Current Phenomenological Know-How and Modeling of Emulsion

Ind. Eng. Chem. Res. 2000, 39, 2665-2676

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Current Phenomenological Know-How and Modeling of Emulsion Inversion Jean-Louis Salager,* Laura Ma´ rquez, Alejandro A. Pen ˜ a,† Miguel Rondo´ n,‡ ‡ Fe´ lix Silva, and Eric Tyrode FIRP Laboratory, Universidad de Los Andes, Me´ rida 5101, Venezuela

This paper encompasses classic trends as well as recent advances in the understanding of emulsion inversion phenomena. The generalized formulation issue is first discussed from hydrophilic-lipophilic balance to the most recent concepts. The so-called standard inversion line on the formulation-composition map exhibits several branches, referred to as transitional and catastrophic inversions, that bound normal and abnormal emulsion regions. Dynamic inversion is also discussed with its hysteresis zones, where both types of emulsions may be attained, depending upon the system’s previous history of the formulation-composition map. Recent findings are reported concerning the effect of variables with practical relevance (i.e., stirring energy, viscosity of phases, surfactant concentration, and partitioning) on the standard and dynamic inversion patterns. State-of-the-art emulsion inversion modeling is briefly discussed. Morphological AspectssEmulsion Types and Inversion An emulsion is a dispersed system made of a liquid phase (called internal or dispersed phase), which is fragmented in the form of drops that are suspended inside another liquid phase (called continuous or external phase) essentially immiscible with the former. To be an emulsion, the dispersed system must exhibit some stability against coalescence. This requires a third component (usually referred to as an emulsifier), which is most often a surfactant. There are two simple emulsion morphologies or types, i.e., O/W and W/O, which correspond respectively to the dispersion of oil drops in water and vice versa. Both morphologies are found at the same time in a multiple or double emulsion, which may be considered as an emulsion inside an emulsion.1 There are also two types of multiple emulsions, that is, o/W/O and w/O/W, where the lower case indicates the most internal phase. In most activities, except petroleum production, O/W are the normal or common emulsions and W/O the inverted ones. Passing from one of the simple morphologies to the other is referred to as emulsion inversion. If an emulsion made under certain specified conditions has one morphology, while another emulsion made under slightly different conditions exhibits the other morphology, it may be said that the inversion frontier or line passes somewhere between the two sets of conditions. Such a separation line between the two cases would be called the “standard” inversion frontier or line, which delineates the sets of conditions that result in a O/W region and a W/O region on an appropriate map, as considered later. On the other hand, a pre-existing emulsion can be subjected to a continuous or lumpwise change (generally * To whom correspondence should be addressed. Tel./Fax: (++58-74) 40.29.54. E-mail: [email protected]. † Current address: Chemical Engineering Department, Rice University, Houston, TX 77005. ‡ Current address: PDVSA-INTEVEP, Los Teques, Venezuela.

under constant stirring) until its original type switches to the other in an event called “dynamic” inversion. As in the previous case, the conditions just before and just after the inversion are slightly different, and a dynamic inversion frontier may be defined between them. The term “condition” refers to everything that may influence the type of emulsion and can be described quantitatively in some scientific way (e.g., the value of a variable such as the temperature, the proportion of oil in the mixture, the concentration of electrolytes in the water phase, or the rotational speed of the stirring device, among other factors). The current understanding of the effect of these and other variables upon the kind of emulsion that is obtained when oil, water, and an emulsifier are mixed is summarized subsequently. Accounting of Variables From the point of view of the emulsion maker, the preparation of an emulsion involves many degrees of freedom as far as the formulation and the emulsification are concerned because the type and amount of ingredients to use and the procedure to follow must be set. These degrees of freedom could be classified as variables, parameters, or properties that are susceptible to influencing the final emulsion product. There are three kind of factors or variables: (1) “formulation variables” that depend on the nature of the components; (2) “composition variables” that quantitatively describe the composition of the system in terms of weight or volume fractions; and (3) the ones that describe the way the emulsion has been prepared, that is, the stirring and other “emulsification protocol” conditions. The physicochemical variables that depend on the nature of the different ingredients are those that are able to alter the prevailing physicochemical condition at the liquid-liquid interfaces. There are at least four such variables, which correspond to the two liquid phases, the surfactant, and the temperature. Theoretically, pressure should have some influence on the physical chemistry, too, but it is not likely to be important in these liquid-state systems unless ex-

10.1021/ie990778x CCC: $19.00 © 2000 American Chemical Society Published on Web 07/11/2000

