Journal of Membrane Science 268 (2006) 48–56
Mass transfer in osmotic membrane distillation Naveen Nagaraj a , Ganapathi Patil a , B. Ravindra Babu a , Umesh H. Hebbar a , K.S.M.S. Raghavarao a,∗ , Sanjay Nene b a
Department of Food Engineering, Central Food Technological Research Institute, Mysore 570013, India b Chemical Engineering Division, National Chemical Laboratory, Pune 411008, India Received 18 November 2004; received in revised form 20 May 2005; accepted 5 June 2005 Available online 21 July 2005
Abstract Osmotic membrane distillation is a novel athermal membrane process that facilitates the maximum concentration of liquid foods under mild operating conditions. In the present study, the effect of various process parameters such as type, concentration and flow rate of the osmotic agent; type (polypropylene membranes) and pore size (0.05 and 0.2 m) of the membrane; temperature with respect to transmembrane flux was studied. Experiments were performed with real systems (pineapple/sweet lime juice) in a flat membrane module. Osmotic agents namely sodium chloride and calcium chloride at varying concentrations are employed. For both the osmotic agents, higher transmembrane flux was observed at maximum osmotic agent concentration. In comparison with sodium chloride, higher transmembrane flux was observed in case of calcium chloride. A mass transfer-in-series resistance model has been employed, considering the resistance offered by the membrane as well the boundary layers (feed and brine sides) in case of real systems for the first time. The model could predict the variation of transmembrane flux with respect to different process parameters. © 2005 Elsevier B.V. All rights reserved. Keywords: Transmembrane flux; Juice; OMD; Modeling; Mass transfer-in-series resistance model
1. Introduction Concentration of liquid foods by conventional methods such as evaporation results in product deterioration with respect to loss of flavors, taste and nutritive components resulting in low quality end product [1]. Further, evaporative concentration is energy intensive since it involves phase change of water. Hence, in recent years, membrane processes such as microfiltration (MF) ultrafiltration (UF) and reverse osmosis (RO) are being employed for clarification and concentration of fruit juices [2]. The limitations of these membrane processes are maximum attainable concentration (only up to 25–30 ◦ Brix), concentration polarization, and membrane fouling [3]. Even, the newer membrane process such as membrane distillation (MD), which operates at lower temperature and pressure, also suffers from relatively low flux
∗
Corresponding author. Tel.: +91 821 2513910; fax: +91 821 2517233. E-mail address:
[email protected] (K.S.M.S. Raghavarao).
0376-7388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2005.06.007
due to temperature polarization [4]. Hence, there is a need to develop an alternate/complementary membrane process. Osmotic membrane distillation (OMD) has such potential since it facilitates the concentration of liquid foods under mild operating conditions [5–9]. In the earlier work on OMD, attempts were made to consider the mass transfer on feed side; however, in some of them, the estimation of feed boundary layer resistance was not undertaken. In the present work, the feed boundary layer resistance is accounted, in addition to that of brine boundary layer and membrane, in the mass transfer-in-series resistance model for real systems (pineapple and sweet lime juice) The effect of various process parameters such as type, concentration and flow rate of the osmotic agent; type (polypropylene membranes) and pore size (0.05 and 0.2 m) of the membrane; temperature with respect to transmembrane flux have been studied for real systems. Mass transfer in the boundary layer is estimated as function of dimensionless numbers, whereas, the mass transfer through the membrane is accounted based on either by Knudsen or molecular diffusion. The use of dimensionless
N. Nagaraj et al. / Journal of Membrane Science 268 (2006) 48–56
numbers enables the quantification of the hydrodynamics on the feed as well as OA boundary layers, Based on the overall resistance estimated, the model could predict reasonably well the effect of the process parameters on the transmembrane flux.
