Mixed film theory

As discussed before (4) it is perhaps convenient to classify these theories into three main categories interfacial or mixed film theories, solubilisation theories and thermodynamic theories. Below a brief description of each of these classes will be given with particular emphasis on the role of surfactant nature and structure. 

Mixed film theories (4-8) The essential feature of the mixed film theories is to consider the film as a liquid, two dimensional third phase in equilibrium with both oil and water, implying that such a monolayer could be a duplex film, i.e., one giving different properties on the water side than on the oil side (4). According to these theories, the interfacial tension Y is given by the expression,... 

The approach taken is semi-empirical. Point efficiencies are estimated making use of the two-film theory , and the Murphree efficiency estimated allowing for the degree of mixing likely to be obtained on real plates. 

Predicted and calculated flux of fenitrothion from water were similar although values were arrived at independently. Both results suggest that volatilization from water is slow compared to other paths of degradation of the insecticide which confirms predictions of the two-film theory of volatilization (17)(18). Losses of fenitrothion from surface films have been shown to be very rapid (2 ) but a surface film was not formed in the present work because the insecticide was mixed into the upper 10 cm of the water column. 

Film theory predicts that the mass transfer coefficient for a phase (or the overall mass transfer coefficient) is proportional to the diffusion coefficient and inversely proportional to the thickness of the stagnant zone. The diffusion coefficient can be calculated from either the Wilke-Chang or the FSG equations. However, 6 is difficult (if not impossible) to determine. Hence, mass transfer coefficients are often determined from empirical correlations. Also, Film theory is based on the assumption that the bulk fluid phases are perfectly mixed. While this might approach reality for well-mixed turbulent systems, this is certainly not the case for laminar systems. 

In the film theory the complete resistance to mass transfer from the interface to the bulk of the liquid is confined to a fictitious film along the interface. The bulk of the fluid is considered to be perfectly mixed in the direction perpendicular to the interface, i.e. the concentration of A is uniform beyond the film. Figure 7.13 shows the concentration profile of A according to the film theory. 

The film theory is the simplest model for interfacial mass transfer. In this case it is assumed that a stagnant film exists near the interface and that all resistance to the mass transfer resides in this film. The concentration differences occur in this film region only, whereas the rest of the bulk phase is perfectly mixed. The concentration at the depth I from the interface is equal to the bulk concentration. The mass transfer flux is thus assumed to be caused by molecular diffusion through a stagnant film essentially in the direction normal to the interface. It is further assumed that the interface has reached a state of thermodynamic equilibrium. 

According to the thermodynamic theory of microemulsion formation, the total interfacial tension of the mixed film of surfactant and cosurfactant must approach zero. The total interfacial tension is given by the following equation. 

DISTILLATION PLATE EFFICIENCY. The two-film theory can be applied to mass transfer on a sieve tray to help correlate and extend data for tray effieiency. The bubbles formed at the holes are assumed to rise through a pool of liquid that is vertically mixed and has the local composition x. The bubbles change in composition as they rise, and there is assumed to be no mixing of the gas phase in the vertical direction. For a unit plate area with a superficial velocity the moles transferred in a thin slice dz are... 

A theory which incorporates some of the principles of both the two-film theory and the penetration theory has been proposed by TOOR and Marchello The whole of the resistance to transfer is regarded as lying within a laminar film at the interface, as in the two-film theory, but the mass transfer is regarded as an unsteady state process. It is assumed that fresh surface is formed at intervals from fluid which is brought from the bulk of the fluid to the interface by the action of the eddy currents. Mass transfer then takes place as in the penetration theory, except that the resistance is confined to the finite film, and material which traverses the film is immediately completely mixed with the bulk of the fluid. For short times of exposure, when none of the diffusing material has reached the far side of the layer, the process is identical to that postulated in the penetration theory. For prolonged periods of exposure when a steady concentration gradient has developed, conditions are similar to those considered in the two-film theory. 

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