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tremely high pressures are considered, which is an uncommon situation.2 The nature of the phases may additionally produce an effect, via such physical properties as the density and the viscosity of both liquids. It is probable that the interfacial tension between the pure liquid phases plays a role as well because it is a measurement of their incompatibility. However, the interfacial tension depends even more upon the presence of adsorbed surfactant, which is taken into account as part of the physicochemical formulation. The influence of these physical properties is relatively easy to handle from an intuitive point of view, and it will be discussed later, as a corrective effect. For purposes of the following discussion, only physicochemical variables will be included as formulation variables. Different kinds of variables may affect the interfacial physical chemistry. The quantification of their influence is not straightforward, as demonstrated by scores of experiments carried out in enhanced oil recovery studies in the 1970s.3-6 These studies have allowed selection of a reasonable set of variables to describe the physicochemical formulation. The nature of the oil phase may be characterized by its alkane carbon number (ACN) when it is an alkane and by its equivalent ACN when it is not, as detailed later. The physicochemical parameter that renders the nature of the aqueous phase is its ionic strength or salinity, which in turn depends on the nature and content of the electrolyte, that is, at least two variables. The characterization of the physicochemical nature of the surfactant requires at least one parameter, for example, its “hydrophilic-lipophilic balance” (HLB) number. In most cases, however, it is more convenient to assign one parameter to its hydrophilic group and another parameter to its hydrophobic or lipophilic part. With inclusion of the temperature as a variable, which is susceptible to influencing most interactions, the number of required formulation variables rises to at least 5 or 6. Furthermore, an alcohol or a hydrotrope is usually added to improve the solubility of some substances or to inhibit the formation of mesophases. Long hydrocarbon chain alcohols may also act as cosurfactants by modifying the physicochemical interaction of the surfactant with the oil and water phases. On the other hand, the surfactant is often a mixture of different species, either for cost reasons or by design to attain an intermediate or synergistic property. Most commercially used oils are mixtures, usually containing hundreds or thousands of components such as petroleum crude oils. In most practical cases, the water phase contains several electrolytes. All of this means that the number of degrees of freedom may be quite high, only as far as the formulation variables are concerned. The consequences of this multiplicity in the number of variables are overwhelming. For example, a systematic study with 10 values of each of 10 variables would require a staggering 10 billion experiments, a dead end eventuality. Physicochemical FormulationsFrom Early Concepts to Current Quantification Obviously, random trial-and-error procedures are to be ruled out. In the past 50 years, a lot of research has been dedicated to quantification of the physicochemical formulation concepts or effects in a simple way.7

The first yardstick to be proposed, in 1949, was the still famous HLB number,8,9 which is related to the surfactant structure and to some extent to some oilphase properties. The HLB empirical approach is still popular because of its extreme simplicity. but it lacks accuracy and does not take into account the effects of the kind and concentration of electrolyte, temperature, and other factors. The next milestone in the understanding of the physicochemical formulation was the introduction by Winsor10 of the “ratio of the interaction energies” between the adsorbed surfactant molecules and the oil and water molecules, as a general and overall description of the physicochemical conditions prevailing at the interface. Winsor’s R ratio depends on all formulation variables in a way that may be qualitatively ascertained according to the general laws of molecular interactions. Winsor was thus able to experimentally verify his theoretical proposal in a systematic way. A dozen of reports published in the late 1940s and early 1950s and resumed in his book10 showed that the state and properties of the system at equilibrium were directly related to the R ratio, that is, a particular combination of the effects, rather than the effects themselves. This was extremely important in practice because it was a hint that the formulation could be represented somehow by a single parameter. Winsor’s R ratio framework is still the best pedagogical presentation to explain the effect of the physicochemical formulation on a surfactant-oil-water system. However, Winsor’s R ratio could not be numerically evaluated, which is a serious drawback, as far as its practical applications were concerned. Some years later, Shinoda11-13 introduced the concept of the “phase inversion temperature” (PIT), which was the first single experimental parameter that was able to describe, in numerical terms, Winsor’s theoretical approach. However, application of the PIT concept was limited to relatively balanced nonionic surfactant systems. In the 1970s, enhanced oil recovery research, particularly the experimental work carried out in R. S. Schechter and W. H. Wade laboratory at the University of Texas at Austin, led to the development of empirical correlations14-18 that numerically describe the conditions for attaining ultralow interfacial tension and enabling oil mobilization. The correlation was soon recognized as a numerical expression of the relative contributions of the different formulation variables to a global generalized formulation concept. This was subsequently related to the “surfactant affinity difference” (SAD), that is, the difference between the standard chemical potentials of the surfactant in the oil and water phase,19,20

SAD ) µw* - µo* ) ∆Goilfwater ) -RT ln Kp (1) where Kp is the partition coefficient of the surfactant between water and oil at the corresponding temperature, and can thus be measured. Analogous to the experimental correlation for the attainment of optimum formulation, the numerical expression for SAD as a function of the formulation variables was reported to be that shown in eqs 2 and 3 for ionic and nonionic surfactant systems, respectively: 21,22

SAD/RT ) ln(S) - K × ACN - f(A) + σ - aT∆T + Constant (2)

