constant, Kp (Eq. (13)) Viscosity of solvents Solvent size Membrane pore size Dielectric constant of solvent Dielectric constant of membranes Surface tension of solvent Surface tension of membrane
Estimated during modeling Estimated during modeling Estimated during modeling Literature data Calculated from [34] Manufacture data sheet Literature data from [25] Literature data from [18] Literature data from [25] Determined with DSA 10 Mk2 (Krüss)
for the solubility parameter, which shows solvent affinity to the membrane. Polarity could be expressed as dielectric constant, which is an easy measurable physical property. Non-dimensional polarity coefficients (˛) for hydrophilic and hydrophobic SRNF membrane have been already presented elsewhere [33]. In case of ceramic membranes, this coefficient can be improved, since dielectric constant of ceramic membrane materials are available. The modified polarity coefficient for the hydrophilic and hydrophobic membrane is assumed as: Dielectric constant of solvent Dielectric constant of membrane
˛hydrophilic =
Dielectric constant of membrane Dielectric constant of solvent
(9)
˛hydrophobic =
(7)
Solvent diffusivity in the membrane matrix can be related to viscosity of solvent through the following approximation [8,36]:
2 rs rp
Obtained by
(6)
When the effect of surface tension, is combined with the effect of pore size (rp ) and solvent molecular size (rs ), one can obtain the following equation: Rs = ks
Parameter
(8)
where ks is a constant determined during the fitting. Rm presents the solubility and diffusivity resistance together. For the calculation of the molecular size, and energetic optimization procedure was used base on approach indicated elsewhere [34]. Reddy et al. [35] showed that the solubility parameter cannot correlate their experimental data. Polarity can be a relevant replacement
Diffusivity ˛
1
(10)
(11)
From the above approach, the ceramic matrix resistance, Rm is given by Rm = km
˛
(12)
is the viscosity of the solvent and km is a constant depends on porosity and tortuosity of the ceramic membrane. The value of Rm for tight pores membranes is lower than loose pores ones.
Fig. 6. Comparison of experimental and fitting value of the permeability of series solvent through a HITK275 ceramic membrane, using the new model.
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51
Fig. 7. Comparison of experimental and fitting value of the permeability of series solvent through a HITK2750 ceramic membrane, using the new model.
Finally, the pores resistance Rp is given base on the capillary flow approach:
2
Rp = kp
rs rp
(13)
kp is also a geometric membrane constant. The value of Rp for tight nanoporous membranes is higher than for loose nanoporous ones. The overall resistance Rm can be evaluated by substituting Eqs. (8), (12) and (13) in Eq. (4). The flux of solvent through membrane calculated by substituting, Rm in Eq. (5). Ks , Km and Kp are experimentally determined parameter. These results from permeation study were used to obtain the transport model coefficient. Therefore, the suggested transport model was implemented in mathematical computing software (Matlab R2006b) and a least square fit was used to obtain the values of the unknown parameters (Ks , Km and Kp ). In Table 3 the parameters necessary for the modeling are summarized. In attempts to correlate the extensive data obtained with Eq. (5), it was found that the constant parameters Ks , Km and Kp were constant for all solvents and each membrane type, and therefore, they characterize intrinsic membrane properties. The best regression values of Ks , Km and Kp were obtained for HITK275 and for HITK2750. Fig. 6 shows plot of permeability data measured for HTIK275. It can be seen that proposed model gives a very good fit to the experimental data. The model provides a reasonable approximation for the permeation data for different class of solvent through tight nanoporous ceramic membrane. Fig. 7 compares the calculated permeability data with the experimental data for HITK2750. HITK275 is made of TiO2 , which is a hydrophilic material. In contrast, HITK2750 is made of ZrO2 , a more hydrophobic material (as confirmed by contact angle measurement). In this context, it was appropriate to use the equation for hydrophobic membranes. The new model shows a very high correlation over the entire range of solvents. The new model did not show any problem when dealing with all different solvent, different number of varying solvent properties. The error variances were found to be between 0.5 and 4.2% for the new model. This confirms that the proposed model is able to predict the pure solvent flux for tight nanoporous and ceramic membrane rightly. 5. Conclusions The main objective of the current paper was to develop a model for predicting the flux of organic solvents permeating through ceramic NF membranes from membrane and solvent parameters.
A semi-empirical correlation is presented which describes solvent transport properties through a ceramic NF membrane, governed by surface, pore and membrane matrix resistances. The model embodies three fitting parameters, Ks , Km and Kp . The model have been evaluated for ceramic NF membranes. Two different ceramic membranes (tight and loose nanoporous) have been tested. A good fit for a large number of different solvent, was obtained. In conclusion, the semi-empirical model presented in this paper provides an appropriate framework for practical as well as theoretical research interest. Acknowledgment The Research Council of the K.U. Leuven is gratefully acknowledged for their financial support to this work (OT/2006/37). References [1] L.S. White, Transport properties of a polyimide solvent resistant nanofiltration membrane, Journal of Membrane Science 205 (1–2) (2002) 191–202. [2] X.J. Yang, A.G. Livingston, L. Freitas dos Santos, Experimental observations of nanofiltration with organic solvents, Journal of Membrane Science 190 (1) (2001) 45–55. [3] I.F.J. Vankelecom, et al., Physico-chemical interpretation of the SRNF transport mechanism for solvents through dense silicone membranes, Journal of Membrane Science 231 (1–2) (2004) 99–108. [4] J.D.B. Katleen Boussu, D. Charles, W. Marc, G.L. Kelvin, D. Diederik, A. Steliana, I.F.J. Vankelecom, C. Vandecasteele, B. Van der Bruggen, Physico-chemical characterization of nanofiltration membranes, ChemPhysChem 8 (3) (2007) 370–379. [5] L.E.M. Gevers, et al., Physico-chemical interpretation of the SRNF transport mechanism for solutes through dense silicone membranes, Journal of Membrane Science 274 (1–2) (2006) 173–182. [6] J. Geens, et al., Polymeric nanofiltration of binary water–alcohol mixtures: influence of feed composition and membrane properties on permeability and rejection, Journal of Membrane Science 255 (1–2) (2005) 255–264. [7] D.R. Machado, D. Hasson, R. Semiat, Effect of solvent properties on permeate flow through nanofiltration membranes: Part II. Transport model, Journal of Membrane Science 166 (1) (2000) 63–69. [8] D. Bhanushali, et al., Performance of solvent-resistant membranes for nonaqueous systems: solvent permeation results and modeling, Journal of Membrane Science 189 (1) (2001) 1–21. [9] K. Li, Ceramic Membranes for Separation and Reaction, John Wiley, Chichester, England; Hoboken, NJ, 2007, x, 306 p. [10] N. Stafie, D.F. Stamatialis, M. Wessling, Effect of PDMS cross-linking degree on the permeation performance of PAN/PDMS composite nanofiltration membranes, Separation and Purification Technology 45 (3) (2005) 220–231. [11] L.G. Peeva, et al., Effect of concentration polarisation and osmotic pressure on flux in organic solvent nanofiltration, Journal of Membrane Science 236 (1–2) (2004) 121–136. [12] E. Gibbins, et al., Observations on solvent flux and solute rejection across solvent resistant nanofiltration membranes, Desalination 147 (1–3) (2002) 307–313. [13] J.P. Robinson, et al., Solvent flux through dense polymeric nanofiltration membranes, Journal of Membrane Science 230 (1–2) (2004) 29–37.
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