Christel Pierlot
email: christel.pierlot@univ-lille1.fr

Jesus F Ontiveros

Maxime Royer

Marianne Catté

Jean-Louis Salager

Emulsification of viscous alkyd resin by catastrophic phase inversion with nonionic surfactant

Keywords: Emulsion, alkyd, viscous, catastrophic phase inversion, torque

The addition of water to hydrophobic alkyd resin containing an hydrophilic nonionic surfactant (polyethoxylated-20-oleyl alcohol) was used to produce the emulsion morphology change from W/O to O/W in a small thermostated reactor (50 mL). The so-called catastrophic phase inversion of the water/alkyd resin system was detected by monitoring both the viscosity through a torque measurement and the electrical conductivity, until an equal weight fraction of water and resin is attained (f w = 0.5). The two methods provide similar values of the phase inversion point (PIP). Although the determination of the PIP exhibits a small inaccuracy, it is clear that different torque profiles and PIP are observed depending on the resin neutralization level, the surfactant concentration and the water addition rate. For the non neutralized resin, both PIP and emulsion drop size decreases with surfactant concentration increase. The completely neutralized resin could be emulsified using a minimum of 2 wt% of surfactant in the final emulsion. In such a case the water fraction at which inversion occurs, is independent (f w , inv = 0.36) of the surfactant concentration and a small resin drop diameter (< 200 nm) can be obtained. A more precise study of the reached drop size of the emulsion versus resin neutralization (0, 25, 50, 75, 100 and 125%) indicates that a minimum diameter is obtained around 90-100% neutralization, with no effect of over neutralization. For non-neutralized resin, a maximum f w,Inv (0.25) can be obtained by reducing water addition rate allowing the production of 0.5 μm droplets in a longer process.

Introduction

Alkyd resins

Alkyd resins are polyesters obtained from polycondensation of polyacids (as phthalic anhydride), polyalcohols (as glycerol), and fatty acids with double bounds, as indicated in Fig. 1. They are synthesized and formulated in different ways and generally classified according to the vegetable oil length [START_REF] Martens | Alkyd resins[END_REF][START_REF] Van Gorkum | The oxidative drying of alkyd paint catalysed by metal complexes[END_REF][START_REF] Oldring | Resins for Surface Coatings, Alkyds & Polyesters[END_REF][START_REF] Lin | [END_REF][START_REF] Gooch | Emulsification and polymerization of alkyd resins[END_REF]. They are well known for performance as a coating for paint films, and have developed considerably since 1929 as reported in details elsewhere [START_REF] Hofland | Alkyd resins: From down and out to alive and kicking[END_REF]. By changing the nature of the monomers, and the length of the oil unsaturated fatty acid side groups for crosslinking, alkyd resins are suitable for a wide range of applications, in particular for metal paints. Another advantage of this polyesters is that they are compatible with other polymers like acrylic, silicone phenolic or epoxy resins. In the 1950's the environment concern tended to eliminate the volatile organic compound (VOC) solvents from the paints and to develop water-borne systems, i.e. polymer drop in water emulsified systems. This was not very easy for high viscosity oil phases as it is the case of alkyd and epoxy resins, because even a very energetic turbulent stirring is not effective in producing very small oil drops O/W emulsion [START_REF] Grace | Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems[END_REF]. It was however shown in empirical cosmetic studies [START_REF] Lin | Low-energy emulsification I: Principles and applications[END_REF] that paradoxically, a low energy emulsification could be a way to produce a very effective emulsification in some particular circumstances. This was however somehow mysterious until systematic studies of emulsion properties versus formulation variables were carried out in the 1980's [START_REF] Jarry | Inversion of Surfactant-oil-brine emulsified Systems: Generalized mapping and Property transitions[END_REF], and made general during the next decade [START_REF] Salager | Guidelines for the formulation, composition and stirring to attain desired emulsion properties (type, droplet size, viscosity and stability)[END_REF]. This is why the basic know-how on emulsion properties which can be found in details elsewhere [START_REF] Salager | Emulsion formulation engineering for the practitioner[END_REF], has to be quickly reviewed before entering the particular waterborne resin dispersion case dealt with in the present article.

Basic influence of formulation, composition and other variables on emulsion formation and properties

The probably most determinant effect on emulsion type is the nature of the emulsifier compound, i.e. the surfactant species. The original Banckrof's rule introduced 100 years ago has been improved through the physicochemical formulation concept which takes into account the interactions of the surfactant adsorbed at interface with both liquid phases, so called oil (O) and water (W) in what follows. This rule essentially stated that the external phase of the emulsion is most of the time the one in which the surfactant is most soluble. It was improved by in the late 1940 by the introduction of tech HLB empirical scale for the surfactant which was used for decade even if it is inaccurate for not taking into account the exact nature of the other ingredients. The Winsor's R ratio original notion introduced in the 1950's was that if the interaction of the adsorbed surfactant at interface was greater for the water (respectively oil) than for the oil (respectively water) the most likely emulsion to be produced was O/W (respectively WO). Winsor improvement was to show that such interaction ratio was depending of all the characteristics of the system, i.e. the oil nature (its degree of polarity), the water nature (its salinity, i.e. ionic concentration), the nature of the surfactant head and tail groups, as well as the temperature, and even pressure. Although Winsor's R theory was an excellent concept, important in discussing the observed effects, it was not very useful in practice because the interactions in R could not be calculated accurately.

In the 1970's the enhanced oil recovery research and development studies required to improve the formulation concept accuracy to attain the so-called optimum formulation at which the OW interfacial tension undergoes through a low minimum, which is the situation where the interactions of the interfacially adsorbed surfactant for the O and W phases are exactly equal. This optimum formulation also corresponds to the occurrence of a triphase system with a bicontinuous microemulsion in equilibrium with excess oil and excess water, as well as very specific properties of the emulsified systems, i.e. their type change (inversion), their minimum persistence (instability) and their minimum viscosity.

As first proposed a long time ago [START_REF] Wade | Interfacial tension and phase behavior of surfactant systems[END_REF] and recently discussed elsewhere [START_REF] Salager | How to attain ultralow interfacial tension and three-phase behavior with surfactant formulation for enhanced oil recovery: a review. Part 1. Optimum formulation for simple surfactant-oil-water ternary systems[END_REF] the attainment of an optimum formulation, may be represented by a zero difference of standard chemical potential of the surfactant for the two phases, i.e. its surfactant affinity difference SAD or its dimensionless expression so-called the Hydrophilic-Lipophilic Deviation HLD [START_REF] Salager | Partitioning of ethoxylated octylphenol surfactants in microemulsion-oil-water systems: influence of temperature and relation between partitioning coefficient and physicochemical formulation[END_REF][START_REF] Salager | Formulation des microémulsions par la méthode du HLD[END_REF]. The HLD = 0 situation was found to happen as a numerical correlation was accurately satisfied.

For a polyethoxylated surfactant, the correlation for optimum formulation was found to be [START_REF] Bourrel | A correlation for phase behavior of nonionic surfactants[END_REF]

SAD/RT = HLD = α -EON -k.ACN + (a.A) + t (T -25) + (b.S) (1)
where α is a characteristic parameter of the surfactant tail that linearly increases with its length, and EON is the average degree of ethoxylation of the surfactant. ACN is the alkane carbon number (or, eventually, its equivalent EACN for non-alkane oils). S and A are the salt and alcohol concentrations and T is the temperature of the system in °C; k, a, t and b are characteristic constants depending of the type of surfactant, salt and alcohol.