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SAD/RT ) R - EON + bS - k × ACN - φ(A) + cT∆T + Constant (3) In these relationships, S is the salinity (as wt % NaCl in the aqueous phase), ln(S) is the natural logarithm of the salinity or some equivalent,23 ACN (alkane carbon number) or the equivalent ACN (EACN) if the oil is not an alkane is a characteristic parameter of the oil phase,24,25 f(A) and φ(A) are functions of the alcohol type and concentration,14,26 σ and R are characteristic parameters of the surfactant structure,15 and EON is the average number of ethylene oxide groups per molecule of nonionic surfactant.16 ∆T is the temperature deviation from the ambient reference temperature (25 °C); b, k, K, aT, and cT are empirical constants that depend on the nature of the system. The “Constant” is the value of SAD/RT for a reference system that is at “optimum formulation”, as discussed in the next paragraph. This reference value may be calculated by entering the experimental Kp value at optimum formulation into eq 1. However, if SAD is taken as the deviation from the reference case, the “Constant” is then always zero. For the sake of simplicity, this “deviation” definition is taken in what follows. Each term can be viewed as an energy-related contribution to the overall interaction balance, expressed as an algebraic sum, instead of a ratio as in Winsor’s R. The positive contributions (including the alcohol effect because the functions f(A) and φ(A) are negative for long-chain alcohols) tend to promote the transition in one direction (from R < 1 to R > 1) while the effect of negative terms tends toward the opposite direction.27,28 Whether SAD is respectively positive or negative, the dominant affinity of the surfactant is respectively for the oil or water phase. At SAD ) 0 the surfactant affinity for the water phase exactly equilibrates its affinity for the oil phase and the so-called optimum formulation is attained. Enhanced oil recovery researchers selected the word “optimum”, in the early 1970s, because this condition corresponds to the simultaneous occurrence of both an ultralow minimum in interfacial tension and the best petroleum recovery performance.29,30 As far as the generalized formulation concept is concerned, SAD ) 0 corresponds to R ) 1, while SAD < 0 is equivalent to R < 1, and vice versa. The sign of SAD indicates the dominant affinity of the surfactant, whereas its value denotes the magnitude of deviation from optimum formulation, that is, from balanced interactions. Equations 2 and 3 indicate that SAD accounts for the relative and compensating effects of the different formulation variables; therefore, it can be changed in a number of ways. Additional effects have been reported31-37 to complement these equations. For the sake of simplicity, these effects are not discussed here. Formulation Scan and Associated Properties In the development of empirical correlations for SAD, phase behavior studies were carried out by changing one variable at the time through a procedure that is usually referred to as “unidimensional formulation scan”.27,28,38 In the studies of the associated properties of surfactant-oil-water (SOW) systems along a unidimensional formulation scan, the actual formulation variable used to perform the scan does not matter because the

Figure 1. Regions of existence of normal (bold characters) and abnormal emulsions in a bidimensional formulation-composition plot and in corresponding triangular phase diagrams for SAD > 0 and SAD < 0.

physicochemical condition that prevails at the interface is due to a combination of effects, as mentioned earlier. Therefore, such a variable is generally chosen as being the most convenient one, from the experimental point of view; for example, water-phase salinity for ionic surfactant systems and temperature or EON for ethoxylated nonionic ones. When the properties of the SOW systems were monitored, either at equilibrium or after emulsification, it was found that, along a unidimensional formulation scan, the optimum formulation corresponds to a very peculiar situation for practically any system property.39,40 It is now well-established that, at optimum formulation, the minimum in interfacial tension is accompanied by the following transitions: (1) the emulsion morphology is interchanged from one type to the other,41,42 as observed a long time ago by Bancroft;43,44 (2) the emulsion stability passes through a deep minimum,41,45-48 which has been interpreted in different ways;23,49-52 and (3) the emulsion viscosity undergoes a minimum, also.53,54 Because these patterns are always the same, independent of the variable that is used to produce the scan, they are associated not with the particular scanned variable but with the generalized formulation SAD. Consequently, it may be said that the effect of the 10 or more formulation variables can be summarized according to the value of a single parameter such as SAD. This drastic reduction in the number of degrees of freedom paved the way for additional systematization in the phenomenology by making space to introduce other variables. Influence of CompositionsBidimensional Mapping Composition variables are easier to handle. In the case of a true ternary system, there are only two independent variables, often selected as the surfactant concentration and the relative amount of oil and water, typically expressed either as the water-to-oil ratio or as the water or oil content. In a simplified SOW ternary-phase diagram (Figure 1, upper graph) one can see that a single-phase region extends from the S apex down to the W and O apexes along both SW and SO sides. Because W and O are

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Figure 2. Formulation-composition plots showing a schematic representation for phase behavior and emulsion morphology (after refs 38 and 39).

immiscible phases, there is always a multiphase region in the center, the “height” of which corresponds to the minimum amount of surfactant that is required to cosolubilize the oil and water into a microemulsion single phase. This minimum surfactant concentration ranges usually from a low 5% to 30% or more. Consequently, two-phase behavior is exhibited and an emulsion can be made upon stirring when the surfactant concentration is taken to be low enough, say 0.5% or 5% in practice, with little phenomenological change as far as the emulsion properties are concerned. Thus, the “main” composition variable is not the surfactant concentration but the water-oil proportion. Upon mixing, most systems in the two-phase region produce the so-called “normal” emulsion type, which corresponds to the preferred morphology according to Bancroft’s rule,43 oriented-wedge theory,55,56 or modern counterparts such as Kabalnov’s hole stability concept.57 These normal emulsions exhibit O/W morphology for Winsor’s type I systems (R < 1 or SAD < 0) and W/O for Winsor’s type II case (R > 1 or SAD > 0), as indicated in large letters in the center of the two-phase region of the ternary diagrams. However, at one corner of the two-phase region of the triangular diagram, the preferred morphology cannot be attained because the preferred-continuous-phase content is too low. In this case, so-called “abnormal” emulsions are obtained. The abnormal emulsion regions are indicated on a side of the two-phase region. They show water as the external phase at SAD > 0 and high water content, and oil as the external phase at SAD < 0 and high oil content, and for now they are indicated as small lettering of O/W and W/O, respectively. They typically represent from one-third to one-forth of the two-phase region. The line that separates the normal from abnormal emulsions is the inversion line. Figure 1 (lower graph) indicates a formulationcomposition bidimensional diagram where the formulation is indicated along the ordinate as a generalized parameter such as SAD. Along the abscissa is the selected composition variable, which is the water/oil content at low surfactant concentration, says 1 or 2 wt %, so that the surfactant may be neglected in the mass inventory. The horizontal dashed line in the center of the graph indicates the SAD ) 0 formulation and separates the regions where the hydrophilic and lipophilic tendencies dominate. The arrows indicate the correspondence between the formulation in the lower graph and the diagram type (upper graphs). The bold lines represent the water-oil content for emulsion inversion in all graphs. Bidimensional diagrams have been used to plot the phase behavior,58 emulsion type, 59 and other properties as a function of the two most significant variables, that