2. Theoretical aspects Osmotic membrane distillation is an athermal membrane process, which employs hydrophobic membrane to separate two aqueous solutions having different osmotic pressures. The driving force for the mass (water) transfer is the difference in vapor pressure of the solvent (water) across the membrane. Water evaporates from the surface of the solution having higher vapor pressure, diffuses in the form of vapor through the membrane, and condenses on the surface of the solution [10]. The evaporation process requires the supply of the latent heat of vaporization at the upstream meniscus. This is provided as sensible heat via conduction or convection from the bulk upstream liquid, or via conduction across the solid phase comprising the membrane. Conversely, at the downstream face of the membrane, condensation of water vapor into the osmotic agent solution occur releasing heat of condensation. The thermal conductance of membrane should be sufficiently high, so that all the energy of vaporization can be supplied by conduction across the membrane at a low temperature gradient. As a consequence, under normal operating conditions, the temperature difference between the liquids on either sides of the membrane is quite small (≈2 ◦ C) [6], and the process could be considered as isothermal in certain cases. 2.1. Mass transfer aspects
Knudsen diffusion or molecular diffusion depending on the pore size [11]. When the mean free path is significant relative to the pore size, the diffusing molecules collide more frequently with the pore wall and the diameter of the pore is important. Such mass transfer is termed as Knudsen diffusion and the membrane diffusion coefficient (KmK ) is given by [12] rε M 0.5 (3) KmK = 1.064 χδ RT When the membrane pore size is relatively large, the collisions between the diffusing molecules themselves are more frequent. Such mass transfer is termed as molecular diffusion and the membrane diffusion coefficient is expressed as [13] Kmm =
1 Dε M Yln χδ RT
(4)
where ‘D’ is the Fick’s diffusion coefficient and can be predicted by D=
0.001858T 3/2 (1/MA + 1/MB )1/2 2 Ω PσAB D
(5)
Both these approaches are useful for predicting the mass transfer through the membrane mainly depending on the membrane pore size. However, each of them has its own limitations. The Knudsen equation requires details of membrane pore geometry (such as pore radius, membrane thickness, tortuosity). Molecular diffusion does not hold at low partial pressure of the air, as ‘Yln ’ tends to 0 and hence, molecular diffusion is clearly undefined; thereby diffusion mechanism approaches Knudsen diffusion [12]. 2.3. Mass transfer across the boundary layers
The basic equation, which relates the transmembrane flux (J) to the driving force represented by the difference in vapor pressures of the bulk liquids (feed and OA) and is given by J = K P
49
(1)
where ‘K’ is the overall mass transfer co-efficient which accounts for all the three resistances for water transport and is given by 1 1 −1 1 + + (2) K= Kf Km KoA
The boundary layers are present in the feed and the OA on either side of the membrane. These layers may offer significant resistance to mass transfer, depending on the physical properties of the solution (feed and OA) as well as the hydrodynamic conditions of the systems. The liquid mass transfer coefficients in the boundary layers of feed and OA (Kf and KOA ) can be estimated by using empirical equations given below, involving only physical properties and hydrodynamic conditions of the solutions. Sh = b1 Reb2 Scb3
(6)
where Kf , Km and KoA are the mass transfer resistances in feed layer, membrane and osmotic agent layer, respectively.
where b1 , b2 and b3 are the constants and are to be selected appropriately for the given hydrodynamic conditions, and
2.2. Mass transfer through the membrane
Sh =
The resistance for the diffusive transport of water vapor across the microporous hydrophobic membrane is offered by the membrane pore structure as well as air present in the pores. The diffusion of water vapor through this stagnant gas phase (air) of the membrane pore can be described either by
where Dw is the water diffusion coefficient and can be estimated by using following empirical equation [14,15]. Dw =
ki L , Dw
Re =
uLρ µ
and
(117.3 × 10−18 )(ϕMw )0.5 T 0.6 µνA
Sc =
µ ρDw
(7)
(8)
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Table 1a Water activity coefficients for the osmotic agents at various concentrations [20] Concentration (M)
Activity coefficient (CaCl2 ·2H2 O)
Activity coefficient (NaCl)
2 3 4 5 6 8 10 12 14
0.879 – 0.681 – 0.444 0.323 0.105 0.105 0.105
0.679 0.718 0.788 0.878 0.988 – – – –
3. Materials and methods 3.1. Membranes
In order to obtain Kf and KoA in the same units of Km the following equation was used [6], Ki =
In the present case, the module, which was employed to conduct the experiments, is plate and frame, where the feed and OA solutions were circulated on either side of the membrane at different flow rates with the help of peristaltic pumps. Small temperature gradient that could exist across the membrane has not been considered due to very short contact times involved.
