Pervaporation separation of ethanol–water mixtures through sodium alginate membranes

Pervaporation separation of ethanol–water mixtures through sodium alginate membranes

Desalination 229 (2008) 68–81 Pervaporation separation of ethanol–water mixtures through sodium alginate membranes Swayampakula Kalyania, Biduru Smit...

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Desalination 229 (2008) 68–81

Pervaporation separation of ethanol–water mixtures through sodium alginate membranes Swayampakula Kalyania, Biduru Smithab, Sundergopal Sridharb*, Abburi Krishnaiaha a

Biopolymers and Thermo physical Laboratory, Department of Chemistry, Sri Venkateswara University, Tirupati 517 502, India b Membrane Separations Group, Chemical Engineering Division, Indian Institute of Chemical Technology, Hyderabad 500 007, India Tel. +91 (40) 27193142; Fax +91 (40) 27193626; email: [email protected]

Received 3 March 2006; accepted revised 16 July 2007

Abstract A sodium alginate (SA) dense membrane was prepared by the casting and drying of sodium alginate solutions on an acrylic plate, followed by crosslinked with phosphoric acid for the separation of ethanol–water mixtures at 30°C by the pervaporation method. The membrane containing 3 wt.% of sodium alginate shows the highest separation selectivity of 2182 with a substantial flux of 0.035 kg m–2 h–1. Permeation flux increased with an increase in weight percentage of water in the feed mixture, but separation selectivity decreased. The effect of experimental factors, such as the concentration of the feed solutions, membrane thickness and the operating permeate pressure on SA membrane performance were evaluated. The membranes were also subjected to sorption studies to evaluate the extent of interaction and degree of swelling in pure as well as binary feed mixtures. Further, ion exchange capacity (IEC) studies were carried out for all the crosslinked and uncrosslinked membranes to determine the total number of interacting groups present in the membranes. Keywords: Pervaporation; Sodium alginate membrane; Ethanol/water azeotrope; Phosphoric acid

1. Introduction Presently, the dehydration of organic mixtures is the most important application for pervaporation. Research efforts have been directed to the *Corresponding author.

selection of proper membrane materials. A good pervaporation membrane material should have high permeation flux and separation factor for the pervaporation dehydration of alcohol. It has long been recognized that hydrophilic polymers are selected as membrane material for the dehydration of various solvents because the water molecule is

0011-9164/08/$– See front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.desal.2007.07.027

S. Kalyani et al. / Desalination 229 (2008) 68–81

easily sorbed by the hydrophilic polymeric membrane. According to the solution-diffusion mechanism, separation in the pervaporation process takes place in two steps: selective sorption of liquid molecules into the membrane surface on the feed side and selective diffusion of them through the membrane due to differences in both the solubilities and diffusivities of permeating constituents, respectively. From these points of view, natural high polymers, polysaccharides, are worthy of consideration as a membrane materials for dehydration. They possess good affinity toward water molecules as shown in several studies dealing with the dehydration of alcohols through polysaccharide membranes. Alginic acid membrane [1] and generated cellulose membrane [2] are reported to show a good selectivity in the dehydration of water–alcohol mixture. Chitosan membrane [3], one of the cationic polysaccharide membranes, also yielded high selectivity when its amino group was neutralized by poly basic acids or when it was cross-linked using H2SO4 [4]. Among the hydrophilic polysaccharide type polymers, alginate membrane has gained special interest because it showed the highest flux and separation factor among the hydrophilic materials tested for the pervaporation dehydration [5,6]. However, a very high hydrophilicity of sodium alginate resulting from both of its carboxyl and hydroxyl groups, leads to a significant swelling of membrane in aqueous solution, followed by a remarkable decline of selectivity and mechanical strength. To overcome these drawbacks, several researchers have modified the alginate membranes for the effective dehydration performance. Yeom and Lee [7], crosslinked the sodium alginate membrane with glutaraldehyde for the separation of water–isopropanol mixture. Haung and co-workers [8] prepared a novel two-ply dense composite membranes using successive casting of sodium alginate and chitosan for the dehydration of isopropanol and ethanol. However, the performance of a pure sodium alginate membrane was still not satisfactory because of a large free volume be-