is, the formulation and the water-oil composition, at a constant surfactant concentration and constant emulsification protocol. Provided that the surfactant concentration is within the proper range, the phase behavior map (Figure 2, left) exhibits a central three-phase behavior strip that is the optimum formulation zone (SAD ) 0). This strip ends up in two single-phase regions located at both extremes of the composition axis. Unless the surfactant concentration is high, these single-phase regions are very narrow because they correspond to the mutual solubilities of oil and water with a small amount of surfactant. Below and above the three-phase region the biphasic Winsor’s type I and type II phase behavior regions are encountered. A mnemotechnical labeling proposed by the University of Minnesota EOR group60 is also used. The number 2 indicates two phases, and the position of the bar (top or bottom) indicates the phase that contains most the surfactant when the equilibrated system is placed in a vertical test tube. This convention assumes that the oilphase density is lower than the water-phase density. In some maps, the plotting of the formulation as a particular formulation variable value induces a slanting of the three-phase band. This slanting is related to the selective partitioning of the different surfactant species or to the uneven partitioning of the alcohol and surfactant in the water and oil phase.61,62 In such cases, the interfacial composition of the surfactant mixture is altered when the water-to-oil ratio is changed. It occurs when the surfactant mixture does not behave as a pseudocomponent, a usual case with ethoxylated nonionic surfactants.20 Because SAD ) 0 corresponds to the center of the three-phase region, changing the particular formulation variable scale to a SAD scale would straighten up this problem, if necessary. Figure 2 (right) shows a schematization of the emulsion-type map in which the standard inversion line appears as a stair.59 When conditions correspond to one side of the standard inversion line, stirring of an equilibrated SOW system leads to the O/W morphology, while on the other side of the line, a W/O emulsion is attained instead. The formulation-composition map is divided into six zones (A+, A-, B+, B-, C+, and C-). On one hand, regions are labeled as “+” or “-” depending upon the sign of SAD, that is, on the formulation case. On the other hand, zones labeled as “A”, “B”, or “C” differ in the water (or oil) content. While systems with a water-to-oil ratio near unity are in the A+/A- regions, low-water-content systems (usually below 30% water) are in the B+/B- zones and high-water-content systems (typically above 70% water) are the in C+/C- zones. The standard inversion line stair shape has been found to be typical of most systems, as extensively reported in the literature.59,63-65


The horizontal branch in the center of the diagram closely follows the optimum formulation (SAD ) 0). Therefore, in this central region, the emulsion morphology only depends on the physicochemical formulation. In such a case, the emulsion type is referred to as “normal”. The normal-to-normal emulsion change in morphology, from one side of the horizontal branch to the other, is called a “transitional inversion”,21 for reasons that will be discussed later. At SAD > 0 (respectively, < 0), the normal emulsion is W/O (respectively, O/W) up to a high internal-phase proportion, say 70% water (respectively, oil) content. Beyond this internal-phase proportion, the emulsion assumes the other morphology and becomes an “abnormal” emulsion. Thus, at low water or oil content, the standard inversion line is almost vertical; that is, the emulsion type essentially depends on the phase proportion. Abnormal emulsions are often multiple emulsions, noted w/O/W in the C+ region and o/W/O in the Bregion. In abnormal multiple emulsions, it is the most external emulsion that is abnormal, whereas the most internal one is normal, in the sense that it obeys the preferred morphology according to the current formulation. As a reminder that the amount of the most internal phase is often very small, the labeling symbol uses a lower case letter to represent this phase, as in o/W/O and w/O/W. Consequently, it can be said that the formulation dominates the emulsion type up to some high internal-phase proportion that is about 70%, while above this figure the composition dominates, and it is the phase that is present in a greater amount that becomes the external phase. As a rule of thumb, it can be said that when there is a conflict between the formulation and composition requirements, abnormal multiple emulsions are produced as a way to partially satisfy both requirements. The vertical branches of the inversion line separate a normal emulsion region from an abnormal one. This inversion pattern has been called “catastrophic”21 because its generally sudden occurrence could be modeled by using catastrophe theory, as discussed later. Although all the formulation variables have been reduced to a single one (SAD), there are still many degrees of freedom in addition to the formulation and water-oil composition. Other variables that are likely to affect the systems are the surfactant concentration, phase viscosity, and all variables that account for the emulsification conditions, particularly those related to stirring. It has been found, thus far, that none of these variables significantly influenced the position of the horizontal branch, provided that it was located as SAD ) 0 in the appropriate scale. In contrast, a change in these variables can shift the location of the “vertical” branches of the standard inversion line, and even turn them from vertical to slanted, as a consequence of a coupled formulation-composition effect. Figure 3 indicates some currently available trends in a three-dimensional scheme that shows the distortion of the standard inversion line in several cases39,40,66-67 and corrects previously published misleading information.39 As the surfactant concentration increases, the central region tends to expand, while the opposite happens as the stirring energy is increased. In some extreme cases, such effects can reverse the stair shape,66 as in Figure 4 (left) in which the change in the aqueousphase viscosity from an essentially 1 cP sodium chloride solution in water to a 100 cP carboxymethyl cellulose

