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Langmuir 2007, 23, 1052-1056
Modelization of the Release from a Tetradecane/Water/Hexadecane Multiple Emulsion: Evidence of Significant Micellar Diffusion M. Stambouli,*,† J. R. Avendano-Gomez,‡ I. Pezron,‡ D. Pareau,† D. Clausse,‡,§ and J. L. Grossiord§,| Laboratoire de Ge´ nie des Proce´ de´ s et Mate´ riaux, Ecole Centrale Paris, 92295 Chaˆ tenay-Malabry Cedex, Laboratoire Ge´ nie des Proce´ de´ s Industriels, UniVersite´ de Technologie de Compie` gne, UMR CNRS 6067, B.P. 20529, 60205 Compie` gne, and Laboratoire de Physique Pharmaceutique, Centre d’Etudes Pharmaceutiques, UniVersite´ de Paris Sud, UMR CNRS 8612, 92296 Chaˆ tenay-Malabry, France ReceiVed February 20, 2006. In Final Form: September 25, 2006 The release of tetradecane from a multiple emulsion of the type tetradecane/water/hexadecane was studied experimentally using the differential scanning calorimetry technique. The kinetics of the tetradecane release was measured for three formulations containing different concentrations of hydrophilic surfactant (2%, 4%, and 7%). A new mass transfer model derived from the shrinking core model was developed. The values of the model parameters deduced from the least-squares fittings led to the determination of the tetradecane diffusivity. Thus, the preponderant mechanism of mass transfer was proved to be micellar diffusion and not molecular diffusion. This conclusion was confirmed by considering the effect of the change in the hydrophilic surfactant concentration.
Introduction Multiple emulsions of the oil/water/oil (O1/W/O2) type are systems in which aqueous globules are dispersed within an oil continuous phase (O2). Those aqueous globules contain microdroplets of a second oily phase (O1), commonly known as the internal phase. The organic phase in which the aqueous globules are dispersed is denoted the external phase. In this manner, the physical morphology of the O1/W/O2 multiple emulsion allows the presence of two oily phases separated by an aqueous membrane. This property of the multiple emulsion could find important applications in separation processes as an alternative to liquid-liquid extraction systems.1-3 In a previous study,4 some authors of this paper considered the mass transfer in oil/water/oil multiple emulsions. In the emulsion system studied, the internal oil phase was composed of tetradecane microdroplets encapsulated within the aqueous phase. The aqueous globules were dispersed into the hexadecane continuous bulk. Each sample was submitted to a slight magnetic agitation during the whole duration of the kinetics analysis. Differential scanning calorimetry was employed to monitor the time-dependent changes of the O1/W/O2 multiple emulsion. The crystallization behaviors of the internal and the external phases were analyzed to deduce and describe the evolution of the emulsion, thanks to an established correlation between the freezing temperature of the undercooled phases and their composition. Thus, a very simplistic model was used to fit the release of tetradecane for a Tween 20 concentration of 7% (w/w).4 The agreement was quite good if taking into account the very approximate nature of the model. The assumption that the multiple globule radius was constant during the whole release was of †
Ecole Centrale Paris. Universite´ de Technologie de Compie`gne. § These authors contributed equally to this work. | Universite ´ de Paris Sud. ‡
(1) Li, N. N. Ind. Eng. Chem. Process Des. DeV. 1971, 10, 215. (2) Hamoudeh, M.; Seiller, M.; Chauvierre, C.; Auche`re, D.; Lacour, B.; Pareau, D.; Stambouli, M.; Grossiord, J.-L. J. Drug DeliVery Sci. Technol. 2006, 16 (3), 223. (3) Draxler, J.; Fu¨rst, W.; Marr, R. J. J. Membr. Sci. 1988, 38, 281. (4) Avendano-Gomez, J. R.; Grossiord, J.-L.; Clausse, D. J. Colloid Interface Sci. 2005, 290, 533.
