Whitman two-film theory

According to the Whitman Two-Film theory, the actual concentration profiles, as shown in Fig. 1.28 are approximated for the steady state with no chemical reaction, by that of Fig. 1.29. 

Fig. 1.28 Concentration gradients according to the Whitman Two-Film theory.

Mass transfer in real absorption equipment resembles a molecular diffusion process only in the basic idea of a concentration difference driving force. However, the two-film theory of Whitman can be used to construct a model similar in many respects to molecular diffusion equations. Fig. 1 is a schematic representing the Whitman two-film theory ... 

The mechanism clearly involves diffusion inside one phase to the phase boundary , across the phase boundary , and into the second phase, but it is sometimes complicated by a chemical reaction such as a solvation stepi2 at the phase boimdary . Neglecting chemical reactions, the Whitman two-film theory of gas absorptions is applicable to liquid-liquid systems. This suggests that the phase boundary should be considered as a film of phase A in contact with another film of phase B. Diffusion through the boundary films is controlled by an equation of the type ... 

A number of attempts have been made to relate the values of kA obtained for one system with those for other systems. The coefficients involve resistances to mass transfer for both the vapor and the liquid phases, and it has been customary to apply relations based on the Lewis and Whitman two-film theory. It is doubtful that such a theory is applicable in this case since it is difficult to visualize the conditions inherent in this theory for a liquid phase in a packed tower. Further studies of the mechanism of mass transfer between the vapor and the liquid for systems approximating the conditions in a packed tower are needed to furnish a sound basis for correlating the over-all mass-transfer coefficients. 

Whitman two-film theory Atheoryused in gas adsorption to describe the mass trans-fer of a solute from a gas into a liquid in which either side of the interface exists a stagnant gas film and a similar stagnant liquid film (see Fig. 57). The two films are assumed to offer the only resistance to mass transfer hi the bulk gas and liquid, the soludon pardal pressure... 

Two-film theory (Lewis and Whitman, 1924) the theory is based on molecular diffusion through two stagnant films, a liquid and a gas film, at the air-water interface. 

Although mass transfer across the water-air interface is difficult in terms of its application in a sewer system, it is important to understand the concept theoretically. The resistance to the transport of mass is mainly expected to reside in the thin water and gas layers located at the interface, i.e., the two films where the gradients are indicated (Figure 4.3). The resistance to the mass transfer in the interface itself is assumed to be negligible. From a theoretical point of view, equilibrium conditions exist at the interface. Because of this conceptual understanding of the transport across the air-water boundary, the theory for the mass transport is often referred to as the two-film theory (Lewis and Whitman, 1924). 

The preceding analysis of the process of absorption is based on the two-film theory of Whitman 11. It is supposed that the two films have negligible capacity, but offer all the resistance to mass transfer. Any turbulence disappears at the interface or free surface, and the flow is thus considered to be laminar and parallel to the surface. 

There are several theories concerned with mass transfer across a phase boundary. One of the most widely used is Whitman s two-film theory in which the resistance to transfer in each phase is regarded as being located in two thin films, one on each side of the interface. The concentration gradients are assumed to be linear in each of these layers and zero elsewhere while at the interface itself, equilibrium conditions exist (Fig. 5). Other important theories are Higbie s penetration theory and the theory of surface renewal due to Danckwerts. All lead to the conclusion that, in... 

The film model referred to in Chapters 2 and 5 provides, in fact, an oversimplified picture of what happens in the vicinity of interface. On the basis of the film model proposed by Nernst in 1904, Whitman [2] proposed in 1923 the two-film theory of gas absorption. Although this is a very useful concept, it is impossible to predict the individual (film) coefficient of mass transfer, unless the thickness of the laminar sublayer is known. According to this theory, the mass transfer rate should be proportional to the diffusivity, and inversely proportional to the thickness of the laminar film. However, as we usually do not know the thickness of the laminar film, a convenient concept of the effective film thickness has been assumed (as... 

Lewis and Whitman (1924) proposed that this resistance to mass transfer across an interface is the sum of the resistances in each phase. They called this concept the two-film theory. As Treybal (1968) pointed out, their two-film theory does not depend on which model is used to describe the mass transfer in each phase, therefore, the two-resistance theory would be a more appropriate name. It would also cause less confusion, since the names film theory (mass transfer in one phase) and two-film theory (mass transfer between... 

