Kinetic analysis on membrane-based reverse micellar extraction of lysozyme from aqueous solutions

Journal of Membrane Science 281 (2006) 636–645

Kinetic analysis on membrane-based reverse micellar extraction of lysozyme from aqueous solutions Ruey-Shin Juang ∗ , Hsiang-Chien Kao, Chiau-Lin Shiau Department of Chemical Engineering and Materials Science, Yuan Ze University, Chung-Li 320, Taiwan Received 16 January 2006; received in revised form 17 April 2006; accepted 21 April 2006 Available online 28 April 2006

Abstract The extraction of lysozyme from aqueous solutions through a flat-sheet microporous membrane (pore size 0.45 ␮m, thickness 147 ␮m, porosity 0.75) into an isooctane solution of sodium bis(2-ethylhexyl)sulfosuccinate (AOT) reverse micelles was examined. Batch liquid–liquid extraction experiments were first conducted at different lysozyme concentrations (250–1000 mg L−1 ), KCl concentrations (0.1–1.2 M), pH (2–12) and AOT concentrations (0.01–0.1 M) to obtain equilibrium relationships. Effective extraction of lysozyme was achieved in the KCl concentration range of 0.1–0.4 M and pH range of 4–9. More than 90% of lysozyme could be stripped to an aqueous phase of high alkalinity (pH 11.5) and high KCl concentration (1.5 M). A mass transfer model was proposed that considers all diffusion in the aqueous stagnant layer, membrane and reverse micellar stagnant layer to predict the transport flux of lysozyme in the present membrane-based extraction process. The solubilization of lysozyme from aqueous phase to the AOT/isooctane reverse micelles was assumed to attain equilibrium instantaneously. A good agreement between the calculated and measured fluxes was obtained under the ranges studied (standard deviation, 11%). © 2006 Elsevier B.V. All rights reserved. Keywords: Reverse micellar extraction; Lysozyme; AOT; Membrane-based extraction process; Mass transfer modeling

1. Introduction In recent years, many separation techniques have been developed in biotechnology to achieve a highly efficient and economical process. One novel technique with the ability to be scaled up easily, to be operated continuously, and to be highly selective is liquid–liquid extraction using microemulsions [1–4]. The aggregates of surfactant molecules are spontaneously generated in organic solvents as a result of molecular self-assembly. These aggregates can solubilize water in their polar cores giving rise to water-in-oil microemulsions, commonly referred to as reverse micelles. It has been proven that proteins can be solubilized within these reverse micelles in active form [5]. This method is more suitable for separating proteins than conventional liquid–liquid extraction or other methods that were used in the past because the transfer of proteins into solvents often results in irreversible denaturation and loss of biological activity [4].

∗

Corresponding author. Tel.: +886 3 4638800x2555; fax: +886 3 4559373. E-mail address: [email protected] (R.-S. Juang).

0376-7388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2006.04.035

Traditional liquid–liquid reverse micellar extraction processes have been operated in devices, such as spray column, rotating disc contactor, packed towers, etc. [6–8], which seek to maximize contact area for mass transfer. The mild or intimate mixing that usually occurs in these devices might lead to the possible formation of emulsions of the two phases, thereby inhibiting phase separation and product recovery. These shortcomings could be minimized or eliminated using non-dispersive solid membrane-based processes, such as membrane contactors and supported liquid membranes [9,10]. They use a flat-sheet or hollow fiber microporous membranes soaked with the organic carriers to separate the aqueous feed phase and the organic phase or even the aqueous strip phase. Besides the non-dispersive nature, hollow fiber membrane-based extractions are substantially faster than those possible in traditional equipments and the extraction is not compromised by flooding and loading because the flows of reverse micelles and raffinate are almost completely independent [9]. In this work, the reverse micellar extraction of proteins from aqueous solutions using a flat-sheet microporous membrane was experimentally and theoretically examined. The system of lysozyme-bis(2-ethylhexyl)sulfosuccinate (AOT)/isooctane

