Formulations equilibrium phase behavior

As we have seen, the optimal salinity or PIT concept based on the equilibrium phase behavior provides much useful insight in formulating emulsions and... 

Structured Surfactant Formulations take advantage of basic aqueous surfiictant phase behavior. Figure 1 shows a schematic of general surfiictant aqueous equilibrium phase behavior as a function of sur ctant concentration. 

Phase Behavior. The surfactant formulations for enhanced oil recovery consist of surfactant, alcohol and brine with or without added oil. As the alcohol and surfactant are added to equal volumes of oil and brine, the surfactant partitioning between oil and brine phases depends on the relative solubilities of the surfactant in each phase. If most of the surfactant remains in the brine phase, the system becomes two phases, and the aqueous phase consists of micelles or oil-in-water microemulsions depending upon the amount of oil solubilized. If most of the surfactant remains in the oil phase, a two-phase system is formed with reversed micelles or the water-in-oil microemulsion in equilibrium with an aqueous phase. 

A sudden increase in research effort on microemulsion systems was driven by the economic impact of the oil embargo in the early 1970s and the development of the so-called enhanced oil recovery processes that followed. The plentiful research funding available from both industry and governmental agencies resulted in an unprecedented improvement in the basic and advanced knowledge of very complex phenomena, in particular the surfactant-oil-water phase behavior in all its intricacies. It was found that the interfacial tension could be lowered to an ultralow 0.001 mN/m in many systems provided that a particular physicochemical condition was attained. It turned out that this so-called first optimum salinity, and then optimum formulation, coincides with the occurrence of three-phase behavior in which a bicontinuous microemulsion is in equilibrium with oil and water excess phases, i.e., the Winsor III case [20,21,109,110]. 

Figure 16 Mixed bidimensional (formulation-composiiion) map showing the phase behavior at equilibrium and the emulsion iso eonductivLty contours (left). Simplified map patterns with inversion locus and region labels (right). (After Reference 8,1.)...

Each phase behavior type is associated with an emulsion type, but near optimum formulation either a monophasic (micioemulsion) or triphasic (microemulsion at equilibrium with excess oil and water) is exhibited, dqiending on the amphiphile surfactant/alcohol mixture (S -f- A) concentration. When lempenituie... 

The whole phenomenology of phase behavior and emulsion inversion was interpreted wifli a butterfly catastrophe model with amazing quahtative matching between theory and experiment. The phase behavior model used the Maxwell convention which allows the system to split into several states, i.e., phases at equilibrium. On the other hand, the emulsion-type model allows for only one state (emulsion type) at the time, with eventually catastrophic transition and hysteresis, according to the perfect delay convention. The fact that the same model potential permits the interpretation of the phase behavior and of the emulsion inver sion (204, 206) is a symptomatic hint that both phe-nomenologies are linked, probably through formulation and water/oil composition which are two of the four manipula-ble parameters in the butterfly catastrophe potential. 

Before going into the topic of formulation, it is wordi remembering some basic concepts about phase equilibria. Since emulsions are two-phase systems, ihcir physicochemical formulation should be such that there are two phases in equilibrium, which are in due time stirred to make it a dispersion. Thus, formulation is to be studied according to its influence on the phase behavior of the SOW system, with emphasis on cases where two (or more) phases coexist in equilib-riunt. The well-known phase rule can be slated as ... 

Physicochemical formulation refers to intensive variables, which are characteristics of the nature of the components, along with temperature and pressure. They determine the affinity or negative of the standard chemical potential of the different species—particularly the surfactant—in all phases at equilibrium. They determine the phase behavior, as well as interfacial properties such as tension or natural cmvature. 

The purpose of a formulation scan is to switch from HLD < 0 to HLD > 0, or vice versa, by changing a single formulation variable in a monotonous way. When the HLD < 0 the affinity of the smfactant for the aqueous phase dominates, and a so-called Winsor type I phase behavior is exhibited in which a surfactant-rich aqueous phase (micellar solution or microemulsion) is in equilibrium with an essentially pure oil phase. When the HLD > 0, a Winsor type II phase behavior is exhibited, and this time it is the oil phase that contains most of the surfactant. At the intermediate HLD = 0 formulation, the affinity of the surfactant is the same for both phases, and a very low minimum of interfacial tension is exhibited, which is the reason why the researchers involved in enhanced oil recovery in the 1970s called it the optimum formulation. This label has been conserved ever since even for other applications [13]. 