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tween the molecular chains [9]. Its membrane performance has been improved by modifying alginate with different methods such as blending [10], grafting [11] and cross-linking [12]. In this paper, we prepared a novel composite membrane from sodium alginate (SA) crosslinked in a novel fashion with phosphoric acid, for water/ethanol mixtures separation by pervaporation. The work also explores the effect of varying water concentration in the binary feed mixture on membrane flux and selectivity. Furthermore, the diffusion coefficient and pervaporation results have been explained on the basis of solution-diffusion principles. 2. Experimental 2.1. Materials Sodium alginate, having an average molecular weight of 5,00,000, was purchased from Aldrich Chemicals, Mumbai, India. Ethanol of purity 99.9%, isopropanol and phosphric acid were purchased from Loba Chemicals, Mumbai. Demineralised water (conductivity = 0.02 S cm–1), which was used for the preparation of feed solution, was generated in the laboratory itself. 2.2. Preparation of membranes Sodium alginate membranes were prepared by solution casting and solvent evaporation method. The 3 wt.% solution of sodium alginate in aqueous medium was prepared, stirred and filtered to remove the undissolved matter. A bubble-free solution was cast on a clean acrylic plate/Petri dish to the desired thickness and dried in atmospheric conditions at room temperature followed by vacuum drying for a period of 5 h at the elevated temperature (50°C) in an oven to remove the last traces of solvent. The so formed membrane was crosslinked for 3 h in an isopropanol–water bath (90/10 vol.%) containing 3.5 vol.% of phosphoric acid. After removing the membrane from the cross-linking bath, it was washed with water re-

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peatedly and dried in an oven at 80°C to eliminate the presence of residual acid, if any. The membrane thickness as measured by a micrometer screw gauge was in the range of 35–40 μm. The dried membranes were utilized in PV experiments. The stability of the membrane was analyzed by bending the membrane before and after PV studies. The experiment performed for the duration of 3 months during which the membrane was found to be stable. After this period, the membrane was bent to ensure its mechanical stability and it was noted that despite bending completely the membrane did not break. Hence, the membrane durability and stability appears to be reasonably good [13].

2.3. Membrane characterization 2.3.1. Fourier transform infra red (FTIR) studies The FTIR spectra of unmodified and phosphoric acid crosslinked NaAlg membranes were scanned in the range 400–4000 cm–1 using a Nicolet–740, Perkin–Elmer 283B FTIR spectro photometer by KBr pellet method. 2.3.2. XRD analysis A Siemens D 5000 powder X-ray diffractometer was used to assess the solid-state morphology of phosphorylated sodium alginate (P-NaAlg) in powdered form. X-rays of 1.54 Å wavelengths were generated by a CuK source. 2.3.3. Thermal gravimetric analysis (TGA) Thermal stability of the polymer membranes was examined (Seiko 220TG/DTA analyzer) in the temperature range of 25–700°C at a heating rate of 10°C min–1 with continuous flushing using pure nitrogen gas at 200 ml min–1. The samples were subjected to TGA both before and after phosphorylation to determine the thermal stability and decomposition characteristics.

2.4. Sorption characteristics In order to evaluate membrane-liquid affinities, weighed samples of circular pieces of the polymer membranes (3 cm dia) were soaked in pure water and ethanol as well as their binary mixtures of various concentrations. The membranes were taken out after different soaking periods and quickly weighed, after carefully wiping off excess liquid, to estimate the amount absorbed at the particular time “t”. The membrane was then quickly placed back in the solvent. The process was repeated until the membranes attained steady state as indicated by constant weight after a certain period of soaking time. Degree of swelling was calculated using Eq. (1):

DS =

Ms Md

(1)

The percentage sorption was calculated using Eq. (2):

Sorption [%] =

Ms − Md × 100 Md

(2)

2.5. Determination of the ion exchange capacity (IEC) The ion exchange capacity (IEC) indicates the number of milliequivalents of ions in 1 g of the dry polymer. To determine the degree of substitution by acid groups, the phosphorylated membranes and unphosphorylated specimens of similar weight were soaked in 50 ml of 0.01 N NaOH solution for 12 h at ambient temperature. Then, 10 ml of the solution was titrated with 0.01 N H2SO4. The sample was regenerated with 1 M HCl, washed free of acid with water and dried to a constant weight. The IEC was calculated according to Eq. (3) [14]