R.-S. Juang et al. / Journal of Membrane Science 281 (2006) 636–645

was exemplified. In contrast to a large number of studies investigating liquid–liquid extraction of lysozyme [11–17], little attention has been paid to examining reverse micellar extraction in solid membrane-based processes [9,18]. For example, Tsai et al. [18] have studied the extraction of ␣-chymotrysin by supported liquid membranes using AOT reverse micelles as carriers. Only a phenomenological model was proposed to describe the mass transfer. In fact, the extraction and separation of lysozyme with AOT reverse micellar the so-called bulk liquid membrane, a process without solid membrane support, have been reported [19,20]. The chemistry involved in membrane-based reverse micellar extraction process is essentially the same as that in liquid–liquid extraction process, and the overall membrane process is governed not only by equilibrium parameters but also by kinetic parameters. It is thus possible to model such membrane process from a good knowledge of extraction chemistry and transport properties of the relevant geometry [21]. In practice, the extraction equilibrium behavior is rather complicated. The distribution of proteins between the micellar phase and aqueous phase is largely determined by the environments of bulk aqueous phase, i.e., pH, ionic strength and type of salt. Parameters related to the organic phase also affect the distribution of protein, such as type and concentration of surfactant, presence of co-surfactant and type of solvent [1–5]. By controlling these parameters, the extraction efficiency can be varied via the variations of protein-micelle electrostatic, hydrophobic and steric interactions. Among these, electrostatic interaction is considered as the dominant driving force especially in forward extraction process [1]. To obtain consistent results and convincible conclusions under controlled conditions, batch liquid–liquid reverse micellar extraction experiments were first made to get equilibrium relationships. The membrane-based extraction experiments were then performed, in which the membrane and bulk organic phases were the same as the organic phase used in liquid–liquid extraction systems. A mass transfer model was proposed that takes into account diffusion in the aqueous-phase stagnant layer, membrane and micelle-phase stagnant layer to describe the extraction of lysozyme in the present membrane-based process. The validity of the proposed model was justified by comparing with the measured transport fluxes of lysozyme under various conditions.

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rate from 0.1 M KCl solution of pH 6.5 to a reverse micellar phase was governed by diffusion in the aqueous film and the solubilization at the aqueous–organic interface. Using a similar device, Kinugasa et al. [11] have reported that in the stripping of lysozyme from the micellar solution there is a main resistance to leave it at the organic–aqueous interface; however, they indicated that the forward extraction rate of lysozyme into AOT reverse micellar phase at pH values below its pI is limited only by diffusion through the boundary layers. Although the role of solubilization reaction during the extraction is inconsistent in these two studies, the resistance of lysozyme solubilization at the interface to the overall extraction process is assumed to be negligibly small in the present flat-sheet microporous membrane-based extraction system. This is particularly valid in this case because of the use of a thicker membrane support (thickness 147 ␮m) here [21], in which membrane diffusion would play a crucial role. The concentration profiles of the specie near and within the microporous membrane are shown in Fig. 1. If all the concentration profiles are linear and the diffusion process is described by Fick’s equation, the transport flux of each step is given as follows: 1. Diffusion of lysozyme from the feed bulk phase through aqueous layer to the aqueous-membrane interface, in which lysozyme instantaneously solubilizes into AOT reverse micelles, J1 = ka,Lys ([Lys]a − [Lys]ai )

(1)

2. Diffusion of lysozyme present in the AOT reverse micelles through the membrane, m

m

J2 = km,micelle ([Lys]ai − [Lys]oi )

(2)

where the overbar refers to the membrane (reverse micellar) phase and the superscript m refers to the membrane side adjacent to the aqueous- or organic-membrane interface. That is, Lys denotes the lysozyme that solubilizes in the AOT reverse micelles for simplicity.

2. Modeling of the mass transfer 2.1. Mass transfer in the membrane extraction process For the kinetic studies on the extraction of lysozyme (1000 mg L−1 ) by the AOT-isooctane reverse micelles across a flat liquid–liquid interface, Nishiki et al. [14] have indicated that the rate constant of lysozyme release (i.e., the dissociation of lysozyme-AOT complex) at the aqueous–organic interface is two orders smaller than that of lysozyme solubilization (i.e., the formation of lysozyme-AOT complex). They found that the release process at the interface is rate limiting for the stripping of lysozyme from reverse micellar phase to an aqueous phase of higher KCl concentration. On the other hand, the extraction

Fig. 1. Concentration profiles of lysozyme and its AOT reverse micelle near and within a flat microporous membrane support.