Figure 3. Effect of several variables upon the relative position of the inversion locus on a formulation-composition map. Arrows indicate the change that is observed after an increase in the corresponding variable.

brine considerably reduces the extension of the Aregion where normal O/W emulsions are found. Figure 4 (right) indicates that it is the A+ region (where normal W/O emulsions are found) that is decreased by an increase in oil-phase viscosity, as documented elsewhere,66,68 for up to very viscous oil phases, for which the stair essentially disappears. Indeed, it may be said that as the viscosity of one phase increases, it becomes more difficult to make an emulsion in which this phase is the continuous one, in the sense that the map region where it happens is reduced. It is worth noting that in Figure 4 the optimum formulation (dashed) line, that is, SAD ) 0, is shifted by the change in the water- and oil-phase nature. When carboxymethylcellulose (a polyelectrolyte) is added, the optimum salinity is reduced as a consequence (left graph). When high-molecularweight lube oil is added to kerosene, the oil equivalent ACN is increased, which requires a corresponding increase in salinity (right graph) according to eq 2. The disposition of the standard inversion line on the bidimensional formulation-composition map that corresponds to the imposed conditions is of paramount importance for the emulsion maker because it indicates, in a very straightforward way, where certain specific properties can be attained, as explained elsewhere.40,68-71 Dynamic Inversion When an emulsion is subjected to a change in formulation or composition, under constant stirring, its representative point is displaced on the bidimensional map according to a continuous or lumpwise motion. When such a displacement does not cross the standard inversion line, no morphology change is exhibited, and other properties of the emulsion are likely to change according to the specific characteristics of the visited regions. This emulsion shift is a typical treatment for adjusting the mean value of the emulsion drop size, apparent viscosity, or stability. When the path of the representative points of the emulsion, on the formulation-composition map, crosses the standard inversion line and wanders onto the other side, a dynamic inversion is likely, though not inevitably, to occur.21 Experimental evidence indicates that when the formulation, including temperature, is changed, to cross the horizontal branch separating the normal A regions of the formulation-composition map, then dynamic inversion takes place exactly at the point of transition across the standard inversion line, that is, at the optimum formulation, whatever the position and direction of change (white arrows in Figure 5 left) . This is consistent with the extremely low interfacial tension and low emulsion stability exhibited in this region. In effect, it may be conjectured that any formed emulsion

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Figure 4. Effect of the viscosity of the water and oil phase (µw and µo, respectively) upon the position of the standard inversion line (after ref 66). The optimum formulation line is also displaced because a new compound is present in the viscous phase. Consequently, the nature of such phase is slightly altered.

Figure 5. Dynamic inversion patterns (adapted from ref 40).

breaks up very quickly and can be reformed very quickly because of the prevailing low interfacial tension.72,73 On one hand, recent research has shown that mass transfer is also very rapid in this formulation region74 so that any surfactant shift from one phase to the other (which is driven by the change in the partitioning coefficient with SAD) is likely to take place very rapidly. Very rapid changes are essentially equivalent to instantly equilibrated phenomena in which case the physicochemical conditions prevail over the kinetic or time-dependent phenomena. On the other hand, it has been known from a long time ago75 that when the vertical branches are crossed by a continuous change in the water-to-oil ratio, emulsion inversion does not take place immediately. Instead, it is delayed with respect to the standard inversion line (indicated in Figure 5 by a dashed line), in the sense that the emulsion can take up an amount of dispersed phase beyond that achievable through standard emulsification. If the change is an increase in the internalphase ratio from a normal emulsion to an abnormal emulsion, that is, from A+ to C+ at SAD > 0 and from A- to B- at SAD < 0 (Figure 5, left), the dynamic inversion delay feature tends to increase the width of the A region. Conversely, if the change is from an abnormal to a normal emulsion (Figure 5, center), then the dynamic inversion delay feature tends to restrict the A region extension. Therefore, the delay occurs in both directions of crossing. Moreover, it depends on the formulation; that is, the farther from SAD ) 0, the larger the dispersed-phase fraction that the emulsion can take up before inversion happens. Because there is a delay in both directions of crossing, the standard inversion line lies between the dynamic inversion lines for the two composition scans, that is, at an intermediate position within the triangular zones that are formed by superposition of the dynamic inversion boundaries21,76 (Figure 5, right).

