Mass transfer interfacial resistances

Prediction methods attempt to quantify the resistances to mass transfer in terms of the raffinate rate R and the extract rate E, per tower cross-sectional area Af, and the mass-transfer coefficient in the raffinate phase and the extract phase times the interfacial (droplet) mass-transfer area per volume of tower a [Eqs. (15-32) and (15-33)]. 

As the interface offers no resistance, mass transfer between phases can be regarded as the transfer of a component from one bulk phase to another through two films in contact, each characterized by a mass-transfer coefficient. This is the two-film theory and the simplest of the theories of interfacial mass transfer. For the transfer of a component from a gas to a liquid, the theory is described in Fig. 6B. Across the gas film, the concentration, expressed as partial pressure, falls from a bulk concentration Fas to an interfacial concentration Ai- In the liquid, the concentration falls from an interfacial value Cai to bulk value Cai-... 

The enhanced rate expressions for regimes 3 and 4 have been presented (48) and can be appHed (49,50) when one phase consists of a pure reactant, for example in the saponification of an ester. However, it should be noted that in the more general case where component C in equation 19 is transferred from one inert solvent (A) to another (B), an enhancement of the mass-transfer coefficient in the B-rich phase has the effect of moving the controlling mass-transfer resistance to the A-rich phase, in accordance with equation 17. Resistance in both Hquid phases is taken into account in a detailed model (51) which is apphcable to the reversible reactions involved in metal extraction. This model, which can accommodate the case of interfacial reaction, has been successfully compared with rate data from the Hterature (51). 

Supersaturation has been observed to affect contact nucleation, but the mechanism by which this occurs is not clear. There are data (19) that infer a direct relationship between contact nucleation and crystal growth. This relationship has been explained by showing that the effect of supersaturation on contact nucleation must consider the reduction in interfacial supersaturation due to the resistance to diffusion or convective mass transfer (20). 

Designed to obtain such fundamental data as chemical rates free of mass transfer resistances or other complications. Some of the heterogeneous reactors of Fig. 23-29, for instance, employ known interfacial areas, thus avoiding one uncertainty. 

A non-ideal MSMPR model was developed to account for the gas-liquid mass transfer resistance (Yagi, 1986). The reactor is divided into two regions the level of supersaturation in the gas-liquid interfacial region (region I) is higher than that in the main body of bulk liquid (region II), as shown in Figure 8.12. 

Later publications have been concerned with mass transfer in systems containing no suspended solids. Calderbank measured and correlated gas-liquid interfacial areas (Cl), and evaluated the gas and liquid mass-transfer coefficients for gas-liquid contacting equipment with and without mechanical agitation (C2). It was found that gas film resistance was negligible compared to liquid film resistance, and that the latter was largely independent of bubble size and bubble velocity. He concluded that the effect of mechanical agitation on absorber performance is due to an increase of interfacial gas-liquid area corresponding to a decrease of bubble size. 

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. 

As the agitation of the reaction mixture was very intensive, interfacial mass transfer resistance is suppressed, and the concentration in gas and liquid are related by the phase equilibrium... 

Consider an extreme case in which there is no resistance to reaction and all of the resistance is due to mass transfer. The rate of mass transfer is proportional to the interfacial area and the concentration of the driving force. An expression can be written for the rate of transfer of Component i from gas to liquid through the gas film per unit volume of reaction mixture ... 

Interfacial contact area, 10 755-756 Interfacial effects, in CA resists, 15 182 Interfacial energy, 24 157 colloids, 7 281-284 Interfacial forces, in foams, 12 4 Interfacial free energy, 24 119 Interfacial in situ polymerization, in microencapsulation, 16 442 446 Interfacial mass-transfer coefficients,... 

The possible existence of an interface resistance in mass transfer has been examined by Raimondi and Toor(12) who absorbed carbon dioxide into a laminar jet of water with a flat velocity profile, using contact times down to 1 ms. They found that the rate of absorption was not more than 4 per cent less than that predicted on the assumption of instantaneous saturation of the surface layers of liquid. Thus, the effects of interfacial resistance could not have been significant. When the jet was formed at the outlet of a long capillary tube so that a parabolic velocity profile was established, absorption rates were lower than predicted because of the reduced surface velocity. The presence of surface-active agents appeared to cause an interfacial resistance, although this effect is probably attributable to a modification of the hydrodynamic pattern. 