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3. Diffusion of lysozyme/AOT reverse micelles through the organic layer to the organic bulk phase, J3 = ko,micelle ([Lys]oi − [Lys]o )

(3)

At pseudo-steady state, the following equalities hold [21,22]: J1 = J2 = J3 = JLys

(4)

If the equilibrium relationships for reverse micellar extraction and the mass transfer coefficients were available, the steadystate flux JLys could be calculated by combining Eqs. (1)–(4) using the NEQNF program (FORTRAN version 5.0). 2.2. Measurement of transport parameters from simple diffusion experiments It was reported that a microporous hydrophobic membrane with a high porosity and pore diameters between 10−3 and l02 ␮m is not wetted by water [23]; however, hydrocarbons and most organic solvents readily wet it. The diffusion boundarylayer resistance at both sides of the membrane in membranebased transport processes could be determined from simple diffusion experiments, particularly for the solutes of acetic acid and iodine [23–25]. This is because they have sufficiently low and high distribution coefficients (m), respectively, defined as the ratio of equilibrium solute concentration in the organic phase to that in the aqueous phase. The concentration profiles of acetic acid (HA) and iodine (B) across a flat-sheet membrane-based diffusion cell are shown in Fig. 2. The solute concentrations at both sides of the membrane-

organic interface are assumed to the same because this interface is basically homogeneous due to the high porosity of the membrane used [24,25]. In isooctane/water system, the distribution coefficients of acetic acid (mHA ) and iodine (mB ) was measured to be 1.2 × 10−3 and 38.4, respectively, in the solute concentration ranges of 0.01–0.1 M and 2–11 mM. When acetic acid is transferred from the organic to aqueous phases, the transfer rate is given by:
 Vo d[HA]o − = ko ([HA]o − [HA]oi ) A dt m

m

= km ([HA]oi − [HA]ai ) = ka ([HA]ai − [HA]a ) = Ko ([HA]o − mHA [HA]a )

(5)

and mHA 1 1 1 = + + Ko ka ko km

(6)

where ko , km and ka are the individual mass-transfer coefficients (m s−1 ) and Ko is the overall mass-transfer coefficient based on the organic-phase concentration (m s−1 ). Because mHA is small enough, the terms (mHA [HA]a ) and (mHA /ka ) in Eqs. (5) and (6) are negligible compared to [HA]o and (1/ko + 1/km ), respectively [23–25]. Hence, the simplified relationships are obtained:
 [HA]o,0 A ln Ko t = (7) Vo [HA]o,t 1 1 1 = + Ko ko km

(8)

When iodine (B) is transferred from the aqueous to organic phases, the following relationships are similarly obtained:
 Va d[B]a m m − = ka ([B]a − [B]ai ) = km ([B]ai − [B]oi ) A dt
 [B]o (9) = ko ([B]oi − [B]o ) = Ka [B]a − mB and 1 1 1 1 = + + Ka ka m B ko m B km

(10)

where Ka is the overall mass-transfer coefficient based on the aqueous-phase concentration (m s−1 ). Since mB is sufficiently large, the terms ([B]o /mB ) and 1/(mB ko ) in Eqs. (9) and (10) are ignored in contrast to [B]a and (1/ka + 1/mB km ), respectively. Here, the term 1/mB km is not omitted because km is smaller than ko , e.g., by up to one order in the diffusion of iodine from water across a microporous hydrophobic PVDF membrane (pore size 0.22 ␮m, thickness 125 ␮m, porosity 0.75) to kerosene [25]. Thus, we have
 [B]a,0 A ln Ka t = (11) [B]a,t Va Fig. 2. Concentration profiles of acetic acid and iodine near and within a membrane support.

1 1 1 = + Ka ka m B km

(12)

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As indicated in Eqs. (7) and (11), Ko and Ka can be obtained from the slope of the semi-log plot of ([HA]o,0 /[HA]o,t ) and ([B]a ,0 /[B]a ,t against t, respectively. In this work, diffusion of species through the membrane pore is approximated by diffusion through a cylindrical wall (because the membrane used is symmetric); thus, the membrane mass-transfer coefficient can be expressed as [23]: km =

εm Dj τm L

(13)