Table 1. Volume Fractions of Hexadecane, Water, and Tetradecane in the O1/W/O2 Multiple Emulsion phase
volume fraction
hexadecane phase (O2) aqueous membrane (W) tetradecane phase (O1)
0.392 0.326 0.282
course open to criticism. In a more general way, the model used was not based on unquestionable and very clear hypotheses. Therefore, a more rigorous analysis is now undertaken to correlate the tetradecane release with its solubility and diffusion coefficients in the aqueous membrane, by using the experimental results of the reference paper.4 Materials and Methods Multiple Emulsion Compositions. The composition of the multiple emulsion O1/W/O2 is given in Table 1. The aqueous membrane included a hydrophilic surfactant, namely, Tween 20 (polyoxyethylene sorbitan monolaureate), which was used at three different concentrations (2%, 4%, and 7%, w/w). The initial mean diameters of the internal oily droplets and the multiple globules were measured and found to be around 5 µm and 1 mm, respectively. Mass Transfer by DSC Analysis. To monitor the changes in composition of the internal and external phases of the multiple emulsion in isothermal conditions (18 ( 1 °C), a sample of the multiple emulsion is taken and submitted to a cooling experiment. The details of the DSC analysis were thoroughly presented in the reference paper.4 Nevertheless, for clarity, the principle will briefly be summarized here. The signal recorded from a cooling experiment allows two characteristic peaks corresponding to the crystallization of each oily phase to be distinguished. The composition of the phases and their corresponding volumes determine the crystallization temperature. Therefore, during the cooling experiment, the hexadecane crystallizes before the tetradecane, as illustrated in Figure 1, which provides an example of a crystallization thermogram for the multiple emulsion. At a lower temperature, the crystallization of the tetradecane microdroplets is observed. On grounds of simplification, the water crystallization peak was not reported on the graph. A sample of the emulsion was analyzed from time to time to point out the mass transfer. As an example, Figure 2 provides the evolution of the crystallization thermogram in the case of a 4% (w/w)
10.1021/la060486i CCC: $37.00 © 2007 American Chemical Society Published on Web 12/29/2006
Release from a Tetradecane/Water/Hexadecane Emulsion
Langmuir, Vol. 23, No. 3, 2007 1053
Figure 1. Example of a DSC thermogram for a O1/W/O2 multiple emulsion: (a) crystallization of the internal phase O1 (tetradecane microdroplets); (b) crystallization of the external phase O2 (hexadecane).
Figure 2. Evolution of the crystallization thermogram of the O1/W/O2 multiple emulsion tetradecane/water/hexadecane containing 4% (w/w) Tween 20 in the aqueous membrane. concentration of Tween 20. The evolution of the crystallization thermogram reveals a transfer of tetradecane from the internal phase toward the external phase (decrease in the tetradecane peak); i.e., the tetradecane is released through the aqueous phase and is integrated into the bulk phase, which is initially composed of pure hexadecane (shift of the hexadecane peak). After 15 days there is only one peak left, corresponding to a mixture of both hydrocarbons. The hexadecane peak is shifted toward lower temperatures and increases in intensity (defined as the area under the curve), clearly proving a significant transfer of tetradecane into the hexadecane phase. Simultaneously, the tetradecane peak decreases significantly with time. A slight shift of this peak toward higher temperatures is also observed, probably related to a slight counterdiffusion of hexadecane. However, this phenomenon is less important than the first one. This observation could be explained by taking into account the interfacial areas: that available for tetradecane transfer through the internal droplets (about 5 µm diameter) is 2-3 orders of magnitude
larger than the external one available for hexadecane transfer (globule about 1 mm in diameter). The rate of the tetradecane mass transfer into the water shell is then evidently higher than that of hexadecane. Thus, we can assume that only tetradecane is transferred. The fraction of tetradecane release is directly related to the AUC (area under the curve) of the crystallization peak illustrated in the thermograms. The experimental results are then fitted with our new model derived from the shrinking core model, commonly applied to heterogeneous reactions.5,6 This model has been modified and applied to the special case of the emulsions under study. Shrinking Core Model. Owing to the complex physical structure of the multiple emulsions, some simplifications should be stated to simplify the mathematical treatment. Thus, the internal microdroplets (5) Froment, G.F.; Bischoff, K. B. Chemical Reactor. Analysis and Design, 2nd ed.; Wiley: New York, 1990. (6) Lidell, K. C. Hydrometallurgy 2005, 79, 62.
