Lewis-Whitman theory

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). 

For plane, unstirred cells, the theoretical equations are (21) and (25) and for plane stirred cells there are the theories of Lewis and Whitman, Kishinevskii, Danckwerts, and Levich, and Eqs. (14) and (16) of the present writer. In particular, if Eqs. (7) and (11) represent processes... 

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 theories vary in the assumptions and boundary conditions used to integrate Fick s law, but all predict the film mass transfer coefficient is proportional to some power of the molecular diffusion coefficient D", with n varying from 0.5 to 1. In the film theory, the concentration gradient is assumed to be at steady state and linear, (Figure 3-2) (Nernst, 1904 Lewis and Whitman, 1924). However, the time of exposure of a fluid to mass transfer may be so short that the steady state gradient of the film theory does not have time to develop. The penetration theory was proposed to account for a limited, but constant time that fluid elements are exposed to mass transfer at the surface (Higbie, 1935). The surface renewal theory brings in a modification to allow the time of exposure to vary (Danckwerts, 1951). 

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. 

The film theory, once developed for equimolar binary mass transfer in non-reactive systems (Lewis and Whitman, 1924), was free from contradictions. Nowadays, it is widely applied for much more complicated processes, and therefore, additional assumptions have to be made. These assumptions are in some conflict with physical backgrounds, and thus, application of this theory becomes problematic (Kenig, 2000). 

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

Film theory goes back to work by Lewis and Whitman [1.27] from 1924. In order to explain the principles we will assume that a substance A is transferred from a quiescent solid or liquid surface, shown as a hat plate in Fig. 1.48, to flowing fluid B. The concentration of A drops from cA0 at the plate surface to cAi in the fluid. Film theory comes from the assumption that mass transfer takes place in a thin him of thickness S near the wall, hence the name. Concentration and velocity should only change in the y direction, but not, as is further assumed, with time or in any other coordinate direction. In steady how this results in a constant molar flux hA = cAwA of A being transferred in the y direction. If this were not the case, more A would how into a volume element of the fluid than out of it, and therefore the concentration of substance A would change with the time, or material A could also be howing in the x direction which would therefore cause a concentration difference in another coordinate direction. However neither of these scenarios are admissible in terms of the prerequisites for the application of him theory. Therefore according to him theory... 

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... 

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... 

This theory, developed by Lewis and Whitman, supposes that motion in the two phases dies out near the interface and the entire resistance to transfer is considered as being contained in two fictitious films on either side of the interface, in which transfer occurs by purely molecular diffusion. It is postulated that local equilibrium prevails at the interface and that the concentration gradients are established so rapidly in the films compared to the total time of contact that steady-state diffusion may be assumed. 

Several models have been proposed to describe the phenomenon occurring when a gas phase is brought into contact with a liquid phase. The model that has been used most is the two-film theory proposed by Whitman [1923] and by Lewis and Whitman [1924]. In this theory a stagnant layer is supposed to exist in both phases along the interface. In the gas phase the component A experiences a resistance to its transfer to the interface which is entirely concentrated in the film. At the interface itself there is no resistance so that Henry s law is satisfied ... 

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. 

The two-film (or two-resistance) theory was first proposed in a landmark paper by W.K. Lewis and W.G. Whitman over 80 years ago Ind. Eng. Chem. 16,1215 [1924]). In spite of sporadic criticism, particularly of the assumption of interfacial equilibrium, it has survived remarkably well and continues to serve as one of the mainstays in the design of industrial separation processes. 

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