The generalized formulation HLD is a single factor that influences the type of emulsion when an equilibrated SOW system is stirred, i.e. O/W (respectively W/O) when HLD < 0 (respectively HLD > 0) when the volumes of the two fluids are not very different, e.g. typically from 30 to 70% of oil or water. However, if there is a very large amount of one of the fluids, the stirring tends to have this fluid as the emulsion continuous phase with the dispersion of the other one as drops, even if the formulation condition, i.e. the HLD sign, favors the opposite.

These two effects are represented in a formulation-composition bidimensional map shown in Fig. 2 as proposed a long time ago [START_REF] Salager | Surfactant-oil-water systems near the affinity inversion. Part III: The two kinds of emulsion inversion[END_REF]. phase. In the central WIII zone (at and close to optimum formulation HLD = 0) the microemulsion middle phase is in equilibrium with oil and water excess phases.

Emulsion type attained in the corresponding formulation-composition zones in the map are separated by the steplike boundary, so-called "standard" inversion line [START_REF] Salager | Surfactant-oil-water systems near the affinity inversion. Part III: The two kinds of emulsion inversion[END_REF]. The central A zone corresponds to similar amount of oil and water, say from 30 to 70%, while B and C zones are for emulsions with an excess of oil or water, which is the most external phase in a multiple emulsion morphology. The + or -associated with the letter indicates the sign of SAD or HLD, i.e. whether the surfactant is rather lipophilic (+) or hydrophilic (-) in the conditions.

Emulsions in the mid composition range (A) were labeled as "normal" as there are spontaneously formed by stirring and relatively stabilized by the presence of surfactant at interface, with the exception of the HLD ~0 thin region where they are very unstable. Emulsions in the B + and C -zones are also normal, because their type corresponds to the formulation effect, with a high external phase content. The B -and C + zones were labeled as "abnormal" because the tendencies of the formulation and composition influences are in conflict. What is the dominating influence depends on the way the emulsion is formed as will be discussed later in this article. As a matter of fact, a double satisfaction is more or less produced by the occurrence of a multiple emulsion as indicated as o/W/O or o/W/O in Fig. 2, with a stable inner emulsion of droplets in drops and an unstable outer one of drops in a continuous phase.

Formulation and composition variables have the most important influence on emulsion type and inversion, but there are not the unique ones. Unfortunately, all others variables dealt with in emulsions have essentially a similar effect on the formulation-composition phenomenology, i.e. they increase or decrease the width of the A zone. Increasing the surfactant concentration tends to widen it [START_REF] Silva | Dynamic inversion hysteresis of emulsions containing anionic surfactants[END_REF], while increasing the stirring energy tends to narrow it, by widening the B and C zones [START_REF] Peña | Effect of stirring energy upon the dynamic inversion hysteresis of emulsions[END_REF][START_REF] Rondón-Gonzaléz | 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[END_REF].

For a system located in a multiple emulsion zone (C + or B -), with a fixed formulation-composition, i.e. constant position in the Fig. 2 map, a continuous stirring for a long time tends to favor the normal inner emulsion and thus to increase the width of the A zone. As a consequence the inversion from the abnormal multiple emulsion to the simple normal emulsion type takes place [START_REF] Rondón-González | Emulsion inversion from abnormal to normal morphology by continuous stirring without internal phase addition: effect of surfactant mixture fractionation at extreme water-oil ratio[END_REF][START_REF] Rondon-Gonzalez | Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 6. Effect of the Phase Viscosity on the Inversion Produced by Continuous Stirring[END_REF][START_REF] Rondon-Gonzalez | Emulsion catastrophic inversion from abnormal to normal morphology. 7. Emulsion evolution produced by continuous stirring to generate a very high internal phase ratio emulsion[END_REF][START_REF] Arenas-Calderon | Preparation of highly concentrated bitumen emulsions by catastrophic phase inversion: Follow-up of the emulsification process[END_REF].

Increasing the viscosity of one of the phase tends to narrow the normal emulsion zone where the more viscous phase is the external one, i.e. A + for a more viscous oil phase and A -for a more viscous aqueous phase [START_REF] Brooks | Phase inversion in non-ionic surfactant-oil-water systems-III. The effect of the oil-phase viscosity on catastrophic inversion and the relationship between the drop sizes present before and after catastrophic inversion[END_REF][START_REF] Salager | Current phenomenological know-how and modeling of emulsion inversion[END_REF]. This is a consistent mechanical influence which has been explained in absence of formulation preference, by a higher momentum transfer in the more viscous phase [START_REF] Selker | Factors affecting which phase will disperse when immiscible liquids are stirred together[END_REF].These viscosity effects on the vertical parts of the standard inversion line in Fig. 2 could be extremely important in some cases [START_REF] Salager | Current phenomenological know-how and modeling of emulsion inversion[END_REF]. The type and location of the stirring device have also some influence [START_REF] Lin | Effect of initial surfactant location on emulsion phase inversion[END_REF][START_REF] Salager | Influence of the stirrer initial position on emulsion morphology. Making use of the local water-to-oil ratio concept for formulation engineering purpose[END_REF].

All these effects, may be incorporated into a three dimensional map in which the Fig. 2 formulation-composition is modified by a third influence, i.e. those of any or all of the other variables. Even if Fig. 3 concept is not really very easy to assimilate, it is actually an extremely simplifying presentation, since it allows to interpret the phenomenology of emulsion inversion and properties with respect to a score of variables, e.g. in a space with more than 10 dimensions.

Dynamic inversion

The standard inversion line (in Fig. 2) or surface (in Fig. 3) is limiting by the zones where the attained emulsion is one type or another according to the influence of all variables at the corresponding place in the 2D or 3D

diagram. Passing from one side of the boundary to the other side by changing one (or more) of the variables dealt with in Fig. 2 and 3 diagrams is called a dynamic inversion. It can be produced in several ways which are quickly reviewed here, but which are discussed in details elsewhere [START_REF] Salager | Current phenomenological know-how and modeling of emulsion inversion[END_REF].

The first one is by changing the formulation HLD sign through a variation of one or more of the variables appearing in equation 1. This crossing of the A + /A -line or surface one direction or the other, according with the white end arrows in Fig. 4, has been called "transitional" inversion [START_REF] Salager | Encyclopedia of emulsion technology[END_REF] because it is linked with a phase behavior transition which is reversible, particularly if the change can be easily carried out both way, as in the case of temperature for which the process was called the phase inversion temperature (PIT) a long time ago [START_REF] Shinoda | The correlation between phase inversion temperature in emulsion and cloud point in solution of nonionic emulsifier[END_REF][START_REF] Shinoda | The comparison between the PIT system and the HLB-value system to emulsifier selection[END_REF][START_REF] Shinoda | Stability of O/W [oil/water] type emulsions as functions of temperature and the HLB [hydrophile-lipophile balance] of emulsifiers: the emulsification by PIT [phase inversion temperature]-method[END_REF][START_REF] Shinoda | Encyclopedia of emulsion technology[END_REF].

