Thermodynamic three phase interface

The bubble point tests conducted in methanol/water mixtures were worked up to show properties of the three-phase interfaces along the complex contact line in SS304 LAD screens. In particular, the variation with F2 of the solid/vapor interfacial tension /sv differed from that of the solid/liquid interface j/sl- The data are consistent with the Langmuir isotherm description of the thermodynamics of adsorption. The result of the analysis is that the co-areas Amin are 0.32 nm /molecule for the SS304— vapor interface and 1.77 nm /molecule for the SS304—solution interface. This implies that that methanol molecules form a dense, liquid-like monolayer at the interface of SS304 with the vapor phase, while the methanol molecules are very dilute in the interface between SS304 and the solution of methanol/water. 

The preceding condition of thermodynamic equilibrium implies that the curvature of the dispersed phase becomes zero at the transition from two to three phases. In the middle-phase microemulsion, the pressures p and p2 fluctuate in time and space because of the instability of the interface between the two media (see below), and intuition suggests that Eqs. (37) and (40) be replaced with their average, hence that the condition of zero curvature be replaced with the condition of mean (with respect to time) average curvature. 

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°)... 

Rotenberg, Y., Boruvka, L. and Neumaim, A.W., J. Colloid Interface Sci., 93(1983)169 Scheludko, A., Tchaljovska, S. and Fabrikant, A., Disc. Faraday Soc., (1970)1 Scheludko, A., Schulze, H.J. and Tchaljovska, S., Freiberger Forschungshefte, A484(1971)85 Scheludko, A., Toshev, B.V. and Platikanov, D., "On the mechanism and thermodynamics of three-phase contact line systems", in "The Modem Theory of Capillarity", Akademie-Verlag, Berlin, 1981... 

Evidently if S > 0 then k>+1. Were S>0 so that > o-, + a, this would imply that the solid-gas interface would immediately coat itself with a layer of the liquid phase and replace the supposedly higher free energy per unit area of direct solid-gas contact, cr g, by the supposedly lower sum of the free energies per unit area of solid-liquid and liquid-gas contacts, cr i + cr, thereby lowering the free energy of the system. However, in thermodynamic equilibrium this cannot be realized (Gibbs 1906, Rowlinson Widom 1982). Therefore, for a spreading film in thermodynamic equilibrium k = +1 S = 0), and locally there is a state of mechanical equilibrium at the contact line between the three phases. 

In such a thermodynamic analysis, it is necessary to use Equations (6.4) and (6.5), and the fact that in the system the sum of the areas of solid-vapor (Asv) and solid-hquid (Asl) interfaces remains constant. Using the equations, it can be shown that the change in free energy SG caused by a change in position of the three-phase boundary by a distance 8s can be represented as... 

The interplay of phase separation and polymer crystallization in the multi-component systems influences not only the thermodynamics of phase transitions, but also their kinetics. This provides an opportunity to tune the complex morphology of multi-phase structures via the interplay. In the following, we further introduce three aspects of theoretical and simulation progresses enhanced phase separation in the blends containing crystallizable polymers accelerated crystal nucleation separately in the bulk phase of concentrated solutions, at interfaces of immiscible blends and of solutions, and in single-chain systems and interplay in diblock copolymers. In the end, we introduce the implication of interplay in understanding biological systems. 

Hydrodynamics, mass, and heat transfer in the commonly used three-phase fixed-bed reactors were briefly outlined. Also, scale-up rules and alternative ways to scale down trickle-bed reactors are discussed. In spite of the extensive studies on the hydrodynamics, mass, and heat transfer in three-phase fixed-bed reactors, clearly, a lot of work remains to be done in providing a fundamentally based description of the effect of pressure on the parameters of importance in three-phase fixed-bed reactors operation, design, and scale-up or scale-down. It is evident that atmospheric data and models/correlations cannot, in general, be extrapolated to operation at elevated pressures. The physics conveyed by the standard two-phase flow models is minimalistic because it insufficiently describes the role and presence of interfaces and their thermodynamic properties. The explicit inclusion of interfaces and interfacial properties is essential because they are known to have a significant role in determining the thermodynamic state of the whole system. 