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Figure 3. (a) Schematic picture of the tetradecane/water/hexadecane multiple emulsion. (b) Modelization of the multiple emulsion globule as a virtual coalesced subdrop surrounded by a spherical aqueous shell. (c) Typical tetradecane concentration profile in the multiple emulsion. are assumed to form one virtual coalesced subdrop encapsulated in an aqueous spherical shell (Figure 3a,b). Figure 3c shows a typical concentration profile for diffusive transport across the aqueous membrane. The following notations were used: cI, tetradecane concentration in phase I (pure tetradecane); cII, tetradecane concentration in phase II (tetradecane + hexadecane); c′I, tetradecane concentration in the aqueous phase at interface I; c′II, tetradecane concentration in the aqueous phase at interface II; c′(r), tetradecane concentration in the aqueous phase at radius r; rI, internal tetradecane drop radius; rII, aqueous globule radius. Two partition coefficients can be defined as the ratios between the tetradecane concentrations in the aqueous membrane and the oily phases, if equilibrium is assumed at both interfaces: KI )
c′I cI
KII )
c′II cII
membrane at interface I can be written as
(dc′dr )
J ) -4πrI2D′e
(4)
d(FIVI) ) -J dt where FI and VI are, respectively, the tetradecane density and the volume of phase I. With dVI ) 4πrI2 drI and using eq 4
(1) c′II - c′I FI4πrI2 drI ) 4πrID′e dt 1 - (rI/rII) so that
J(r) ) -4πr2D′e(dc′/dr)
(2)
where D′e is the effective diffusion coefficient of tetradecane in the aqueous phase, it is then possible to write the material balance equation under pseudo-steady-state approximation: d 2 dc′ leading to r D′e )0 dr dr
(
c′II - c′Ι ) -4πrID′e 1 - (rI/rII)
Writing the material balance of tetradecane at interface I between time t and t + dt, it follows that
By considering the expression of the tetradecane flux through the aqueous spherical shell of radius r
J(r) ) J(r + dr)
r)rI
)
(3)
It is assumed that the slight magnetic agitation could maintain a homogeneous repartition of the multiple globules without any effect on the internal circulation. The tetradecane droplets can then be considered as immobile inside the water globules, but able to release hydrocarbon molecules across the water membrane into the outer hexadecane phase. Therefore, the transport phenomenon is probably either pure molecular or pure micellar diffusion. This equation can be integrated using the boundary conditions at the inner and outer interfaces of the water spherical shell. Thus (1 - rI/r)
c′(r) - c′I ) (c′II - c′I) (1 - rI/rII) so that the expression of the tetradecane flux through the aqueous
( )
rI 1 -
rI D′e drI ) ∆c′ dt rII FI
(5)
where ∆c′ ) c′I - c′II. y and z0 can be defined as follows: y)
rI rI0
z0 )
[] rII0
3
rI0
where rI0 and rII0 are, respectively, the initial tetradecane droplet and aqueous globule radii. The integration of eq 5 accounting for the water material balance and using the boundary conditions across the water spherical shell leads to
∫ y dy - ∫ y [ -1 + y y
1
y 2
1
3
+ z0]-1/3 dy ) -
D′e
(∆c′)t (6)
FI(rI0)2
By noticing that y3 is proportional to the fraction of tetradecane still encapsulated at time t and that x ) 1 - y3 represents the fraction
Release from a Tetradecane/Water/Hexadecane Emulsion
Langmuir, Vol. 23, No. 3, 2007 1055 Table 2. Best Fitting Parameters Tween 20 concentration (%, w/w) t1 (h) [D′e(∆c)/FI] × 1010 (cm2 s-1) regression coefficient
2 875 1.03 0.995
4 451 2.00 0.980
7 318 3.10 0.833
Table 3. Values of the Initial Rate of the Tetradecane Release for the Three Tween 20 Concentrations Tween 20 concentration (%, w/w) 2 4 7 (dx/dt)t)0 × 106 (s-1) experimental 0.62 1.12 2.25 model 0.91 1.77 2.51 Table 4. Partition and Diffusion Coefficient Values Tween 20 concentration (%, w/w) KI × 103 D′e × 107 (cm2 s-1)
2 0.61 1.7
4 1.2 1.7
7 2.1 1.5
Results and Discussion Taking into account that
z0 ≡
Figure 4. (a, top) Evolution of the release fraction x versus time t for 2% (w/w) Tween 20 at constant temperature, 18 ( 1 °C. (b, middle) Evolution of the release fraction x versus time t for 4% (w/w) Tween 20 at constant temperature, 18 ( 1 °C. (c, bottom) Evolution of the release fraction x versus time t for 7% (w/w) Tween 20 at constant temperature, 18 ( 1 °C. of tetradecane which was released at the same time, it follows from eq 6, after integration, that t)
FI(rI0)2
[(z0 - x)2/3 - (1 - x)2/3 + 1 - z02/3]
2D′e(∆c′)
(7)
It is worth noting that this equation can be written in the following equivalent form: t)
t1
[(z0 - 1)
2/3
[(z0 - x)2/3 - (1 - x)2/3 - (z02/3 - 1)] - (z02/3 - 1)] (8)
where t1 is the complete tetradecane release time (x ) 1).
