Mixture critical curve

Glassification of Phase Boundaries for Binary Systems. Six classes of binary diagrams have been identified. These are shown schematically in Figure 6. Classifications are typically based on pressure—temperature (P T) projections of mixture critical curves and three-phase equiHbria lines (1,5,22,23). Experimental data are usually obtained by a simple synthetic method in which the pressure and temperature of a homogeneous solution of known concentration are manipulated to precipitate a visually observed phase. 

Analysis of correlation length and density fluctuations in pure and solvent-modified SCFs, in particular around the mixture critical curve (P - PJ. Also measurement of the mean nuclei size and microscale mixing segregation (8). 

Figure 2 P-T mixture critical curve (solid line) for ethanol-C02 modeled from the Peng-Robinson equation of state, also shown in relation to the extension of the gas-liquid coexistence curve for pure CO2 (dashed line) (8).

Supercritical conditions above P > Fm) or below P < P ) the mixture critical curve lead to different crystallization and aggregation mechanisms (7,20). In the first case there is no interfacial tension, and mass transfer is determined by the flow-molecular diffusion interactions during mixing, defined here as jet mixing. In the second case, there is interfacial tension between the phases, and the mixing mechanism is based on atomization to small droplets while energy and species are being transferred between the... 

Liquid-Fluid Equilibria Nearly all binary liquid-fluid phase diagrams can be conveniently placed in one of six classes (Prausnitz, Licntenthaler, and de Azevedo, Molecular Thermodynamics of Fluid Phase Blquilibria, 3d ed., Prentice-Hall, Upper Saddle River, N.J., 1998). Two-phase regions are represented by an area and three-phase regions by a line. In class I, the two components are completely miscible, and a single critical mixture curve connects their criticsu points. Other classes may include intersections between three phase lines and critical curves. For a ternary wstem, the slopes of the tie lines (distribution coefficients) and the size of the two-phase region can vary significantly with pressure as well as temperature due to the compressibility of the solvent. 

Mixtures of equisized charged spheres were also treated by the MSA. Such a system is then uniquely characterized by the ratio of the critical temperatures of the pure components. Harvey [235] found that a continuous critical curve from the dipolar solvent to the molten salt is maintained until the critical temperature of the ionic component exceeds that of the dipolar component by a factor of about 3.6. This ratio is much higher than theoretically predicted for nonionic model fluids. We recall that for NaCl the critical line is still continuous at a critical temperature ratio of about 5. Thus, the MSA of the charged-hard-sphere-dipolar-hard-sphere system captures, at least in part, some unusual features of real salt-water systems with regard to their critical curves. 

Mixtures approximating curve (2), in which the critical locus is almost linear, usually are formed when the components have similar critical properties and form very nearly ideal mixtures. A minimum in the critical locus, as in curve (3), occurs when positive deviations from Raoult s law occur that are fairly large, but do not result in a (liquid + liquid) phase separation. Some (polar + nonpolar) mixtures and (aromatic + aliphatic) mixtures show this type, of behavior. 

A PT diagram for the ethane/heptane system is shown in Fig. 12.6, and a yx diagram for several pressures for the same system appears in Fig. 12.7. According to convention, one plots as y and x the mole fractions of the more volatile species in the mixture. The maximum and minimum concentrations of the more volatile species obtainable by distillation at a given pressure are indicated by the points of intersection of the appropriate yx curve with the diagonal, for at these points the vapor and liquid have the same composition. They are in fact mixture critical points, unless y = x = 0 or y = x = 1. Point A in Fig. 12.7... 

Solid-Fluid Equilibria The phase diagrams of binary mixtures in which the heavier component (the solute) is normally a solid at the critical temperature of the light component (the solvent) include solid-liquid-vapor (SLV) curves which may or may not intersect the LV critical curve. The solubility of the solid is very sensitive to pressure and temperature in compressible regions where the solvent s density and solubility parameter are highly variable. In contrast, plots of the log of the solubility versus density at constant temperature exhibit fairly simple linear behavior. 

It is important to note that while SCWO is formally defined in terms of the critical point of pure water, addition of any other constituents to the water will alter the critical point, and the system may or may not be supercritical with respect to this mixture critical point. Rather than a single critical point, for a binary system a critical curve exists that in the simplest cases joins the critical point of pure water to the critical point of the second substance across the composition space. For ternary mixtures the critical curve becomes a critical surface, and so on. In general, mixtures of water with higher volatility substances such as noncondensable gases or liquid organics will remain supercritical, while mixtures of water with lower-volatility substances such as salts will become subcritical and liquid or solid phases will precipitate from the vapor/ gas phase. 

A very important aspect of phase behavior in a system consisting of a volatile organic solvent, such as ethanol, and a supercritical fluid, such as CO2, is that the mixture critical pressure coincides with the liquid vapor phase transition. This means that above a single phase exists for all solvent compositions, whereas the (ethanol-rich and C02-rich) two-phase region lies below this curve. This fact has important implications for the mass transfer and precipitation mechanisms. Complete miscibility of fluids above P means that there is no defined or stable vapor liquid or liquid liquid interface, and the surface tension is reduced to zero and then thermodynamically becomes... 