where εm , τ m and L are the porosity, tortuosity and thickness of membrane support, respectively. A reasonable value of τ m of 2 is adopted here [25]. As indicated by Levich [26], the individual mass-transfer coefficients ko and ka are proportional to Dj2/3 ν−1/6 and km is proportional to Dj as shown in Eq. (13), where ν is the kinematic viscosity of the medium. The values of ko , km and ka can be thus calculated from Eqs. (8) and (12) because they are interchangeable when Dj ’s of acetic acid and iodine in various media and the ν values are available. 3. Materials and methods 3.1. Reagents and solutions Lysozyme powder from chicken egg white (95% purity, MW 14.4 kDa, pI 11.1, activity 46,400 unit mg−1 solid) was obtained from Sigma–Aldrich Co. Also, the anionic surfactant AOT (sodium bis(2-ethylhexyl)sulfosuccinate) was purchased from Sigma–Aldrich Co. and was used as received. The solvent isooctane was supplied by Fluka Chemie GmbH. Kerosene (Union Chemical Co., Taiwan) was washed twice with 20 vol% H2 SO4 to remove aromatics and then with deionized water (Millipore Milli-Q) three times. Other analytical reagent-grade inorganic chemicals including KCl, Na2 HPO4 , NaH2 PO4 , I2 , KI, NaOH and HCl were all supplied by Merck Co. In liquid–liquid extraction experiments, the aqueous phase contained various amounts of lysozyme (250–1000 mg L−1 ) and KCl (0.1–1.2 M) in deionized water. The aqueous pH was adjusted in the range of 2–12 by adding small amount of 0.1 M NaOH or HCl solution. The organic solution was prepared by diluting various amounts of AOT (0.01–0.1 M) in isooctane. The strip phase tested consisted of different amounts of KCl (0.3–2.4 M) and its pH was changed in the range of 8–12.5. 3.2. Sample analysis The concentration of lysozyme in the aqueous phase was determined by measuring the absorbance at 280 nm with an UV/visible spectrophotometer (Jasco V-550, Japan). The enzymatic activity of lysozyme in the aqueous phase was measured following the method of Davies et al. [16,27]. A solution containing 0.3 g L−1 of dry Micrococcus lysodeikticus substrate (Sigma–Aldrich Co.) was prepared in 50 mM phosphate buffer at pH 7. The temperature of the UV cells was 25 ◦ C and the wavelength was 450 nm. The substrate solution (3 cm3 ) was pipetted into both the reference and the sample cuvettes, which were held

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in the spectrophotometer for 5 min to allow them to reach 25 ◦ C. The phosphate buffer (0.1 cm3 ) was pipetted into the reference cuvette. Then, 0.1 cm3 of the lysozyme solution was added to the sample cuvette, and the decrease in the absorbance of substrate solution was monitored for 3 min. One activity unit of lysozyme will decrease the absorbance by 0.001 per minute at 25 ◦ C and pH 7 under the specified conditions. The water content of reverse micellar phase (W0 ) was determined by Karl-Fischer titration using a volumetric titrator (Mettler Toledo DL-38), which is defined as the molar concentration ratio of water to AOT in the reverse micellar phase. The KarlFischer reagents used were CombiTitrant 5 (one-component reagent) and combiSolvent (methanol-free solvent with onecomponent reagent) purchased from Merck Co. (Germany). A 1.0-cm3 solution was injected using a syringe and the coefficient of variation was ±5%. 3.3. Batch extraction and stripping of lysozyme The extraction experiments were carried out using an aqueous phase containing lysozyme and KCl in a 25-cm3 stoppered conical flask at 25 ◦ C. Equal volumes (10 cm3 ) of aqueous phase and the organic phase (AOT reverse micelles/isooctane) were mixed and stirred at 157.0797 × 10−1 rad s−1 (150 rpm) for 20 min. After phase separation by centrifugation at 4188.792 × 10−1 rad s−1 (4000 rpm) for 10 min, the aqueous samples were taken and the organic phase was gathered for the following stripping process. To prevent the interference of other species during UV measurements, the sample analysis was performed against appropriate blank solutions, which were prepared simultaneously with the lysozyme sample. The aqueous pH was measured using a pH meter (Horiba F-23, Japan). Each experiment was at least duplicated under identical conditions. Reproducibility of the measurements was within 6% (mostly, within 3%). The extraction yield, E (%), was calculated as follows: ⎛ ⎞ equilibrium concentration of lysozyme ⎜ in the organic phase ⎟ ⎜ ⎟ E(%) = 100 × ⎜ ⎟ ⎝ initial concentration of lysozyme ⎠ in the aqueous phase (14) In the stripping process, the organic (reverse micellar) phase that had been loaded with lysozyme from the extraction runs was in contact with an equivalent volume (10 cm3 ) of a new aqueous phase in a 25-cm3 stoppered conical flask at 25 ◦ C, which contained a fixed KCl concentration and pH. The mixture was stirred at 157.0797 × 10−1 rad s−1 (150 rpm) for 60 min, and then centrifuged for 10 min at 4188.792 × 10−1 rad s−1 (4000 rpm). The concentration and activity of lysozyme in the aqueous phase were determined. The activity recovery was calculated by: activity recovery (%) 
activity of recovered lysozyme (units mg−1 ) = 100 × activity of feed lysozyme (units mg−1 ) (15)