IEC =

B − P × N NaOH × 5 m

(3)

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where IEC is the ion exchange capacity (meq g–1), B the amount of 0.01 M sulfuric acid used to neutralize unmodified sodium alginate, P the amount of 0.01 M sulfuric acid used to neutralize the crosslinked membrane, 5 the factor corresponding to the ratio of the amount of NaOH taken to dissolve the polymer to the amount used for titration, and m the sample mass in g. 2.6. Pervaporation procedure Experiments were carried out on a 100 ml batch level with an indigenously constructed pervaporation manifold (Fig. 1) operated at a vacuum as low as 0.05 mm Hg in the permeate line. The membrane area in the pervaporation cell assembly was approximately 20 cm2. The experi-

mental procedure is described in detail elsewhere [15]. Permeate was collected for a duration of 8– 10 h. Tests were carried out at room temperature (30±2°C) and repeated twice using fresh feed solution to check for reproducibility. The collected permeate was weighed after allowing it to attain room temperature in a sartorius electronic balance (accuracy: 10–4 g) to determine the flux and then analyzed by gas chromatography to evaluate the membrane selectivity. 2.6.1. Flux and selectivity equations In pervaporation the flux J of a given species, say faster permeating component i of a binary liquid mixture comprising of i (water) and J (ethanol) is given by Eq. (4)

SM

SM - Stirrer Motor M - Membrane FC - Feed Chamber C1& C2 - Condensers DF- Dewar Flask V1, V2, V3- Control valves VG- Mcleod Guage VP- Vacuum Pump ATM - Atmosphere

M

FC PV Cell

C2 C1

V1

V2

VG

V3

ATM

DF

ATM

VP

Fig. 1. Schematic of laboratory vacuum pervaporation set-up.

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Ji =

S. Kalyani et al. / Desalination 229 (2008) 68–81

Wi At

3. Results and discussion (4)

In the present study, though different membrane thicknesses were utilized, the flux has been calculated for the thickness of the membrane to 10 μm (normalized flux) and is given by Eq. (5).

Normalized flux flux × membrane thickness = 10 μm

(5)

The membrane selectivity is the ratio of permeability coefficients of water and ethanol and can be calculated from their respective concentrations in feed and permeate as given in Eq. (6)

α=

y (1 − x )

x (1 − y )

(6)

Pervaporation separation index (PSI) is a measure of the separation capability of a membrane and is expressed as a product of selectivity and flux [16], which was given in Eq. (7). PSI = J × α

(7)

3.1. Ion exchange capacity (IEC) The amount of residual acetate and hydroxyl groups present after crosslinking was estimated from IEC studies. It was noted that unmodified sodium alginate showed an IEC of 1.26 meq g–1 whereas phosphoric acid crosslinked polymer exhibited an IEC of 0.75 meq g–1. The IEC is equivalent to the total number of free acetate groups (considering the fact that acetate groups are more interactive than hydroxyl groups), R-COONa present in the membrane, which decreased upon crosslinking [17]. This result shown that almost 50% of the acetate groups present in the unmodified sodium alginate has now formed the crosslinks with phosphoric acid. A model of the possible interaction is shown in Fig. 2. IEC and FTIR studies prove the occurrence of crosslinking. Hence, phosphoric acid will establish a linkage with NaAlg through ester formation as confirmed by FTIR (Fig. 3). To the best of our knowledge, it is the first kind of study wherein phosphoric acid is employed as a crosslinking agent and the membrane could withstand the solvent environment and pervaporation employed in this study. 3.2. FTIR studies

2.7. Analytical procedure The feed and permeate samples were analyzed using a Nucon Gas Chromatograph (Model 5765) installed with Thermal Conductivity Detector (TCD) and packed column of 10% DEGS on 80/100 Supelcoport of 1/8″ ID and 2 m length. The oven temperature was maintained at 70°C (isothermal) while the injector and detector temperatures were maintained at 150°C each. The sample injection size was 1 μl and pure hydrogen was used as a carrier gas at a pressure of 1 kg cm–2. The GC response was calibrated for this particular column and conditions with known compositions of ethanol–water mixtures and the calibration factors were fed into the software to obtain correct analysis for unknown samples.

