Ind. Eng. Chem. Res. 2009, 48, 2913–2919
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Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 8. Effect of Formulation on the Inversion Produced by Continuous Stirring Marianna Rondo´n-Gonza´lez,*,†,‡ Luis F. Madariaga,†,‡ Ve´ronique Sadtler,† Lionel Choplin,† and Jean-Louis Salager‡ Centre de Ge´nie Chimique des Milieux Rhe´ologiquement Complexes (GEMICO), Nancy–UniVersité, Nancy, France, and Laboratorio FIRP, Ingenierı´a Quı´mica, UniVersidad de Los Andes, Me´rida, Venezuela
This paper deals with the influence of the global formulation of a water-oil-surfactant system, expressed by the hydrophilic-lipophilic difference (HLD), on the emulsion inversion produced just by the continuous stirring of an abnormal system, without any internal phase addition or any composition change. Evidence confirms that, under stirring, a w/O/W multiple emulsion is formed by the continuous inclusion of the external water phase inside the dispersed drops, which results in an increase of the effective dispersed phase volume until a critical value at which the inversion is triggered. Results suggest that the stability of the most internal emulsion determines the kinetics of inclusion and the stirring time required to induce inversion. However, it is the stability of both internal (w/O) and external (O/W) emulsions which determines the dispersed phase fraction at which the inversion is triggered. When different water fractions are used, the change of the critical dispersed phase fraction reveals that this process is affected by the partitioning of the surfactant mixture species between phases and results confirm that the critical dispersed phase fraction is a property related to the interfacial formulation of the system. Introduction Emulsion inversion is the change in the emulsion morphology from oil-in-water (O/W) to water-in-oil (W/O), or vice versa. It is an attractive process because it generally allows the formation of a smaller drop size than a conventional emulsification process with a lower energy input. Different methods are used to prepare emulsions by a phase inversion process.1 Some are based on the change of a composition variable, such as the addition of the internal phase, and are known as “catastrophic inversion”. Others result from a change in a formulation variable such as the surfactant hydrophilicity or the temperature, and are called “transitional inversion”. The present paper, as the three previous ones in this series,2-4 deals with a different process to induce catastrophic inversion: the inversion produced by continuous stirring, also known as the “static inversion protocol”.5 This protocol consists in submitting an abnormal emulsion, i.e., a system in which the external phase is not the phase predicted by the formulation (according to the Bancroft’s rule),6 to continuous stirring without any internal phase addition nor any change in formulation (e.g., temperature, salinity, or HLB), until inversion takes place at a critical dispersed phase value.5,7,8 This process could be identified in a formulation-composition map9 (Figure 1a). In this map, the stairlike line is the standard inversion frontier that separates the regions in which O/W and W/O emulsions are formed as the result of the stirring of an equilibrated surfactant-oil-water system. In the central part, this map is divided by a horizontal branch of the inversion line; in the upper region the surfactant affinity for the oil phase dominates and in the lower region it is the affinity for the water phase which dominates. The map is also divided according to the position of the vertical branches of the inversion line, which * To whom correspondence should be addressed. E-mail:
[email protected]. † Nancy–Université. ‡ Universidad de Los Andes.
are typically located at 30 and 70% water. Zones A+, A-, B+, and C- are called normal regions because the emulsion type corresponds to the normal curvature requirement of the interface, according to Brancoft’s rule. The formation of abnormal (and usually multiple) emulsions inside the C+ and B- regions of this map corresponds to a formulation-composition conflict. For instance, in region C+, formulation favors the formation of a normal W/O emulsion, but there is not enough oil phase to be the external phase, and the stirring tends to disperse oil in water. Consequently, a multiple emulsion which consists in a combination of both morphologies is usually formed; the most external emulsion is imposed by the composition and it is abnormal, and the most internal one (droplets in drops) follows Bancroft’s rule and is thus normal and stable. In the continuous stirring protocol, because there is no formulation or composition change, the inversion is represented by the displacement of the inversion line over the representative point of the system (Figure 1b). At the beginning of the stirring, the system corresponds to a simple or slightly multiple abnormal system, located inside the C+ (B-) region of the map (filled circle), but as the stirring goes on, the system morphology becomes more and more multiple by the inclusion of external phase as droplets inside the dispersed phase drops. Consequently, the inversion A+/C+ line is displaced more and more toward the right of the map (or leftward for the B-/A- line), until it crosses over the system representative point. In a three-
Figure 1. (a) Formulation-composition map. (b) Inversion produced by continuous stirring represented in the bidimensional formulation-composition map. (c) Three-dimensional representation of the inversion produced by continuous stirring.
