Transfer between phases

Chemical reaction always enhances the rate of mass transfer between phases. The possible magnitudes of such enhancements are indicated in Tables 23-6 and 23-7. They are no more predictable than are specific rates of chemical reactions and must be found experimentally for each case, or in the relatively sparse literature on the subject. 

Mass Transfer Mass transfer in plate and packed gas-liquid contactors has been covered earHer in this subsection. Attention nere will be limited to deep-bed contactors (bubble columns and agitated vessels). Theory underlying mass transfer between phases is discussed in Sec. 5 of this handbook. 

Coalescence The coalescence of droplets can occur whenever two or more droplets collide and remain in contact long enough for the continuous-phase film to become so thin that a hole develops and allows the liquid to become one body. A clean system with a high interfacial tension will generally coalesce quite rapidly. Particulates and polymeric films tend to accumulate at droplet surfaces and reduce the rate of coalescence. This can lead to the ouildup of a rag layer at the liquid-hquid interface in an extractor. Rapid drop breakup and rapid coalescence can significantly enhance the rate of mass transfer between phases. 

An impeller with a high fluid head is one with high peripheral velocity and discharge velocity. Such impellers are useful for (I) rapid reduction of concentration differences in the impeller discharge stream (rapid mixing), (2) production of large interfacial area and small droplets in gas-hquid and immiscible-liquid systems, (3) sohds deagglomeration, and (4) promotion of mass transfer between phases. 

The efficiencies which may be obtained can consequently be calculated by simple stoichiometry from the equilibrium data. In the ease of countercurrent-packed columns, the solute can theoretically be completely extracted, but equilibrium is not always reached because of the poorer contact between the phases. The rate of solute transfer between phases governs the operation, and the analytical treatment of the performance of such equipment follows closely the methods employed for gas absorption. In the ease of two immiscible liquids, the equilibrium concentrations of a third component in each of the two phases are ordinarily related as follows ... 

Rushton (R11) in 1954 presented a graph showing contacting efficiency as a function of impeller diameter at constant power input. He found that the rate of mass transfer between phases increased to a maximum and then decreased as the impeller diameter increased. The optimum occurred at a ratio of impeller to tank diameter of about 0.25, a ratio which is much smaller than that found for liquid blending. 

Note that ai will gradually increase during the course of the reaction and will reach its saturation value, agjKu, when B is depleted. Dropping the accumulation term for ai i) represents a form of the pseudo-steady hypothesis. Since component B is not transferred between phases, its material balance has the usual form for a batch reactor ... 

The broken vertical line denotes an area of contact between any two ionic conductors, particularly between liquid ionic conductors (electrolyte-electrolyte interface or liquid junction). Ions can transfer between phases by diffusion across such a boundary hence, circuits containing such an interface are often called circuits or cells with transference. 

None of the terms of this equation can be determined experimentally. The equation represents a generalization of Eq. (2.6) for the case where charge transfer between phases is attended by an electrochemical reaction. 

The role of mixing in heterogeneous reactions is obvious. In multiphase processes mixing imposed by a stirrer or an external pump is necessary to increase the interface through which reactants pass to meet their partner in the other phase and/or to intensify mass transfer between phases. Mixing can also play a significant role in the case of homogeneous reactions. Chemical reactions occur at the molecular level. Reactant molecules introduced into a reactor encounter the environment in the vicinity of the inlet. The composition of the mixture there is obviously... 

Annular flow, smooth interface (Henry et al., 1969) Since the interface is relatively small compared to dispersed flow and assumed to be smooth, there is no significant momentum transfer or mass transfer between phases. Under such conditions, the change of slip ratio with pressure is... 

Mist flow, one component In a one-component system with finely dispersed drops in the mist flow, the mass transfer between phases over a large interfacial area has to be considered. For the compression wave the frozen state can be assumed to be subcooled liquid, superheated vapor conditions generated by the wave are fairly stable, and the expressions for the two-component system are valid (Henry, 1971) ... 

Adiabatic conditions may be assumed and heat transfer between phases neglected. 

The simplest mechanism postulated for transfer between phases is that a concentration gradient exists only across a stagnant film between phases. Then the rate of transfer is proportional to the interfacial area and a difference of concentrations across the film. For a power law chemical rate, at steady state,... 

Sherwood TK, Woertz BB. The role of eddy diffusion in mass transfer between phases. Trans Am Inst Chem Eng 1939 35 517-540. 

Since mass transfer between phases occurs for all time t, the mass and volumes of each phase are non-constant in the interval between initial and final reaction times [tospectroscopic results and data analysis, particularly when calculating moles present. 

In Chapter 17 we pointed out that the treatment of heterogeneous reaction required the consideration of two factors in addition to those normally encountered in homogeneous reactions the modification of the kinetic expressions resulting from the mass transfer between phases and the contacting patterns of the reacting phases. 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

These empirical correlations were originally based mainly on data obtained for isothermal horizontal flow at pressures close to atmospheric (to 50 psi), normal temperatures, and pipe diameters to one inch using air and eight different liquids. In order to apply these equations to singlecomponent two-phase flow with mass transfer between phases, Martinelli... 

For no mass transfer between phases, the acceleration loss is approximately,... 

In the case of single-component two-phase flow, such as in vaporizing water, physical equilibrium is commonly assumed and seems to yield reasonable results, even though it might seem that supersaturation could occur. The rate of mass transfer between phases, therefore, is not a limiting process for single component flow. 

Chemical species can transfer between phases, and this represents the coupling between the mass-balance equations. This geometry looks like a membrane reactor in which a permeable area A (dashed lines) separates the phases, but all multiphase reactors can be described by this notation. 

In the preceding sketches the reactors are coupled through the interface between them. In a single-phase system the only ways that a species could change were by flow in entrance and exit pipes and by reaction. Now we also have the possibihty of a species entering or leaving the reactor by transferring between phases within the reactor. 

Fig. 24.5 Transfer between phases in the two-phase system described by Larroche et al. [71, 72]...

Mathematical models of packed bed reactors can be classified into two broad categories (1) one-phase, or pseudohomogeneous, models in which the reactor bed is approximated as a quasi-homogeneous medium and (2) two-phase, or heterogeneous, models in which the catalyst and fluid phases and the heat and mass transfer between phases are treated explicitly. Although the... 

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