The second type of dynamic inversion is the crossing of the B -/A -or the A + /C + lines or surfaces, passing from an abnormal emulsion to a normal one, or vice-versa. This corresponds in Fig. 2 to an "horizontal" change of the water-to-oil ratio at a constant formulation. In Fig 4 plots a black end arrow indicates the path in the original zone until the morphology changes (at its end). As it is seen in the central plot B -→ A -path, which is the inversion type of interest in the present case, the change from the original abnormal W/O type to the final normal O/W type (produced by adding water under constant stirring) takes place not at the crossing of the standard inversion (dashed) line but at a higher amount of added water, i.e. on the right of the standard inversion line. It is also seen that the delay with respect to the crossing of the standard line increases as the formulation departs from optimum, i.e. as HLD is more negative, due to the cusp bifurcation widening [START_REF] Salager | Encyclopedia of emulsion technology[END_REF] and verified by the data [START_REF] Silva | Dynamic inversion hysteresis of emulsions containing anionic surfactants[END_REF][START_REF] Rondon-Gonzalez | Emulsion catastrophic inversion from abnormal to normal morphology. 7. Emulsion evolution produced by continuous stirring to generate a very high internal phase ratio emulsion[END_REF][START_REF] Rondón-González | Emulsion catastrophic inversion from abnormal to normal morphology. 8. Effect of formulation on the inversion produced by continuous stirring[END_REF]. If the change is now produced in the other A -→ B -direction path, i.e. from the normal O/W to the abnormal W/O type (by adding oil under constant stirring) the change is again delayed, this time at a higher content of oil.

Consequently, there is a zone, indicated as a shaded zone in Fig. 4 right plot where the actual emulsion type (O/W or W/O) depends on the story of the process. This memory feature is called hysteresis and corresponds to a cusp catastrophe model [START_REF] Dickinson | Interpretation of emulsion phase inversion as a cusp catastrophe[END_REF] which is a simple irreversible change. In the present case two cusps appears in the map, and a butterfly catastrophe bifurcation had to be used to model both the phase behavior [START_REF] Salager | Phase behavior of amphiphile-oil-water systems related to the butterfly catastrophe[END_REF] and the emulsion inversion [START_REF] Schuster | Encyclopedia of Emulsion Technology: Basic theory, measurement, applications[END_REF], proposing the terms transitional and catastrophic inversions and explaining the difference between the two types in a relatively simple way [START_REF] Salager | Encyclopedia of emulsion technology[END_REF]. Since the addition of water or oil to an emulsion can locally produce a variation in water-to-oil ratio and surfactant concentration at a small scale, i.e. in a local volume the size of a few drops, the actual process of addition of a phase can result in the occurrence of both types of emulsion from place to place. This is why multiple emulsions are likely to occur in the B -and C + abnormal and unstable emulsion zones, and consequently in the hysteresis regions during an inversion from abnormal to normal morphology.

It is well known that an emulsion viscosity increases when the internal phase content becomes high and when the drop size is smaller and monodispersed. The formation of multiple emulsions can result in an increase of the volume of drops because of their stuffing by smaller droplets coming from the external phase [START_REF] Jahanzad | Catastrophic phase inversion via formation of multiple emulsions: A prerequisite for formation of fine emulsions[END_REF]. Such multiple emulsion become pseudoplastic and even viscoelastic, i.e. often much more viscous than the oil phase. In such a case the accumulation of the shear on the viscous oil drop, so-called high internal phase ratio mechanism, and the shearing model [START_REF] Yuan | A general approach for modelling complex fluids: its application to concentrated emulsions under shear[END_REF][START_REF] Li | A numerical study of the shearing motion of emulsions and foams[END_REF] allows to emulsify very viscous oil phases at low stirring conditions as discussed elsewhere [START_REF] Pérez | Surfactant-oil-water systems near the affinity inversion. XII. Emulsion drop size versus formulation and composition[END_REF], being to more efficient than a low tension [START_REF] Sajjadi | Formation of fine emulsions by emulsification at high viscosity or low interfacial tension; A comparative study[END_REF].

There are many possible mechanisms, particularly concerning the evolution of the multiple emulsion intermediate situation during the inversion from an abnormal to a normal emulsion. Many specific studies have been reported in details by different research groups and a very valuable information is available [START_REF] Rondón-Gonzaléz | 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[END_REF][START_REF] Rondon-Gonzalez | Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 6. Effect of the Phase Viscosity on the Inversion Produced by Continuous Stirring[END_REF][START_REF] Rondon-Gonzalez | Emulsion catastrophic inversion from abnormal to normal morphology. 7. Emulsion evolution produced by continuous stirring to generate a very high internal phase ratio emulsion[END_REF][START_REF] Brooks | Phase inversion in non-ionic surfactant-oil-water systems-III. The effect of the oil-phase viscosity on catastrophic inversion and the relationship between the drop sizes present before and after catastrophic inversion[END_REF][START_REF] Jahanzad | Catastrophic phase inversion via formation of multiple emulsions: A prerequisite for formation of fine emulsions[END_REF][START_REF] Brooks | Dynamics of liquid-liquid phase inversion using non-ionic surfactants[END_REF][START_REF] Brooks | Phase inversion in non-ionic surfactant-oil-water systems-II. Drop size studies in catastrophic inversion with turbulent mixing[END_REF][START_REF] Zerfa | Phase behaviour of non-ionic surfactant-p-xylene-water systems during the phase inversion process[END_REF][START_REF] Sajjadi | Morphological Change in Drop Structure with Time for Abnormal Polymer/Water/Surfactant Dispersions[END_REF][START_REF] Zerfa | Phase behaviour of polymer emulsions during the phase inversion process in the presence of non-ionic surfactants[END_REF][START_REF] Sajjadi | Dynamic behaviour of drops in oil/water/oil dispersions[END_REF][START_REF] Sajjadi | Phase Inversion in Abnormal O/W/O Emulsions: I. Effect of Surfactant Concentration[END_REF][START_REF] Sajjadi | Phase Inversion in Abnormal O/W/O Emulsions. 2. Effect of Surfactant Hydrophilic-Lipophilic Balance[END_REF][START_REF] Klahn | On the escape process during phase inversion of an emulsion[END_REF][START_REF] Bouchama | On the mechanism of catastrophic phase inversion in emulsions[END_REF][START_REF] Zambrano | Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 1. Effect of the Water-to-Oil Ratio Rate of Change on the Dynamic Inversion Frontier[END_REF][START_REF] Mira | Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 2. Effect of the Stirring Intensity on the Dynamic Inversion Frontier[END_REF][START_REF] Tyrode | Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 3. Conditions for Triggering the Dynamic Inversion and Application to Industrial Processes[END_REF][START_REF] Fernandez | Nano-emulsion formation by emulsion phase inversion[END_REF][START_REF] Tyrode | Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 4. Following the Emulsion Viscosity during Three Inversion Protocols and Extending the Critical Dispersed-Phase Concept[END_REF][START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF].

However, the complexity is extreme and a very small change in the conditions can result in a large difference in the result, which is not unexpected in a catastrophic phenomenon. This is in particular the case for very viscous oil cases, for which the information is limited.

As discussed in a review on the inversion techniques used in industrial practice [START_REF] Salager | Using emulsion inversion in industrial processes[END_REF] and the from the previously mentioned trends, high viscosity oil O/W emulsions are generally prepared by the catastrophic inversion from the B -abnormal to the A -normal one. The method has been used for many viscous oil cases such as alkyd polyester [START_REF] Watson | The rheology of aqueous emulsions prepared by direct emulsification and phase inversion from a high viscosity alkyd resin[END_REF], polyisobutylene [START_REF] Sajjadi | Phase Inversion in Abnormal O/W/O Emulsions: I. Effect of Surfactant Concentration[END_REF], epoxy resins [START_REF] Yang | Preparation of waterborne dispersions of epoxy resin by the phase-inversion emulsification technique. 2. Theoretical consideration of the phase-inversion process[END_REF][START_REF] Yang | Preparation of waterborne dispersions of epoxy resin by the phase-inversion emulsification technique. 1. Experimental study on the phase-inversion process[END_REF], polydimethylsilicone oils [START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF] or bitumen [START_REF] Arenas-Calderon | Preparation of highly concentrated bitumen emulsions by catastrophic phase inversion: Follow-up of the emulsification process[END_REF]. The reported conditions are variable from case to case, with some apparently favorable trends like a slow addition of water, continuously or by very small amounts, at low stirring energy during a long time, and with a surfactant in the oil phase providing a negative HLD formulation. However, each case seems to exhibit some specificity, with a variety of mechanisms which are able to influence the results.