10.1021/ie801225h CCC: $40.75 2009 American Chemical Society Published on Web 02/17/2009
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dimensional representation of the formulation-composition map, this protocol could be represented by the displacement of the representative point of the system through the inversion surface as the stirring time increases (Figure 1c). Inclusion and Escape Mechanisms. The formation of a multiple emulsion and the increase of the dispersed phase volume during the continuous stirring protocol are the consequences of the balance between the inclusion of the external phase as droplets inside the dispersed drops and their escape. If inclusion dominates over escape, inversion occurs. However, if the system reaches a steady state in which the rate of inclusion balances the rate of escape, inversion will not take place.10 Different mechanisms have been proposed in the literature to explain the inclusion and escape phenomena. Brooks and Richmond investigated the inclusion by studying the emulsion inversion produced by internal phase addition in the B- f Adirection on the formulation-composition map. Two of these mechanisms have been proposed by Sajjadi et al. to explain the inclusion of droplets when the inversion is produced by continuously stirring an abnormal system,7,11 i.e., the drop coalescence and the drop deformation. In the first mechanism, internal droplets are formed from the continuous phase trapped between drops during their collision and coalescence. The second mechanism occurs because of the deformation of the external unstable emulsion. Ohtake et al.12 suggested that when abnormal emulsion drops are exposed to any deformation, the surfactant present at the interface tends to develop a concave surface curvature, causing the external phase to be caught in the concavity and form a droplet of the external phase inside the internal phase. However, the inclusion produced by any of these mechanisms is opposed by the escape of inner droplets. Klahn et al. concluded that escape depends on the rate of drainage of the film formed between the inner droplet and the wall of the surrounding one.13 Groeneweg et al. put forward two mechanisms:10 In the first one, the surrounding drop becomes deformed by the flow, and a large inner droplet might become elongated and squeezed between walls of the surrounding drop. If the film between the inner droplet and the continuous phase ruptures, the droplet escapes. In the second mechanism, the inner droplet moves within the surrounding drop. If the inner droplet approaches the wall boundary of the surrounding drop and remains there for a sufficient time, the film between the inner droplet and the continuous phase wall could become thin enough and rupture, leading the droplet to escape. Because inclusion is favored by Bancroft’s rule and escape is opposed, both phenomena are expected to be affected by the formulation of the system, and probably by composition and stirring conditions, too.7,12 Formulation Effect. Usually, a variation of the system formulation, e.g., by changing the temperature or the surfactant the hydrophilic-lipophilic balance (HLB) or the ethylene oxide number (EON), is carried out in order to induce a transitional inversion. However, a formulation change can also affect the way in which the catastrophic inversion takes place. Sajjadi et al. have reported, for inversions produced by internal phase addition, that the inclusion of continuous phase into the dispersed phase tends to increase as the optimum formulation is approached.14 It was noted in part 3 of this series15 that the dispersed phase fraction at which the inversion is triggered seems to depend on the system formulation when inversion is induced by the continuous addition of internal phase. Finally, in the last paper
of this series,2 it was shown how the change in the formulation of the system (when the lipophilicity of the system decreases) reduces the propagation time, i.e., the stirring time required once the inversion is triggered in order to complete the inversion of a highly concentrated system, when the emulsion inversion is induced by the continuous stirring of the system. On the other hand, the effect of formulation on normal emulsions, such as the present inner emulsion, is well-known. As the system approaches optimal formulation, i.e., the formulation at which the surfactant has the same affinity for water and oil phases, the emulsion stability decreases and the coalescence of drops takes place essentially upon contact. This minimum of emulsion stability has been attributed to the trapping of the surfactant in the microemulsion phase,16 as well as other mechanisms.17-19 The aim of this paper is to complete these studies by elucidating the influence of formulation on the inversion produced by continuous stirring through the formation of a multiple emulsion and its evolution by inclusion of external phase droplets inside drops. Furthermore, the influence of the water fraction is presented in order to complete the results discussed in previous papers of this series.4,5 Experimental Section System Formulation. The experimental setup and procedure used to produce the emulsion inversion are similar to those described in previous parts of this series.2-4 The oil phase is a kerosene cut (equivalent alkane carbon number EACN ) 10 and viscosity ) 0.001 Pa · s), supplied by Fluka. The aqueous phase consists of a purified water (Milli-Q Millipore, France) in which 1 wt % NaCl (purity >98%, Aldrich) is added to increase the water phase conductivity and allow the detection of the formation of the multiple emulsion and the inversion point. Two different surfactant system are used: (1) The system consists of a mixture of two commercial polyethoxylated nonylphenol surfactants, Igepal CO-210 (with an average ethylene oxide number EON ) 2) and Igepal CO630 (EON ) 9), supplied by Aldrich, at a total concentration of 2 wt %. 