k i C t Mw (xs )lm γP ∗
(9)
where Ct is the molar concentration of the solution, γ activity co-efficient (Table 1a shows, the activity coefficients of osmotic agent solutions at various concentrations) and P* the saturation vapor pressure, the values of which were obtained from literature [16,17]. 2.4. Thermal effect on mass transfer In osmotic membrane distillation, as the water evaporates on feed side of the membrane and condenses on osmotic agent (OA) side of the membrane, the feed cools down and the OA solution warms up. This results in temperature gradient across the membrane, which adversely affects the driving force and in turn has an effect on mass flux. This problem has been discussed in the literature [6,7]. According to these authors, the thermal effect lead to over prediction of the water flux across up to 26%. Gostoli [7], has attempted to integrate the thermal effect in the mass transfer equation by introducing a sort of efficiency coefficient η, which represents the fraction of the driving force really effective for mass transfer through the membrane. The author had used stirred membrane cell to evaporate pure water at 25 ◦ C with NaCl solution, where concentration polarization was neglected. At these conditions, the value of η was reported as 0.85 and the membrane permeability was observed to be 15% lower than the experimental values.
Hydrophobic polypropylene membranes of pore sizes 0.05 and 0.2 m and average thickness of 150 m manufactured by Accurel, Enka, Germany (obtained from NCL, Pune) were used in the study. The membrane porosity and the tortuosity of the pores were considered to be 0.75% and 2, respectively, as commonly done in the literature [6]. The pore sizes as well as the type of the membrane were selected based on our earlier work [3]. 3.2. Chemicals Sodium chloride (NaCl, B.No: 1033D01), calcium chloride dihydrate (CaCl2 ·2H2 O, B.No: 6HBV0134B) were obtained from Ranbaxy Ltd., India, whereas pectinase (Aspergillus niger, B.No: T: 826160) was obtained from SISCO Research Laboratories Pvt. Ltd., Mumbai, India. Distilled water (Millipore, Inc.) was used for all the experiments. 3.3. Methods 3.3.1. Preparation of fruit juice The fresh pineapple (Annanus comasus) and sweet lime (Citrus sinesis Osbeck) fruits were purchased from local market and juice was extracted (after peeling) using Food Processor (Singer # FP-450). The extracted juice was clarified using pectinase [18]. The physical properties such as viscosity and density of the feed and OA solutions were calculated by using Ostwald viscometer and specific gravity bottle respectively, and the values obtained are mentioned in Table 1b.
Table 1b Physical properties of feed and OA solutions Osmotic agent
Density (×10−3 kg m−3 )
Viscosity (×103 Pa s)
Density (×10−3 kg m−3 )
Viscosity (×103 Pa s)
Pineapple juice CaCl2 ·2H2 O NaCl
1.29 1.26
4.66 1.35
1.02 1.03
1.37 1.35
Sweet lime juice CaCl2 ·2H2 O NaCl
1.30 1.25
4.67 1.36
1.02 1.03
1.60 1.58
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Fig. 1. Flat membrane module.
3.3.2. Experimental procedure Experiments were performed using a flat membrane module having a membrane area of 0.0116 m2 , shown in Fig. 1. The module consists of microporous hydrophobic polypropylene membrane (0.05 or 0.2 m), a polyester mesh (on OA side) and a Viton gasket (on feed side) supported between two stainless steel (SS 316) frames. Feed solution (pineapple or sweet lime juice) and osmotic agent solution were circulated on either side of the membrane in co-current mode using peristaltic pumps. The transmembrane flux was calculated, by measuring the increase in volume of osmotic agent solution once in every hour. All the experiments were performed for a period of 5 h and the average values of the flux were reported. All the experiments unless otherwise mentioned were carried out at the temperature of 28 ± 0.5 ◦ C. The feed flow rate as well as OA flow rate was maintained constant (100 ml/min) during the entire study.
Fig. 2. Effect of OA concentration on transmembrane flux: (a) pineapple, calcium chloride, 0.05 m; (b) pineapple, sodium chloride, 0.05 m.