The shrinking extension of the delayed inversion zone (shaded) as optimum formulation is approached may be related to the previously commented fact that optimum formulation systems are readily equilibrated and are thus basically insensitive to any temporal effect. Thus, it may be said that the delayed inversion (which is essentially a time-related effect) is defeated by the “immediate” equilibration features that prevail as optimum formulation is approached. These wedge-shaped regions are called “hysteresis” zones,75 analogous to magnetic phenomena, because any of the two emulsion morphologies may be found within them, depending on the direction of the dynamic process. In these regions, the current emulsion type depends on the previous history of the system, particularly the change in water/oil composition. Recent Advances in Dynamic Inversion As with the standard inversion line, the selective partitioning of the species contained in a surfactant mixture can produce a strong slanting of the phase boundary when a formulation variable is used instead of SAD.59,77 Figure 6 shows such a distorted map for an ethoxylated nonionic system when EON is the formulation variable.78 It is known that these commercial surfactants contain a variety of oligomers, which in the present case may range from nonethoxylated nonylphenol to a nonylphenol with 15 ethylene oxide groups. Such large differences results in extreme partitioning, with sometimes more than 80% of the surfactant fractionating into the oil phase. This is by the way why the three-phase behavior (dotted) zone disappears at a low degree of ethoxylation (EON < 4). The overall map topology remains the same, but in this example the A+ zone essentially vanishes because it is squeezed between two converging lines, that is, the optimum formulation line (SAD ) 0) and the A+/C+ vertical branch of the inversion line. The slanting indicates that, at higher water content, the surfactant mixture at the interface is more lipophilic because it requires a higher overall EON value to reach a balanced affinity at the center of the three-phase region. The position of the hysteresis zone and its extension are found to change with variables that are not taken


Figure 8. Three-dimensional schematic plot showing the normalto-abnormal (D f E) and abnormal-to-normal (F f G) inversion patterns for emulsions made within the hysteresis zone, after an increase in stirring energy.

Figure 6. Phase behavior and dynamic inversion patterns in a system highly affected by the partitioning of the surfactant between the oil and aqueous phase.

Figure 7. Effect of stirring upon the extension of the hysteresis zone.

into account in the bidimensional map. First are the variables that are able to change the position that corresponds to the standard inversion line. Recent studies have shown that an increase in surfactant concentration tends both to widen the hysteresis zone and to shift it to extreme composition, thus extending the area of the normal A regions.76 In contrast, an increase in stirring energy tends to produce the opposite effect,79 as indicated in Figure 7. A more spectacular reduction has been reported for anionic systems, which often exhibit a lower interfacial tension.80 This effect of stirring energy may be quite important as far as some industrial applications are concerned, for example, pipeline transport of 100 000 bbl/day of extraheavy bitumen-in-water emulsions over long distances in Eastern Venezuela.81 In this case, a high internalphase ratio O/W emulsion is located at point D in the bottom of the formulation-composition diagram (Figure 8) that corresponds to low stirring energy. Such an emulsion lies inside the hysteresis region (shaded) and could be of any type, though its manufacturing process ensures an O/W morphology. If it is subjected to high

shear, such as in a centrifugal pump, the formulationcomposition diagram changes into the upper one in which the hysteresis region extension is reduced and slightly shifted toward a higher water composition. The emulsion representative point E is now in the W/O (actually o/W/O) region, which means that the emulsion gets inverted by the excessive stirring. A way to avoid this would be to produce an increase in surfactant concentration, to shift the hysteresis zone to the left (and to expand it). This would result in additional expense; thus, the practical solution in this case was to avoid high-shear pumping. This could be the situation for any high internal-phase ratio emulsion such as those manufactured for food, paint, or cosmetic conditioning. Figure 8 also shows that a similar, but opposite, situation can happen in the case indicated by arrow FG. At low stirring energy, a W/O emulsion can be made on the left side of point D in the B- region and then shifted to point F with increasing of its water content (though not enough to reach the right frontier of the hysteresis zone). An increase in stirring will shift the situation to point G in the upper diagram, where an O/W emulsion is produced. In this case, the increase in stirring energy has produced a dynamic inversion from W/O to O/W, just the opposite of the previous case. This example illustrates why in the past emulsion inversion was regarded as a whimsical phenomenon. Recent investigations have shown that, in some cases, the inversion delay can be extended and consequently the hysteresis zone can be extremely expanded. No systematization is available yet concerning the factors (or combinations of factors) that might control the width of the hysteresis zone. Nevertheless, the emulsification protocol, the stirring method, the position of the impeller with respect to the interface, and the way that the composition is shifted (i.e., its programming) have been recognized as significant elements.66,67,79,82-87 What happens when the emulsion representative point is shifted through the hysteresis zone is only partially known and seems to depend on the dynamic inversion protocol. In the abnormal-to-normal inversion path, an evolution through the formation of multiple emulsions is often detected,64,86-88 as evidenced in Figure 9 by the region of emulsion intermediate conductivity, which is lower than expected for the corresponding normal O/W emulsion with the same composition. The occurrence of multiple emulsions as an intermediate stage may be expected in this case because the original emulsion is most often multiple. Additionally, recent studies86,87 indicate that the same intermediate situation could happen in the other direction of change, that is, when a normal-to-abnormal emulsion inversion path is followed. Several drop inclusion mechanisms89,90 have been proposed to justify the occurrence

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Figure 9. Detection of multiple emulsions through electrical conductivity measurements in a dynamic composition scan in the direction B- f A- (see inserted map). Multiple emulsions exhibit conductivity values between those expected for the W/O and O/W morphologies (dashed lines).

