Two Phase Systems

One-phase systems have been investigated in detail in the earlier chapters of this book. In the following sections we extend these studies to two-phase systems. 

If a system is formed of two phases, we draw the mass-balance schematic diagram as follows. 

To change the above mass-balance equations into design equations we just replace r - by V r j and fj by V r), where r) and r are the rates of reaction per unit volume of reaction mixture or per unit mass of catalyst for catalytic reactions, etc. 

Notice that the equations (6.24) and (6.25) are coupled through the term RMi. 

The Clapeyron equation, first introduced in Sec. 4.2, follows from tliis equality. If tire temperature of a two-phase system is clianged, tlien tire pressure must also cliange in accord witli tire relation between vapor pressure and temperature if tire two pliases continue to coexist in equilibrium. Since Eq. (6.66) applies tliroughout tliis cliange, 

The entropy change A 5 and tlie volume change A are tlie changes wliich occur when a unit amount of a pine chemical species is transferredfrom phase a to phase at tlie equilibrium temperature and pressure. Integration of Eq. (6.8) for this change yields tlie latent heat of phase transition  

The Antoine equation, which is more satisfactory for general use, has the form  

A principal advantage of this equation is that valnes of the constants A, B, and C are readily available for a large number of species. Each set of constants is valid for a specified temperature range, and should not be used outside of that range. 

The accurate representationof vapor-pressuredata over a wide temperature range requires an equationof greatercomplexity. The Wagnerequationis one of the best available it expresses the reduced vapor pressure as a function of reduced temperature  

Aliphatic ethers with branched side chains such as MTBE (methyl t-butyl ether), especially, deactivate enzymes only to a very small degree in incubation experiments for example, the BAL mentioned above has a half-life h/2 of up to 500 h in aqueous-organic two-phase systems (see Fig. 3.1.6) [21]. This may not hold true for a special enzyme/solvent combination under process conditions. When incubated at higher temperatures or even in the presence of the substrate benzaldehyde the deactivation of the enzyme is much higher (see Table 3.1.2) 

There is a destabilizing effect on the BAL from the temperature, the organic solvent, and the substrate. These influences are summarized in Fig. 3.1.7. 

When the enzyme is incubated at 4 °C with aqueous buffer, a very small deactivation constant is found. In the presence of a second phase of MTBE, deactivation is 30% higher (4 °C). The highest increase in enzyme deactivation is due to the temperature the deactivation constants are 22-fold (1.3 x 17) or 255-fold (15 X 17) higher when incubating the enzyme at 20 °C in pure buffer or in a two-phase system respectively. In the presence of the substrate benzaldehyde almost the entire enzyme is deactivated within 1 h. This deactivation in a two-phase system is to some extent dependent on the size of the phase boundary and can 

Buffer/MTBE (90mL 50mM TEA, pH 8)/25mL MTBE 0.197 0.372 

Buffer/MTBE and substrate (as above, -l-20mM benzaldehyde in organic phase) 0.887 1.578 

For faceted grains in a liquid matrix, the dihedral angle is not uniquely defined because of torque on a facet, contrary to the case of rounded 

Reeently, some attempts have been made to explain abnormal grain growth in a liquid matrix. The explanation is based on theoretical and 

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Fig. V-15. Volta potentials Galvani potentials 0, and surface potential jumps x in a two-phase system. (From Ref. 187.)...

Applied to a two-phase system, this says that the change in pressure with temperature is equal to the change in entropy at constant temperature as the total volume of the system (a + P) is increased, which can only take place if some a is converted to P ... 

The above approximation, however, is valid only for dilute solutions and with assemblies of molecules of similar structure. In the event that concentration is high where intemiolecular interactions are very strong, or the system contains a less defined morphology, a different data analysis approach must be taken. One such approach was derived by Debye et al [21]. They have shown tliat for a random two-phase system with sharp boundaries, the correlation fiinction may carry an exponential fomi. 

If we consider the scattering from a general two-phase system (figure B 1.9.10) distinguished by indices 1 and 2) containing constant electron density in each phase, we can define an average electron density and a mean square density fluctuation as ... 

Kang S Y and Kim K 1998 Comparative study of dodeoanethiol derivatized nanopartioles prepared in one and two phase systems Langmuir 14 226... 

