Mass transfer interfacial

Interfacial transfer of chemicals provides an interesting twist to our chemical fate and transport investigations. Even though the flow is generally turbulent in both phases, there is no turbulence across the interface in the diffusive sublayer, and the problem becomes one of the rate of diffusion. In addition, temporal mean turbulence quantities, such as eddy diffusion coefficient, are less helpful to us now. The unsteady character of turbulence near the diffusive sublayer is crucial to understanding and characterizing interfacial transport processes. 

The flux rate will be constant with z, unless we are very close to equilibrium or there are sources or sinks of hydroxylbenzene in the container. At the interface, equilibrium is assumed between the air and water phases. This equilibrium may only exist for a thickness of a few molecules, but is assumed to occur quickly compared with the time scale of interest. The concentrations at this air-water interface are related by the following equation  

In the diffusive sublayer, flux is due purely to diffusion. Then, we can utilize the fact that mean flux is constant with distance  

Because Jhb is constant and Dhba and Dhbw are also constant, assuming the thermodynamic parameters such as temperature and pressure do not change, the solution to equation (8.4) is 

As noted previously, most environmental flows are turbulent. The diffusive sublayer, where only diffusion acts to transport mass and the concentration profile is linear, is typically between 10 /xm and 1 mm thick. Measurements within this sublayer are not usually feasible. Thus, the interfacial flux is typically expresses as a bulk transfer 

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Interfacial Mass-Transfer Coefficients. Whereas equiHbrium relationships are important in determining the ultimate degree of extraction attainable, in practice the rate of extraction is of equal importance. EquiHbrium is approached asymptotically with increasing contact time in a batch extraction. In continuous extractors the approach to equiHbrium is determined primarily by the residence time, defined as the volume of the phase contact region divided by the volume flow rate of the phases. 

Effective Interfacial Mass-Transfer Area a In a packed tower of constant cross-sectional area S the differential change in solute flow per unit time is given by... 

The concentrations of the coffee, both in the granules and in the liquid flowing through the bed, will vary continuously both with distance and with time. The behaviour of the packed bed is therefore best approximated by a series of many uniform property subsystems. Each segment of solid is related to its appropriate segment of liquid by interfacial mass transfer, as shown in Fig. 1.9. 

Rate of interfacial mass transfer of i from phase G into phase L... 

In the case of an input of component i to the system by interfacial mass transfer, the balance equation now becomes ... 

In this type of apparatus, the two phases do not come to equilibrium, at any point in the contactor and the simulation approach is based, therefore, not on a number of equilibrium stages, but rather on a consideration of the relative rates of transport of material through the contactor by flow and the rate of interfacial mass transfer between the phases. For this, a consideration of mass transfer rate theory becomes necessary. 

Note that the transfer rate equation is based on an overall concentration driving force, (X-X ) and overall mass transfer coefficient, Kl. The two-film theory for interfacial mass transfer shows that the overall mass transfer coefficient, Kl, based on the L-phase is related to the individual film coefficients for the L and G-phase films, kL and ko, respectively by the relationship... 

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... 

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,... 

It must be emphasized that the above considerations were made in the absence of reaction. Interfacial mass transfer followed by reaction requires further consideration. The Hatta regimes classify transfer-reaction situations into infinitely slow transport compared to reaction (Hatta category A) to infinitely fast transport compared to reaction (Hatta category H) [42]. In the first case all reaction occurs at the interface and in the second all reaction occurs in the bulk fluid. Homogenous catalytic hydrogenations, carbonylations etc. require consideration of this issue. An extreme example of the severity of mass transport effects on reactivity and selectivity in hydroformylation has been provided by Chaudari [43]. Further general discussions for homogeneous catalysis can be found elsewhere [39[. 

Chapter 9 Air-Water Mass Transfer in the Field. The theory of interfacial mass transfer is often difficult to apply in the field, but it provides a basis for some important aspects of empirical equations designed to predict interfacial transport. The application of both air-water mass transfer theory and empirical characterizations to field situations in the environment will be addressed. 

Table 5.1 shows that, with the boundary conditions present in most environmental flows (i.e., the Earth s surface, ocean top and bottom, river or lake bottom), turbulent flow would be the predominant condition. One exception that is important for interfacial mass transfer would be very close to an interface, such as air-solid, solid-liquid, or air-water interfaces, where the distance from the interface is too small for turbulence to occur. Because turbulence is an important source of mass transfer, the lack of turbulence very near the interface is also significant for mass transfer, where diffusion once again becomes the predominant transport mechanism. This will be discussed further in Chapter 8. 

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