Phase boundary line

At any point along a boundary line, the two phases on either side of the line coexist in a state of d Tiamic equilibrium. The normal freezing point and normal boiling point of a substance (shown by red dots) are the points where the phase boundary lines intersect the horizontal line that represents P = atm. 

If there is an inert electrode present, then show where the inert electrode is with its phase boundary. If the electrode components are in the same phase, then separate them by commas if not, a vertical phase boundary line. For example, consider the following redox reaction ... 

The energy increase related to a compositional fluctuation resulting in a two-phase splitting may be considered as an energy threshold of activation of the de-mixing process. The spinodal curve thus defines a kinetic limit, not a phase boundary line. 

Figure 9.20. Vertical section through Cu-Ni-Ag, at a constant IOat%Ni, showing definition of phase-boundary lines.

The relationship Young s equation describes is the interplay of forces (liquid surface tension, solid surface tension, liquid-solid surface tension) at the three-phase boundary line. It is regarded as if these forces interact along a line. Experimental data show that this is indeed true. The magnitude of 9 is thus only dependent on the molecules nearest the interface, and is independent of molecules much farther away from the contact line. 

A reaction path can proceed in two principally different directions after it has crossed a phase boundary 1) (0juo/0j Bo)paih > (0//o /0 no)eq and 2) (0 o/0 Bo)paii. < (0/Wo/0 Bo)eq- In the second case, the reaction path will re-enter the field of the reduced phase which it just left and can then oscillate along the phase boundary line in Figure 7-8 for some length. A morphologically stable interface between the oxidized and the reduced phase can not develop in this case, and a part of the oxide layer is expected to consist of a mixture of two phases. 

Use the Plot tab on CSMGem (add intervals required) to plot the sll phase boundaries with and without methanol using MS Excel. After combining the calculated data, the final plot should look like Figure A.7. The solutions are the intersection of the expansion line and sll phase boundary lines. 

The parallel tie-lines in the two-phase region indicate the phase split of a system with a composition in the two-phase region into two phases with compositions at the intersections with the phase boundary line. 

Phase boundaries Lines on a phase diagram the two phases on either side of a phase boundary are in equilibrium (coexist) at the phase-boundary. 

Plot all the expressions resulting from step 3 as phase boundary lines on the same graph. 

Calculate the compositions of the exiting raffinate and extract streams. Replot (or trace) Fig. 9.1 without the tie lines (Fig. 9.3). On Fig. 9.3, plot the mean-concentration point M. Now from mass-balance considerations, the exit concentrations must lie on the two phase-boundary lines and on a straight line passing through the mean concentration point. We know we want the water phase to have an exit concentration of 3 wt % alcohol. Such a concentration corresponds to point Ln on the graph. At point LN. the ether concentration is seen to be 7.6 wt % (this can be found more accurately in the present case by numerical extrapolation of the water-phase data in Table 9.1). Therefore, the composition of the raffinate stream is 3% alcohol, 7.6% ether, and (by difference) 89.4% water. 

The phase boundary lines for supercritical ethane at 250 and 350 bar are shown in Figure 2. The surfactant was found to be only slightly soluble in ethane below 200 bar at 37 C, so that the ternary phase behavior was studied at higher pressures where the AOT/ethane binary system is a single phase. As pressure is increased, more water is solubilized in the micelle core and larger micelles can exist in the supercritical fluid continuous phase. The maximum amount of water solubilized in the supercritical ethane-reverse micelle phase is relatively low, reaching a W value of 4 at 350 bar. 

As schematically shown in Figure 7a, initial PEVD reaction and product nucleation occurs at the three-phase boundary of solid electrolyte (E), working electrode (W) and the sink vapor phase (S) which contains vapor phase reactant (B). Only here are all reactants available for the half-cell electrochemical reaction at the sink side of a PEVD system. Although the ionic and electronic species can sometimes surface diffuse at elevated temperature to other sites to react with (B) in the vapor phase, the supply of the reactants continuously along the diffusion route is less feasible and the nuclei are too small to be stabilized under normal PEVD conditions. Only along the three phase boundary line are all the reactants available for further growth to stabilize the nuclei. Consequently, initial deposition in a PEVD process is restricted to certain areas on a substrate where all reactants for the sink electrochemical reaction are available. 

While Eq. (25.3) describes the force balance at the three-phase boundary line, our major concern is the interface between a polymer and liquid water without an air phase, which may be described by Eq. (25.4). 

Slope of the solid-liquid phase boundary line... 

Figure 4.2 Variation of the vapor pressure, Pv, of a substance with the temperature, 7, showing the phase transition between solid, liquid and vapor phases. Two phases can coexist in equilibrium only at pressures and temperatures defined by the phase boundary lines in the phase diagram, such as liquid-vapor, solid-liquid and solid-vapor lines. The liquid-vapor phase boundary terminates at the critical point, 7C. All three phases can coexist in equilibrium only at the triple point, 73, which is the intersection of the three two-phase boundaries.

The Clapeyron equation is exact and applies rigorously to all first-order phase transitions. It shows how pressure and temperature vary with respect to each other (temperature or pressure) along the phase boundary line, and in that sense, it defines the phase boundary line. 

According to the McCabe-Thiele method, the system for separation is considered on a quasi-binary basis. In this approach, it must be possible to neglect the influence of the solvent, which is acceptable if the phase boundary lines (solubilities) do not change much with concentration during separation. In this case, the number of theoretical stages, the minimal reflux (ratio), the minimum number of theoretical stages, and their mutual dependence can be determined. 

When two phases are in equilibrium they are both represented by a point with co-ordinates (/>, T) on a phase boundary line of the phase diagram. At such a point the Gibbs free energies of the two phases must be equal, = G, and they will remain equal if conditions move to a nighbouring point on the phase boundary. Hence... 

Fig. 1 Methane hydrate, which is stable belou- and to the left of the phase boundary line. Also shovra is the geothermal gradient in permafrost as well as marine environments. Where the curves intersect, natural methane hydrate is stable. Natural methane hydrates are found in the lightly shaded region. BSR labels the "bottom-simulating reflector." an unexpected interface found by sonic exploration techniques and usually associated with the interface between sediments with and without hydrate. View this art in color at...

Fig. 11. Effect of a local defect, y, on the three phase boundary line, where d is a measure of the defect size and ti(x) and y , are parameters of the disturbance (Ref.

In addition to marking the phase boundary, line FC expresses the relationship between saturation pressure and temperature. The saturation pressure generally increases quickly with temperature up to the critical point. There is no vapor-liquid transition above the critical point therefore, the relationship between saturation pressure and temperature exists only below the critical point. The saturation pressure of pure component is an important physical property and a required parameter in many calculations of phase equilibria. Several equations have been developed to describe the mathematical relationship between saturation pressure and temperature. One of the most widely used is the Antoine equation ... 

The preceding discussion was concerned with capillary forces in a system containing only the liquid of interest and a second fluid phase. It has been stated, however, that the systems of most practical interest involve a third phase (usually a solid) resulting in a three-phase boundary line. The situation can be represented as a drop of liquid resting on a flat solid surface and... 

Therefore, a large number of published phase diagrams suffer from the drawback that the phase boundary lines have to be extracted from data wiiich are clearly affected by flux pinning, or even worse, that phase boundaries are added, which are not related to the thermodynamic state at all, but exclusively determined by the strength of the pinning potential ( irreversibility line , Malozemoff et al. 1988). 

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