Consequently, in practice it is thus important to monitor the morphology changes taking place during the inversion, to understand the influence of the actual conditions during the water addition process. Any method able to detect drop size, optical or electrical properties or viscosity change is likely to be a candidate to monitor the phase inversion, and to pinpoint it with accuracy.

The classical way to detect the emulsion inversion consists in measuring its electrical conductivity. Conductivity of O/W emulsions in which the more conductive phase is the continuous phase have been modeled by mathematical model [START_REF] Lira | Electrical conductivities of concentrated emulsions and their fit by conductivity models[END_REF]. Conductivity is typically high for the O/W morphology and low for the W/O one, particularly if the aqueous phase contains some electrolytes as often the case in practice. Equations have been established for the determination of the electrical conductivity on dispersions of three-phase emulsions, from volume fractions of each dispersed phase [START_REF] Lee | Morphologies of three-phase emulsions of the ternary nonionic amphiphile/oil/water systems and their determination by electrical method[END_REF][START_REF] Smith | An experimental test of catastrophe and critical-scaling theories of emulsion inversion[END_REF][START_REF] Lee | Formation of two-phase multiple emulsions by inclusion of continuous phase into dispersed phase[END_REF]. However for highly viscous emulsions on-line conductivity measurements are sometimes difficult because unsure renewal of fluid between the platinum plate of the cell.

Moreover, although the conductivity remains the usual method to track the inversion, the difficulties to clearly distinguish between multiple emulsions, gives importance to other methods as dielectric spectroscopy, ultrasonic, rheology, optical and torque/viscosity measurements. Table 1 summarizes different works related to the determination of the inversion phase of viscous emulsion system. Isopropyl myristate/Brij Shear stress versus shear rate profil with temperature (out and on line measurement) [START_REF] Pierlot | Cone-Plate Rheometer as Reactor and Viscosity Probe for the Detection of Transitional Phase Inversion of Brij30-Isopropyl Myristate-Water Model Emulsion[END_REF] Torque/Viscosity Kerosen/Tween Home made "rheomixer" reactor. Couette model to convert torque into viscosity (on line measurement) [START_REF] Allouche | Simultaneous Conductivity and Viscosity Measurements as a Technique To Track Emulsion Inversion by the Phase-Inversion-Temperature Method[END_REF] Bitume/ Tallow diamine and fatty acid Home made "rheomixer" reactor.

(on line measurement) [START_REF] Arenas-Calderon | Preparation of highly concentrated bitumen emulsions by catastrophic phase inversion: Follow-up of the emulsification process[END_REF] Rosin ester/Rosin acid Home made reactor. Metzner-Otto approach to convert torque into viscosity (on line measurement) [START_REF] Song | Role of operating conditions in determining droplet size and viscosity of tackifier emulsions formed via phase inversion[END_REF] Even if the high viscosity of alkyd resins makes difficult the measurement of their conductivity in a reactor, their profuse use in the coating industry stimulates the research in order to study the effect of variables that influence the catastrophic inversion process to obtain O/W emulsions. The purpose of this article is to obtain information by estimating the viscosity variations through the measurement of a torque on the stirring device. The variables to be analyzed will be the surfactant concentration, the neutralization of the carboxylic acid groups, and the added water flow rate. The results to be related will be the size of the resin final droplets and the water fraction needed to get the inversion. The analysis will be carried out in terms of the formulation (as hydrophilic lipophilic deviation HLD) to try to understand the chemical and physical parameters effects causing the morphology changes in the BrijO20/Alkyd resin/Water emulsion.

Materials and methods

Materials

Technical grade polyoxyethylene oleyl ether with an average of 20 ethylene oxide group per molecule was supplied by Sigma-Aldrich as BrijO20 (HLB = 15). The HLD surfactant parameter calculated according to a recent accurate relationship [START_REF] Salager | Trends to attain a lower interfacial tension in a revisited pure alkyl polyethyleneglycol surfactant-alkane-water ternary system. Basic concepts and straightforward guidelines for improving performance in enhanced oil recovery formulations[END_REF] is β = α -EON = -12.

Alkyd resin was synthetized according to described protocol [START_REF] Roussel | Production of alkyd resin from a bio-source[END_REF] and has an acid value of 8.7 (8.7 mg KOH are needed to neutralize 1 g of resin). Sodium chloride NaCl (purity ≥ 99.5%) was obtained from Acros Organics. Concentrated Potassium hydroxide (47 wt%) was purchased from Prolabo. Demineralized water (conductivity 1.34 S.cm -1 at 21 °C) was used in the aqueous phase.

Rheological experiments

A 1 mL alkyd resin sample is placed in the gap of a cone-plate (4 cm, 2°) Kinexus rheometer (Malvern). A shear stress gradient 0 to 500 Pa is applied in 1 min followed by the opposite, all at constant temperature. The linear profiles obtained allows the determination of the viscosity (shear stress divided by shear rate) in the studied scale.

Torque measurements

Torque are measured with Heidolph RZR 2051control at 50°C at 400 rpm and recorded via specific software (Watch/Control 200) provided by Heidolph.

Conductivity experiments

The conductivity is measured with a Radiometer Analytical CDM 210 conductimeter fitted with a CDC741T platinized platinum probe those geometry prevents accumulation of drops on the platinum plates.

Droplet Size and Size Distribution.

The emulsion average droplet size, i.e the volume-weighted median D (v, 0.5) , and the size distribution were determined by the laser diffraction instrument MasterSizer3000 (Malvern Instrument). The emulsion sample was diluted (1/1000 or 1/100 depending of the obscuration level) with distilled water to until correct 10% obscuration was obtained. Heidolph. For the conductivity experiments, and as a consequence of small losses of material when the cell is cleaned, a 30.0 g quantity of resin was used to maintain a suitable level in the reactor.

Emulsification experiments

Definitions

The surfactant weight fraction is defined by: Where m W and m O are the weights of water and alkyd resin respectively. f w,Inv is the mass fraction of water at which the inversion takes place.

Results and discussions

Choice of experimental conditions

Resins neutralized at 50% and 100% have been prepared by mixing alkyd resins with appropriate amounts of concentrated potassium hydroxide solution. The resin phase viscosity is measured with a cone-plate rheometer.

Shear stress versus shear rate plots exhibit a linear profil (not showed) indicating a newtonian behavior of the alkyd resin whatever the neutralization level (0, 50 or 100%) at the studied temperature range (from 25 to 75°C). However, no significant drop in viscosity with the degree of neutralization is found in Fig. 5 data. It is seen that in all neutralization cases, the viscosity is reduced from 37 Pa.s at work temperature (50 °C) to 3 Pa.s at 75°C. The Arrhenius law applied to the viscosity can be written as follows

η = η 0 exp(E a /RT) ( 3
)
where T is the temperature, η 0 a coefficient, Ea the activation energy and R is the universal gas constant. Fig. 5B plot linearity indicates that the resin is a first order fluid. The slope of the straight line allows to estimate the activation energy at E a =104 kJ.mol -1 .