The FTIR spectrum of the pure and the crosslinked NaAlg are shown in Fig. 3. The spectrum of NaAlg shows the prominent peaks of C=O stretching of the carboxylic group at 1651 cm–1 and the characteristic peak of free hydroxyl group is observed in the range of 3188 cm–1 to 3583 cm–1 are shown in Fig. 3a. The spectrum of crosslinked NaAlg showed a shift in the C=O peak from 1651 cm –1 in the uncrosslinked membrane to 1759 cm–1 for the modified membrane. This shift may be attributed to the formation of –OC–O–P bond due to the interaction of hydroxyl group of phosphoric acid with acetate group of NaAlg. It can also be noted that the P=O remains intact and does not participate in the reaction. This can be confirmed by the presence of a peak of 960 cm–1

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S. Kalyani et al. / Desalination 229 (2008) 68–81 OH HO

O

O

O

O C OH O

HO

OH O O

H3PO4

C

O

O

P

O

O COONa

Sodium alginate

HO

O

O

O

O

C

Phosphoric acid

O

O O

OH

O

HO

P

Na Alg

Fig. 2. Structural representation of Sodium alginate membrane crosslinked with phosphoric acid.

Fig. 3. FTIR spectra of uncrosslinked NaAlg (a) and Crosslinked NaAlg (b).

which corresponds to P=O. The formation of a new peak (Fig. 3b) at 1419 cm–1 corresponds to the interaction of hydroxyl group of phosphoric acid with carboxyl group present in the NaAlg

resulting in the formation of –P–O–C bond. Such a changes in the spectrum confirmed the successful crosslinking of membrane.

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3.3. XRD studies The XRD spectra of uncrosslinked and crosslinked NaAlg are shown in Fig. 4. From the spectra of unmodified (Fig. 4a) and crosslinked (Fig. 4b) sodium alginate it can be noted that the XRD pattern of uncrosslinked sodium alginate membrane appears to be amorphous in nature, whereas the XRD pattern of crosslinked membrane appears to be semi crystalline in nature. From Fig. 4a it can also be seen that there are two distinct peaks at 9° and 15° of 2 θ. The peak at 15° of 2 θ indicates the presence of crystallinity as reported by Yang et al. [18]. These two peaks are related to two types of crystals: crystal 1 and crystal 2. Crystal 1, is responsible for the separation, since it corresponds to the hydroxyl functional group. A reduction in d–spacing value from 7.2 Å for un-crosslinked to 6.88 Å in crosslinked

polymer gives an indication of reaction between the carboxylic groups of sodium alginate with hydroxyl groups of phosphoric acid, which would improve the selective permeation of the membrane. 3.4. TGA studies The TGA curves of the uncrosslinked and crosslinked NAALG membranes are shown in Fig. 5. The TGA curve of NaAlg (Fig. 5a) shows the beginning of weight loss at 220°C followed by a final decomposition at 260°C. Fig. 5b shows that P–NaAlg begins to undergo a weight loss starting at 180°C followed by the final decomposition at 250°C. This observation indicates that there is no considerable difference in thermal stability before and after crosslinking. Hence the crosslinked membranes could be used for PV studies even at high temperatures.

Fig. 4. X-RD diffractograms of uncrosslinked NaAlg (a) and crosslinked NaAlg (b).

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Fig. 5. TGA curves for uncrosslinked NaAlg (a) and crosslinked NaAlg (b).

3.5. Sorption studies The effect of equilibrium sorption percentage and degree of swelling data of the membrane in aqueous ethanol of different compositions is shown in Table 1. The crosslinked membrane showed a high degree of sorption (42.6%) in pure water, with a relatively negligible sorption for pure ethanol. From Fig. 6, it can be seen that the weight percentage water uptake of the binary feed mixtures increased from 12.02 to 42.63% with increase in feed water concentration from 5.2 to 38.6 wt.%

signifying the possibility of attaining enhanced flux using these membranes. However, absorption of large amounts of water at higher feed concentrations could cause increased swelling and subsequent fall in membrane selectivity due to plasticization of the polymer chains. 3.6. Influence of operating conditions It is well know that separation characteristics of a membrane depend upon the interaction between solvent to be separated and the membrane

Table 1 Effect of feed concentration on degree of swelling, permeate water concentration and water flux

No.