4. Results and discussion The effect of various process parameters such as type, concentration and flow rate of the osmotic agent; type (polypropylene membranes) and pore sizes (0.05 and 0.2 m) of the membrane; temperature with respect to transmembrane flux across the membrane are discussed in the following sections. 4.1. Effect of concentration of the osmotic agent The concentration of OA solutions was varied over 2–6 M (sodium chloride), and 2–14 M (calcium chloride). During the experiments, osmotic solution flow rate was maintained constant (100 ml/min). The values of transmembrane flux observed at different concentrations of osmotic solution are shown in Figs. 2–4. In both the cases (NaCl and CaCl2 ·2H2 O) transmembrane flux has increased with an increase in OA concentration. This increase is mainly due to higher vapor pressure difference across the membrane, which results in an
Fig. 3. Effect of OA concentration on transmembrane flux: (a) pineapple, calcium chloride, 0.2 m; (b) pineapple, sodium chloride, 0.2 m.
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Fig. 5. Effect of flow rate on transmembrane flux.
Fig. 4. Effect of OA concentration on transmembrane flux: (a) sweet lime, calcium chloride, 0.2 m; (b) sweet lime, sodium chloride, 0.2 m.
increase in the driving force for water transport through the membrane. The theoretical fluxes were predicted by accounting the individual mass transfer resistances for water transport through the boundary layers (both feed and OA side) and also through the membrane based on molecular or Knudsen diffusion. 4.2. Effect of flow rate of the osmotic agent Experiments were performed at varying flow rates (25–100 ml/min) by maintaining OA solution at its saturation level (CaCl2 ·2H2 O—14 M; NaCl—6 M). The transmembrane flux has gradually increased with an increase in flow rate as shown in Fig. 5. This can be attributed to reduction in concentration polarization layer (due to the reduction in hydrodynamic boundary layer thickness). This confirms the detrimental effect of concentration polarization in reducing the driving force across the membrane and its decrease with an increase in flow rate. 4.3. Effect of membrane pore size To analyze the effect of pore size on transmembrane flux, experiments were performed using hydrophobic polypropylene membranes of 0.05 and 0.2 m pore size. The osmotic solutions namely CaCl2 ·2H2 O (2–14 M) and NaCl (2–6 M)
Fig. 6. Effect of membrane pore size of transmembrane flux.
were circulated at constant flow rate of 100 ml/min, employing pineapple juice as feed. The results are shown in Fig. 6 and it can be observed that the transmembrane flux did not show any dependency on pore size in the range studied. However, from the theoretical calculations it was observed that mode of diffusion mechanism (and in turn the transmembrane flux) depends on the membrane pore size employed, which has been explained later in the discussion. 4.4. Effect of type of osmotic agent on transmembrane flux Two OA’s namely NaCl and CaCl2 ·2H2 O of different concentration (2–14 M for CaCl2 ·2H2 O and 2–6 M for NaCl) were employed during OMD experiments. The calcium chloride has showed higher transmembrane flux at all the concentrations when compared to that of sodium chloride. This is mainly due to the higher osmotic activity (ratio of its water solubility to its equivalent weight) of CaCl2 ·2H2 O, which has resulted in higher vapor pressure gradient across the membrane. 4.5. Effect of temperature Experiments were carried out by varying feed (pineapple/sweet lime juice) temperature in the range of 30–38 ◦ C
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Table 3 Values of mass transfer coefficient at different concentrations of osmotic agent Kfeed (×106 m s−1 )
Concentration (M)
(a) For pineapple juice, CaCl2 ·2H2 O, 0.05 m 2 1.65 4 1.59 6 1.64 8 1.58 10 1.62 12 1.61 14 1.59 (b) For pineapple juice, NaCl, 0.05 m 2 1.67 3 1.67 4 1.67 5 1.65 6 1.65
Fig. 7. Effect of temperature on transmembrane flux.
while keeping the OA temperature constant at 28 ± 0.5 о C employing constant temperature water bath (this study will be useful for the concentration of liquids that are not temperature sensitive). For these experiments both feed and osmotic solutions (CaCl2 ·2H2 O; 14 M) were circulated at constant flow rate of 100 ml/min. From the results it was observed that the transmembrane flux across the membrane has increased significantly with an increase in temperature (Fig. 7). It is known that the mass transfer coefficient in transport processes shows Arrhenius dependency on temperature. Similar behavior was observed in the present study. The rise in feed temperature results in an additional driving force that works synergistically with driving force generated due to the concentration gradient.