2-Butanol, supplied by Prolabo, is added to the system in a concentration of 2 wt % to avoid the formation of liquid crystals and to accelerate the equilibration process. Unless otherwise explicitly specified, this is the system used. (2) The system is formulated with only one surfactant. Either Igepal CO-520 (EON ) 5), supplied by Aldrich, or Igepal CO210 (EON ) 2) is used separately depending on the formulation required, in a total concentration of 1 wt %. In this case no alcohol is added to the system. Inversion Protocol. Systems with different formulations (HLD value as defined later) and different water fractions (fw ) 0.6, 0.7, 0.8, 0.95) to make up 70 mL are prepared inside the C+ region of the formulation-composition map. Phases are prepared separately and left to equilibrate 24 h. The lipophilic surfactant (Igepal CO-210 or Igepal CO-520) is dissolved in the oil phase, while the hydrophilic one (Igepal CO-630) is added to the water. Just before the experiment, phases are put into contact, and in most cases 2-butanol is added. Then, systems are initially emulsified with an Ultra-Turrax turbine blender (IKA T25 Basic with Dispersion Tool S25-NK-19G, Germany) rotating at 8000 rpm for 40 s. Then, the preemulsified systems are submitted to the continuous stirring protocol, at 25 °C, inside the “rheomixer” device, described in detail elsewhere,8 until the phase inversion is detected by abrupt changes in conductivity
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Figure 2. Inversion mechanism scheme based on results presented by Sajjadi et al.,7 and microscopic observations (not shown) made on systems used in part 5 of this series.5
and viscosity. The overall mixing is assured by a rotational speed of the vessel corresponding to an effective shear rate of 200 s-1, and an additional stirring is provided by an Ultra-Turrax turbine blender (DI 25 basic with dispersion tool S25N-10G, from IKA Germany) rotating at 9500 rpm. In order to follow up the morphology of the system under stirring, the conductivity is monitored with a CDM 210 conductimeter and a bipolar conductivity cell CDC 749 (Radiometer Analytical, France). The apparent dispersed phase fraction (φ) is calculated from the conductivity of the system under stirring, by applying Bruggeman’s equation k ) kw(1 - φ)3 ⁄ 2
(1)
where k is the emulsion conductivity and kw is the aqueous phase conductivity. Results and Discussion All inversion experiments are carried out from an abnormal w/O/W or O/W emulsion to a normal W/O one, in the C+ f A+ direction of the bidimensional formulation-composition map. In this case, emulsified systems before inversion are intrinsically unstable, because the external O/W interface is not favored by the formulation, which is globally lipophilic. In all systems presented here, inversion takes place through the formation of a multiple emulsion, at which the external phase (W) is included as droplets (w) inside the dispersed oil drops (O) until a critical dispersed phase fraction is reached and the inversion is triggered, as described in Figure 2. This trend has been demonstrated by the decrease of the conductivity and the increase of the viscosity of previously studied abnormal water-surfactant-oil systems, not shown here but described in detail in others papers of this series.3,4 In the present work, formulation is expressed in a generalized way as the hydrophilic-lipophilic difference (HLD), given by20,21 HLD ) R - EON + bS - k(ACN) + t(T - 25) + aA
(2)
where R, k, and t are surfactant parameters, as well as EON, which is the average degree of ethoxylation; ACN is the alkane carbon number (or eventually its equivalent EACN for nonalkane oils), S and A are the salt and alcohol concentrations, b and a are the characteristic constants of each type of salt and alcohol, and T is the temperature of the system (in degrees Celsius). HLD is positive if surfactant exhibits a stronger affinity by the oil phase, it is negative in the opposite case, and HLD ) 0 if surfactant has the same affinity for both phases (known as optimal formulation). Inversion Time. For systems prepared at a fixed water fraction (fw ) 0.7) but different HLD values (globally lipophilic inside the C+ region), the stirring time required to trigger the inversion, i.e., the inversion time, is affected by the HLD of the system as shown by Figure 3. In this figure, HLD values in the abscissa decrease from left to right as the lipophilicity of the surfactant mixture decreases and optimal formulation (at
Figure 3. Influence of global formulation (HLD) on inversion time and on internal phase (W) separation (which represents the emulsion instability) of W/O final emulsions after inversion. fw ) 0.7.