Feed water concentration (wt.%)

Degree of swelling

% of sorption

Permeate water concentration (wt.%)

Water flux (kg/m2.h)

PSI

1. 2. 3. 4. 5. 6.

5.22 9.74 15.65 20.52 31.57 38.6

1.12 1.20 1.26 1.32 1.38 1.43

12.03 19.78 25.80 32.30 38.53 42.63

99.16 98.76 96.03 93.71 88.30 80.50

0.035 0.048 0.051 0.065 0.071 0.080

535 242 47 26 7 4

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45 40

% Sorption

35 30 25 20 15 10 5

10

15

20

25

30

35

40

Feed water concentration (wt%) Fig. 6. Effect of feed water concentration on % sorption.

matrix. Hydrophilic membrane like chitosan and sodium alginate can develop hydrogen bond interaction with water leading to preferential sorption and diffusion of water through the barrier membrane [7]. The influence of feed composition, membrane thickness and permeate pressure on membrane performance has been examined in detail. 3.6.1. Effect of feed composition The relation between liquid feed composition and pervaporation performance over a wide range of feed mixtures at 30°C was investigated using crosslinked membranes. For this study, the membrane thickness and permeate pressure were kept constant at 70 mm and 0.5 mm Hg respectively. The pervaporation performance of P-sodium alginate membrane was investigated for varying feed water compositions comprising of 5.2– 38.6 wt.% water keeping other operating parameters such as permeate pressure and membrane thickness constant. Expectedly, a rise in the feed concentration of water produced an increase in

the water-normalized flux from 0.245 to 0.553 kg m–2 h–1 (10 μm)–1 (Fig. 7). At higher feed water concentrations, the membrane swells appreciably because of the availability of more water molecules for sorption and diffusion. The preferential interaction with water molecules causes the membrane to swell, leading to plasticization and unrestricted and quicker transport of both volatile components through the barrier. On swelling, the polymer chains become more flexible and hence the transport through the membrane becomes easier for both the feed components resulting in high flux [19]. Hence the selectivity decreased from 2182 at 5.2 wt.% feed water concentration to 6.58 at 38.6 wt.%. Higher water concentrations render greater swelling of the membranes that enables permeation of both components into the downstream side yielding higher flux but a drop in selectivity. Thus the swelling increases with increasing water concentration leading to reduction in membrane selectivity. However, it is worth mentioning that the membrane showed promising results for dehydrating feeds having 5–25% water. Moreover, the azeo-

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2500

1500 0.4 1000

2

Membrane selectivity

0.5

Normalized fulx (Kg/m . hr. 10 μm)

2000

500

0.3

0

2

4

6

0.2 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

Feed water concentration (Wt%) Fig. 7. Effect of feed water composition on PV performance of NaAlg (membrane thickness 70 μm and permeate pressure at 0.5 mm Hg).

tropic composition of 96 wt.% ethanol was easily broken by pervaporation with >99% water concentration in the permeate. 3.6.2. Effect of membrane thickness The effects of varying membrane thickness on separation performance was studied at constant feed composition (azeotropic) and permeate pressure (0.5 mm Hg) by synthesizing membranes of thickness ranging from 30 μm to 120 μm. With an increase in the membrane thickness a gradual reduction in the flux from 0.102 to 0.016 kg m–2 h–1 can be clearly evidenced from Fig. 8. Though the availability of polar groups enhances with an increase in the thickness, flux decreases since diffusion becomes increasingly retarded as the feed molecules have to travel a greater distance to reach the permeate side. The permeate concentration of water varied from 96.2 to 99.4 wt.% which meant that the selectivity increased from 469 to 3182. In pervaporation process, the upstream layer of the membrane is swollen and plasticized due to

absorption of feed liquid and allows unrestricted transport of feed components. In contrast, the downstream layer is virtually dry due to continuous evacuation in the permeate side and therefore this layer forms the restrictive barrier which allows only interacting and smaller sized molecules such as water to pass through. It is expected that the thickness of the dry layer would increase with an increase in the overall membrane thickness resulting in improved selectivity as observed in the present case. 3.6.3. Effect of permeate pressure The permeate pressure was varied from 0.5 to 8 mm Hg, to study the permeation characteristics at a constant thickness of 70 μm and azeotropic feed composition. At lower pressures (high vacuum) the influence of the driving force on the diffusing molecules in the membrane is high, and will result in the components being swept out immediately from the permeate side resulting in high mass transfer rates. Fig. 9 shows that the

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S. Kalyani et al. / Desalination 229 (2008) 68–81 3500 0.10

0.08

2500

0.06

2000

0.04

2

1500

Flux (Kg/m . hr)

Membrane Selectivity

3000

1000 0.02 500 0.00 20

40

60

80

100

120

Membrane thickness (μm) Fig. 8. Effect of membrane thickness on PV performance (azeotropic feed composition 4 wt.% of water and permeate pressure at 0.5 mm Hg).

