Curve binodal

The thermodynamics and physical properties of the mixture to be separated are examined. VLE nodes and saddles, LLE binodal curves, etc, are labeled. Critical features and compositions of interest are identified. A stream is selected from the source Hst. This stream is either identified as meeting all the composition objectives of a destination, or else as in need of further processing. Once an opportunistic or strategic operation is selected and incorporated into the flow sheet, any new sources or destinations are added to the respective Hsts. If a strategic separation for dealing with a particular critical feature has been implemented, then that critical feature is no longer of concern. Alternatively, additional critical features may arise through the addition of new components such as a MSA. The process is repeated until the source Hst is empty and all destination specifications have been satisfied. 

Figure 3 illustrates the thermodynamic interplay of polymer crystallization and liquid-liquid demixing in polymer solutions. The liquid-liquid binodal curve is primarily determined by the B value. With the increase of Ep values, the liquid-liquid binodal curves shift slightly upward. On the other hand, the... 

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A line is drawn from Rn through M to give Ex on the binodal curve and ExF and SR to meet at the pole P. It may be noted that P represents an imaginary mixture, as described for the leaching problems discussed in Chapter 10. 

In an ideal stage, the extract Ex leaves in equilibrium with the raffinate Rx, so that the point Rx is at the end of the tie line through Ex. To determine the extract E2, PRi is drawn to cut the binodal curve at E2. The points R2, E3, R3, E4, and so on, may be found in the same way. If the final tie line, say ER4, does not pass through R , then the amount of solvent added is incorrect for the desired change in composition. In general, this does not invalidate the method, since it gives the required number of ideal stages with sufficient accuracy. 

The TMS system PC/dodecane/p-xylene shows the phase behaviour depicted in Fig. 6 representing a system with a closed miscibility gap, which shows a strong temperature dependence. Possible solvent compositions are defined by the area between the two binodal curves at the temperatures of 25 °C and 80 °C. 

Figure 45 shows the glass transition temperature of solvent-modified networks prepared with various amounts of cyclohexane. It is seen, that Tg is independent of, or varies only slightly with, the initial amount of cyclohexane after the heat treatment. The T -values of solvent-modified epoxy networks are lower than for the fully crosslinked network, which is a result of the cyclohexane dissolved in the matrix, with a concentration given by the binodal curve and therefore is independent of the initial amount of cyclohexane. 

The binodal curve has been calculated and is shown in Fig. 10.2 as a solid line. Furthermore, the calculated distribution of acetic acid between both phases is shown in Fig. 10.3. From these figures, it can be seen that the fitting to experimental data is good. 

Usually, the modeled binodal curves reproduced the experimentally observed data (with different constant nonrandomness factor, a) to a satisfactory degree [96-98,112,131,134]. 

If k - oo then equilibrium is instantaneously reached and the system evolves along the binodal curve (trajectory a and a ). On the other hand, if k —> 0, then no phase separation will... 

On the basis of these relationships, using the expressions of the chemical potentials of the components at the level of approximation of the second virial coefficients, the binodal curve can be expressed by the following set of equations (Edmond and Ogston, 1968) ... 

In practice, it turns out that it is an extremely time-consuming procedure to calculate the binodal curve. 

As well as the spinodal and binodal curves, the phase diagram of the system is characterized by the coordinates of the critical point. This is the single common point of intersection of the spinodal and binodal curves. 

Figure 3.3 Illustration of the calculation of the phase diagram of a mixed biopolymer solution from the experimentally determined osmotic second virial coefficients. The phase diagram of the ternary system glycinin + pectinate + water (pH = 8.0, 0.3 mol/dm3 NaCl, 0.01 mol/dm3 mercaptoethanol, 25 °C) —, experimental binodal curve —, calculated spinodal curve O, experimental critical point A, calculated critical point O—O, binodal tielines AD, rectilinear diameter,, the threshold of phase separation (defined as the point on the binodal curve corresponding to minimal total concentration of biopolymer components). Reproduced from Semenova et al. (1990) with permission.

Data could be obtained from such a graph to construct a McCabe-Thiele type diagram. Tie line points on the binodal curve would provide data for an equilibrium curve, and data could be obtained to construct an operating line (from lines drawn from 0 through the binodal curve). 

On a ternary equilibrium diagram like that of Figure 14.1, the limits of mutual solubilities are marked by the binodal curve and the compositions of phases in equilibrium by tielines. The region within the dome is two-phase and that outside is one-phase. The most common systems are those with one pair (Type I, Fig. 14.1) and two pairs (Type II. Fig. 14.4) of partially miscible substances. For instance, of the approximately 1000 sets of data collected and analyzed by Sorensen and Arlt (1979), 75% are Type I and 20% are Type II. The remaining small percentage of systems exhibit a considerable variety of behaviors, a few of which appear in Figure 14.4. As some of these examples show, the effect of temperature on phase behavior of liquids often is very pronounced. 

Figure 14.6. Construction of points on the distribution and operating curves Line oh is a tieline. The dashed line is the tieline locus. Point e on the equilibrium distribution curve, obtained as the intersection of paths be and ade. Line Pfg is a random line from the difference point and intersecting the binodal curve in /and g. Point j is on the operating curve, obtained as the intersection of paths gj and fhj.

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