HLD ) 0) is approached. Along this variation, the inversion time first decreases, undergoes through a minimum, and then increases. Because the inversion process passes through the formation of a multiple emulsion, it could be inferred that the inversion time depends on the capacity of the system to include the external phase as droplets and on the stability of the resulting inner emulsion. The resistance to coalescence of these inner w droplets in the multiple w/O/W system before inversion could be associated with the stability of the normal W/O emulsion after inversion since the W drops after inversion mostly correspond to the inner w droplets before inversion.22 For three W/O normal emulsions after inversion, prepared at different HLD values, the volume fraction of water separated as a function of time was measured after 4 1/2 months and plotted in Figure 3. This separation time corresponds to the instability of the system, i.e., the opposite of the stability data usually reported in the literature. The data match the inversion time variation: as the system moves toward optimum formulation, the W/O emulsion first becomes more stable (the fraction of separated water decreases), then passes through a stability maximum (minimum separation near HLD ) 1.8), and finally becomes unstable (HLD < 1.5) as the formulation approaches optimum. This result, which was also observed for other water fractions, strongly suggests that when inversion is induced by the continuous stirring of an abnormal w/O/W multiple emulsion, the inversion time is directly linked to the stability of the inner (w/O) emulsion. The decrease in the stability as the optimal formulation is closely approached has been known for more than two decades.16,23-25 On the other hand, it is worth noting that the decrease in the stability when systems are too far from optimum formulation is much less discussed in the literature, though it appears to have been mentioned for the first time quite a long time ago.26 As a matter of fact, it may be attributed to a reduction of the interface-seeking drive of the amphiphile molecule which is more likely to migrate into the bulk phase. The HLD value at which the minimum of inversion time is observed, denoted HLDm, represents the minimum stirring time required to trigger inversion, and also corresponds to the smallest amount of energy input, a key factor for industrial applications. This HLDm tendency is also observed for water fractions of 0.6, 0.8, and 0.9 (not presented here). Because this system contains two surfactants with highly different hydrophilicities, the appropriate HLD value at which the inversion time is minimal could appear to be the consequence of the segregation of the two species between the two
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Figure 4. A+/C+ branches of the standard inversion line for systems prepared with one and two commercial surfactants. The HLD of the systems is calculated from the overall mixture composition using eq 2 with b ) 0.13, a ) -0.05, R ) 9.5, k ) 0.15, and t ) 0.06.21
interfaces of the multiple emulsion. However, this is not the case as the following study carried out with only one surfactant will show. Inversion Time: One (Commercial) Surfactant Study. In order to study the formulation influence in a system prepared with only one surfactant, a single commercial ethoxylated nonionic surfactant was chosen. In such a case, the HLD of the system can be changed as a function of temperature, either Igepal CO-520 for 0 < HLD < 3 or Igepal CO-210 for 3 < HLD < 5. However, experiments should be carried out at a higher water fraction (fw ) 0.95) because the abnormal C+ region is much less extended, compared with the C+ region in the presence of two surfactants, as shown in Figure 4. Surfactants used in this work are not single species, but are commercial technical grade products consisting of a mixture of oligomers. However, the two surfactants used in the first study have oligomer distributions whose modes are far from each other (because of a large difference between their average ethoxylation degrees). Compared with the system prepared with only one commercial surfactant, this two-surfactant system is more likely to exhibit partitioning. Figure 4 shows the inversion lines for systems prepared with one or two surfactant systems, obtained by the stirring of equilibrated systems as described elsewhere.9 For the twosurfactant system, the inversion line is strongly displaced to the low water fraction side (shift indicated by the arrow), as a consequence of the well-known partitioning of surfactant mixtures which induces a deviation of interfacial formulation from the bulk counterpart.27 The observations made during the phase inversion of systems prepared with only one surfactant indicate that, at high water fractions, the complete inversion of the system does not take place immediately once the conductivity and viscosity indicate the triggering of the inversion, but after some additional stirring time, the so-called propagation time, elapses to complete the inversion of the whole system.2 Then, results presented here correspond to the time at which the inversion is triggered, which corresponds to inversion time if propagation time were zero. Despite the fact that inversion time results observed with both systems (one or two surfactants) cannot be compared on a numerical basis due to the difference in water fraction, Figure 5 reveals that the system prepared with only one surfactant exhibits the same trend in inversion time as the system prepared with two surfactants; i.e., a minimum of inversion time is also observed. Certainly, the nonionic surfactant used, either Igepal CO-520 or Igepal CO-210, is not actually an isomerically pure substance, but a mixture of oligomers. Nevertheless, it doubtfully
Figure 5. Formulation influence on inversion time of systems prepared using one nonionic surfactant. HLD is varied changing the temperature of systems. fw ) 0.95. HLD is calculated using eq 2 and constant values given in Figure 4 caption.