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3.4. Apparatus and membrane The membrane-based stirred cell used here was identical to that described previously but with a slightly larger dimension [28]. Two chambers (250 cm3 each) separated by a membrane support with an area of 9.6 cm2 were stirred at the same rate (209.4396 × 10−1 rad s−1 (200 rpm)) but in opposite directions. This stirring speed was selected such that the organic phase soaked within the membrane pores could not be washed out. The entire cell was immersed in a water bath controlled at 25 ◦ C. The PVDF microporous membrane used (Durapore, Millipore) had a mean thickness (L) of 147 ␮m, a mean pore size of 0.45 ␮m and a porosity (εm ) of 0.75. 3.5. Simple diffusion experiments In simple diffusion experiments, the pores in microporous membrane were pre-filled with the AOT-free isooctane or kerosene under vacuum as reported earlier [25,28]. The membrane was clamped and the apparatus was assembled. For measuring organic-layer mass transfer coefficient, acetic acid (0.1 M) was transferred from the organic to aqueous phases and the aqueous and organic samples were taken at a certain time intervals. The concentrations of acetic acid in the aqueous and organic phases were determined by titrating with water and isopropyl alcohol solution of KOH, respectively, using phenolphthalein as indicator to check whether the mass balance was fulfilled. For measuring aqueous-layer mass transfer coefficient, on the other hand, iodine (2 mM) was transferred from the aqueous to organic phases and the aqueous samples were withdrawn. The concentration of iodine in the aqueous phase was analyzed with an UV/visible spectrophotometer at a wavelength of 460 nm [29]. Here, the organic sample was not taken because only the iodine concentration in the aqueous phase is needed in determining Ka as shown in Eq. (11). 3.6. Membrane-based extraction experiments In membrane-based extraction experiments, the pores in microporous membrane were filled with AOT reverse micelles under vacuum before use. The membrane was then clamped and the device was assembled. The aqueous phase containing lysozyme and KCl and the organic AOT reverse micellar phase (250 cm3 , each) were introduced into the left and right chambers, respectively, and the stirring was started. When pseudo steady state was reached (within about 40 min), samples (2.5 cm3 ) were taken from the aqueous phase at preset time intervals and the original aqueous phase was immediately added to maintain the volume unchanged. The concentration of lysozyme in aqueous phase was determined, and corrections due to the volume replacement were also made. 4. Results and discussion 4.1. Batch extraction of lysozyme The effect of aqueous pH on lysozyme solubilization into reverse micellar phase is shown in Fig. 3. More than 80% of

Fig. 3. Effect of aqueous pH on the forward extraction of lysozyme.

lysozyme is extracted into the reverse micelles at pH < pI (11.1) since lysozyme is positively charged and is attracted by the AOT head-groups under such conditions [11]. This is not the case at higher KCl concentration (>0.5 M), which will be further discussed below. Proteins are transferred to the reverse micelles only at pH at which their net charge is opposite to that of the surfactant head-groups since solubilization is usually steered by electrostatic interactions between protein molecule and the surfactant head-group [5,11]. It is found from Fig. 3 that the solubilization drastically reduces to 12% and even 1% at pH 12 because lysozyme is negatively charged at this pH and hence results in electrostatic repulsion from the negatively charged AOT head-groups. It was suggested that the solubilization of lysozyme into an AOT reverse micelle consists of two steps: formation of lysozyme-AOT complex to precipitate from the aqueous phase and the solubilization of lysozyme-AOT complex into the reverse micellar phase [17]. The low extraction at low KCl concentration (0.1 M) and low pH (<4) is possibly a result of the formation of stable precipitates of lysozyme-AOT complex in the aqueous phase, thereby inhibiting soluilization and extraction. In this case, the fewer amounts of chloride counterions compete with AOT to bind with the positively charged lysozyme, and the dissociation of AOT anion from its counterion (potassium) increases. Generally speaking, effective extraction of lysozyme (>95%) is achieved in the pH range of 4–9 and KCl concentration range of 0.1–0.4 M, as we will see in Fig. 4. Another factor affecting protein solubilization is the ionic strength. Forward extraction was carried out at pH 4.2 using an aqueous phase containing various amounts of KCl. The ionic strength effect on the amount of lysozyme solubilizing into the reverse micelles is shown in Fig. 4. It is found that the solubilization of lysozyme is significantly retarded when KCl concentration is higher than 0.5 M. This is also the case in the AOT concentration ranges of 0.01–0.1 M (Fig. 5a). Such behavior can be explained in terms of two effects due to a change in the thickness of electric double layer [11,15,17]. One is a size exclusion effect. The electric double layer adjacent to the hydrophilic AOT head-groups is thinned with an increase in ionic strength, and thus the electrostatic repulsive force between