Example of multiphase flash and stability analysis. We will, in detail, discuss the stability analysis of a three-component system of Ci/CO /nCif at T = 294.0K and P — 67 bar with — 0.05. 2 co.> = 0.90, and = 0.05. At fixed temperature and pressure, from the phase rule F — c - -2 — p, there can be a maximum of three phases when the interface between the phases is flat. The first question is what types of phases may exist—gas, liquid, or solid. As we will see in Chapter 5, a solid phase does not exist for the above system. Therefore one might expect (1) a single gas phase or a single liquid phase, (2) gas and liquid phases, (3) liquid and liquid phases, or (4) gas-liquid-liquid phase separation. The difficulty in liquid-liquid (L-L) and vapor-liquid-liquid (V-Lr-L) and higher-phase equilibria (for more than three components) is how many phases should be considered for flash calculations. One approach is to determine whether one, two, or more phases are to be considered without prior knowledge of the true number of phases. In certain cases, as we will see in the next chapter, it is possible from thermodynamic stability analysis to determine the true number of phases a priori without performing a flash. However, in general, we do not know the true number of phases. One may, therefore, follow a sequential approaches outlined next for the Ci/C02/nCiQ example. 

In 1805 Young established a relationship between the contact angle of a drop of liquid and the interfacial tensions at the three-phase contact line between a solid, a liquid, and its vapor at equilibrium (Eq. 10.1). J. Willard Gibbs in 1928 then derived the contact angle 9, from thermodynamic quantities, the surface free energies for the three interfaces. Substantial refinements in terms of the nature of the forces involved in the wetting process have been made since then, and interested readers can consult fundamental texts on surface forces. ... 

We have so far been concerned mainly with the structure and thermodynamics of the interface between two phases, and we have seen in outline, and sometimes in detail, the elements of the molecular theories that account for or predict that structure and thermodynamics. Macro-scopically, the interface between two bulk phases is two-dimensional and locally planar—although at the molecular level it has a discernible three-dimensional structure, which we have studied and related to the thermodynamics. 

Finally, in 8.6, we come to consider the nature of the three-phase contact line. We sketch briefly the thermodynamics of that line and the associated line tension, in parallel with our earlier discussion of the thermodynamics of two-phase interfaces and the interfadal tension. Tbe statistical mechanics of the three-phate line, even at the phenomenological level of the van der Waals theory, is not nearly so extensively developed as that of the two-phase interface, but we outline what has been done and we mention some work in progress. Experimentally, also, the three-phase line is not nearly so well studied as is the two-phase interface. There are many fewer results on line tension than on interfadal tension measurements of the former are intrinsically more difficult because the tensions are so small 10 " to 10 N, that is, excess free energies of 10 " to 10 Jm. Unlike surface tension, line tension can be of either sign, as both theory and experiment show. Indeed, we shall refer to recent experiments that show that it can change sign with continuous change in the thermodynamic state. 

In the language of the one-density van der Waals theory of Chapter 3, we have in a c-component system a density of excess free energy, - W, as a function of some density or composition variable, x, at fixed vsdues of the c +1 thermodynamic fields (of which only c - p+2 are independent if p phases are in equilibrium). The function W(x) here is like the W(p) in Fig. 3.2, except that now, to describe three-phase equilibrium, it must have three equal maxima, as in Fig. 8.5. In this figure the variable x in the bulk a, p, and y phases is shown to take the respective values x , x, and x as determined by the prescribed values of the c -1 (because p = 3) independent fields. Those are the points x at which W has its three maxima, and where W=0. The remaining c densities—those other than X—are imagined merely to follow the variations in x through the various interfaces just as they would vary with x in a bulk phase. Hiat is the essence of this one-density version of the theory, as explained in 3.3. 

We have continued to use the Gibbs convention V = 0 and we have assumed that we are in the macroscopic limit, in whidi the three-phase line may be treated as linear so that curvature terms piay be ne ected in (8.29) and (8.36)—just as curvature terms were ne ected in the analogous equations for the surface thermodynamic functions in 2.3, where we assumed planar interfaces. 

Irrespective of the precise origin of an instability, the amplification of the capillary waves leads to the deformation of the free surface (film-air interface) and results in localized flow of liquid from the thinner parts to the thicker parts of the film [38, 56-168]. This phenomenon eventually results in the rupture of the film with the formation of dry patches or holes, when the growing amplitude of the capillary wave spectrum equals the film thickness [65]. As the film ruptures, the two distinct interfaces (film-air and film-substrate) merge and a three phase contact line (film-air-substrate) is formed. Depending on the thermodynamics of the system. 

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