Mixing within phases

Mixing within phases and mixing between phases frequently has a dominant effect. 

In the classical set-up of bulk liquid membranes, the membrane phase is a well-mixed bulk phase instead of an immobilized phase within a pore or film. The principle comprises enantioselective extraction from the feed phase to the carrier phase, and subsequently the carrier releases the enantiomer into the receiving phase. As formation and dissociation of the chiral complex occur at different locations, suitable conditions for absorption and desorption can be established. In order to allow for effective mass transport between the different liquid phases involved, hollow fiber... 

Hicks (H6) and Frazer and Hicks (F3) considered the ignition model in which exothermic, exponentially temperature-dependent reactions occur within the solid phase. Assuming a uniformly mixed solid phase, the one-dimensional unsteady heat-flow equation relates the propellant temperature, depth from the surface, and time by the nonlinear equation ... 

Stirred tanks are often used for gas-liquid reactions. The usual geometry is for the liquid to enter at the top of the reactor and to leave at the bottom. The gas enters through a sparge ring underneath the impeller and leaves through the vapor space at the top of the reactor. A simple but effective way of modeling this and many similar situations is to assume perfect mixing within each phase. 

On the basis of different assumptions about the nature of the fluid and solid flow within each phase and between phases as well as about the extent of mixing within each phase, it is possible to develop many different mathematical models of the two phase type. Pyle (119), Rowe (120), and Grace (121) have critically reviewed models of these types. Treatment of these models is clearly beyond the scope of this text. In many cases insufficient data exist to provide critical tests of model validity. This situation is especially true of large scale reactors that are the systems of greatest interest from industry s point of view. The student should understand, however, that there is an ongoing effort to develop mathematical models of fluidized bed reactors that will be useful for design purposes. Our current... 

A toluene water wash process is shown in Figure 10-12. This process is used to clean water-soluble impurities from contaminated toluene. The separation is achieved with a Podbielniak centrifuge, or Pod, because of a difference in densities. The light phase (contaminated toluene) is fed to the periphery of the centrifuge and travels to the center. The heavy phase (water) is fed to the center and travels countercurrent to the toluene to the periphery of the centrifuge. Both phases are mixed within the centrifuge and separated countercurrently. The extraction is conducted at 190°F. 

Assuming ideal mixing within the simple regions, the principle of equality of potentials between phases at equilibrium reduces to... 

To improve mixing within in the reactor by allowing gravity to cause flows of phases relative to each other. 

Another type of nonideal SEC behavior, which will not be covered in this chapter, is related to the use of mixed mobile phases (multiple solvents). Because solute-solvent interactions play a critical role in controlling the hydrodynamic volume of a macromolecule, the use of mixed mobile phases may lead to deviations from ideal behavior. Depending on the solubility parameter differences of the solvents and the solubility parameter of the packing, the mobile phase composition within the pores of the packing may be different from that in the interstitial volume. As a result, the hydrodynamic volume of the polymer may change when it enters the packing leading to unexpected elution results. Preferential solvation of the polymer in mixed solvent systems may also lead to deviations from ideal behavior (11). 

Equation (4.11) applies provided that the gas phase resistance to the transfer of HTO is limiting. This requires that the accommodation coefficient of molecules at the surface, the solubility, and the liquid phase diffusion, or mixing, within the drop, are all sufficiently high. 

Different chromatographic conditions, sometimes very unusual ones, have been tested for the analysis of TFA-methyl ester derivatives. Hagen and Black [208] applied Carbo-wax 20M as the stationary phase, injected the sample at room temperature, and within 2—3 min increased the temperature to 270°C they detected in the chromatogram even Lys, Arg, Trp and His, thus succeeding where other workers failed, especially as far as His is concerned. The best separation of TFA-methyl esters of amino acids was obtained on a glass column (3.25 m X 2.5 mm I.D.) packed with Diatoport S coated with 2.5% of a mixed silicone phase (XE-60—QF-1—MS-200,46 27 27), both with a temperature programme and under isothermal conditions [211]. 

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