The radial distribution function can also be used to monitor the progress of the equilibration. This function is particularly useful for detecting the presence of two phases. Such a situation is characterised by a larger than expected first peak and by the fact that g r) does not decay towards a value of 1 at long distances. If two-phase behaviour is inappropriate then the simulation should probably be terminated and examined. If, however, a two-phase system is desired, then a long equilibration phase is usually required. 

When polymers or other water-soluble substances are present in the sample, it is advantageous to add a small amount of chloroform to the initial reaction mixture after the subsequent addition of water, a two-phase system results which may be titrated in the usual way to a starch end point or by observing the disappearance of the iodine colour in the chloroform layer. 

Safrole can be oxidized to safrole epoxide with H2O2 in a two-phase system, using a quaternary phosphotungstic PTC. The formed safrole epoxide is then isomerized to MDP2P with Lil. 

Elastomeric Modified Adhesives. The major characteristic of the resins discussed above is that after cure, or after polymerization, they are extremely brittie. Thus, the utility of unmodified common resins as stmctural adhesives would be very limited. Eor highly cross-linked resin systems to be usehil stmctural adhesives, they have to be modified to ensure fracture resistance. Modification can be effected by the addition of an elastomer which is soluble within the cross-linked resin. Modification of a cross-linked resin in this fashion generally decreases the glass-transition temperature but increases the resin dexibiUty, and thus increases the fracture resistance of the cured adhesive. Recendy, stmctural adhesives have been modified by elastomers which are soluble within the uncured stmctural adhesive, but then phase separate during the cure to form a two-phase system. The matrix properties are mosdy retained the glass-transition temperature is only moderately affected by the presence of the elastomer, yet the fracture resistance is substantially improved. 

Cyclohexane, produced from the partial hydrogenation of benzene [71-43-2] also can be used as the feedstock for A manufacture. Such a process involves selective hydrogenation of benzene to cyclohexene, separation of the cyclohexene from unreacted benzene and cyclohexane (produced from over-hydrogenation of the benzene), and hydration of the cyclohexane to A. Asahi has obtained numerous patents on such a process and is in the process of commercialization (85,86). Indicated reaction conditions for the partial hydrogenation are 100—200°C and 1—10 kPa (0.1—1.5 psi) with a Ru or zinc-promoted Ru catalyst (87—90). The hydration reaction uses zeotites as catalyst in a two-phase system. Cyclohexene diffuses into an aqueous phase containing the zeotites and there is hydrated to A. The A then is extracted back into the organic phase. Reaction temperature is 90—150°C and reactor residence time is 30 min (91—94). 

Bubbles and Fluidized Beds. Bubbles, or gas voids, exist in most fluidized beds and their role can be important because of the impact on the rate of exchange of mass or energy between the gas and soflds in the bed. Bubbles are formed in fluidized beds from the inherent instabiUty of two-phase systems. They are formed for Group A powders when the gas velocity is sufficient to start breaking iaterparticle forces at For Group B powders, where iaterparticle forces are usually negligible, and bubbles form immediately upon fluidization. Bubbles, which are inherently... 

Butanes are recovered from raw natural gas and from petroleum refinery streams that result from catalytic cracking, catalytic reforming, and other refinery operations. The most common separation techniques are based on a vapor—Hquid, two-phase system by which Hquid butane is recovered from the feed gas. 

Rubber-Modified Copolymers. Acrylonitrile—butadiene—styrene polymers have become important commercial products since the mid-1950s. The development and properties of ABS polymers have been discussed in detail (76) (see Acrylonitrile polymers). ABS polymers, like HIPS, are two-phase systems in which the elastomer component is dispersed in the rigid SAN copolymer matrix. The electron photomicrographs in Figure 6 show the difference in morphology of mass vs emulsion ABS polymers. The differences in stmcture of the dispersed phases are primarily a result of differences in production processes, types of mbber used, and variation in mbber concentrations. 