Fig. 6 presents the measured torque generated by 20.0g of alkyd resin versus different turbine stirring speed at different temperatures (30, 40, 50 65 and 80°C). The torque generated by 20.0 g of water at 25°C which is also plotted will be considered as the background noise. All profiles are essentially linear at the beginning at low stirring, with a slope inversely proportional to the temperature. Then, a maximum torque value is obtained for a stirring speed superior to 400 rpm. At 30°C, the viscosity of the resin (450 Pa.s) is too high and the mechanical device limit is reached, thus it is not possible to stir above 400 rpm. At high temperature (80°C), the difference in torque between the resin and water is small, so that it is difficult to detect the emulsion inversion from W/O to O/W in this condition. It is seen from Fig. 6 that a significant difference between resin and water torque data is observed at moderate temperature (40-65°C) when the stirring rate is higher than 100 rpm. The optimum experimental conditions to study the phase inversion are thus selected to be at 50°C with a stirring speed of 400 rpm. Usually, commercial water-borne alkyd resin emulsions are sold with the same amount of polymer and water, i.e.

at f w = 0.5. To achieve such proportion, the catastrophic inversion must be completed at a lower value of f w,Inv at the end of the B -→ A -path shown in Fig. 4. As it is seen in the data reported in the literature [START_REF] Silva | Dynamic inversion hysteresis of emulsions containing anionic surfactants[END_REF][START_REF] Peña | Effect of stirring energy upon the dynamic inversion hysteresis of emulsions[END_REF][START_REF] Salager | Current phenomenological know-how and modeling of emulsion inversion[END_REF][START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF]] and because of the shape of the hysteresis cusp bifurcation, the B -→ A -boundary which indicates the complete inversion point, moves to the right, i.e. to a higher f w,Inv , as the formulation departs more from HLD = 0. This is inconvenient for the purpose of keeping f w,Inv low. On the other hand, being too close to HLD = 0 has been known a long time ago to result in an unstable final emulsion [START_REF] Salager | Emulsion formulation engineering for the practitioner[END_REF][START_REF] Salager | Surfactant-oil-water systems near the affinity inversion. Part I: Relationship between equilibrium phase behavior and emulsion type and stability[END_REF][START_REF] Anton | Emulsion instability in the three-phase behavior region of surfactant-alcohol-oil-brine systems[END_REF] with rather large drops [START_REF] Pérez | Surfactant-oil-water systems near the affinity inversion. XII. Emulsion drop size versus formulation and composition[END_REF][START_REF] Tolosa | Combined Effects of Formulation and Stirring on Emulsion Drop Size in the Vicinity of Three-Phase Behavior of Surfactant-Oil Water Systems[END_REF], i.e. another inconvenience. It is thus necessary to select a proper intermediate HLD formulation for the best compromise.

A recent study on how to find the appropriate formulation to produce a quick inversion [START_REF] Rondón-González | Emulsion catastrophic inversion from abnormal to normal morphology. 8. Effect of formulation on the inversion produced by continuous stirring[END_REF] reported that it is at some distance from the optimum on the HLD side corresponding to the final normal emulsion, that an optimum compromise is attained in the abnormal emulsion zone before inversion. This optimum formulation occurrence corresponds to the most favorable situation between two opposite effects taking place in a multiple emulsion as found in the abnormal zone where the inversion mechanisms are taking place. The first one is the formation and stabilization of the small droplets-in-drops inner emulsion, which is favored by a formulation far from HLD = 0, thus propagating the formation of the final stable emulsion. The second one is a rapid coalescence of the large drops to complete the inversion, which is accelerated by a formulation close to HLD=0. A complex argumentation proposed elsewhere [START_REF] Rondón | Obtención de biopreparados a partir de lactobacilos autóctonos del tracto digestivo de pollos y evaluación de su efecto probiótico en estos animales[END_REF] indicates that the optimum formulation located at some distance from optimum, typically 2-3 HLD units [START_REF] Salager | Guidelines for the formulation, composition and stirring to attain desired emulsion properties (type, droplet size, viscosity and stability)[END_REF][START_REF] Tolosa | Combined Effects of Formulation and Stirring on Emulsion Drop Size in the Vicinity of Three-Phase Behavior of Surfactant-Oil Water Systems[END_REF], corresponds to the minimum drop size for the final emulsion case, which is of course an additional benefit.

Thus the selected surfactant has been BrijO20, a polyethoxylated surfactant with HLB = 15 or β = α -EON = -12 which is significantly hydrophilic but not too much at 50°C, i.e. probably contributing to reach a HLD close to -3 or -4. It is worth remarking that in industrial processes, the surfactant is introduced in the resin before adding water [START_REF] Roussel | Production of alkyd resin from a bio-source[END_REF][START_REF] Weissenborn | Emulsification, drying and film formation of alkyd emulsions[END_REF][START_REF] Lefsaker | Characterization of alkyd emulsions: Characterization of phase inversion and emulsification properties pre-and post-inversion[END_REF]. Thus, the surfactant concentration is not constant in the semi-batch reactor, but start to be higher, a favorable situation to favor the incorporation of oil droplets in the drops formed by the added water.

In all cases the reported surfactant concentration corresponds to the final concentration when f w =0.5

Torque profile versus water addition

In all experiments the alkyd resin sample is introduced into the reactor at room temperature and is gradually stirred from 100 to 400 rpm in 10 min until the temperature reaches 50°C. Once the value of the torque is stabilized, the required potassium hydroxyde solution quota is added to achieve the selected neutralization. 5 minutes later, the surfactant is introduced into the reactor and the system is maintained under stirring for 5 minutes. The room temperature water is added at the selected flow rate. Fig. 7. shows typical data in which the torque on the impeller is plotted as a function of time and amount of added water (addition rate of 0.5 mL.min -1 ).

Three different experimental conditions have been selected to show the typical torque profiles that can be obtained: i) when there is not inversion probably because the surfactant concentration is too low (Fig. 7A).

Consequently the other experiments are carried out at a higher (8 wt%) surfactant concentration. ii) When inversion takes place with a 100% neutralized resin (Fig. 7B). iii) When inversion occurs with a 0% neutralized resin (Fig. 7C). Theses torque variations based on the volume of added water exhibit similarities with those reported for catastrophic inversion emulsification of viscous polymers such as epoxy resin [START_REF] Akay | Flow-induced phase inversion in the intensive processing of concentrated emulsions[END_REF], polyethylene [START_REF] Akay | Preparation of Colloidal Low-Density Polyethylene Latexes by Flow-Induced Phase Inversion Emulsification of Polymer Melt in Water[END_REF],

polyurethane [START_REF] Saw | Catastrophic phase inversion in region II of an ionomeric polymer-water system[END_REF], rosin resins [START_REF] Song | Role of operating conditions in determining droplet size and viscosity of tackifier emulsions formed via phase inversion[END_REF], silicon resin [START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF] and bisphenol A polyester [START_REF] Goger | In Situ Rheological Measurement of an Aqueous Polyester Dispersion during Emulsification[END_REF] or bitumen [START_REF] Arenas-Calderon | Preparation of highly concentrated bitumen emulsions by catastrophic phase inversion: Follow-up of the emulsification process[END_REF].

The addition of a potassium hydroxide solution rapidly causes a reduction of the torque, which however returns to its original value in less than 5 minutes (Fig. 7A and7B). In contrast, the addition of surfactant causes a decrease in torque without return to its initial level as significantly visible in Fig. 7B andC. Then, when water is added the torque signal becomes relatively unstable with a decreasing trend. At some time the unstability disappear, the torque increases significantly and then decreases and stabilizes. Such torque maximum which may be found to be larger in some cases [START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF], corresponds to the complete inversion occurrence.

Emulsions samples collected before this particular point cannot be dispersed in water, whereas they do after it. In order to corroborate the detection of the phase inversion point from the torque data, conductivity experiments were done using a solution 0.01M NaCl as aqueous phase (to plausibly increase the electrical conductivity of the aqueous phase).

