Interfacial mixed-film theories

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 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. 

Interfacial mass transfer processes can be described by the two-film theory. Both the gas and the liquid phase can be divided into a stagnant film located near the interface and well-mixed bulk phases without concentration gradients. The two-film theory certainly lacks physical reality in postulating the existence... 

Modern attempts to formulate a quantitative theory of emulsions and emulsion stability have looked most closely at the nature of the interfacial region separating the two immiscible phases, especially the chemical and physical nature of the adsorbed film, the role of mixed films and complex formation, interfacial rheology, and steric and electronic factors at the interface. The theoretical foundations for current ideas concerning emulsion formation and stability are presented in several of the references cited in the Bibliography. A few of the most basic ideas, however, are presented below. 

Harriott suggested that, as a result of the effects of interfacial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a tiiin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a film resistance in one phase and a penetration model resistance in the other. It is necessary in equatjon 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then Cai — Cao in place of — 3 Cao, and the mass transfer rate at time t is given for a film thickness L by ... 

Fig. 9.2-2. The surface-renewal theory for mass transfer. This approach tries to apply the mathematics of the penetration theory to a more plausible physical picture. The liquid is pictured as two regions, a large well-mixed bulk and an interfacial region that is renewed so fast that it behaves as a thick film. The surface renewal is caused by liquid flow.

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