Isothermal ternary

In order for this concept to be applicable, the matrix and the reactant phase must be thermodynamically stable in contact with each other. One can evaluate this possibility if one has information about the relevant phase diagram — which typically involves a ternary system — as well as the titration curves of the component binary systems. In a ternary system, the two materials must lie at comers of the same constant-potential tie-triangle in the relevant isothermal ternary phase diagram in order to not interact. The potential of the tie-triangle determines the electrode reaction potential, of course. 

Trial A.F. and Spera F.J. (1988) Natural convection boundary layer flows in isothermal ternary systems role of diffusive coupling. Int. J. Heat Transfer 31, 941-955. 

Equation (5.118) is the condition of mechanical equilibrium. Only two fluxes are independent in the isothermal ternary system. If we choose them to be jA and jB, and the independent forces to be XA and X0, we obtain by inserting Eq. (5.118) into the flux equations for A and B... 

Fig. n.9. Isobaric isothermal ternary phase diagram containing process paths for an asymmetric transformation example. The two enantiomers are labeled R and S, and the solvent is labeled W. 

Related Calculations. Graphic representation of liquid-liquid equilibrium is convenient only for binary systems and isothermal ternary systems. Detailed discussion of such diagrams appears in A. W. Francis, Liquid-Liquid Equilibrium, Interscience, New York, 1963. Thermodynamic correlations of liquid-liquid systems using available models for liquid-phase nonideality are not always satisfactory, especially when one is trying to extrapolate outside the range of the data. 

Case 2 includes many of the example systems studied in this book. For example, reactors with temperature as the only controlled variable fall into this category. Also, the isothermal ternary scheme CS4 shown in Fig. 2.13a has a local composition controller on one of the dominant variables, the composition of component A. However, Case 2 is characterized by the fact that other dominant variables are not controlled at the reactor. Instead, the plantwide control structure plays a significant role in its ability to influence these uncontrolled variables. When the uncontrolled compositions become disturbances and the controlled dominant variables are too weak, we have difficulties. On the other hand, the plantwide control structure can be arranged to provide indirect control of the dominant composition variables, thereby augmenting the unit control loops. The HDA process provides a good illustration. The dominant variables are reactor inlet temperature and toluene composi-... 

For isothermal ternary systems, Geveke and Danner (1991) have modified the Flory-Huggins theory to account for the concentration dependency of the parameters. The reduced total Gibbs free energy of mixing is given by... 

The Zr-B-C isothermal ternary cross sections at 1900 and 2400°C. After Rudy... 

The Hf-B-C system presents a situation that falls somewhat between the Ti and Zr systems [60]. Although the HfB phase is stable in the Hf-B binary system, it melts at 2100°C, below the melting point of the Hf parent metal (2227°C). During a directed metal oxidation reaction of molten Hf with B4C at just above the melting point of Hf, e.g., 2400°C, the Hf-B-C isothermal ternary cross section (Fig. 18) indicates that the molten metal is... 

Fig. 18. The Hf-B-C isothermal ternary cross sections at three different temperatures. Points A and B represent two possible stoichiometries for processing hafnium boride/hafnium carbide composites. After Rudy [57],...

The isothermal ternary diagrams will get stacked one on top the other to build a prism that shows the effect of pressure on the phase behavior. The three sides of the prism are, in fact, the P-x diagrams for each binary pair at the system temperature. The ternary diagrams in this chapter always put the SCF in the lower right-hand corner of the triangle. A, the component least soluble in the SCF, is always placed in the lower left-hand corner B, the third component, is placed at the top of the triangle. We will assume that components A and B have vapor pressures that are less than 5 bar at modest temperatures, typical of organic solvents. 

Isothermal ternary sections of the system H +, NH4+//S042-, NH2S03-, H20 were... 

Representation of (liquid-liquid) equilibrium in an isothermal ternary system by a simple mathematical expression is almost impossible and the best representation of such a case is a graphical one employing triangular co-ordinates. 

Figure 1. Schematic of the isothermal ternary B-C-N phase diagram at temperatures below the decomposition of the stoichiometric compounds and the regimes of composition of some soKd solutions discussed. For explanation of the compounds see text. First published in [152] and reproduced with permission.

For an isothermal ternary extraction problem, the oudet conpositions and flow rates can be calculated from external mass balances used in conjunction with the equilibrium relationship. The mass balances around the entire cascade are... 

The studies reported so far on the surfactant systems with divalent counterions are very few and limited to calcium and magnesium. Here we present the binary phase diagram (composition vs temperature) of the system barium di-2-ethylhexyIsulphosucdnate (BaA2)- iO. We will also make a preliminary report on the isothermal ternary system of barium octylsulphate (BaOS)-decanol- /). 

Figure 56.1 shows an isothermal ternary phase diagram among two diastereomeric salts, B HA and BxjHA, and an achiral solvent L where the crystalline salts are anhydrous and not miscible. Points A and B represent the solubility of undesired and desired salts, BuHA and Bj HA, respectively. E is the eutectic point where a saturated solution is in equilibrium with both salts in solid phases. The maximum separation efficiency is achieved when the system is at point P. At this point, the separation efficiency e, defined here as the ratio of desired salt in the solid phase to the total desired salt in the system, can be calculated directly from the phase... 

Table 13.8 Prediction of Isothermal Ternary VLE from Binary Data (15 Systems) The Effect of Binary Data Accuracy...

---