Single- to Two-Phase Systems

This type of process represents the ideal biphasic method as long as the product can be extracted without contamination from the catalyst and catalyst immobilization solvent. This technique is employed commercially for the production of butyraldehyde from propene, carbon monoxide and hydrogen which is described in detail in Chapter 11 [3], 

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Figure 2.3 A single- to two phase system in which the substrates are initially dissolved in the same phase as catalyst and the product forms a new phase...

The transition from a single- to two-phase system involves enhancing of composition fluctuation and development of microregions of the new phase in a metastable or unstable region of the phase diagram. If the transition proceeds continuously, then the decision on when the system ceases to be a single-phase system is, to a certain extent, arbitrary. 

As an illustration consider a single-component, two-phase system in a potential field. Let the phases be a gas and a liquid phase. Such a system has one degree of freedom, and we then choose the temperature, volume, and moles of the component to be the variables that define the state of the system. The cross section of the container, A, is uniform. Let the bottom of the container be at the position rt in the field. Figure 14.2 illustrates this system where r0 is the position of the phase boundary. With knowledge of the volume of the system and the cross section of the container, (r2 — rt) is known. The unknown quantities are r0 and the moles of the component in each phase. The pressure at the phase boundary is the vapor pressure of the liquid at the chosen temperature. Then the number of moles of the component in the gas phase is... 

For a single-component, two-phase system such as a liquid and vapor of the same substance, the relationship between the vapor pressure p, and temperature is usually of the form shown in Fig. 9.1. The region to the right of the curve represents unsaturated vapor, whereas the region to the left represents liquid underpressure. Along the curve, vapor and liquid coexi.st in equilibrium. Similar considerations apply to solid-vapor equilibria. 

The paper is structured as follows the experimental setup and the obtained results are briefly described in the next section. The third section is then devoted to the description of the results in the single- and two-phase systems. Finally a discussion and comparison with other techniques and previous results is held in a fourth section. 

C" and thus correspond to higher molar Gibbs energy. We conclude then that state A", consisting of a mixture of liquids B" and C", is the most stable among all single or two-phase systems that can be constructed. Accordingly, state C" is identified as liquid phase I (methanol saturated in carbon disulfide) and state B" with liquid phase II (carbon disulfide saturated in methanol). 

The choice of the anion ultimately intended to be an element of the ionic liquid is of particular importance. Perhaps more than any other single factor, it appears that the anion of the ionic liquid exercises a significant degree of control over the molecular solvents (water, ether, etc.) with which the IL will form two-phase systems. Nitrate salts, for example, are typically water-miscible while those of hexaflu-orophosphate are not those of tetrafluoroborate may or may not be, depending on the nature of the cation. Certain anions such as hexafluorophosphate are subject to hydrolysis at higher temperatures, while those such as bis(trifluoromethane)sulfonamide are not, but are extremely expensive. Additionally, the cation of the salt used to perform any anion metathesis is important. While salts of potassium, sodium, and silver are routinely used for this purpose, the use of ammonium salts in acetone is frequently the most convenient and least expensive approach. 

Methods for determining the drop in pressure start with a physical model of the two-phase system, and the analysis is developed as an extension of that used for single-phase flow. In the separated flow model the phases are first considered to flow separately and their combined effect is then examined. 

In the case on the left, a composition exists which in which a minimum melting point exists. Again, A and B form a which partially melts to form a + L. However, two forms of a edso exist, a compositional area known as a "miscibility gap", i.e.- " ai and aa". But at higher temperatures, both of these melt into the single phase, a. Finally, we obtain the melt plus a. Note that at about 80% ttj-20% Uj, a melting point minimum is seen where it melts directly instead of forming the two-phase system, a -i- L. 

For turbulent flow in single-phase systems, the predicted temperature profile is not changed significantly if the Peclet number is assumed to be infinite. Therefore, in turbulent two-phase systems the second-order terms in Eqs. (9) probably do not have a significant effect on the resulting temperature profiles. In view of the uncertainties in the present state of the art for determining the holdups and the heat-transfer coefficients, the inclusion of these second-order terms is probably not justified, and the resulting first-order equations should adequately model the process. 

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