Phase transfer model

The quartz geothermometer (Fournier, 1977) requires that the dissolved silica concentration in an ascending hydrothermal solution becomes quenched in as the fluid approaches the surface. On the other hand, the phase transfer model for the rate of quartz deposition, described in this chapter, requires that the LEA be valid. The conditions for which each of these models is appropriate can be found by calculating values of Da, and Pe. Figure 8.1 shows the temperature range for the transition from LEA to quenched conditions. 

Phase transfer models account for the transfer of material from one phase to another in response to changing intensive or extensive variables. This discussion will be limited to the dissolution or precipitation of minerals in contact with an aqueous solution, but the approach could be used for other scenarios, such as a mineral growing in an igneous melt in response to declining temperature. 

Figure 8.5. Growth rate of a layer of quartz on the wall of a fracture with a 1 cm aperture predicted by the phase transfer model.The quartz is precipitating from an aqueous solution flowing with a Darcy velocity of 1 m/day along a geothermal...

For the analysis heat and mass transfer in concrete samples at high temperatures, the numerical model has been developed. It describes concrete, as a porous multiphase system which at local level is in thermodynamic balance with body interstice, filled by liquid water and gas phase. The model allows researching the dynamic characteristics of diffusion in view of concrete matrix phase transitions, which was usually described by means of experiments. 

Kishinev ski/23 has developed a model for mass transfer across an interface in which molecular diffusion is assumed to play no part. In this, fresh material is continuously brought to the interface as a result of turbulence within the fluid and, after exposure to the second phase, the fluid element attains equilibrium with it and then becomes mixed again with the bulk of the phase. The model thus presupposes surface renewal without penetration by diffusion and therefore the effect of diffusivity should not be important. No reliable experimental results are available to test the theory adequately. 

Weislogel MM, Lichter S (1998) Capillary flow in an interior corner. 1 Eluid Mech 373 349-378 Wu PY, Little WA (1984) Measurement of the heat transfer characteristics of gas flow a fine channels heat exchangers used for microminiature refrigerators. Cryogenics 24 415 20 Xu X, Carey VP (1990) Film evaporation from a micro-grooved surface an approximate heat transfer model and its comparison with experimental data. J Thermophys 4(4) 512-520 Yarin LP, Ekelchik LA, Hetsroni G (2002) Two-phase laminar flow in a heated micro-channels. Int J Multiphase Flow 28 1589-1616... 

PETP flakes produced from used soft drinks bottles were subjected to alkaline hydrolysis in aqueous sodium hydroxide. A phase transfer catalyst (trioctylmethylammonium bromide) was used to enable the depolymerisation reaction to take place at room temperature and under mild conditions. The effects of temperature, alkali concentration, PETP particle size, PETP concentration and catalyst to PETP ratio on the reaction kinetics were studied. The disodium terephthalate produced was treated with sulphuric to give terephthalic acid of high purity. A simple theoretical model was developed to describe the hydrolysis rate. 17 refs. 

Experimental gas-solid mass-transfer data have been obtained for naphthalene in CO2 to develop correlations for mass-transfer coefficients [Lim, Holder, and Shah, Am. Chem. Soc. Symp. Ser, 406, 379 (1989)]. The mass-transfer coefficient increases dramatically near the critical point, goes through a maximum, and then decreases gradually. The strong natural convection at SCF conditions leads to higher mass-transfer rates than in liquid solvents. A comprehensive mass-transfer model has been developed for SCF extraction from an aqueous phase to CO2 in countercurrent columns [Seibert and Moosberg, Sep. Sci. Techrwl, 23, 2049 (1988) Brunner, op. cit.]. 

Although the Lewis cell was introduced over 50 years ago, and has several drawbacks, it is still used widely to study liquid-liquid interfacial kinetics, due to its simplicity and the adaptable nature of the experimental setup. For example, it was used recently to study the hydrolysis kinetics of -butyl acetate in the presence of a phase transfer catalyst [21]. Modeling of the system involved solving mass balance equations for coupled mass transfer and reactions for all of the species involved. Further recent applications of modified Lewis cells have focused on stripping-extraction kinetics [22-24], uncatalyzed hydrolysis [25,26], and partitioning kinetics [27]. 

The design of functionalized polymers with a specific utilization is seen in new polysiloxanes used by Zeldin (p. 199) as phase transfer catalysts. Novel functional polyphosphazenes have been reported as well by Allcock (p. 250). The introduction of transition metal cyclopentadienyl, metal carbonyl and carborane moieties into polyphosphazene macromolecules is representative of truly novel chemistry achieved after careful model studies with corresponding molecular systems. 