would segregate as much as the two surfactants used in the last section, with the HLB corresponding to extreme 13 and 4 values. This result suggests that it is not the presence of two surfactants, eventually stabilizing separately each interface, that explains the existence of a minimum of inversion time at HLDm. It tends to indicate that the effect is due to the global formulation of the system, that, in the case of two surfactants, corresponds probably to mixed interfacial films formed rapidly at both interfaces, because of the low molecular weight of surfactant molecules. Kinetics of Inclusion. In order to compare the kinetics of inclusion of the external water phase as droplets, for systems prepared at different formulations, the evolution of the effective dispersed phase fraction (O, oil drops, + w, water inner droplets) is shown as a dimensionless time function, calculated as the relation between time and inversion time. Figure 6 is split in two graphs, each one showing one of the trends observed in Figure 3: the diminution of inversion time from a far-away HLD (HLD > 3) to the quickest inversion HLD (HLD ) 2.2) and the increase of the inversion time from the quickest inversion HLD to the close-to-optimum zone (HLD ) 0.5). Figure 6 shows that the inclusion of the dispersed phase fraction is dramatically affected by the HLD of the system. From a far-away HLD ) 3 to the quickest inversion HLD ) 2.2, Figure 6a shows the increase of the rate of inclusion; this means that, for a given dimensionless time, the net inclusion is larger as the formulation is closer to optimum. This result could be explained by the increase in stability of the inner w/O emulsion, which shifts the balance between inclusion and escape in favor of inclusion and increases the effective dispersed phase fraction. From the quickest inversion HLD ) 2.2 to the close-tooptimum zone HLD ) 0.5, Figure 6b shows the opposite trend: for a given dimensionless time, the relative importance of inclusion decreases as the formulation approaches optimum. This case could also be explained by the change in the stability of the inner w/O emulsion. As its stability decreases (corroborated by the stability of the final W/O emulsion, exhibited in Figure 3), inclusion weakens in relation to escape and, consequently, the net inclusion declines. Additionally, the decrease of the inclusion could also be affected by the change in system formulation. As HLD decreases, approaching optimum formulation (inside the C+ region), the decrease and fading of a clearcut surfactant lipophilicity makes the formation of inner w/O emulsion less favorable. This particular behavior of the rate of inclusion was also observed for other water fractions (not shown here). Critical Dispersed Phase Fraction. Figure 7 presents the critical dispersed phase fraction (φc),5 i.e., the dispersed phase
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Figure 6. Dispersed phase fraction evolution as a dimensionless time function, as HLD approaches optimum formulation. (A) From far away, HLD ) 3, to the quickest inversion HLD, HLD ) 2.2. (B) From the quickest inversion HLD to the close-to-optimum zone. fw ) 0.7.
Figure 7. Influence of formulation on the critical dispersed phase fraction. fw ) 0.7.
