Mass transfer across interfaces

Inserting these values into the above and rearranging, we have kR 

The dimensionless group raised to the p power is a Peclet number that raised to the y power is a ratio of lengths. 

This correlation will be successful only if we have guessed the right key variables. It may work if the tablets remain intact. It probably won t work if they disintegrate. Still, the analysis gives us a good first step in organizing our results. 

We now turn to mass transfer across interfaces, from one fluid phase to the other. This is a tricky subject, one of the main reasons that mass transfer is felt to be a difficult subject. In the previous sections, we used mass transfer coefficients as an easy way of describing diffusion occurring from an interface into a relatively homogeneous solution. These coefficients involved approximations and sparked the explosion of definitions exemplified by Table 8.2-2. Still, they are an easy way to correlate experimental results or to make estimates using the published relations summarized in Tables 8.3-2 and 8.3-3. 

In this section, we extend these definitions to transfer across an interface, from one well-mixed bulk phase into another different one. This case occurs more frequently than does transfer from an interface into one bulk phase indeed, I had trouble dreaming up the examples earlier in this chapter. Transfer across an interface again sparks potentially major problems of unit conversion, but these problems are often simplified in special cases. 

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One of the benefits of SCCO2 for homogeneous catalysis is that rates or se-lectivities may be significantly higher than in other multi-phase systems or in conventional solvents, because mass transfer across interfaces is enhanced. An example is CO2 hydrogenation that simultaneously uses CO2 as both reaction medium and substrate [114]. 

The formation of emulsions or microemulsions is conneeted with several dynamic processes the time dependence of surface tensions due to the kinetics of adsorption, the dynamic contact angle, the elasticity of adsorption layers as a mechanic surface property influencing the thiiming of the liquid films between oil droplets, the mass transfer across interfaces and so on. Kahlweit et al. (1990) have recently extended Widom s (1987) concept of wetting or nonwetting of an oil-water interface of the middle phase of weakly-structured mixtures and microemulsions. They pointed out that the phase behaviour of microemulsions does not differ from that of other ternary mixtures, in particular of mixtures of short-chain amphiphiles (cf for example Bourrell Schechter (1988). 

Mass transfer across interfaces is ubiquitous in industrial processes. For instance, it occurs in separation processes used in the field of biotechnology, in the extraction of metals from aqueous solutions, in the chemical and pharmaceutical industries and also in the treatment of effluents from the same plants. Ho vever, in the design of the contacting equipment the role of the interface and of interfacial phenomena are not taken into account. Take the example of the industrial effluent streams. These are usually not made up of pure components but are soups containing different chemicals and chemicals with surfactant properties. However, in the design of liquid-liquid contactors those streams are considered to be clean and interfacial phenomena (such as Marangoni and gravitational convection), which may exist, are not taken into account. 

It is difficult to summarize all the phenomena discussed in this volume. However, major topics include ultralow interfacial tension, phase behavior, microstructure of surfactant systems, optimal salinity concept, middle-phase microemuIsions, interfacial rheology, flow of emulsions in porous media, wettability of rocks, rock-fluid interactions, surfactant loss mechanisms, precipitation and redissolution of surfactants, coalescence of drops in emulsions and in porous media, surfactant mass transfer across interfaces, equilibrium dynamic properties of surfactant/oil/brine systems, mechanisms of oil displacement in porous media, ion-... 

Differentiate two-film theory, penetration theory, and surface renewal theory of mass transfer across interfaces. 

In the previous two sections we have presented definitions of mass transfer coefficients and have shown how these coefficients can be found from experiment. Thus we have a method for analyzing the results of mass transfer experiments. This method can be more convenient than diffusion when the experiments involve mass transfer across interfaces. Experiments of this sort include liquid liquid extraction, gas absorption, and distillation. 

As you think about this more carefully, you will realize that the units of pressure or concentration cloud a deeper truth Mass transfer should be described in terms of the more fundamental chemical potentials. If this were done, the peculiar concentration differences would disappear. However, chemical potentials turn out to be difficult to use in practice, and so the concentration differences for mass transfer across interfaces will remain complicated by units. 

The simplest theory involved in mass transfer across an interface is film theory, as shown in Figure 3.10. In this model, the gas (CO) is transferred from the gas phase into the liquid phase and it must reach the surface of the growing cells. The rate equation for this case is similar to the slurry reactor as mentioned in Levenspiel.20... 

In a later publication, Kolbel et al. (K16) have proposed a less empirical model based on the assumption that the rate-determining steps for a slurry process are the catalytic reaction and the mass transfer across the gas-liquid interface. When used for the hydrogenation of carbon monoxide to methane, the process rate is expressed as moles carbon monoxide consumed per hour and per cubic meter of slurry ... 