0.30

2500

0.15 1000

2

Membrane Selectivity

0.20 1500

Normalized flux (Kg/m .hr. 10 μm)

0.25

2000

0.10 500 0.05 0

2

4

6

8

Permeate Pressure (mm Hg) Fig. 9. Effect of permeate pressure on PV performance (azeotropic feed composition 4 wt.% of water and membrane thickness 70 μm).

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membrane exhibits considerable lowering of normalized flux from 0.245 to 0.081 kg m–2 h–1. (10 μm)–1 as well as a reduction in selectivity from 2187.57 to 469, with an increase in permeate pressure from 0.5 mm Hg to 8 mm Hg. Under high vacuum conditions (lower pressures) diffusion through the membrane is the rate determining step of the pervaporation process and the diffusing water molecules experience larger driving force, which enhances the desorption rate at the downstream side. Lower vacuums reduce the driving force, thus slowing desorption of molecules. In such cases the relative volatilities of the two components of the mixture govern the separation factor of the membrane. 4. Comparison of present work with literature Data from literature on selectivity and flux of different membranes for pervaporation separation of ethanol/water system are included in Table 2 [20–24] along with those obtained in the present study. The data in the table indicate that the flux and selectivity of P–SA membranes are comparable with those of other membranes. Further, P– SA has optimum values for selectivity and flux, whereas in the case of other membranes maxi-

mum flux is associated with lower values of selectivity and vice-versa except in case of chitosan membrane. Furthermore, the ease in fabrication of these membranes associated with low cost render them more attractive for pervaporation of aqueous alcohols. 5. Conclusions Sodium alginate membranes were prepared for pervaporation-based dehydration of ethanol water mixture. The efficient water permselective characteristic of alginate could be appropriately utilized to yield good flux, separation factors, and better thermal properties. Sorption studies revealed that the membrane had greater affinity towards water than ethanol. With increasing feed water concentration, the membrane performance was found to be affected substantially by increase in the extent of swelling of the polymer, which resulted in a rise in flux but a reduction in selectivity. The crosslinked membranes were found to show promising performance for dehydration of ethanol containing smaller amounts of water. The azeotropic composition of ethanol water mixture was easily broken by pervaporation. Increasing membrane thickness decreased the flux but had a

Table 2 Comparison of flux and selectivity of PVA–SA blend membrane with values reported in literature No.

Membrane

Feed composition Water (%)

1 2 3 4 5 6 7

Novel two ply composite CS/SA CS/HEC CS/SA Chitosan SA PVA/PVS P–SA

5 10 13.5 10 10 6.2 5.2

Selectivity

Flux (kg m–2 h–1)

Reference

Ethanol (%) 95 90 86.4 90 90 93.8 94.8

1110

0.07

10491 436 8000 120 700 2182

0.11 0.22 0.26 0.29 0.50 0.24

8 20 21 22 23 24 Present work

CS/SA — chitosan/sodium alginate; CS/HEC — chitosan/hydroxyethylcellulose; SA — sodium alginate; poly(vinyl alcohol)/poly (styrene sulfuric acid); P–SA — phosphorylated sodium alginate

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less profound effect on the separation factor. Higher permeate pressure caused a reduction in both flux and selectivity. [5]

Symbols — Membrane area — Amount of sulfuric acid used to neutralize blind sample soaked in NaOH Ji — Flux of water component i m — Mass of the membrane Md — Mass of the dry polymer Ms — Mass of the swollen polymer P — Amount of sulfuric acid used to neutralize the sulfonated membrane soaked in NaOH t — Evaluation time Wi — Mass of water in permeate x,y — Feed and permeate water concentration α — Membrane selectivity (1 – x), (1 – y) — Feed and permeate ethanol concentration A B

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