at inversion formed by the oil drops (O) and the water droplets (w) inside them, as a function of the HLD. HLD values in the abscissa decrease from left to right as in Figures 3 and 4. As for inversion time, two opposite trends are observed. First, the critical dispersed phase fraction increases as the HLD decreases, then reaches a maximum (near HLD ) 1), and then decreases again. The increase of the critical dispersed phase fraction with the decrease of HLD in the left part of the plot indicates that a higher inclusion of water droplets is necessary to trigger the inversion. This result could be interpreted in two ways. The first one is that as the HLD decreases (from 3 to 2.2) the stability of the inner w/O emulsion increases (as shown in Figure 3), which favors the “stuffing” of the dispersed drops by droplets. However, the maximum stability of the inner emulsion (at HLD ) 2.2 in Figure 3) does not correspond to the maximum critical dispersed phase fraction observed in Figure 7 at HLD ) 1. Hence, there is another factor, which is likely to be the stability of the external abnormal emulsion (O/W). The point is that the stability of abnormal emulsions is rarely studied, simply because these systems are highly unstable and usually separate immediately after stirring is stopped. However, Sajjadi et al.14 have reported that the size of the multiple W drops in an o/W/O emulsion in the B- region is found to decrease as the HLB of the system decreases. This means that when optimum formulation is approached, W water drops coalescence slightly slows down. They stated that the presence of an oil soluble-component in the surfactant, even in a low proportion, slightly stabilizes the abnormal W/O emulsion. Then, if this feature is also valid for the C+ region, which is most likely the case because of the phenomenology symmetry with
respect to optimum formulation, the increase of the critical dispersed phase fraction with the decrease of the HLD observed in the present work could be explained by two concomitant effects of the decrease in lipophilicity of the abnormal system. There is not only an increase in stability of the normal inner w/O emulsion, but also a decrease in the intrinsic instability of the external O/W emulsion. As the HLD decreases even more (from 1 to 0.5), the trend reverses and the dispersed phase fraction strongly decreases as the formulation approaches optimum. This diminution could be directly related to the normal emulsion stability plunge as the formulation approaches optimum. In the present case, as the HLD decreases from 1 to 0.5, external drops (O/W) of the multiple emulsion coalesce without delay, and the emulsion inverts at a lower dispersed phase volume.28 Water Fraction (fw): Indirect Formulation Effect. The effect of the water fraction has already been studied in previous papers of this series. It was shown that when the emulsion inversion is produced for systems prepared at the same HLD value but with different water fractions, the inversion time increases with fw. This was interpreted as being due to the higher inclusion of inner droplets required to attain the same critical dispersed phase fraction and trigger the inversion.4,5 However, when a mixture of surfactants of different hydrophilicites is used, the diverse surfactant species partition between phases in different ways. For systems prepared at the same HLD value, this phenomenon generates an indirect change of interfacial formulation with the change in water fraction.27 In a previous paper,8 we have shown the anomalous reduction in the inversion time when the water fraction was increased from 0.8 to 0.85, for systems inverted using the continuous stirring protocol from an abnormal w/O/W emulsion to a normal O/W one. In that work, the reduction of the inversion time was attributed to the change in the partitioning of the surfactant mixture, but also to the formation of liquid crystals due to the high surfactant concentration used (7 wt %). In order to elucidate the partitioning influence in the present work, a lower surfactant concentration (2 wt %) is used and an alcohol, i.e., 2-butanol, is added to the system to prevent the formation of liquid crystals. Figure 8 shows, for systems prepared at the same HLD value (1.84), that the critical dispersed phase fraction (φc) and the inversion time decrease simultaneously as the water fraction increases. This suggests how the actual interface composition changes as the water fraction increases. As the oil fraction decreases (fw increases), more hydrophobic species migrate to the interface and the interfacial mixture formulation becomes more hydrophobic. Consequently, the stability of the external O/W emulsion, which is inherently low, decreases even more
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result corroborates that the critical dispersed phase fraction directly depends on the interfacial composition. Conclusions
Figure 8. Effect of water fraction on inversion time (HLD ) 1.84) and on critical dispersed phase fraction (φc).
Figure 9. Iso-φc line (φc ) 0.84) and optimum formulation of the surfactant-water-oil system.