KoA (×107 m s−1 ) 11.55 9.50 6.73 4.86 4.29 2.68 2.67 9.89 9.57 9.36 9.15 8.27
Kmm = 2.895E−03; KmK = 1.072E−03 in kg m−2 h−1 Pa−1 .
dimensionless numbers (Eq. (6)) was used. The membrane module employed is flat and the flow is laminar (NRe values ranging from 18 to 430) with low mass transfer rates. The values of the constants in Eq. (6) are considered as b1 = 0.664, b2 = 0.5 and b3 = 0.33 [11]. The predicted mass transfer coefficients for both boundary layers at the prevailing hydrodynamic conditions (flat module, laminar flow) are given in Tables 3–5. Mass transport of water through membrane has been estimated based on mode of diffusion mechanism in the pores by Knudsen or molecular diffusion (Eq. (3) or (4)). It is clear that pore size plays an important role in influencing the type of diffusion for water transport through the membrane. The molecular diffusion increases and Knudsen diffusion decreases as the pore diameter becomes larger [4,19]. It may also be noted that in literature, the mechanism of mass transfer in the membrane could not be clearly pointed out to be either Knudsen or molecular [6,7]. This may be mainly due to the fact that the membranes employed by those researchers are composite type where mechanism will be different in the active layer when compared to the support layer. In the present
4.6. Model validation To validate the model in case of real systems, theoretical fluxes were estimated by accounting the individual mass transfer coefficient for boundary layers (feed and OA) as well as for membrane as shown in Table 2. In order to estimate the water transport through the boundary layers (feed as well as OA side), empirical correlation comprising of
Table 2 Mass transfer coefficients values for real systems Osmotic agent
Mass transfer coefficients Kf (×106 m s−1 )
Km (×103 kg m−2 h−1 Pa−1 ) Knudsen
Molecular
KoA (×106 m s−1 )
Pineapple juice CaCl2 ·2H2 O (0.05 m) CaCl2 ·2H2 O (0.2 m) NaCl (0.05 m) NaCl (0.2 m)
1.61 1.57 1.19 1.67
1.072 2.572 1.072 2.572
2.894 1.737 2.894 1.737
6.03 6.14 6.61 9.09
Sweet lime juice CaCl2 ·2H2 O (0.2 m) NaCl (0.2 m)
1.26 1.62
2.572 2.572
1.737 1.737
6.01 8.89
Experimental conditions—flow rate: 100 ml/min (feed and OA); temperature: 28 ± 0.5 ◦ C.
Flow rates (mL/min)
Kfeed (×106 m s−1 )
KoA (×107 m s−1 )
(a) For pineapple juice, NaCl, 0.2 m 100 1.66 75 1.45 50 1.18 25 0.83
8.32 7.13 5.88 4.16
(b) For sweet lime juice, NaCl, 0.2 m 100 1.73 75 1.50 50 1.23 25 0.87
7.76 6.74 5.43 3.83
Kmm = 1.737E−03; KmK = 2.573E−03 in kg m−2 h−1 Pa−1 .
CaCl2 −26 to +62 102–252 128–341 NaCl 81–184 2–88 18–37 CaCl2 90–316 39–144 59–208 NaCl 0.2–0.75 0.47–1.6 0.47–1.6 CaCl2 0.4–2.5 1.01–5.8 0.98–5.7 NaCl 0.3–0.64 0.3–0.62 0.3–0.78
Considering molecular diffusion Experimental flux (kg/m2 h)
Table 5 Values of mass transfer coefficients at different flow rates
Table 6 Comparison of experimental and theoretical flux at different OA concentration
case of unsupported membranes, it was observed that, the Knudsen to be the mode of diffusion when membrane pore size is 0.05 m, whereas the molecular diffusion was the mode of diffusion when pore size is 0.2 m (Table 6). For instance, for 0.05 m membrane the values predicted by Knudsen are more closely matching with the experimental ones. It may be noted that, theoretical values of the transmembrane flux could be estimated after calculating the overall mass transfer resistance (membrane plus boundary layers). The model could predict the variation of transmembrane flux with respect to different process parameters for the real systems, namely pineapple and sweet lime juices. However, there are still deviations from experimental values (Table 6), which could be attributed to the uneven pore distribution of the membrane, porosity, thickness and tortuosity, apart from the complex hydrodynamic nature of the viscous boundary layers. In order to minimize these deviations, there is need for precision analysis of the membrane structure.