() rII0 rI0
3
)
0.282 + 0.326 ) 2.16 0.282
it was possible, by using eq 8 and the least-squares method, to obtain the best fitting of the experimental data relating the tetradecane fraction released x to the time t for the three formulations. Parts a-c of Figure 4 show the experimental points, as well as the best fitting curves obtained from model eq 8, where t1 is the fitting parameter. Thus, the complete release time t1 has been derived for the three formulations. The values of D′e(∆c′)/FI which give the best fitting of the three curves from eq 7 were also deduced, using 0.387 mm as the initial mean radius value rI0 calculated from z0. Table 2 provides these values. As a first approximation, it is possible to consider that c′II is small compared to c′I, at least in the first part of the release process. c′I is indeed the aqueous concentration in equilibrium with tetradecane, whereas c′II is in equilibrium with mixtures of hexadecane and tetradecane. Then, ∆c′ ) KIcI ) KIFI, so that D′e(∆c′)/FI ) KID′e. It is clear that the transport kinetics is strongly dependent on the surfactant concentration, which seems to exclude molecular diffusion as the preponderant mechanism. Moreover, the simple order of magnitude considerations allows confirmation of this assumption. According to Kabalnov et al.,7 in the case of molecular diffusion, the partition coefficient is equal to 3.7 × 10-10 (T ) 25 ( 2 °C). This KI value would lead to an unreasonably high value for the diffusion coefficient D′e of about 1 cm2 s-1. Thus, it is obvious that diffusion occurs, at least partly, by surfactant-facilitated transport. From a more quantitative point of view, this assumption is confirmed by Table 3, which displays the values of the initial rate of the tetradecane release, (dx/dt)t)0. It can be observed that these values are practically proportional to the Tween 20 concentrations, as was anticipated by Kabalnov.8 According to Weiss and McClements,9 the tetradecane solubility in aqueous solutions of Tween 20 is (0.023 g of tetradecane)/(g of Tween 20) at 25 ( 2 °C. Using the pure tetradecane molar concentration (FI ) 3.8 × 10-3 mol cm-3), the values of the partition coefficient KI are obtained for the three formulations. Thus, the diffusion coefficient values have (7) Kabalnov, A. S.; Makarov, K. N.; Pertzov, A. V.; Shchukin, E. D. J. Colloid Interface Sci. 1990, 138, 98. (8) Kabalnov, A. S. Langmuir 1994, 10, 680. (9) Weiss, J.; McClements, D. J. Langmuir 2000, 16, 5879.