Mass transfer rates are increased in the presence of eruptions because the interfacial fluid is transported away from the interface by the jets. For mass transfer from drops with the controlling resistance in the continuous phase, the maximum increase in the transfer rate is of the order of three to four times (S8), not greatly different from the estimate of Eq. (10-4) for cellular convection. This may indicate that equilibrium is attained in thin layers adjacent to the interface during the spreading and contraction. When the dispersed-phase resistance controls, on the other hand, interfacial turbulence may increase the mass transfer rate by more than an order of magnitude above the expected value. This is almost certainly due to vigorous mixing caused by eruptions within the drop. 

K is the overall mass-transfer coefficient based on the liquid phase. A is the total interfacial area in the gas-liquid dispersion. C is the concentration in the liquid phase. C thus corresponds to equilibrium with the gas phase of composition y. H is the Henry coefficient for the gas. In the case of oxygen or a sparingly soluble compound, H is large and resistance to mass transfer is located in the liquid phase. 

In trickle beds, the gas-to-liquid, kigaGL, and liquid-to-particle, kfaLS, coefficients are used to represent the effect of the external mass transfer resistances. The interfacial areas aGl and <2ls refer to the effective mass transfer surface per unit volume of empty reactor. Due to the fact that the coefficients kig and klL cannot be easily estimated independently from the corresponding interfacial areas aGL and aLS respectively, by simple experimental techniques, correlations are normally reported for the products kigaGL and k,a]S (Smith, 1981). 

Immobilization onto a solid support, either by surface attachment or lattice entrapment, is the more widely used approach to overcome enzyme inactivation, particularly interfacial inactivation. The support provides a protective microenvironment which often increases biocatalyst stability, although a decrease in biocata-lytic activity may occur, particularly when immobilization is by covalent bonding. Nevertheless, this approach presents drawbacks, since the complexity (and cost) of the system is increased, and mass transfer resistances and partition effects are enhanced [24]. For those applications where enzyme immobilization is not an option, wrapping up the enzyme with a protective cover has proved promising [21]. 

Extension of analytical solutions for interphase mass transfer, with particular attention to interfacial resistance. 

Experimental study of more systems with interphase mass transfer, with the aim of correlating interfacial resistance with other physical properties. 

The relationships between the overall mass transfer coefficient and the film mass transfer coefficients in both phases are not as simple as in the case of heat transfer, for the following reason. Unlike the temperature distribution curves in heat transfer between two phases, the concentration curves of the diffusing component in the two phases are discontinuous at the interface. The relationship between the interfacial concentrations in the two phases depends on the solubility of the diffusing component. Incidentally, it is known that there exists no resistance to mass transfer at the interface, except when a surface-active substance accumulates at the interface to give additional mass transfer resistance. 

In the group with positive spreading coefficients (e.g., toluene-in-water and oleic acid-in-water emulsions), the values ofkj a in both stirred tanks and bubble columns decrease upon the addition of a very small amount of oil, and then increase with increasing oil fraction. In such systems, the oils tend to spread over the gas-liquid interface as thin films, providing additional mass transfer resistance and consequently lower k values. Any increase in value upon the further addition of oils could be explained by an increased specific interfacial area a due to a lowered surface tension and consequent smaller bubble sizes. 

Regime 5 - instantaneous reactions at an reaction plane developing inside the film For very high reaction rates and/or (very) low mass transfer rates, ozone reacts immediately at the surface of the bubbles. The reaction is no longer dependent on ozone transfer through the liquid film kL or the reaction constant kD, but rather on the specific interfacial surface area a and the gas phase concentration. Here the resistance in the gas phase may be important. For lower c(M) the reaction plane is within the liquid film and both film transfer coefficients as well as a can play a role. The enhancement factor can increase to a high value E > > 3. 

---