R.-S. Juang et al. / Journal of Membrane Science 281 (2006) 636–645

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Fig. 6. Effect of aqueous pH on the stripping and activity recovery of lysozyme. Fig. 4. Effect of aqueous KCl concentration on the forward extraction of lysozyme.

the neighboring head-groups is reduced. This factor gives rise to the formation of smaller reverse micelles in the organic phase and is likely to provide the exclusion effect in response to the size of protein molecule. The other is due to electrostatic attractions between the charged protein groups and the AOT head-groups in a reverse micelle. The extraction of protein is lowered with increasing ionic strength because electrostatic attraction is weakened (electrostatic screening effect). The trends of water content (W0 ) in the reverse micelles with KCl concentration can support this argument, at least in the AOT concentrations of 0.05 and 0.1 M, as shown in Fig. 5b [15].

Fig. 5. Effect of organic AOT and aqueous KCl concentrations on (a) the forward extraction of lysozyme and (b) the water content.

Although the effect of AOT concentration on forward extraction of lysozyme may be positive, it is insignificant under the ranges investigated. It was experimentally found that the organic–aqueous interface tends to emulsify at higher AOT concentrations because in this case the reverse micelles possess higher water contents. Consequently, an AOT concentration of 0.05 M is chosen for further membrane-based extraction studies. 4.2. Batch stripping of lysozyme The stripping of lysozyme was carried out using the aqueous phase with different pH values and KCl concentrations. The stripping reaches maximum (>90%) at pH just above pI, that is, pH 11.5, as shown in Fig. 6. The activity recovery of 90% is obtained under the conditions studied. When aqueous pH is higher than 11.5, the solubilized lysozyme becomes more negatively charged. Some cations will readily enter into the reverse micelles to neutralize the negative charges on the enzyme, thereby inhibiting the release of lysozyme [13,16]. Kinugasa et al. [12] have ever observed that the stripping of lysozyme from 0.05 M AOT reverse micelles reaches maximum at pH 11.3. They also indicated that insoluble aggregates composed of lysozyme and AOT molecules are formed at the organic–aqueous interface at pH > 12, leading to a decrease in the extent of stripping; moreover, the activity recovery is drastically reduced using a strip phase for pH above 12. Fig. 7 shows the effect of KCl concentration in the strip phase on the stripping of lysozyme at pH 11.5. The stripping and activity recovery reach maximum at a KCl concentration of 1.5 M. Similar results that the stripping of lysozyme increases with increasing KCl concentration up to 1.5 M have been reported earlier [12]. Increasing KCl concentration increases the concentration of chloride counterions competing with AOT to bind with the positively charged lysozyme, and increases the dissociation of AOT anions from its counterions [17]. It is evident from Fig. 7 that the stripping decreases at a KCl concentration above 1.5 M, likely due to the formation of insoluble aggregates containing AOT and lysozyme molecules at the organic–aqueous interface [13]. At such high KCl concentrations, on the other hand, the amount of chloride ions competing with AOT to bind with the positively charged lysozyme remarkably increases [16]. Hence,

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R.-S. Juang et al. / Journal of Membrane Science 281 (2006) 636–645 Table 1 Values of the parameters used for calculating transport flux of lysozyme in the present membrane-based extraction process at 25 ◦ C Parameter

Fig. 7. Effect of aqueous KCl concentration on the stripping and activity recovery of lysozyme.

there is a possibility that lysozyme tends to exposure in the organic environment during the stripping step and possess a low activity recovery because complex formation between lysozyme and AOT decreases. 4.3. Results of simple diffusion experiments The values of ko , km and ka cannot be readily evaluated from Eqs. (8) and (12) since there are three unknowns but only two equations. A simple diffusion experiment of iodine from water to kerosene solvent was conducted, and an extra equation similar to Eq. (12) is thus obtained. The distribution coefficient of iodine (mB ) between kerosene and water is 60 [25]. Fig. 8 shows the typical results for determining Ko and Ka according to Eqs. (7) and (11), respectively. In this work, the diffusivities of acetic acid and iodine in water at 25 ◦ C are estimated to be 1.48 × 10−9 and 1.31 × 10−9 m2 s−1 , respectively, by the Hayduk and Minhas equation for solutes in aqueous solutions [30], where the molar volumes of acetic acid and iodine at their boiling points are 64.0 and 56.3 cm3 mol−1 , respectively [31]. On the other hand,