of multiple emulsions near the catastrophic inversion, but there is still some uncertainty. As a general comment, it can be said that a multiple emulsion is likely to happen when there is a conflict between the formulation and composition requirements as far as the emulsion type is concerned, whatever the reason for such a conflict. In the case of catastrophic inversion, and depending on the protocol of incorporation of the added phase, the local variations in water-oil content result in local conditions that may be on one side or on the other of the inversion line, thus producing a mixture of the two emulsions. This situation could generate multiple emulsions in which the most internal emulsion is stable while the most external one is not. The width of the region in which multiple emulsions occur seems to vary considerably from case to case and no general trend is known for sure yet, as far as the authors’ unpublished data on the subject show. In any case, the current knowledge on the inversion mechanisms is still fragmentary, although the preparation of fine miniemulsions by such inversion processes has been routinely used in cosmetics manufacturing for decades. The transitional inversion scheme, via the PIT inversion method91,92 or similar miniemulsion-related methods,93-99 seems to be easier to explain than the catastrophic inversion changes through multiple-emulsion occurrence.88-90 Modeling Emulsion Inversion As soon as the knowledge on some topic becomes organized enough, it is convenient to build a model that describes the observed trends and allows the interpretation of its main features; thereafter, the model can be used to predict new situations and to guide further advances. This has been the case in the emulsion inversion phenomenon. However, and because the whole phenomenology is not yet clearly quantified, a universal approach, rather that accurate modeling, has been the trend. The first contributions were registered at the beginning of the 20th century when Ostwald100,101 assumed that the internal-phase volume fraction of an emulsion could not exceed the relative volume occupied by the close-packed sphere configuration (φmax), which is about 0.74 for monodispersed rigid spheres, but could be

higher for polydispersed systems. According to Ostwald’s model, there is only one morphology above φmax and below 1 - φmax, whereas the two morphologies are possible in between. This essentially mechanistic model has the virtue of acknowledging the hysteresis phenomenon, but it does not take into account the surfactant effect, which is known to be of considerable importance in most practical cases. Perhaps as a response to this drawback, Bancroft announced his famous rule that links the relative surfactant affinities for the water and oil phase to the emulsion type.43,44 In modern terms, Bancroft’s rule means that the preferred external phase of an emulsion is the one in which the surfactant is more soluble. Because this rule states a tendency or a preference, some exceptions may be allowed to occur, for example, those according to Ostwald’s rule at extreme oil and water contents. It is amazing to realize that the bases of the current phenomenology framework were set down such a long time ago. It seems that Ostwald’s suggestion was essentially forgotten and that the advances in the following 60 years only addressed the modeling of the surfactant effect on the emulsion morphology according to Bancroft’s rule, as in the wedge theory,55,56 in empirical approaches as in Griffin’s HLB,8,9 or experimental measurements as in Shinoda’s PIT,102 in the correlation for three-phase behavior,14,16,18 and in fundamental concepts such as Winsor’s R,10 the so-called cohesive energy ratio CER,103 or the SAD.21 All these are essentially physicochemical models that give a more or less appropriate description of the interface tendency to bend in one way or the other. All are satisfactory, each at its level of completeness, to interpret most of the transitional inversion characteristics. However, none of them can cope with the hysteresis and other peculiar features exhibited by catastrophic dynamic inversion, such as the existence of two possible states (O/W and W/O) with no intermediate situation, the sudden changes in several properties when the system switches from one of the possible states to the other, and the divergence between the two emulsion types being triggered by an infinitesimal difference in initial conditions. Catastrophe theory evolved from algebraic topology 30 years ago, and it soon wandered out of the mathematicians’ realm to become a handy tool that can describe discontinuous processes, which are very common in nature.104 The catastrophe theory approach makes use of a potential that commands evolution of the system, like the Gibbs free energy. The stable states correspond to the minima of this potential, and the way the system is distributed into the different minima is given by a convention. Thus, it is an essentially physicochemical model in which time plays no part, as discussed elsewhere.21 In 1981, Dickinson105 suggested that the first elementary catastrophe, that is, the so-called “cusp”, might be used to interpret the hysteresis and other features that were exhibited during the emulsion inversion through a change in composition. Dickinson’s cusp catastrophe model was able to interpret the hysteresis, but it failed to render the asymmetrical characteristic of the formulation effect.106,107 An improvement was introduced by using a higher degree catastrophe, the so-called “butterfly”. Salager21,108,109 showed that the same butterfly catas-