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Figure 5. Scheme of a rigid globule.
been derived (Table 4). The experimental value of the diffusion coefficient D′e (at 18 °C) is approximately constant for the three formulations and equal to (1.6 ( 0.1) × 10-7 cm2 s-1. Regarding the D′e values available in the literature, it is worth noting that, to the best of our knowledge, there is only one reference (Mandal et al.10) which has provided a value of 7.8 × 10-7 cm2 s-1. McClements and Dungan11 have just mentioned this previous paper. To obtain this value, Mandal et al.10 determined at first the experimental value of the hydrodynamic radius RH for pure Tween 20 micelles (RH ) 3.16 nm at 25 °C) and then calculated the D′e value according to the Stokes-Einstein relation. It was shown10 that the pure micelle size was quite independent of the Tween concentration, which is likely for diluted micellar solutions. One could expect that the incorporation of tetradecane molecules inside the micelles was likely to increase their size, leading to a smaller value of D′e. Nevertheless, to obtain our value of D′e, the extent of the change would be so high that it is unlikely that the size increase could alone explain the observed difference. Compared to the literature data (7.8 × 10-7 cm2 s-1 at 25 °C), the good agreement observed in terms of the order of magnitude does confirm evidence of a micellar transport mechanism. However, it is pertinent to wonder about the difference between the D′e values, to know if it is significant or if it results from the noncompletely rigorous character of our quantitative analysis. Indeed, some simplifications have been made. (1) Our treatment assumes that c′II is negligible compared to c′I. This hypothesis is obviously relevant in the first part of the kinetics but questionable afterward. However, it is hardly credible that the observed difference results from this assumption: indeed the fit of only the first part of the graphs does not give very different D′e values (deviation less than 15%). (2) Another questionable point concerns the fact that the multiple globule mean diameter is not known with a sufficient accuracy. However, this uncertainty does not explain the D′e value difference. A sensitivity study indeed shows that a deviation of only 21% in the D′e value results from a 10% diameter change. (3) For a rigorous comparison between experimental (T ) 18 °C) and literature (25 °C) data, one should estimate the temperature (10) Mandal, A. B.; Gupta, S.; Moulik, S. P. Indian J. Chem. 1985, 24A, 670. (11) McClements, D. J.; Dungan, S. R. J. Phys. Chem. 1993, 97, 7304.
Stambouli et al.
correction. A simplified calculation shows that the expected correction does not exceed 150%. Thus, even after this correction, the ratio (D′e)this paper/(D′e)literature remains around 1/3. All these simple considerations are not able to explain the differences observed above, so a more accurate discussion of the model is needed. As a matter of fact, to simplify the mathematical treatment, the proposed model assumes that the matrix of very small internal microdroplets is represented by a unique virtual coalesced subdrop (Figure 3). This model is rather consistent with a rigid aqueous globule in which the tetradecane droplets are immobile (Figure 5). The aqueous part of the globule can be divided into two regions: one participating in the transfer with the hexadecane phase (situated close to interface II) and the other which is in contact only with tetradecane (the core of the globule). It is possible to consider that, after a given time (depending on the diffusion rate in the aqueous solution), this second aqueous region is saturated with tetradecane at concentration c′I, because it is completely surrounded by tetradecane. When time goes on, the outer droplets shrink and disappear, the droplets of the core roughly remaining at their initial dimension; the aqueous layer then increases and the core decreases at the same time. The limit of our model is then the consideration of a pure tetradecane drop instead of a mixed “drop” (intact tetradecane droplets and aqueous continuous phase) closer to the actual geometry of the emulsion; the tranfer rate may be a little ill-estimated, resulting in the observed differences. On the contrary, if the globule is well agitated, the droplets exchange themselves instantaneously; it can then be considered that the decrease in the size of the droplets is the same for all of them. The model does not apply in this case. Thanks to the absence of agitation of the system (as the tetradecane droplet mean diameters are higher than 5 µm, it is possible to neglect their motion under Brownian agitation), the assumption of a rigid globule is more relevant; the model is then rather well adapted. One would think that a more accurate model requiring tedious numerical integration would be able to provide a better description of the mass transfer and better agreement with the literature D′e value. However, this approach would need the introduction of adjustable empirical parameters. Therefore, in our case, a better fitting would not necessarily mean a better physical understanding.
Conclusion As a conclusion it could be stated that this paper interestingly contributes to the understanding of mass transfer in multiple emulsions. The extension of a chemical engineering model generally applied for solid-liquid or solid-gas processes has allowed a good description of mass transfer in an oil/water/oil multiple emulsion. This model gives a good fitting with the experimental results. In addition, the diffusion coefficient of tetradecane in the multiple emulsion has been calculated and compared to the available data. Evidence for micellar diffusion is then proved. LA060486I