Diffusivity Acetic acid in water (Da,HA ) Acetic acid in bulk isooctane (Do,HA ) Iodine in water (Da,B ) Iodine in bulk kerosene (Do,B ) Iodine in bulk isooctane (Do,B ) Lysozyme in water (Da,Lys ) Lysozyme-AOT micelle in bulk isooctane (Do,micelle ) Mass transfer coefficient Lysozyme in water (ka,Lys ) Lysozyme-AOT micelle in bulk isooctane (ko,micelle ) Lysozyme-AOT micelle within membrane (km,micelle )

Value ( m s−1 )

Reference

1.48 × 10−9 2.81 × 10−9

This work This work

1.31 × 10−9 2.76 × 10−9 3.23 × 10−9 1.15 × 10−10 1.23 × 10−10

This work This work This work [11,32] This work

2.41 × 10−6 2.12 × 10−6

This work This work

2.96 × 10−7

This work

the diffusivities of acetic acid (existing as dimers) and iodine in isooctane as well as iodine in kerosene are estimated to be 2.81 × 10−9 , 3.23 × 10−9 and 2.76 × 10−9 m2 s−1 , respectively, by the Hayduk and Minhas equation for non-aqueous solutions [30]. The kinematic viscosities of isooctane and kerosene are 7.1 × 10−7 and 7.9 × 10−7 m2 s−1 , respectively, at 25 ◦ C. The molar volumes of isooctane and kerosene at their boiling points are 185 and 278.5 cm3 mol−1 , respectively [31]. The parachors of acetic acid dimer, iodine, isooctane and kerosene are estimated to be 258.6, 180.6, 406.5 and 512 cm3 g1/4 s−1/2 , respectively, by the method of additive group contributions [30]. Under the given cell geometry and agitation conditions for the membrane-based stirred cell, the following transport parameters are obtained (Table 1): ka,B (iodine in water) = 1.22 × 10−5 m s−1 ; ko,B (iodine in isooctane) = 1.87 × 10−5 m s−1 ; km,B (iodine in isooctane-filled membrane) = 7.78 × 10−6 m s−1 . 4.4. Validity of the mass transfer model As indicated in Section 2.1, the steady-state flux JLys could be calculated by simultaneously solving Eqs. (1)–(4) if the masstransfer coefficients and extraction equilibrium relationships were available. Once the individual mass-transfer coefficients of iodine are known, that of lysozyme in water and reverse micelles in isooctane can be estimated by the following equations [11,26]:

 ka,Lys Da,Lys 2/3 = (16) ka,B Da,B 

Do,micelle 2/3 ko,micelle = (17) ko,B Do,B

Fig. 8. Determination of mass transfer coefficients in the membrane-based transport process.

Table 1 lists the correlated results. The diffusivity of lysozyme in water consisting of 0.1 M NaCl is 1.15 × 10−10 m2 s−1 at 25 ◦ C [11,32]. The diffusivity of lysozyme as the AOT

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Fig. 9. Effect of aqueous pH value on (a) the time profiles of lysozyme concentration and (b) the calculated and measured fluxes in the membrane-based extraction process.

complex in isooctane reverse micelle is estimated to be 1.23 × 10−10 m2 s−1 by the Stokes–Einstein equation [11]: Do,micelle

kB T = 3πdη

(18)

is the Boltzmann’s constant where kB (=1.38 × 10−23 kg m2 s−2 K−1 ), T the absolute temperature (K), η the viscosity of isooctane (=4.81 × 10−4 kg m−1 s−1 ) and d is the diameter of the reverse micelle (m). Here, the d value of 7.4 nm is adopted according to the measured water content [15]. Secondly, solubilization equilibrium of lysozyme is assumed at the aqueous-membrane interface; thus, we have m

[Lys]ai =

E [Lys]ai 100 − E

(19)

It is noticed that the extraction yield E (%) depends on pH, KCl and lysozyme concentrations in the aqueous phase, as well as AOT concentration in the organic phase, as shown in Figs. 3–5. Figs. 9a–11a illustrate time profiles of the extraction of lysozyme by AOT reverse micelles using the membrane-based process at different aqueous pH values, KCl concentrations and organic AOT concentrations, respectively. In Figs. 9a–11a, the transport fluxes of lysozyme JLys are calculated based on the