An experimental investigation of equilibrium behavior of the systems composed of methylcyclohexane + ethylbenzene + methanol was carried out at 288.2 K. The liquid-liquid phase diagrams exhibit type 1 systems and indicate that methanol is totally miscible with the gasoline in a wide interval. Therefore, methanol may be considered as a good candied in gasoline formulations for vehicular fuels. 

When mixing two surfactants species in a SOW system, an equilibrium takes place between the oil and water phases and the interface for each species. Since the two species do not necessarily exhibit the same affinity for the interface and the oil and water bulk phases, the compositions of the surfactant mixtures at interface and in the phases might be different. For instance if a very hydrophilic species is mixed with a very lipophihc one, as often recommended in the old formulation literature, then the hydrophihc surfactant has a strong tendency to partition in water, whereas the lipophihc one would partition in the oil. In this case the surfactant mixture in water will contain a large majority of hydrophilic species, i.e., it will be very hydrophilic, whereas the oil phase will predominantly contain the hpophihc species, with the remaining adsorbing at interface. This situation in which each species actuates on its own, more or less independently of the other, has been called non-collective behavior. Since the surfactant mixture composition at interface is often the one that commands the actual property of the system, such as the interfacial tension or the stabihty of the emulsion, it is most important to know how to calculate or measure the characteristics of the mixture present at interface. Such methods will be discussed in the next section. 

Determination of T y. In the formulation of the phase equilibrium problem presented earlier, component chemical potentials were separated into three terms (1) 0, which expresses the primary temperature dependence, (2) solution mole fractions, which represent the primary composition dependence (ideal entropic contribution), and (3) 1, which accounts for relative mixture nonidealities. Because little data about the experimental properties of solutions exist, Tg is usually evaluated by imposing a model to describe the behavior of the liquid and solid mixtures and estimating model parameters by semiempirical methods or fitting limited segments of the phase diagram. Various solution models used to describe the liquid and solid mixtures are discussed in the following sections, and the behavior of T % is presented. 

A general formulation of the problem of solid-liquid phase equilibrium in quaternary systems was presented and required the evaluation of two thermodynamic quantities, By and Ty. Four methods for calculating Gy from experimental data were suggested. With these methods, reliable values of Gy for most compound semiconductors could be determined. The term Ty involves the deviation of the liquid solution from ideal behavior relative to that in the solid. This term is less important than the individual activity coefficients because of a partial cancellation of the composition and temperature dependence of the individual activity coefficients. The thermodynamic data base available for liquid mixtures is far more extensive than that for solid solutions. Future work aimed at measurement of solid-mixture properties would be helpful in identifying miscibility limits and their relation to LPE as a problem of constrained equilibrium. 

The goal of a subctitical VLE calculation is to quantitatively predict or correlnte the various kinds of behavior illustrated by Fig. 1.5-1 or by its iso baric or multicomponent coimlerparta. The basis for the calculation is phase-equilibrium formulation of Section 1.2-5, whare liquid-phase fogaciries are elimienled in favor of liquid-phase activity coefficients, aed vapor-pbase fugaciries in favor of vapor-phase fugacity coefficients. Raoult s Law standard states are chosen (tor all components in the liquid phase hence, (fTf- = f > and Eq. (1.2-63) becomes... 

The pseudophase-separation model for surfactant solutions (84, 132, 135) states that a surfactant solution above its critical micelle concentration (CMC) consists of two pseudophases in equilibrium with each other singly dispersed surfactant monomer molecules and micelles. When the surfactant solution is in contact with a solid, the adsorbed phase constitutes a third pseudophase (40). Strong experimental evidence suggests that surfactant adsorption takes place from the surfactant monomer phase but not from the micelles (84), behavior that leads to competition of both the micelles and the adsorbed phase for surfactant molecules from the monomer phase. Adsorption from a surfactant solution above the CMC then depends not only on the affinity of the surfactant for the solid surface but also on its tendency to form micelles. If a mixture can be formulated such that at least one of the surfactants is incorporated into micelles preferentially over the adsorbed phase, then the micelles act as a sink for the surfactant and thus prevent it from being adsorbed. 

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