Coincidence of Torque and Conductivity profiles versus water addition

In Fig. 8 it is seen that the quick conductivity change indicating the phase inversion coincides with the maximum torque peak. Knowing the volume of water added at that point it is possible to calculate the water fraction f w,Inv attained at the inversion from W/O to O/W morphology.

Fig. 8 indicates the data for two cases with extreme resin neutralization level (0 and 100%). It is worth remarking that the conductivity monitoring could not be carried out continuously, because the high viscosity of the emulsion prevents a regular renewal of the fluid on the platinum covered electrodes, thus possibly resulting in a preferential oil wetting. Consequently, the cell has to be periodically taken out of in the reactor and cleaned before re-imersing it. As reported for catastrophic inversion of emulsions with viscous rosin methyl ester [START_REF] Greiner | Spontaneous formation of a water-continuous emulsion from aw/o microemulsion[END_REF],

epoxy resin [START_REF] Xu | Catastrophic Emulsification of Epoxy Resin Using Pluronic Block Copolymers: Preinversion Behavior[END_REF], or polydimethylsiloxane [START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF] the increase in conductivity is relatively slow from the initial oil external morphology (W/O or o/W/O) to the final one (O/W).

Fig. 8 data clearly confirm that the start of catastrophic inversion, indicated by the sudden rise in conductivity, matches the start of the maximum torque peak.

Fig. 8. Evolution of torque and conductivity during emulsification process of 30.0 g alkyd resin versus water addition at 50 °C, agitator speed of 400 rpm, 5.6% BrijO20, water (NaCl 10 -2 M) addition rate of 0.2 mL.min -1 alkyd resin neutralized at 0% (A) and 100% (B).

Effect of Neutralization on the water fraction at inversion f w,Inv and on the emulsion drop size.

Fig. 9 shows the variation of f w,Inv and emulsion droplet average size D (v,0.5) at f w = 0.5 versus the percentage of neutralization of the alkyd resin, using 8 and 10% wt. of BrijO20 and a 0.5 mL .min -1 rate of water addition. It is seen that the water fraction needed to inverse the emulsion "f w,Inv " increases from 0.13 to 0.33 when the rate of neutralization increases from 0 to 75%, and then remains constant even beyond the complete neutralization to 125%, which could result in some charge excess or salinity effect. Since the chosen surfactant (BrijO20) is relatively hydrophilic (HLB = 15) it gives a negative HLD, and an inversion from abnormal W/O (or o/W/O) emulsion to normal O/W emulsion effectively take place at low f w (0.15 to 0.35). This low f w,Inv values are in agreement with the general discussion on this kind if emulsification by catastrophic inversion [START_REF] Pérez | Surfactant-oil-water systems near the affinity inversion. XII. Emulsion drop size versus formulation and composition[END_REF], i.e. that the HLD < 0 formulation favors the O/W morphology and that both the slow stirring motion (400 rpm) required by the high viscosity oil phase and the low water flow rate addition (0.5 mL.min) tend to shift the B -/A -inversion locus branch to the left. All these effects are known to be even stronger when the oil viscosity is increased [START_REF] Rondón | Obtención de biopreparados a partir de lactobacilos autóctonos del tracto digestivo de pollos y evaluación de su efecto probiótico en estos animales[END_REF].

As far as the actual result is concerned, the f w,Inv values in Fig. 9 are quite lower than the required f w < 0.5 value and it is thus satisfactory in practice. Now, the change due to the neutralization evidenced in Fig. 9, is a slight increase in f w,Inv , i.e. a slight increase in the extension of the B -region, and it is worth trying to find some explanation for it according to the known trends. Since the neutralization is generating some polarity on the resin, it is likely to reduce the EACN of the oil phase. The extra charges due to the neutralization process could eventually produce a slight salinity effect. It happens that both effets, i.e. the reduction in EACN and the increased in salinity, tend to increase HLD according to equation [START_REF] Martens | Alkyd resins[END_REF]. Since HLD is negative, such an increase would tends to shift the formulation toward the HLD = 0 optimum, whose result is in general to reduce the width of the hysteresis zone [START_REF] Silva | Dynamic inversion hysteresis of emulsions containing anionic surfactants[END_REF][START_REF] Peña | Effect of stirring energy upon the dynamic inversion hysteresis of emulsions[END_REF], and thus to reduce the f w,Inv value, i.e. the opposite of what is evidenced in Fig. 9. Although the change of the hysteresis zone with the formulation might be inexistent in some cases [START_REF] Salager | Current phenomenological know-how and modeling of emulsion inversion[END_REF][START_REF] Sajjadi | Phase Inversion in Abnormal O/W/O Emulsions. 2. Effect of Surfactant Hydrophilic-Lipophilic Balance[END_REF], Fig. 9 change cannot be explained by the oil change effect on HLD.

Another explanation may be suggested as a similarity with the asphaltenes polar oil role at crude oil/water interface. It is possible that some short resin molecules, when neutralized, actually become quite hydrophilic anionic surfactant species that are able to adsorb at interface to mix with the BrijO20 and to change the HLD to make it more negative [START_REF] Mendez | Surfactant-oil-water systems near the affinity inversion. Part XI. pH sensitive emulsions containing carboxylic acids[END_REF]. This would move the formulation away from optimum, with the widening of the hysteresis zone.

When the neutralization of the resin increases from 0 to 100% the size of the final emulsion drop slightly increases first from 0.8 μm to 2 μm at 50% neutralization, and then decreases in a notable way to 0.2 μm at 100% neutralization. The slight initial increase is probably due to the increase in the f w,Inv as a well known effect of the internal phase ratio [START_REF] Pérez | Surfactant-oil-water systems near the affinity inversion. XII. Emulsion drop size versus formulation and composition[END_REF]. In the second part, where the f w,Inv is remaining constant, the expected displacement of the HLD toward optimum tends to reduce the tension and thus the attained drop diameter, an effect which is known to become exceptional at some distance from optimum [START_REF] Tolosa | Combined Effects of Formulation and Stirring on Emulsion Drop Size in the Vicinity of Three-Phase Behavior of Surfactant-Oil Water Systems[END_REF], where the best compromise concerning a small drop diameter is attained.

The alkyd droplet size which starts again to slightly increase with the addition of more KOH than was necessary for deprotonation of all the carboxylic acid groups (0.3 μm for 125% Neutralization) might be due to an increase in salinity or of the pH, both producing a small change in HLD away from optimum.