Theoretical flux (kg/m2 h)
Kmm = 1.737E−03; KmK = 2.573E−03 in kg m−2 h−1 Pa−1 .
NaCl 0.52–1.82 0.3–1.17 0.3–1.15
9.67 9.26 8.91 8.69 7.94
CaCl2 0.6–1.6 0.5–1.75 0.4–1.54
(b) For sweet lime juice, NaCl, 0.2 m 2 1.71 3 1.67 4 1.72 5 1.65 6 1.34
CaCl2 1.1–6.6 0.69–4.0 0.68–4.0
11.11 9.21 7.10 4.91 4.40 2.95 2.40
Systems Pineapple (0.05 m) Pineapple (0.2 m) Sweet lime (0.2 m)
(a) For sweet lime juice, CaCl2 ·2H2 O, 0.2 m 2 1.25 4 1.30 6 1.20 8 1.30 10 1.28 12 1.26 14 1.21
KoA (×107 m s−1 )
Deviation for molecular diffusion (%)
Kfeed (×106 m s−1 )
Considering Knudsen diffusion
Concentration (M)
Deviation for Knudsen diffusion (%)
Table 4 Values of mass transfer coefficient at different concentrations of osmotic agent
NaCl −26 to +17 46–166 68–108
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5. Conclusions The influence of various process parameters such as type, concentration and flow rate of the osmotic agent; type (polypropylene membranes) and pore size (0.05 and 0.2 m) of the membrane; temperature with respect to transmembrane flux were studied for real systems. Resistance-in-series model was employed for analyzing the mass transfer in OMD. The model could predict the transmembrane flux and also the effect of the parameters. The feed and OA boundary layer resistances could not be ignored even though they were low. The observed deviations of the predicted values from the experimental values of the transmembrane flux could be attributed to uneven pore distribution, geometry of the membrane and complex hydrodynamic nature of the boundary layer (feed and OA).
µ ρ ϕ χ ΩD
viscosity of the fluid (Pa s) density of the fluid (kg m−3 ) association factor, 2.26 for water tortuosity factor (–) ˚ collision integral (A)
Subscripts f feed m membrane mK Knudsen diffusion mm molecular diffusion oA osmotic agent w water
Appendix A Acknowledgements We thank Dr. V Prakash, Director, CFTRI, for the encouragement and keen interest in separation processes. We acknowledge DST, Government of India for funding the project on Osmotic Membrane Distillation # III.5 (76)/2000ET. Naveen Nagaraj and Ganapathi Patil gratefully acknowledge CSIR, Government of India for the Senior Research Fellowships.
Nomenclature D J k K K L M P P* r R T u xs Yln
diffusion coefficient (m2 s−1 ) flux (l m−2 h−1 ) mass transfer coefficient in boundary layer (m s−1 ) mass transfer coefficient (feed and OA) (kg m−2 h−1 Pa−1 ) overall mass transfer co-efficient (kg m−2 h−1 Pa−1 ) length of the membrane (m) molecular weights of constituents (kg mol−1 ) vapor pressure (kPa) saturated vapor pressure (kPa) membrane pore radius (m) gas constant (kJ mol−1 K−1 ) temperature (K) velocity of the fluid (m s−1 ) osmotic agent molar agent mole fraction of air (log-mean) (–)
Greek letters δ membrane thickness (m) ∆ difference ε porosity (–) σ AB Lennard–Jones force constant for the binary
The following steps are performed in order to calculate the mass transfer coefficients and flux across the membrane: Step 1 Mass transfer through the membrane (a) For molecular diffusion. The Ficks diffusion coefficient (D) was calculated from Eq. (5) and substituted in Eq. (4) in order to get Kmm (b) For Knudsen diffusion. The KmK was calculated directly from Eq. (3) Step 2 Mass transfer through the boundary layers (a) The diffusion coefficient (Dw ) was calculated from Eq. (8) and Re and Sc were calculated from Eq. (7). The values obtained were substituted in Eq. (6) in order to get ki for both feed as well as osmotic agent solutions with their respective physical properties and hydrodynamic conditions. (b) The values obtained in the above step were substituted in Eq. (9) in order to get Ki of both feed and OA in the same units as that of Km . Step 3 Calculation of theoretical flux (a) By considering as molecular diffusion or Knudsen diffusion. The theoretical fluxes were calculated using Eq. (1) by substituting overall mass transfer coefficient (K), which has been calculated from Eq. (2).