643

Fig. 10. Effect of aqueous KCl concentration on (a) the time profiles of lysozyme concentration and (b) the calculated and measured fluxes in the membrane-based extraction process.

initial-rate concept, that is

 d[Lys]a A JLys = − Va dt t→0

(20)

Under the conditions investigated, it is evident that there is a maximum flux at pH 7–8 or an AOT concentration of 0.05 M, but the flux decreases with increasing KCl concentrations from 0.1 to 0.7 M. Critical comparisons of the fluxes with literature results appear difficult because to our best knowledge few data are documented using equivalent apparatus. However, the same trends of pH and organic AOT concentration on the amount of lysozyme transferred, calculated after 24 h of operation, through a bulk liquid membrane have been reported [19]. The agreement between the measured and predicted fluxes is acceptably good under the ranges studied, where the standard deviation (S.D.) defined in Eq. (21) is less than 11%. 2



cal /J exp t ) − 1 (JLys  Lys S.D.(%) = 100 (21) N −1 where N is the number of data point. It is proved that the resistance of lysozyme solubilization into AOT reverse micelles at the aqueous–organic interface to the overall mass transfer in membrane-based extraction process is negligibly small. The deviations are likely due to the complicated nature of lysozyme-

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extraction process, the calculated fluxes reasonably agreed with the measured ones (standard deviation, 11%). The kinetics of lysozyme solubilization from aqueous phase to the AOT reverse micelles at the aqueous–organic interface had little effect on the mass transfer in such membrane-based extraction process. Acknowledgement Financial support for this work by the National Science Council, ROC, under Grant NSC94-2214-E-155-001 is gratefully acknowledged.

Nomenclature effective membrane surface area (m2 ) iodine diameter of the reverse micelles (m) diffusivity of species j in bulk liquid phase (m2 s−1 ) E extraction yield defined in Eq. (14) (%) HA acetic acid JLys transport flux of lysozyme (mol m−2 s−1 ) ka individual mass-transfer coefficient in the aqueous layer (m s−1 ) kB Boltzmann’s constant (=1.38 × 10−23 kg m2 s−2 K−1 ) individual mass-transfer coefficient within the km membrane (m s−1 ) ko individual mass-transfer coefficient in the organic (reverse micellar) layer (m s−1 ) Ka overall aqueous-layer mass transfer coefficient defined in Eq. (9) (m s−1 ) Ko overall organic-layer mass transfer coefficient defined in Eq. (5) (m s−1 ) L thickness of membrane support (m) Lys lysozyme Lys lysozyme in the AOT/reverse micellar phase mB , mHA distribution coefficients of iodine and acetic acid between the organic and aqueous phases, respectively t time (s) T absolute temperature (K) V volume of the solution (m3 ) W0 water content in the reverse micellar phase A B d Dj

Fig. 11. Effect of AOT concentration in the reverse micelles on (a) the time profiles of lysozyme concentration and (b) the calculated and measured fluxes in the membrane-based extraction process.

AOT reverse micelles in isooctane like aggregate formation and configuration change, compared to iodine solute [9,12]. This leads to inaccurate estimation in the km value of lysozymeAOT reverse micelles. Further studies on improving model predictions are highly desired including; for example, the addition of various amounts of AOT into the organic phase to repeat the simple diffusion experiments (Section 3.5). This is because the individual mass-transfer coefficients of ka , km and ko may slightly decrease with increasing AOT concentrations [11]. 5. Conclusions Kinetic studies on reverse micellar extraction of lysozyme from aqueous solutions using AOT in isooctane in a microporous membrane-based process were made. Mass transfer was analyzed that considers all diffusion processes but neglects the resistance of solubilization process. A model was presented to predict the transport flux of lysozyme on the basis of a good knowledge of extraction chemistry and transport properties of the relevant geometry. The former data including equilibrium and kinetic relationships were obtained from batch liquid–liquid extraction experiments, whereas the latter data were mainly provided from simple diffusion experiments of specific solutes coupled with some correlations. For the present membrane-based

Greek letters εm porosity of membrane support η viscosity of the medium (kg m−1 s−1 ) ν kinematic viscosity of the medium (m2 s−1 ) τm tortuosity of membrane support Superscript m membrane side adjacent to the aqueous- or organic-membrane interface

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Subscripts 0 initial condition (t = 0) or total basis a, m, o aqueous feed, membrane and organic (reverse micellar) phases, respectively i liquid-membrane interface Lys lysozyme micelle lysozyme-AOT reverse micelle t any time t

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