CA DFT correction on the TSp u is based on the error of AMl/d-PhoT model at the TSpti+Nu> 1 n which the nucleophilic attack (TS ra) is concerted with the proton transfer (TS/>/ ] ) in the gas phase. dUncatalyzed model reaction in solution. eCatalyzed reaction in the hairpin ribozyme. 

Ishii, M., and G. Kocamustafaogullari, 1983, Two-Phase Flow Models and Their Limitations, p. 1, NATO Adv. Sci. Inst. Ser., Advances in Two-Phase Flow and Heat Transfer, S. Kakac and M. Ishii, Eds., Marinus Nijkoff, Brussil. (3)... 

Staub, F. W., 1967, The Void Fraction in Subcooled Boiling—Prediction of the Initial Point of Net Vapor Generation, ASME Paper 67-HT-36, National Heat Transfer Conf., ASME, New York. (3) Staub, F. W., 1969, Two Phase Fluid Modeling, The Critical Heat Flux, Nuclear Sci. Eng. 3J.T 90-199. (5)... 

The solution of Eqs. (9) is straightforward if the six parameters are known and the boundary conditions are specified. Two boundary conditions are necessary for each equation. Pavlica and Olson (PI) have discussed the applicability of the Wehner-Wilhelm boundary conditions (W3) to two-phase mass-transfer model equations, and have described a numerical method for solving these equations. In many cases this is not necessary, for the second-order differentials can be neglected. Methods for evaluating the dimensionless groups in Eqs. (9) are given in Section II,B,1. 

An alternate to the concept of cluster renewal discussed above is the concept of two-phase convection. This second approach disregards the separate behavior of lean and dense phases, instead models the time average heat transfer process as if it were convective from a pseudo-homogeneous particle-gas medium. Thus h hcl, hh and hd are not... 

Catalysis, enzymatic, physical organic model systems and the problem of, 11,1 Catalysis, general base and nucleophilic, of ester hydrolysis and related reactions, 5,237 Catalysis, micellar, in organic reactions kinetic and mechanistic implications, 8,271 Catalysis, phase-transfer by quaternary ammonium salts, 15,267 Catalytic antibodies, 31,249... 

The simplest model compound is cyclohexene oxide III. Monomers IV, V and VII represent different aspects of the ester portion of I, while monomers VII and VIII reflect aspects of both the monomer I and the polymer which is formed by cationic ring-opening polymerization. Monomers IV-VII were prepared using a phase transfer catalyzed epoxidation based on the method of Venturello and D Aloisio (6) and employed previously in this laboratory (7). This method was not effective for the preparation of monomer VIII. In this specific case (equation 4), epoxidation using Oxone (potassium monoperoxysulfate) was employed. 

Our discussion of multiphase CFD models has thus far focused on describing the mass and momentum balances for each phase. In applications to chemical reactors, we will frequently need to include chemical species and enthalpy balances. As mentioned previously, the multifluid models do not resolve the interfaces between phases and models based on correlations will be needed to close the interphase mass- and heat-transfer terms. To keep the notation simple, we will consider only a two-phase gas-solid system with ag + as = 1. If we denote the mass fractions of Nsp chemical species in each phase by Yga and Ysa, respectively, we can write the species balance equations as... 

When the two liquid phases are in relative motion, the mass transfer coefficients in either phase must be related to the dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive transfer to the Schmidt number. Another complication is that such a boundary cannot in many circumstances be regarded as a simple planar interface, but eddies of material are transported to the interface from the bulk of each liquid which change the concentration profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most industrial circumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass transfer model must therefore be replaced by an eddy mass transfer which takes account of this surface replenishment. 

C. Hofstetter, P. S. Wilkinson, T. C. Pochapsky, NMR Structure Determination of Ion Pairs Derived from Quinine A Model for Templating in Asymmetric Phase-Transfer Reductions by BH4" with Implications for Rational Design of Phase-Transfer Catalysts , J. Org. Chem 1999, 64, 8794-8800. 

Belokon et al. (261) subsequently found that salen-Cu(II) complexes are effective catalysts for the asymmetric alkylation of amino acid derivatives. Excellent se-lectivities are observed with 1 mol% of 88b-Cu in toluene at ambient temperature, Eq. 225. Although no stereochemical model is advanced to account for the selec-tivities, these workers suggest the catalyst may be acting as a chiral phase-transfer agent. 

The two-phase kinetic model developed by Karickhoff (65) is capable of fitting either the sorption or desorption of a sorbing solute. For linear isotherms, the mathematical description given by Karickhoff (1) and others (67, 70, 71) is virtually identical to that of a mass transfer process (72). 

The phase equilibria of the most important compounds will be described in the following section. In the sections thereafter, we will treat mass transport in melt-phase polycondensation, as well as in solid-state polycondensation, and discuss the diffusion and mass transfer models that have been used for process simulation. 

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