Figure 9. Critical lines for a binary mixture of components with several critical points. Solid lines (A, B, C) indicate binary mixture critical lines dashed lines are phase existence curve of pure components Cn rn are the m critical point ( w > i) for the pure component (n = 1,2% m = 1 identifies the vapor-liquid critical point m > 1 corresponds to the fluid-fluid critical points.

Figure 1. Liquid-vapor phase diagram for pure liquid (1, 2) and binary mixture (3, 4) the lines of attainable superheat (1, 3), binodals Ts(p c = const) (2, 4) and liquid-gas critical curve (5). Symbols CP indicate the critical point, "w — the way of superheating ofpure liquid.

Figure 4. The approximation for the liquid-vapor critical curve for PPG-425/water and PPG-425/CO2 mixtures. The indicated numbers are the CO 2-saturation pressure values in MPa (open circles) ami water weightfraction (filled circles).

To examine gle at elevated pressures we return to Figure 4.10. At T, which is below the critical temperature of both A and B, the bubble- and dew-point curves both start at the low-pressure end at the vapor pressure of B, which is the less volatile component. At higher pressure, the two curves diverge and finally both end at the vapor pressure of A, the more volatile component. At T2, which is between the critical temperatures of A and B, the bubble- and dew-point curves at the low-pressure end stiU start at the vapor pressure of B, but at the higher-pressure side they meet at the mixture critical state. The critical points of mixtures of varying composition form the mixture critical loci, a space curve that connects the critical states of A and B. 

Constituents from a particular homologous series, such as the normal paraffins, usually deviate from type-I phase behavior only when the size difference between them exceeds a certain value. This is because the constituents are so close in molecular structure that they cannot distinguish whether they are surrounded by like or unlike species. It is important to remember that the critical curve depicted in figure 3.1a is only one possible representation of a continuous curve. It is also possible to have continuous critical mixture curves that exhibit pressure minimums rather than maximums with increasing temperature, that are essentially linear between the critical points of the components (Schneider, 1970), and that exhibit an azeotrope at some point along the curve. 

If an experiment is performed at an overall composition equal to x in figure 3.2d, the vapor-liquid envelope is first intersected along the dew point curve at low pressures. The vapor-liquid envelope is again intersected at its highest pressure, which corresponds to the mixture critical point at T2 and x. This mixture critical point is identified with the intersection of the dashed curve in figure 3.2b and the vertical isotherm at T2. At the critical mixture point, the dew point and bubble point curves coincide and all the properties of each of the phases become identical. Rowlinson and Swinton (1982) show that P-x loops must have rounded tops at the mixture critical point, i.e., (dPldx)T = 0. This means that if the dew point curve is being experimentally determined, a rapid increase in the solubility of the heavy component will be observed at pressures close to the mixture critical point. The maximum pressure of the P-x loop will depend on the difference in the molecular sizes and interaction energies of the two components. 

If the temperature is raised to Tj, the phase behavior shown in figure 3.7e occurs. This temperature is greater than the UCEP temperature, therefore two phases exist as the pressure is increased as long as the critical mixture curve is not intersected. The two branches of the vapor-liquid phase envelope approach each other in composition at an intermediate pressure and it appears that a mixture critical point may occur. But as the pressure is further increased, a mixture critical point is not observed and the two curves begin to diverge. To avoid confusion, the phase behavior shown in figure 3.7e is not included in the P-T-x diagram. 

Most of the studies reported in this chapter fail to include the phase behavior of the reacting mixture. Since multiple phases can occur in the mixture critical region, reaction studies need to be complemented with phase behavior studies so that we may gain an understanding of the fundamentals of the thermodynamics and kinetics of chemical reactions in solution. Chapter 5 describes how a simple cubic equation of state can be used to extend and complement the phase behavior studies. An equation of state can be used to determine the location of phase-border curves in P-T space and, with transition-state theory, to correlate the pressure dependence of the reaction rate constant when the pressure effect is large (i.e., at relatively high pressures). 

Figure 10.3-7 Vapor-liquid equilibrium of the carbon dioxide (l)-isopentane (2) system. The experimental data of G. J. Besserer and D. B. Robinson [J. Chem. Eng. Data. 20, 93 (1976)] are shown at 271.59 K (r = liquid and a = vapor) and 377.65 K ( = liquid and = vapor). The dashed curves are the predictions using the Peng-Robinson equation of state and the van der Waals mixing rule with kn = 0, and the solid lines are the correlation using the same equation of state with ij = 0.121. Thq points o and are the estimated mixture critical points at 377.65 K using the same equation of state with k 2 = 0 and 0.121, respectively.

However, unlike the case for the pure fluid, this inflection point is not the real mi.xture critical point. The mixture critical point is the point of intersection of the dew point and bubble point curves, and this must be determined from phase equilibrium calculations, more complicated mixture stability conditions, or experiment, not simply from the criterion for mechanical stability as for a pure fluid. 

---