Aside the so-called main formulation effect producing a stable emulsion at some distance from optimum formulation [START_REF] Salager | Emulsion formulation engineering for the practitioner[END_REF], an important second order factor should be mentioned in the present case. It is the electrostatic repulsion as a mechanism of stabilization, which can affected by the ionic strength due to an excess of K + and HO -ions that can shield of the carboxylic acid group charges. Weissenborn [START_REF] Weissenborn | Emulsification, drying and film formation of alkyd emulsions[END_REF] found the same drop size versus neutralization profile showed on Fig. 9 with the minimum size (0.6 μm) around 100 % neutralization, with an increase in size due to excessive neutralization. It was observed [START_REF] Jowkar-Deriss | Morphologies and droplet sizes of alkyd-acrylic hybrids with high solids content[END_REF] that alkyd resins with viscosity of 1 Pa.s resulted in emulsions with larger droplet size as compared to the lower viscosity (about 10 mPa.s) alkyds. In the present case the alkyd resin viscosity is higher (about 450 Pa.s at 50°C) and there is no viscosity alteration with the neutralization (Fig. 5). Consequently, the difference in drop size observed on Fig. 9 is probably due to some physico-chemical formulation effect. D (v,0.5) diameter data plotted Fig. 9 correspond to median values calculated from the size distributions shown in Fig. 10. For neutralization percentages from 0 to 75%, the distribution is polydisperse with an average particle size diameter between 0.4 and 2 µm. However, two peaks appear to detach from these profiles: one corresponding to a size of population between 1 to 2 µm and a smaller one at 0.3-0.5 µm. When the neutralization is increased from 0 to 100%, the relative heights of the two peaks are reversed and the size distribution becomes smaller and narrower. A unimodal distribution is obtained for 100% and 125 neutralization with a minimum D (v,0.5) of 0.18 μm and 0.30 μm respectively. The bimodal distribution is probably due to the two different origins of the drops in the final O/W emulsion. First, the small resin droplets formed by inclusion inside the water drops, and secondly the larger oil droplets formed by the rupture of the oil film between stuffed water drops at the end of the inversion propagation [START_REF] Sajjadi | Phase Inversion in Abnormal O/W/O Emulsions: I. Effect of Surfactant Concentration[END_REF][START_REF] Salager | Using emulsion inversion in industrial processes[END_REF]. When the neutralization is complete, practically all drops are likely to be small ones formed by inclusion according to Fig. 9 data. The final o/W/O multiple emulsion just before the inversion is completed, is likely to be a foam like morphology according to the higher torque reported in Fig. 7 and elsewhere [START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF]. The few large drops formed at inversion by the oil film rupture, are broken very efficiently in a very viscous high internal phase ratio O/W emulsion in the A -zone close to the B -/A -boundary [START_REF] Pérez | Surfactant-oil-water systems near the affinity inversion. XII. Emulsion drop size versus formulation and composition[END_REF][START_REF] Sajjadi | Formation of fine emulsions by emulsification at high viscosity or low interfacial tension; A comparative study[END_REF], and do not appear anymore in the distribution which appears to be unimodal. According to the observations from Fig. 10 and the formulation/composition bidimensional map in Fig. 2, Fig. 11 shows how the typical propagation of the inversion through a multiple emulsion [START_REF] Tyrode | Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 4. Following the Emulsion Viscosity during Three Inversion Protocols and Extending the Critical Dispersed-Phase Concept[END_REF][START_REF] Salager | Using emulsion inversion in industrial processes[END_REF][START_REF] Yang | Preparation of waterborne dispersions of epoxy resin by the phase-inversion emulsification technique. 1. Experimental study on the phase-inversion process[END_REF][START_REF] Salager | Emulsion phase inversion phenomena[END_REF] actually evolves at different neutralization level of the alkyd resin.

It is worth remarking that multiple emulsion formation seems to be a necessary condition to obtain a catastrophic phase inversion from B -to A -as discussed in the literature [START_REF] Jahanzad | Catastrophic phase inversion via formation of multiple emulsions: A prerequisite for formation of fine emulsions[END_REF][START_REF] Brooks | Dynamics of liquid-liquid phase inversion using non-ionic surfactants[END_REF]. When a too low amount of surfactant is used, there is not enough surfactant in the mixture to allow the emulsification of the two liquids, and only few large water droplets will be formed. Further addition of water will result in a concentrated resin with small quantity of resin dispersed in aqueous phase (Fig. 11A).

Effect of the surfactant concentration on the catastrophic inversion point

The evolution of the water fraction at which the inversion occurs (f w,Inv ) as function of surfactant concentration is shown in Fig. 12. When the resin is not neutralized f w,Inv decreases from 0.27 to 0.15 when the surfactant concentration ranges from 0.5 to 3% and then remains constant. The behavior is different for the 100% neutralized resin as f w,Inv is a constant at a higher value (f w,Inv =0.37) between 1 and 5.3% surfactant. For each experiment of Fig. 12, the corresponding mean diameter D (v,0.5) (Fig. 13) and size distribution measurement (Fig. 14) were performed at f w = 0.5 The trend is essentially the same, independently of the resin neutralization. Nevertheless, the lower drop size attained with neutralized resin is probably due to a HLD closer to optimum formulation because of a reduction of the resin EACN as discussed before. This HLD shift is resulting in a lower interfacial tension, with the possibility of corresponding to the minimum drop size attainable at some distance from HLD = 0 as shown elsewhere [START_REF] Tolosa | Combined Effects of Formulation and Stirring on Emulsion Drop Size in the Vicinity of Three-Phase Behavior of Surfactant-Oil Water Systems[END_REF]. The decrease in drop size when the surfactant concentration is increased, is probably due to a faster diffusion and adsorption, i.e. a kinetics effect, which seems to be significant below 3-4% wt of surfactant.

The results from Fig. 12 and 13 suggest that in practice small size drops (around 0.2 μm), are associated with a higher f w,Inv at about 0.3-0.4, although not too high, in the case of a 100% neutralized resin with at least 2 wt% of surfactant. Independently of the tension effect, it is possible that a higher water drop content favors the mechanism of foam like o/W/O multiple emulsion before the inversion is completed [START_REF] Jahanzad | Catastrophic phase inversion via formation of multiple emulsions: A prerequisite for formation of fine emulsions[END_REF]. showing the statistical distribution. Even with a high surfactant concentration (> 4 wt%), the emulsion made with the non-neutralized resin is exhibiting a wide size distribution, thus indicating a non homogeneous mixing in the production of small droplets. On the contrary, for the neutralized resin, a very narrow distribution is exhibited when the surfactant concentration is at 2% or above, indicating an efficient process of producing a monodisperse oil droplet inclusion in the water drops, which are by the way in a larger volume. This is consistent with a lower interfacial tension occurrence.

Effect of the water flow rate on the catastrophic inversion point and drop size

Fig. 15 shows the influence of the added water flow rate on the inversion point f w,Inv and on the emulsion drop size for the non-neutralized resin case with 2.9% wt. BrijO20. Experiments for 0.19, 0.29 and 0.5 mL.min -1 have been replicated to estimate the experimental inaccuracy on both f w,Inv and D (v, 0.5) . Fig. 15 indicates that f w,Inv remains constant (f w,Inv ~0.18) above a flow rate of 0.2 mL.min -1 . The size of the emulsion droplets tends to increase from 0.5 μm to 2-3 μm when the water flow rate increases from 0.1 to 0.5 mLmin -1 . Although a minimum D (v,0.5) of 0.5 μm can be reached at a very low flow rate (0.05-0.1 mL.min -1 ), it is not appropriate in practice because it requires more than 6 h of processing to attain the final f w = 0.5.

The reduction of f w,Inv when the internal phase addition rate increases seems to be a general trend. It has been already observed for different oil/surfactant systems, in particular less viscous oil phases such as Kerosene [START_REF] Zambrano | Emulsion Catastrophic Inversion from Abnormal to Normal Morphology. 1. Effect of the Water-to-Oil Ratio Rate of Change on the Dynamic Inversion Frontier[END_REF],

polydimethylsiloxane [START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF], paraffin oil [START_REF] Bouchama | On the mechanism of catastrophic phase inversion in emulsions[END_REF] and cyclohexane [START_REF] Brooks | Phase inversion in non-ionic surfactant-oil-water systems-II. Drop size studies in catastrophic inversion with turbulent mixing[END_REF].

With the multiple emulsion formation early triggered by a slow water addition rate, the propagation process occurs slowly, with the stuffing of rather small "W" drops by "o" droplets, but at still low apparent water volume so that there is a small probability of contact between the W dispersed drops. This results in a high f w,Inv and small droplet size [START_REF] Galindo-Alvarez | Viscous Oil Emulsification by Catastrophic Phase Inversion: Influence of Oil Viscosity and Process Conditions[END_REF].