trophe could be used to model both the phase behavior of SOW systems by using the Maxwell convention, and the emulsion phase inversion, by using the perfect delay convention. Such a coincidence of the bifurcation maps with experimental maps is a telltale sign that the emulsion inversion driving force has some fundamental roots in thermodynamics, although intuition tends to point toward a time-related mechanism. The butterfly catastrophe model allows interpretation of the two cases of emulsion inversion (transitional and catastrophic) as a function of the generalized formulation, and the two composition variables, that is, surfactant concentration and water-oil proportion. It is currently accepted as the model that best mimics the entire inversion phenomenology in all its complexity. Although it may seem to be complicated at first sight, the butterfly catastrophe model is easy to handle, and it is enlightening insofar as the intrinsic mechanism is concerned.21 Recently, it was suggested that some emulsion inversion mechanisms could be modeled according to an intermediate convention, so-called imperfect delay,80 which is reminiscent of the incoherent inversion proposed some years ago,110 in relation to competitive kinetics phenomena. Davies111 was the first to propose this other important approach when explaining emulsion inversion as a competition between the coalescence tendencies of the two types of emulsions. The one with the highest coalescence rate would disappear and the other would prevail. Davies linked the rate of coalescence with the HLB number111 and proposed its famous group contribution approach to calculate it. The kinetic approach that has been proposed to describe the inversion phenomenon is quite satisfactory from the physical point of view, but it is extremely difficult to handle, quantitatively, because drop breaking and coalescence are extremely intricate phenomena that involve many variables whose effects are not yet mastered, despite scores of experimental studies and simulation trials.112-125 The interpretation of the hysteresis feature for the catastrophic inversion with a kinetic model is not a straightforward matter. In an attempt to address this issue, Vaessen and co-workers98,126-128 recently proposed a model in which the inversion is related to the degree of abnormality of the emulsion. While their consolidated vision of the complex kinetics behind the catastrophic inversion phenomena is an interesting contribution, it becomes clear that the eventual ability of a kinetic model to account for the hysteresis pattern would require an even more intricate approach because it is necessary for this kind of model to embrace the formation of multiple emulsions. In any case, kinetic models do not seem to offer yet the clear-cut perception provided by the butterfly catastrophe model. Conclusions Emulsion inversion has been for a long time a whimsical phenomenon that could not be tackled by any means. Although much research is still required to master it for emulsion production purposes, much of the know-how that leads to a general phenomenology of emulsion inversion has accumulated in recent years. The influence of physicochemical formulation may be rendered satisfactorily through a generalized variable that takes into account all formulation variables and temperature. The water-oil content is the second most

important parameter. Its effect is sometimes in conflict with the formulation effect, in which case an abnormal, often multiple emulsion, is formed. The formulationcomposition map is a handy tool to study the emulsion inversion, both standard and dynamic types. This map is found to be altered by other variables such as stirring, surfactant concentration, and phase viscosity. A great deal of practical information has been gathered and allows the formulator to carry on his work in the right direction. However, on one hand, more experimental research is needed to ascertain the generality of these results, and eventual exceptions, particularly on the effect of stirring equipment and the way it is used, that is, the emulsification protocol. On the other hand, the inversion mechanism and the hysteresis phenomena associated with catastrophic dynamic inversion still require much research undertaking to be rationalized. The models using catastrophe theory or competitive kinetics are able to provide some hints and to interpret some phenomena, but they are still far away from a quantitative prediction. Because emulsion inversion is often used in industrial processes, as in cosmetics and paint manufacture, the indispensable additional research effort is probably worthwhile. Acknowledgment The authors would like to express their appreciation to the University of the Andes Research Council for sponsoring the FIRP Laboratory research program in Emulsion Science in general and Emulsion Inversion in particular (Grant CDCHT-I-635-99), to Dr. Norman Carnahan (Rice University) for his valuable comments on this paper, and to the Venezuelan National Research Council (CONICIT) and the Venezuelan Petrochemical Society (PEQUIVEN) for providing scholarships to L.M. and E.T., respectively. Literature Cited (1) Becher, P. Emulsions: Theory and Practice; Reprint; R. Krieger: Huntington, New York, 1960. (2) Fotland, P.; Skange, A. Ultralow Interfacial Tension as a Function of Pressure. J. Dispersion Sci. Technol. 1986, 7, 563. (3) Mittal, K., Ed. Micellization, Solubilization and Microemulsions; Plenum Press: New York, 1977; 2 vols. (4) Shah, D. O., Schechter, R. S., Eds. Improved Oil Recovery by Surfactant and Polymer Flooding; Academic Press: New York, 1977. (5) Johansen, R. T., Berg, R. L., Eds. Chemistry of Oil Recovery; ACS Symposium Series No. 91; American Chemical Society: Washington, DC, 1979. (6) Shah, D. O., Ed. Surface Phenomena in Enhanced Oil Recovery; Plenum Press: New York, 1981. (7) Salager, J. L. Quantifying the Concept of Physico-Chemical Formulation in Surfactant-Oil-Water Systems. Prog. Colloid Polym. Sci. 1996, 100, 137. (8) Griffin, W. C. Classification of Surface Active Agents by HLB. J. Soc. Cosmet. Chem. 1949, 1, 311. (9) Griffin, W. C. Calculation of HLB Values of Non-ionic Surfactants. J. Soc. Cosmet. Chem. 1954, 5, 249. (10) Winsor, P. A. Solvent Properties of Amphiphilic Compounds; Butterworth: London, 1954. (11) Shinoda, K.; Arai, H. The Correlation between Phase Inversion Temperature in Emulsion and Cloud Point in Solution of Nonionic Emulsifier. J. Phys. Chem. 1964, 68, 3485. (12) Arai, H.; Shinoda, K. The Effect of Mixing of Oils and of Nonionic Surfactants on the Phase Inversion Temperatures of Emulsions. J. Colloid Interface Sci. 1967, 25, 396. (13) Shinoda, K.; Kunieda, H. Phase Properties of Emulsions: PIT and HLB. In Encyclopedia of Emulsion Technology; Becher, P., Ed.; Marcel Dekker: New York, 1985; Vol. 1.

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Received for review October 27, 1999 Revised manuscript received April 17, 2000 Accepted April 18, 2000 IE990778X

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