and the dispersed phase fraction required to trigger inversion (φc) is reduced and the inversion time shortened. The inversion time can be also reduced by a more hydrophobic formulation that favors the inclusion of w droplets in O drops, allowing, in a lower stirring time, the attainment of the critical dispersed phase fraction. Figure 9 shows the optimum formulation of the system and an iso-φc line, i.e., HLD of systems which present the same critical dispersed phase fraction, as a function of fw. The optimum formulation line is obtained from a phase behavior study using a unidimensional formulation scan method.28 The iso-φc line is obtained by applying, for each fw, the static inversion protocol to systems prepared at different HLD. The values of HLD presented in Figure 9 are the values at which the critical dispersed phase fraction at inversion is 0.84. The optimal formulation of the system is not horizontal because the HLD scale was calculated from eq 2 by using the overall composition of the surfactant in the system. This value does not match the interfacial HLD which varies with fw due to the high partitioning of the mixture of surfactants. The interfacial HLD cannot be calculated, but the zero interfacial HLD is detected experimentally from the optimum phase behavior. The variation of the iso-φc line exhibits essentially the same slant as the optimum formulation of the system, certainly because it closely follows the change in partitioning of surfactant between phases with the water fraction variation. If the critical dispersed phase fraction is plotted as a function of an effective HLD, calculated as the difference between the interfacial HLD of the system and the optimal interfacial HLD for a given fw, the isoφc lines will appear perfectly horizontal. In practice, this means that, in order to invert the system at the same dispersed phase fraction, systems must be prepared at the same distance from optimum formulation, i.e., at the same interfacial HLD. This
The presented evidence shows how the global formulation of the system, expressed as the hydrophilic-lipophilic deviation (HLD), affects the inversion produced by continuous stirring of an abnormal system. As the lipophilicity of the surfactant mixture decreases (inside the C+ region of the formulationcomposition map) and the system moves toward optimum formulation, the inversion time decreases, reaches a minimum, and then increases as optimum formulation is closely approached. The evidence suggests that the inversion time and the inclusion kinetics are determined by the stability of the inner w/O emulsion. As such, an appropriate HLD value exists at which the inclusion takes place during all the stirring process and the inversion time is minimal. The critical dispersed phase fraction is also affected by the global formulation of the system. In this case, the stability change of the inner emulsion is not sufficient to explain the overall trend; the experimental evidence reported in the literature suggests that the stability of the external emulsion might vary also in the presence of an hydrophilic surfactant in the mixture. The minimum inversion time occurs when the formulation (noted HLDm) is at some distance from optimum, probably where most emulsified systems exhibit the best compromise between a low interfacial tension and not-too-fast coalescence, to achieve a minimum in drop size.29 It is worth remarking that this HLDm value corresponds to the lower energy input and the smaller drop size for this system, making it attractive for industrial applications. Finally, this work corroborates the existence of a critical dispersed phase fraction at which the inversion is triggered, even in a system in which the surfactant mixture exhibits a considerable partitioning. Acknowledgment The authors would like to thank the Fundayacucho Scholarship Program for helping finance the doctoral studies of M.R.G. and L.F.M. and the Postgraduate Cooperation Program PCP (FONACITsVenezuela and MAEsFrance) for sponsoring professor and graduate student exchanges. Literature Cited (1) Salager, J. L.; Forgiarini, A.; Ma´rquez, L.; Pen˜a, A.; Pizzino, A.; Rodrı´guez, M. P.; Rondo´n-Gonza´lez, M. Using Emulsion Inversion in Industrial Processes. AdV. Colloid Interface Sci. 2004, 108-109, 259. (2) Rondo´n-Gonzale´z, M.; Sadtler, V.; Marchal, P.; Choplin, L.; Salager, J. L. Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 7. Emulsion evolution produced by continuous stirring to generate a very high internal phase ratio emulsion. Ind. Eng. Chem. Res. 2008, 47, 2314. (3) Rondo´n-Gonzale´z, M.; Madariaga, L. F.; Sadtler, V.; Choplin, L.; Salager, J. L. Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 6. Effect of the Phase Viscosity on the Inversion Produced by Continuous Stirring. Ind. Eng. Chem. Res. 2007, 46, 3595. (4) Rondo´n-Gonzale´z, M.; Sadtler, V.; Choplin, L.; Salager, J. L. Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 5. Effect of the Water-to-Oil Ratio and Surfactant Concentration on the Inversion Produced by Continuous Stirring. Ind. Eng. Chem. Res. 2006, 45, 3074. (5) Tyrode, E.; Allouche, A.; Choplin, L.; Salager, J. L. Emulsion catastrophic inversion from abnormal to normal morphology. 4. Following the emulsion viscosity during three inversion protocols and extending the critical dispersed-phase concept. Ind. Eng. Chem. Res. 2005, 44, 67. (6) Bancroft, W. D. The theory of emulsification, V. J. Phys. Chem. 1913, 17, 501.
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ReceiVed for reView August 9, 2008 ReVised manuscript receiVed January 2, 2009 Accepted January 7, 2009 IE801225H