Farkas and Sherwood (FI, S5) have interpreted several sets of experimental data using a theoretical model in which account is taken of mass transfer across the gas-liquid interface, of mass transfer from the liquid to the catalyst particles, and of the catalytic reaction. The rates of these elementary process steps must be identical in the stationary state, and may, for the catalytic hydrogenation of a-methylstyrene, be expressed by ... 

Such a model should take into account at least the following phenomena Mass transfer across gas-liquid interface, mass transfer to exterior particle surface, catalytic reaction, flow and axial mixing of gas phase, and flow and axial mixing of liquid phase. 

The experimental and theoretical work reported in the literature will be reviewed for each of the five major types of ga s-liquid-particle operation under the headings Mass transfer across gas-liquid interface mass transfer across liquid-solid interface holdup and axial dispersion of gas phase holdup and axial dispersion of liquid phase heat transfer reaction kinetics. 

Mass Transfer across Liquid-Solid Interface... 

Morris (M9) has recently reviewed a number of studies of mass transfer across the gas-liquid interface in mechanically agitated systems containing suspended solid particles. These studies [Hixon and Gaden (H7), Eckenfelder... 

Mass transfer across the liquid-solid interface in mechanically agitated liquids containing suspended solid particles has been the subject of much research, and the data obtained for these systems are probably to some extent applicable to systems containing, in addition, a dispersed gas phase. Liquid-solid mass transfer in such systems has apparently not been studied separately. Recently published studies include papers by Calderbank and Jones (C3), Barker and Treybal (B5), Harriott (H4), and Marangozis and Johnson (M3, M4). Satterfield and Sherwood (S2) have reviewed this subject with specific reference to applications in slurry-reactor analysis and design. 

No work on mass transfer across the liquid-solid interface in gas-liquid fluidized beds has come to the author s attention. 

Date for mass transfer across the liquid-solid interface are virtually nonexistent for packed-bed gas-liquid-particle operations. The smaller particle size that may be employed in suspended-bed operations should be an advantage in this respect, but the packed-bed operations have, on the other hand, the advantage of having higher possible relative velocities between liquid and solid. 

The penetration theory has been used to calculate the rate of mass transfer across an interface for conditions where the concentration CAi of solute A in the interfacial layers (y = 0) remained constant throughout the process. When there is no resistance to mass transfer in the other phase, for instance when this consists of pure solute A, there will be no concentration gradient in that phase and the composition at the interface will therefore at all Limes lie the same as the bulk composition. Since the composition of the interfacial layers of the penetration phase is determined by the phase equilibrium relationship, it, too. will remain constant anil the conditions necessary for the penetration theory to apply will hold. If, however, the other phase offers a significant resistance to transfer this condition will not, in general, be fulfilled. 

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. 

Given that, from the penetration theory for mass transfer across an interface, the instantaneous rale ol mass transfer is inversely proportional to the square root of the time of exposure, obtain a relationship between exposure lime in the Higbie mode and surface renewal rate in the Danckwerts model which will give the same average mass transfer rate. The age distribution function and average mass transfer rate from the Danckwerts theory must be deri ved from first principles. 

On the. assumptions involved in the penetration theory of mass transfer across a phase boundary, the concentration Ca of a solute A at a depth v below the interface at a time l after the formation of the interlace is given by ... 

According to the penetration theory for mass transfer across an interface, the ratio of the concentration Ca at a depth y and time r to the surface concentration Ca. if the liquid is initially free of solute, is giver by ... 

Henry s law constant. The overall driving force for mass transfer is Ug—K ay and the rate of mass transfer across the interface is... 

These component balances are conceptually identical to a component balance written for a homogeneous system. Equation (1.6), but there is now a source term due to mass transfer across the interface. There are two equations (ODEs) and two primary unknowns, Og and a . The concentrations at the interface, a and a, are also unknown but can be found using the equilibrium relationship, Equation (11.4), and the equality of transfer rates. Equation (11.5). For membrane reactors. Equation (11.9) replaces Equation (11.4). Solution is possible whether or not Kjj is constant, but the case where it is constant allows a and a to be eliminated directly... 

The rate of mass transfer across a phase boundary or interface can be expressed by N=K. A (AQm... 

Solvent extraction is intrinsically dependent on the mass transfer across the interface and the chemical inversion at the interfacial region. Researchers in the field of solvent extraction, especially in the field of analytical chemistry and hydrometallurgy, observed effects of interfacial phenomena in the solvent extraction systems. This gave them a strong motivation to measure what happened at the interface. 

Both substrate and product have suface-active properties and favor mass transfer across the liquid-liquid interface. Their physicochemical properties modulate the behavior of the reaction in the heterogeneous system. Saturating substrate concentration in the aqueous phase (L aq) was not constant. It increased when using a high initial concentration of LA LA and when the HP concentration increased. The percentage of transferred LA T = LA qlLAf) depended on LA, and HP concentrations ... 

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