References [1] K.B. Petrotos, H.N. Lazarides, Osmotic concentration of liquid foods, J. Food Eng. 49 (2001) 201. [2] B. Girard, L.R. Fukomoto, Membrane processing of fruit juices, and beverages: a review, Crit. Rev. Food Sci. Nutr. 40 (2000) 91. [3] A.V. Narayan, N. Naveen, H.U. Hebbar, A. Chakkaravarthi, K.S.M.S. Raghavarao, S. Nene, Acoustic field-assisted osmotic membrane distillation, Desalination 147 (2002) 149. [4] K.W. Lawson, D.R. Lloyd, Membrane distillation, J. Membr. Sci. 124 (1997) 1.
56
N. Nagaraj et al. / Journal of Membrane Science 268 (2006) 48–56
[5] J.I. Mengual, J.M.O. Zarate, L. Pena, V. Velazquez, Osmotic distillation through porous hydrophobic membranes, J. Membr. Sci. 82 (1993) 129. [6] M. Courel, M. Dornier, G.M. Rios, M. Reynes, Modeling of water transport in osmotic distillation using asymmetric membranes, J. Membr. Sci. 173 (2000) 107. [7] C. Gostoli, Thermal effects in osmotic distillation, J. Membr. Sci. 163 (1999) 75. [8] V.D. Alves, I.M. Coelhoso, Mass transfer in osmotic evaporation: effect of process parameters, J. Membr Sci. 208 (2002) 171. [9] J. Sheng, R.A. Johnson, M.S. Lefebvre, Mass and heat transfer mechanisms in the osmotic distillation process, Desalination 80 (1991) 113. [10] P.A. Hogan, R.P. Canning, P.A. Peterson, R.A. Johnson, A.S. Michales, A new option: osmotic distillation, Chem. Eng. Prog. 94 (1998) 49. [11] C.J. Geankoplis, Principles of Mass Transfer Transport Processes Unit Operations, III ed., Prentice-Hall, London, 1993. [12] R.W. Schofield, A.G. Fane, And C.J.D Fell, Heat and mass transfer in membrane distillation, J. Membr. Sci. 33 (1987) 299. [13] T.K. Sherwood, R.L. Pigford, C.R. Wilke, Mass Transfer, McGrawHill, New York, 1975.
[14] C.R. Wilke, P. Chang, Correlation of diffusion coefficients in dilute solutions, A.I.Ch.E.J. 1 (1955) 264. [15] R.E. Treybal, Mass Transfer Operations, III ed., McGraw Hill, New York, 1980. [16] K.R. Patil, A.D. Tripathi, G. Pathak, S.S. Katti, Thermodynamic properties of aqueous electrolyte solutions. 2. Vapor pressure of aqueous solutions of NaBr, NaI, KCl, KBr, KI, RbCl, CsBr, MgCl2 , CaCl2 , CaBr2 , CaI2 , SrCl2 , SrBr2 , SrI2 , BaCl2 , and BaBr2 , J. Chem. Eng. Data 36 (1991) 225. [17] E. Colin, W. Clarke, D.N. Glew, Evaluation of the thermodynamic functions for aqueous sodium chloride from equilibrium and calorimetric measurements below 154 ◦ C, J. Phys. Chem. Ref. Data 14 (1985) 408. [18] H.C.M. Kester, J. Pisser, Purification and characterization of polygalcturonases produced by hyphal fungus Asperigillus niger, Biotech. Appl. Bio. Chem. 12 (1990) 152. [19] V.D. Alves, I.M. Coelhoso, Effect of membrane characteristics on mass and heat transfer in the osmotic evaporation process, J. Membr. Sci. 228 (2004) 159. [20] J. Ananthaswamy, G. Atkinson, Thermodynamics of concentrated electrolyte mixtures. 5. A review of the thermodynamic properties of aqueous calcium chloride in the temperature range 273.15–373.15 K, Chem. Eng. Data 30 (1985) 120.