Mass transfer disperse-phase volume

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

For quantitative validation of simulation results, it is often necessary to compare predicted profiles (of velocity or other variable of interest) with experimental data X-Y plotting facilities are useful for this purpose. Most post-processors allow the user to import tabulated data for comparison with simulation results. Facilities to calculate the usual global quantities of interest to reactor engineers, such as overall pressure drop, dispersed phase volume fraction, heat or mass transfer rates and so on, are necessary to address reactor engineering concerns. Most codes allow use of user-defined routines to evaluate different quantities of interest, which may then be displayed using the standard tools discussed above. 

Treybal (I960) estimated the overall mass-transfer coefficient and the stage efficiency for a mixer (0.5 m high and 0.5 m diameter, = 0.1963 m, Vrimer 0.09817 m ) extracting benzoic acid from water into solvent pure toluene. The water plus benzoic acid flow rate was Qp = 0.003 m /s, and the toluene flow rate was Qp, = 0.0003 m /s. The tank was well mixed. Toluene was the dispersed phase, ( )e) was estimated as 0.0824. The estimated dispersed-phase surface to dispersed-phase volume ratio ap, = 1940 m dispersed phase/m dispersed phase. The estimated overall dispersed-phase mass-transfer coefficient Kpp, = 2.01 x 10 kmol benzoic/[m s(kmol benzoic/m )]. Additional data. Ptoiuene 865 kg/m, — 92.14 kg/kmol. Equilibrium is — 20.8 ( extract... 

The drop size achieved is important in estimating the mass-transfer surface area developed in the dispersion. In certain situations, the surface area of the dispersion per unit volume of the total liquid phase, a, is available from measurements. The average or mean drop size appropriately defined can then be related to For example, the Sauter mean diameter ( 2 of the drop size number density distribution has been related to via the following relation and the dispersed phase volume fraction... 

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... 

Stainless steel flat six-blade turbine. Tank had four baffles. Correlation recommended for ( ) < 0.06 [Ref. 156] a = 6( )/<, where d p is Sauter mean diameter when 33% mass transfer has occurred. dp = particle or drop diameter <3 = iuterfacial tension, N/m ( )= volume fraction dispersed phase a = iuterfacial volume, 1/m and k OiDf implies rigid drops. Negligible drop coalescence. Average absolute deviation—19.71%. Graphical comparison given by Ref. 153. ... 

For a chemically controlled process, conversion depends only on the residence time and not on which phase is dispersed, whereas the interfacial area and, consequently, the rate or mass transfer will change when the relative volumes of the phases are changed. If a reaction is known to occur in a particular phase, and the conversion is... 

The conversion reaches a maximum at 30 Hz. At a higher rate of rotation the increased separatory power of the centrifuge leads to a reduction of the volume of the mixed phase in which the reaction takes place. At reduced rotational speeds of the centrifuge the mixing process becomes less efficient, resulting in larger average drop sizes in the dispersed phase and thus to reduced mass transfer rates and conversion levels. 

Liquid-phase mass transfer coefficient Gas-liquid interfacial area per unit volume of dispersion Gas volume fraction in dispersion Diffusivity of cyanogen in solution Henry law coefficient... 

Similar factors have been developed for bubble columns, which includes the concept of gas hold-up eG, the fraction of the reactor liquid volume occupied by the gas dispersed in the liquid phase. The number of such factors can be reduced when comparing the mass transfer of just one compound in the same liquid/gas system, e. g. for oxygen or ozone transfer in clean water/air systems the above relationship reduces to the first three terms. 

Inlerfacial Contact Area and Approach to Equilibrium. Experimental extraction cells such as the original Lewis stirred cell are often operated with a flat liquid-liquid interface the area of which can easily he measured. In the single-drop apparatus, a regular sequence of drops uf known diameter is released through the continuous phase. These units are useful for the direct calculation of the mass flux N and hence the mass-transfer coefficient for a given system. In industrial equipment, however, it is usually necessary to create a dispersion of drops in order to achieve a large specific inlerfacial area. u. defined as the inlerfacial conlael area per unit volume of two-phase dispersion. Thus the mass-lransler rale obtainable per unit volume... 

Diffusivity of 02 in liquid xylene Da = 1.4 x 10 9 m2/s Equipment performance characteristics Gas volume fraction in the dispersion (1 - eg) = 0.34 Mean diameter of the bubbles present in the dispersion = 1.0 mm Liquid-phase mass transfer coefficient kL = 4.1 x 10 4 m/s... 

As in Example 4.3 with an agitated tank, let the fraction of chlorine passing through the reactor unreacted be / and, because CI2 is replaced by HCI, / is also the mole fraction of chlorine in the off-gas. Since the total pressure is 1 bar, the partial pressure of the chlorine will be fu bar. Because the gas phase in the reactor is assumed to be well mixed, the equivalent interfacial chlorine concentration Ca, is fJStS, i.e. /u/0.45 = 2.22/ kmol/m3. Considering unit volume, i.e. 1 m3 of dispersion, and following equation 4.17, the rate of mass transfer across the interface is now equated to the rate of the reaction in the bulk of the liquid where the concentration of the chlorine is Qnt ... 

The first-order constant klG will now be expressed in terms of the rate constant kx of the reaction in the liquid phase. From equation 4.14, the rate of transfer of A per unit area of gas-liquid interface is >l(kxDA) CAi i.e. in terms of an enhanced mass transfer coefficient k L = V(kxDA) this rate of transfer is k LCAi. The rate of transfer per unit volume of dispersion JA is thus ... 

Liquid-liquid dispersion involves two phases a continuous phase (one with large volume), and a dispersed phase (one with small volume). When the volume fractions of both phases are nearly the same, phase inversion occurs. In this case, which of the two phases becomes a continuous one depends on the starting conditions as well as the physical properties of the system. The range of volume fraction within which either of two immiscible liquids may be continuous is primarily a function of the viscosity ratio it is not strongly dependent upon vessel characteristics or stirring speed (Selker and Sleicher, 1965). Here we briefly evaluate the minimum speed of rotation required to disperse one phase completely into the other, the interfacial area, and the mass-transfer coefficient in liquid-liquid dispersion. 

When two liquids are immiscible, the design parameters include droplet size distribution of the disperse phase, coalescence rate, power consumption for complete dispersion, and the mass-transfer coefficient at the liquid-liquid interface. The Sauter mean diameter, dsy, of the dispersed phase depends on the Reynolds, Froudes and Weber numbers, the ratios of density and viscosity of the dispersed and continuous phases, and the volume fraction of the dispersed phase. The most important parameters are the Weber number and the volume fraction of the dispersed phase. Specifically, dsy oc We 06(l + hip ), where b is a constant that depends on the stirrer and vessel geometry and the physical properties of the system. Both dsy and the interfacial area aL remain unaltered, if the same power per unit volume (P/V) is used in the scale-up. 

The "plug-like velocity flow profile for electrokinetically pumped capillary columns (see Figure 1) is important in minimizing resistance to mass transfer within the mobile phase (4). Hydrostatically-pumped capillaries, have parabolic flow profiles which tend to severely disperse solute bands unless extreme narrow-bore (i.d.s less than 10 pm) capillaries are employed (12). Fortunately, larger capillaries, with less stringent detector volume requirements, can be efficiently used in MECC. 

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