Three phase model thermodynamics

VIII. THERMODYNAMIC PROPERTIES BASED ON THE THREE-PHASE MODEL... 

The three phase model was exposed in the previous chapter. Basically, besides the solute exchange between the stationary and the mobile phase, the micelles introduce a secondary chemical equilibrium. Each equilibrium, micelle-aqueous phase, stationary phase-aqueous phase and stationary phase-micelles, has its thermodynamic constant, P, P s and PsM, respectively, linked together and to the micellar concentration, [M], the phase ratio, (j), and the surfactant molar volume, v, by the Armstrong equation [18]. 

In 1959, J. H. Schulman introduced the term microemulsion for transparent-solutions of a model four-component system [126]. Basically, microemulsions consist of water, an oily component, surfactant, and co-surfactant. A three phase diagram illustrating the area of existence of microemulsions is presented in Fig. 6 [24]. The phase equilibria, structures, applications, and chemical reactions of microemulsion have been reviewed by Sjoblom et al. [127]. In contrast to macroemulsions, microemulsions are optically transparent, isotropic, and thermodynamically stable [128, 129]. Microemulsions have been subject of various... 

Note that the conditions for the phase transition to a quark phase and thermodynamic equilibrium with the nucleon component, as it is seen from our analysis, are realized only for eleven EoS from the considered twenty four ones. Furthermore, for all the three used models of neutron matter the equilibrium and simultaneous coexistence with the quark EoS variants e, g and h having high values of emm, is impossible. 

In this paper, a molecular thermodynamic approach is developed to predict the structural and compositional characteristics of microemulsions. The theory can be applied not only to oil-in-water and water-in-cil droplet-type microemulsions but also to bicontinuous microemulsions. This treatment constitutes an extension of our earlier approaches to micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in the oil phase and the excluded-volume interactions among the droplets. Illustrative results are presented for an anionic surfactant (SDS) pentanol cyclohexane water NaCl system. Microstructur al features including the droplet radius, the thickness of the surfactant layer at the interface, the number of molecules of various species in a droplet, the size and composition dispersions of the droplets, and the distribution of the surfactant, oil, alcohol, and water molecules in the various microdomains are calculated. Further, the model allows the identification of the transition from a two-phase droplet-type microemulsion system to a three-phase microemulsion system involving a bicontinuous microemulsion. The persistence length of the bicontinuous microemulsion is also predicted by the model. Finally, the model permits the calculation of the interfacial tension between a microemulsion and the coexisting phase. 

Contact angle — The contact angle is the angle of contact between a droplet of liquid and a flat rigid solid, measured within the liquid and perpendicular to the contact line where three phases (liquid, solid, vapor) meet. The simplest theoretical model of contact angle assumes thermodynamic equilibrium between three pure phases at constant temperature and pressure [i, ii]. Also, the droplet is assumed to be so small that the force of gravity does not distort its shape. If we denote the - interfacial tension of the solid-vapor interface as ysv. the interfacial tension of the solid-liquid interface as ySL and the interfacial tension of the liquid-vapor interface as yLV, then by a horizontal balance of mechanical forces (9 < 90°)... 

The thermodynamic modeling and calculation procedures for S-L-V equilibrium in binary systems for RESS/PGSS involve simultaneous solution of the phase equilibrium relations for the two components, namely, the SCF solvent, 1, and the solid solute, 3, for all three phases, S, L, and V, as given by the following equations ... 

The prediction of the performance of three-phase multistage separation processes is dependent on the ability to describe the thermodynamics of three-phase behavior. The mathematical solution of three-phase distillation columns is similar to two-phase vapor-liquid columns, the difference being in the model used to calculate the /(-values. If the A -valuc model predicts two liquid phases, two liquid profiles must be considered in the column instead of one. 

Macroscopic thermodynamic models have been presented to give the Gibbs energy profile of the particle, as a function of its position along the interfacial normal [198, 199]. If the aqueous phase (z < 0) is treated as the reference state and line tension at the three-phase boundary is neglected, then... 

In the current study we are mainly interested in describing the gas solubility in pure water, under two-phase equihbrium (H-Lw) conditions. Gases of interest to this study include methane and carbon dioxide, and we report results mainly for the case of methane. To this purpose we couple different published thermodynamic models that are based on (i) the van der Waals-Platteeuw (vdWP) theory [9, 10] from Statistical Thermodynamics to describe three-phase (H-Lw-V) equihbria, (ii) Equations of State (EoS) for fugacity calculations, and (iii) models of gas solubihty in the aqueous phase. The considered approach is described in detail by Tsimpanogiannis et al., [11]. The authors conducted an extensive review of experimental and theoretical studies related to the solubility of gases in the aqueous phase under hydrate equilibrium conditions. Here, we report additional results that were not included in the original publication. 

F.P. Tomasella and L.J. Cline-Love, Thermodynamic Properties in MLC based on the Three-Phase Equilibrium Model, Anal Chem., 62 1315 (1990). 

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