Conclusion

Phase inversion emulsification experiments were carried out by adding water to a viscous alkyd resin oil phase containing a nonionic BrijO20 hydrophilic surfactant in a small thermostated reactor (50 mL). Experimental conditions of temperature (50°C) and agitation (400rpm) were chosen in order to optimize the inversion process to attain a final inverted O/W emulsion with equal resin and water content in a reasonable time. The propagation of the catastrophic phase inversion was followed in many different process conditions by monitoring the torque and the electrical conductivity, and the final product quality was characterized by the drop size distribution.

For the non-neutralized alkyd resin, a 1 µm droplet polydispersed emulsion was found to be produced with about 3 wt% of surfactant at a low water injection rate, i.e. through a rather long process. For an alkyd resin close to be neutralized with potassium hydroxide, a better product performance is attainable, i.e. 0.2-0.3 µm monodispersed emulsions produced with a higher injection rate and thus a shorter process.

Since there are many variables influencing the final product characteristics, the exact optimum conditions for the inversion process are to be determined by using the cost information for raw material and on industrial operations.

Fig. 1 .

 1 Fig. 1. Typical alkyd resin structure with phthalic acid, glycerol and linoleic side chain.

Fig. 2 .

 2 Fig. 2. Phase behavior at equilibrium and emulsion type zones for surfactant-oil-water systems in a 2D formulation-composition map.

Fig. 3 .

 3 Fig. 3. Emulsion type zones for surfactant-oil-water systems in a 3D map: formulation and composition in the horizontal cut and three kind of other variables in the vertical direction.

Fig. 4 .

 4 Fig. 4. Emulsion dynamic inversion line in the formulation-composition map. The tip of the arrows indicates the place where the emulsion type changes.

  20.0 g of alkyd resin is introduced into the 50 mL glass reactor at room temperature. Hot water regulated at 50 °C by a Julabo F25-HL cryostat is circulated in the reactor jacket in order to reduce the viscosity. The stirring of the turbine (70 mm) is gradually increased to 400 rpm with the Heidolph RZR 2051control until torque remains constant. A concentrated (47 wt%) Potassium hydroxide aqueous solution quota (typically : 0.248 mL to attain 100% neutralization) is first added to the 20.0 g resin sample and 5 min later the surfactant is added to the mixture. After torque stabilization, water is introduced at a constant flow rate (0.05 to 0.5 mL;min-1) with a Masterflex pomp Easy-Load 3. Torque is recorded via specific software (Watch/Control 200) provided by

( 2 )

 2 Where m S, m O and m W are the weights of surfactant, alkyd resin and water respectively. The indicated surfactant concentration in each experiment corresponds to the final concentration of surfactant (when the emulsion contains the same water weight as alkyd resin) .The water weight fraction f w is calculated by :(3)

Fig. 5 .

 5 Fig. 5. A : Viscosity of alkyd resin versus temperature for different neutralization ratio (0% :•; 50%: ⬜; 100% : △). B : Ln[Viscosity in Pa.s] versus inverse of temperature (K -1 ) for 50% neutralization alkyd resin.

Fig. 5A shows

  Fig. 5A shows the variation of the viscosity of alkyd resins at different temperatures. The neutralization converts carboxylic groups into carboxylates, and this might change the interactions between the polymer molecules [79].

Fig. 6 .

 6 Fig. 6. Measured torque generated by 20.0g of alkyd resin versus different turbine stirring speed at 30, 40, 50 65 and 80°C. The torque generated by 20.0 g of water at 25°C is also plotted as black circle dots.

Fig. 7 .

 7 Fig. 7. Evolution of torque during emulsification process of 20.0 g alkyd resin, versus time and water addition at 50 °C, with agitator speed of 400 rpm., water addition rate of 0.5 mL.min -1 for three different experimental conditions (A, B or C). A: 0.5% of BrijO20, 100% neutralization. B: 8.0% of BrijO20, 100% neutralization. C: 8.0% of BrijO20, 0% neutralization.

Fig. 9 .

 9 Fig. 9. Mass fraction of water at which the inversion takes place (f w,Inv ) and emulsion droplet size D (v, 0.5) at f w, =0.5 versus Neutralization. Emulsification carried out using on 20.0 g alkyd resin with 8% (⬛,•) or 10% (⬜, ) BrijO20.

Fig. 10 .

 10 Fig. 10. Size distribution of emulsion droplet size at f w, =0.5 versus Neutralization %. Emulsification were carried out using 20.0 g alkyd resin with 8% BrijO20 (0, 25, 50, 75 and 100% Neutralization) and 10% BrijO20 (125% Neutralization).

Fig. 11 .

 11 Fig. 11. Evolution of droplet size and morphology of emulsion during water addition according two different patways, with very low concentration surfactant (A), with high surfactant concentration with low (B) or high (C) level of neutralization.

Fig. 12 .

 12 Fig. 12. Mass fraction of water at which the inversion takes place (f w,Inv ) versus surfactant % for 0% ( ) and 100% (•) neutralization.

Fig. 13 .

 13 Fig. 13. Emulsion droplet size (D (v, 0.5) ) at f w = 0.5 versus surfactant % for 0% ( ) and 100% (•) neutralization.

Fig 14 brings

 14 Fig 14 brings some more information on the possible reasons for the difference in drop size in Fig. 13, by

Fig. 14 .

 14 Fig. 14. Size distribution of emulsion droplet size at f w, =0.5 for 1.1 (△), 2.1 (⬜), 1.9 ( ) and 4.2% (•) surfacatant for 0% (A) or 100% (B) level of neutralization. Emulsification were carried out with 20.0 g alkyd resin at 50 °C, with agitator speed of 400 rpm and with water addition rate of 0.5 mL.min.

Fig. 15 .

 15 Fig. 15. Mass fraction of water at which the inversion takes place ( , f w,Inv ) and emulsion droplet size (•, D(v, 0.5) at f w = 0.5 versus water flow rate. Emulsification process have been carried out with 20.0 g alkyd resin at 50 °C, with an agitator speed of 400 rpm and with 2.9% BrijO20.

Table 1 .

 1 Method, viscous emulsion system, operating method, out or on line measurements and reference.

	Method	Viscous emulsion system	Operating method.	Reference
			Out or on line measurements.
	Dielectric	Toluene/ triton X-100	Slope of real part of impedance	[68,69]
	spectroscopy		(frequencies scan : 1Hz < f < 1 MHz). On
			line measurements
		Paraffin oil/Span, Brij	Dielectric constant measured at 100 kHz.	[70]
			One line measurements
		Epoxy resin/Polymeric	Phase angle of dielectric constant at 300	[63]
		surfactant	Hz frequencies. On line measurements
	Ultrasonic	Alkyd resin/No surfactant	Measurement of ultrasonic propagation	[71]
		(Ultraturrax emulsification	through emulsions
		process)	On line measurements
	Rheology	Heavy crude oil with	Shear stress versus shear rate profil with	[72]
		asphalten/Span	temperature
			(out line measurement)
		Paraffin oil/Span, Brij	Shear stress versus shear rate profil with	[70]
			temperature
			(out line measurement)
		Alkyd resin/non ionic	Dynamic oscillatory shear tests	[61]
		surfactant	(out line measurement)
		Epoxy resin/Block	Dynamic oscillatory shear tests	[73]
		Copolymer	(out-line measurement)

Acknowledgements

Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur et de la Recherche, Région Nord -Pas de Calais and FEDER are acknowledged for supporting and funding partially this work. IFMAS is thanked for taking part in discussions and have approved the list of authors.