The connection between the film mass transfer coefficients and the over-all mass transfer coefficients is provided by the two-film theory from Lewis and Whitman (1924) the total resistance to mass transfer is the sum of the resistances in each phase. 

In addition to qualitative assessment of direction of movement of a chemical using fugacity ratio, quantitative assessment is determined by calculating net gaseous diffusion across air-water interface (Mackay et al. (1986) Baker and Eisenreich, 1990 Achman et al., 1993). The two-film theory as shown in Eq. (3) has been frequently used to determine the gaseous diffusion rate of chemicals (Whitman, 1923 Liss and Slater, 1974). 

Whitman WG (1923) Preliminary experimental confirmation of the two-film theory of gas adsorption. Chem Met Eng 29 146-148... 

Let us consider the diffusion of radicals. According to the two-film theory developed by Lewis and Whitman (1924) for mass tranter across the... 

Whitman, W. G. (1923) The two-film theory for gas adsorption. Ghent. Metall. 

Whitman, W.G. The two film theory of gas absorption. Chem. Metal. 1923, 2, E146-E148. 

The practical applications provided here all involve two phases, with molecules transferring between them. Thus, there are two resistances to transfer, plus possibly a third resistance at the interface itself. We have just discussed transfer within a phase and ending at a phase boundary, such as an interface. It is necessary to couple individual phase resistances to characterize the overall transfer process. The first attempt at this, and indeed a lasting one, was presented by Lewis and Whitman [19] as the two-film theory. More recently it has been called simply the two-resistance theory, eliminating the reqnirement that transport in each phase be handled by the film concept. 

In 1924 Lewis and Whitman 1 suggested that the film theory model could be applied to both die gas and liquid phases during gas absorption. This two-film theory has hed extensive use in modeling steady-state transport between two phases. Transferor species A occurring between a gas phase and liquid phase, each of which may be in turbulent flow, can be described by the individual rate expressions bstween the bulk of each phase and the interface. 

In the remainder of this chapter, the two-film theory with equations of the form of Eq. (13-2) is applied to packed columns and to plate efficiencies. The essence of the two-film theory is the additivity of the vapor and liquid film resistances which was first proposed by Lewis and Whitman.26,37... 

In many separation processes, material must diffuse from one phase into another phase, and the rates of diffusion in both phases affect the overall rate of mass transfer. In the two-film theory, proposed by Whitman in 1923, equilibrium is assumed at the interface, and the resistances to mass transfer in the two phases are added to get an overall resistance, just as is done for heat transfer. The reciprocal of the overall resistance is an overall coefficient, which is easier to use for design calculations than the individual coefficients. 

Professor Whitman is probably best known in technical circles for his development of the two-film theory for gas absorption and for contributions in the corrosion field. His later years were devoted largely to administration of the department and to public services such as the War Production Board, the National Advisory Committee for Aeronautics, Science Advisor to the Department of State, and Secretary General of the U.N. Conference on Peaceful Uses of the Atom. His citation on election... 

The two-film theory of Whitman was the first serious attempt to represent conditions occurring when material is transferred from one fluid stream to another. Although it does not closely reproduce the conditions in most practical equipment, the theory gives expressions which can be applied to the experimental data which are generally available, and for that reason it is still extensively used. 

Mass transfer, an important phenomenon in science and engineering, refers to the motion of molecules driven by some form of potential. In a majority of industrial applications, an activity or concentration gradient serves to drive the mass transfer between two phases across an interface. This is of particular importance in most separation processes and phase transfer catalyzed reactions. The flux equations are analogous to Ohm s law and the ratio of the chemical potential to the flux represents a resistance. Based on the stagnant-film model. Whitman and Lewis [25,26] first proposed the two-film theory, which stated that the overall resistance was the sum of the two individual resistances on the two sides. It was assumed in this theory that there was no resistance to transport at the actual interface, i.e., within the distance corresponding to molecular mean free paths in the two phases on either side of the interface. This argument was equivalent to assuming that two phases were in equilibrium at the actual points of contact at the interface. Two individual mass transfer coefficients (Ld and L(-n) and an overall mass transfer coefficient (k. ) could be defined by the steady-state flux equations ... 

Several models have been proposed to describe the phenomena occurring when a gas phase is brought into contact with a liquid phase. The model that has been used most so far is the two-film theory proposed by Whitman [1] and by Lewis... 

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