Phase dispersion mass transfer

Gases are dispersed in liquids usually to facilitate mass transfer between the phases or mass transfer to be followed by chemical reaction. In some situations gases are dispersed adequately with spargers or porous distributors, but the main concern here is with the more intense effects achievable with impeller driven agitators. 

The continuous phase film mass transfer rate can be increased by electrostatic acceleration of charged droplets of the dispersed phase in the continuous phase. 

When thinking of any electrochemical reaction, it is important to remember that the very act of electron transfer takes place at a surface, whereas the material to be reduced or oxidized is dispersed in a volumetric phase. Thus mass transfer from the bulk of the solution (or to the bulk solution, for the products) plays a central role in electrochemical processes. As such the physical processes of mass transfer (diffusion, migration, and... 

The work discussed in this section clearly delineates the role of droplet size distribution and coalescence and breakage phenomena in mass transfer with reaction. The population balance equations are shown to be applicable to these problems. However, as the models attempt to be more inclusive, meaningful solutions through these formulations become more elusive. For example, no work exists employing the population balance equations which accounts for the simultaneous affects of coalescence and breakage and size distribution on solute depletion in the dispersed phase when mass transfer accompanied by second-order reaction occurs in a continuous-flow vessel. Nevertheless, the population balance equation approach provides a rational framework to permit analysis of the importance of these individual phenomena. 

To simulate the effects of reaction kinetics, mass transfer, and flow pattern on homogeneously catalyzed gas-liquid reactions, a bubble column model is described [29, 30], Numerical solutions for the description of mass transfer accompanied by single or parallel reversible chemical reactions are known [31]. Engineering aspects of dispersion, mass transfer, and chemical reaction in multiphase contactors [32], and detailed analyses of the reaction kinetics of some new homogeneously catalyzed reactions have been recently presented, for instance, for polybutadiene functionalization by hydroformylation in the liquid phase [33], car-bonylation of 1,4-butanediol diacetate [34] and hydrogenation of cw-1,4-polybutadiene and acrylonitrile-butadiene copolymers, respectively [10], which can be used to develop design equations for different reactors. 

We have attempted to present here, in a rather condensed form, a vievc of the present status of the fxmdamentals of preparative and nonlinear chromatography. The fundamental problems and the various models used to model chromatography are discussed first (Chapter 2). As the thermodynamics of phase equilibrium is central to the separation process, whatever model is used, we devote two chapters to the discussion of equilibrium isotherms, for single components (Chapter 3) and mixtures (Chapter 4). A chapter on the problems of dispersion, mass transfer and flow rate in chromatography (Chapter 5) completes the fundamental bases needed for the thorough discussion of preparative chromatography. 

All models take into account the thermodynamic equilibrium and thereby use the relation between the concentration in the mobile phase and loading of the stationary phase. The simplest model in this classification is the ideal model , which considered the convective transport besides the adsorption equilibrium only. Starting from this model, additional kinetic parameters, e.g. axial dispersion, mass-transfer resistances or adsorption kinetics are taken into account at the medium level. 

As the reaction takes place in the catalyst containing phase, the reactants must, first of all, be transferred from the second and eventually gas phase to the reaction phase. Therefore, special attention has to be paid to the mixing and dispersion of one phase within the other and mass transfer efficiency between phases. The mass transfer rate between the different phases depends on the area of the interface and the mass transfer coefficient. Whether the reaction will take place in the bulk of the reaction phase or near the interface depends on the ratio between the characteristic reaction time t ) and the characteristic time for mass transfer (t ). This ratio is known as the Hatta number Ha). 

Efthiamatou C. "Choice of Disperse Phase and Mass Transfer Direction in Liquid/Liquid Extraction" Internal Report,TCL,ETHZ (1980). 

Since both mass transfer rates (see Chapter 16 and setding depend on which phase is dispersed, it is important to know which phase is dispersed. Mass transfer tends to be higher if the phase with the controlling resistance is the continuous phase (this may not be possible). A predictive test that is somewhat more conclusive than Eq. (13=48) can be developed by defining x fFrank et al.. 2008 Jacobs and Penney. 19871... 

The basic concepts for general chromatographic separations (25) can be applied to SEC (9). For separations of polymers, it was proposed that only two column dispersion terms influence H (26,27), namely eddy diffusion in the mobile phase and mass transfer in the stationary phase. The expression for H for a permeating monodisperse high polymer is... 

There are two possibilities fisr determinatirm of the axial mbdng coefllcients, respectively the Pellet numbers. The first is to obtain them fiom mass transfer experiments and the dispersion mass transfer model using optimization procedure. The second is to determine them separate using tracer methods. By the first method the Bodenstein, respectively Peclet, numbers for both phases are calculated together with the volumetric mass transfer coefficients for the gas and the Uquid phas. This leads to enormously grt influence of the primary eiqperimental error on the obtained results. The error is especially great for the cases when the influence of the respective obtained values on the mass transfer in the packing is comparatively slight. That is why the so determined values are reliable only for fee oases they ate obtained in, for mcample for automation purpose. They are not fee best solution for calculation of new apparatuses and new processes. That is why in this book only fee tracer method is considered. 

The phase inversion in such systems can be predicted based on the hold up of dispersed phase and the changes in system properties [13], The authors [12] estimated the phase inversion point, Sauter mean diameter of the droplets in the dispersed phase and mass transfer coefficients for the toluene-HNOj mixtures at various concentrations to characterize the toluene-HNOj dispersion. Their subsequent studies [14] have established the improved catalyst stability in the HNO3 dispersed in toluene medium as compared to toluene dispersed in HNO3 medium. Batch nitration experiments were made under reflux conditions covering a wide range of toluene volume fractions (0.1 to 0.95) to generate the conversion and para selectivity profiles for this volume fraction range (Fig. 2.3). 

Fig. 17. Effect of axial dispersion in both phases on solute distribution through countercurrent mass transfer equipment. A, piston or plug flow B, axial...

For hquid systems v is approximately independent of velocity, so that a plot of JT versus v provides a convenient method of determining both the axial dispersion and mass transfer resistance. For vapor-phase systems at low Reynolds numbers is approximately constant since dispersion is determined mainly by molecular diffusion. It is therefore more convenient to plot H./v versus 1/, which yields as the slope and the mass transfer resistance as the intercept. Examples of such plots are shown in Figure 16. 

The values of k and hence Sb depend on whether the phase under consideration is the continuous phase, c, surrounding the drop, or the dispersed phase, d, comprising the drop. The notations and Sh are used for the respective mass-transfer coefficients and Sherwood numbers. 

In industrial equipment, however, it is usually necessary to create a dispersion of drops in order to achieve a large specific interfacial area, a, defined as the interfacial contact area per unit volume of two-phase dispersion. Thus the mass-transfer rate obtainable per unit volume is given as... 

The role of coalescence within a contactor is not always obvious. Sometimes the effect of coalescence can be inferred when the holdup is a factor in determining the Sauter mean diameter (67). If mass transfer occurs from the dispersed (d) to the continuous (e) phase, the approach of two drops can lead to the formation of a local surface tension gradient which promotes the drainage of the intervening film of the continuous phase (75) and thereby enhances coalescence. It has been observed that d-X.o-c mass transfer can lead to the formation of much larger drops than for the reverse mass-transfer direction, c to... 

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