Such a reaction is controlled by the rate of addition of the acid. The two-phase system is stirred throughout the reaction the heavy product layer is separated and washed thoroughly with water and alkaU before distillation (Fig. 3). The alkaU treatment is particularly important and serves not just to remove residual acidity but, more importantiy, to remove chemically any addition compounds that may have formed. The washwater must be maintained alkaline during this procedure. With the introduction of more than one bromine atom, this alkaU wash becomes more critical as there is a greater tendency for addition by-products to form in such reactions. Distillation of material containing residual addition compounds is ha2ardous, because traces of acid become self-catalytic, causing decomposition of the stiU contents and much acid gas evolution. Bromination of alkylthiophenes follows a similar pattern. 

Biomine in a two-phase system, H2O—CH2CI2, with KHCO can convert sulfides to sulfoxides in good yields (40). 

Cya.nideExcha.nge, Acetone cyanohydrin and methyl isobutyl ketone cyanohydrin [4131 -68-4] dissolved in an organic solvent, such as diethyl ether or methyl isobutyl ketone, undergo cyanide exchange with aqueous cyanide ion to yield a significant cyanide carbon isotope separation. The two-phase system yields cyanohydrin enriched in carbon-13 and aqueous cyanide depleted in carbon-13. Fquilibrium is obtained in seconds. 

Another process for the production of dodecanedioic acid is by oxidation of cyclododecene using a two-phase system in which mthenium tetroxide serves as the oxidizing agent in the organic phase, and is regenerated in the second phase, an aqueous phase containing cerium(IV) ions (75). 

The terminal R groups can be aromatic or aliphatic. Typically, they are derivatives of monohydric phenoHc compounds including phenol and alkylated phenols, eg, /-butylphenol. In iaterfacial polymerization, bisphenol A and a monofunctional terminator are dissolved in aqueous caustic. Methylene chloride containing a phase-transfer catalyst is added. The two-phase system is stirred and phosgene is added. The bisphenol A salt reacts with the phosgene at the interface of the two solutions and the polymer "grows" into the methylene chloride. The sodium chloride by-product enters the aqueous phase. Chain length is controlled by the amount of monohydric terminator. The methylene chloride—polymer solution is separated from the aqueous brine-laden by-products. The facile separation of a pure polymer solution is the key to the interfacial process. The methylene chloride solvent is removed, and the polymer is isolated in the form of pellets, powder, or slurries. 

Recovery. The principal purpose of recovery is to remove nonproteinaceous material from the enzyme preparation. Enzyme yields vary, sometimes exceeding 75%. Most industrial enzymes are secreted by a microorganism, and the first recovery step is often the removal of whole cells and other particulate matter (19) by centrifugation (20) or filtration (21). In the case of ceU-bound enzymes, the harvested cells can be used as is or dismpted by physical (eg, bead mills, high pressure homogenizer) and/or chemical (eg, solvent, detergent, lysozyme [9001 -63-2] or other lytic enzyme) techniques (22). Enzymes can be extracted from dismpted microbial cells, and ground animal (trypsin) or plant (papain) material by dilute salt solutions or aqueous two-phase systems (23). 

The most frequendy used technique to shift the equiUbrium toward peptide synthesis is based on differences in solubiUty of starting materials and products. Introduction of suitable apolar protective groups or increase of ionic strength decreases the product solubiUty to an extent that often allows neady quantitative conversions. Another solubiUty-controUed technique is based on introduction of a water-immiscible solvent to give a two-phase system. Products preferentially partition away from the reaction medium thereby shifting the equiUbrium toward peptide synthesis. 

If the temperature of a two-phase system is changed and if the two phases continue to coexist in equilibrium, then the vapor pressure must also change in accord with its temperature dependence. Since Eq. (4-149) holds throughout this change,... 

This equation may be apphed to a closed, nonreactive, two-phase system. Each phase taken separately is an open system, capable of exchanging mass with the other, and Eq. (4-16) may be written for each phase ... 

The phase rule permits only two variables to be specified arbitrarily in a binaiy two-phase system at equilibrium. Consequently, the cui ves in Fig. 13-27 can be plotted at either constant temperature or constant pressure but not both. The latter is more common, and data in Table 13-1 are for that case. The y-x diagram can be plotted in either mole, weight, or volume frac tions. The units used later for the phase flow rates must, of course, agree with those used for the equilibrium data. Mole fractious, which are almost always used, are appfied here. 

In calciilating the power required for mixers, a reasonable estimate of the average density and viscosity for a two-phase system is satisfactoiy. 

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