Two-phase holes

As shown in Fig. 7.9, for a given vapor pressure P (dotted line), the compositions vBq, xBap of the coexisting phases are found from the intersections (small circles) with the liquid and vapor boundaries of the hatched two-phase region. These intersections are connected by a horizontal tie-line (heavy solid line) that spans the two-phase hole in the diagram. All points along this tie-line represent the same thermodynamic state (i.e., same temperature, pressure, chemical potentials, and compositions of each phase), but each differs only in the relative amounts of each phase (cf. Sidebar 7.2), whether nearly all vapor (at the extreme left of the tie-line), nearly all liquid (at the extreme right), or roughly equimolar amounts of liquid and vapor (near the middle). 

At such a maximum (dotted line) the compositions of coexisting liquid and vapor phases necessarily coincide, and the two-phase hole closes as liquid and vapor curves meet at this point. Examples of such maxima occur frequently, for example, in alcohol-water mixtures, as in the C2H50H/H20 system at vh2o = 0.20. 

Gauter, K., Peters, C.J., Scheidgen, A.L., and Schneider, G.M. (1999) Cosolvency effects, miscibility windows and two-phase holes Ig in three-phase surfaces llg in ternary systems a status report, submitted to Fluid Phase Equilibria. 

Binary and Ternary Mixtures of Carbon Dioxide and Certain Solutes and the Occurrence of Two-Phase Holes... 

As an example for complicated fluid phase behavior in multi-component systems, in the group of Maurer [1,2,3] fluid four-phase behavior liquid-liquid-liquid-gas in ternary and quaternary aqueous systems is examined Thus, already for ternary systems complications can occur. Also Patton et al. [4] encountered unexpected phase behavior in a ternary system. For the system CO2 + 1-decanol + tetradecane they found a so-called two-phase hole ig enclosed in the three-phase surface ttg. 

Quantitatively, the size of the loop of CEP s t= "+g, and with it the size of the two-phase hole g, has become greater by replacing 1-decanol by 1-octanol. The expansion has taken place mainly towards lower mole fraction x . At x close to one (binary system CO2 + tetradecane), the CEP data in both Figures 3 and 4 are very similar, obviously because the two ternary systems involve the same binary system at x =l. The measured CEP data for the ternary system CO2 + 1-octanol + tetradecane are summarized elsewhere [37]. Again, two DCEP s are present where the line of UCEP s t= - -g and the one of LCEP s t= "- g merge. 

In summary it can be concluded that the size of the two-phase holes ig in the three-phase surfaces Ug increase in size with decreasing carbon number of the 1-alkanol for the series CO2 + 1-alkanol + tetradecane. The closed loop character of the holes may got lost when interference with another CEP locus occurs or /and when the axis x =0 or/and x =l intersect the holes. 

In derivation of ternary fluid phase diagrams (Figure 1.35) the experimental observations of an occurrence of two-phase hole L-G (completely bounded by a closed-loop critical curve Li = L2-G) in the three-phase immiscibility region bormded by a critical curve Li = G-L2 from the high-temperature side (quasi-binary cross-sections of type Id) (Peters and Gauter, 1999) are taken into account. In our derivations it was assumed that this two-phase hole L-G may appear in ternary three-phase immiscibility regions that spread from the binary subsystems of types lb and Ic. 

The higher solubility of carbon in y-iron than in a-iroii is because the face-ceiiued lattice can accommodate carbon atoms in slightly expanded octahedral holes, but the body-centred lattice can only accommodate a much smaller carbon concentration in specially located, distorted tetrahedral holes. It follows that the formation of fenite together with cementite by eutectoid composition of austenite, leads to an increase in volume of the metal with accompanying compressive stresses at die interface between these two phases. 

Slug flow must be avoided in all two-phase applications. The designer must be alert for two-phase flow developing in a system. In one case, absorber liquid going to a lower pressure stripper produced a two-phase mixture. The absorber stream entered the stripper in a line that was elled down onto the stripper tray. The two-phase mixture beat out a section of trays. A /4-in. protection plate was provided and this had a hole cut in it in two years. 

A schematic of the apparatus developed is shown in Fig. 3. Stirrers mix and push the lighter and heavier phases in each compartment, with the maximum rotation speed governed by the need to maintain the interface steady. Flow deflectors ensure that the phases are circulated in each chamber and that flow near the interface is laminar. The interfacial plate (thickness 2 mm) is rectangular with a hole at its center. The distance from the interface to the flow deflectors is less than 6 mm. The two phases are analyzed by withdrawing small volumes via sampling holes. 

In a distillation column, vapor is bubbled through the liquid to provide good contact between the two phases. The bubbles are formed when the vapor passes upward through a hole (orifice) in a plate (tray) that is in contact with the liquid. The size of the bubbles depends upon the diameter of the orifice, the velocity of the vapor through the orifice, the viscosity and density of the liquid, and the surface tension between the vapor and the liquid. 

Flashing liquids escaping through holes and pipes require special consideration because two-phase flow conditions may be present. Several special cases need consideration.17 If the fluid path length of the release is short (through a hole in a thin-walled container), nonequilibrium conditions exist, and the liquid does not have time to flash within the hole the fluid flashes external to the hole. The equations describing incompressible fluid flow through holes apply (see section 4-2). 

The first step in the relief sizing calculation for two-phase vents is to determine the mass flux through the relief. This is computed using Equation 4-104, representing choked two-phase flow through a hole ... 

Below 146°C, two phases of Agl exist y-Agl, which has the zinc blende structure, and (3-Agl with the wurtzite structure. Both are based on a close-packed array of iodide ions with half of the tetrahedral holes filled. However, above 146°C a new phase, a-AgI, is observed where the iodide ions now have a body-centred cubic lattice. If you look back to Figure 5.7, you can see that a dramatic increase in conductivity is observed for this phase the conductivity of a-Agl is very high, 131 S m , a factor of 10 higher than that of (3- or y-AgI, comparable with the conductivity of the best conducting liquid electrolytes. How can we explain this startling phenomenon ... 

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