Two-film theory of mass transfer

A relation between dy/dZ and (Ay)/ may be obtained on the basis of the two-film theory of mass transfer. For the vapour film, Fick s law, Volume 1, Chapter 10, gives ... 

As Sherwood and Pigford(3) point out, the use of spray towers, packed towers or mechanical columns enables continuous countercurrent extraction to be obtained in a similar manner to that in gas absorption or distillation. Applying the two-film theory of mass transfer, explained in detail in Volume 1, Chapter 10, the concentration gradients for transfer to a desired solute from a raffinate to an extract phase are as shown in Figure 13.19, which is similar to Figure 12.1 for gas absorption. 

Two-film theory of mass transfer Gas Interface Liquid... 

Calculating fiime scrubber efficiency requires an understanding of mass transfer principles. The reader is referred to Chapter 3 for a more detailed discussion of the two-film theory of mass transfer. 

To produce mass transfer of solute between the two solvents, a driving force is necessary. This driving force usually is expressed in terms of the concentrations of solute in the two phases and the departure from equilibrium values. The two-film theory of mass transfer developed in Chapter 3 for gas absorption also can be applied to liquid extraction. The rate of mass transfer of solute C from the feed (solvent A) to the extract (solvent B) is ... 

Figure 5 shows the concentration profile of cephalosporin anion, P in the emulsion globule. Applying two film theory, the mass transfer rate of P from bulk of phase 111 through the boundary layer of phase III to the III - II interface is given by... 

Applications of the Two-Film Theory to Mass Transfer between Vapor and Liquid Phases... 

This limiting case is sometimes referred to as the two-film theory for mass transfer. The resistances to mass transfer in the vapor and liquid phases are concentrated in the vapor and liquid films. Experimental evidence presented by Tung and Drickamer34 and Emmett and Pigford13 suggest that kt is very large except at very high rates of mass transfer. Thus, for all practical purposes,... 

Two-Film Theory of Mass and Heat Transfer for Fluid-Fluid Reactions in General... 

The transport process, according to the two-film theory, of a volatile component across the air-water interface is depicted in Figure 4.3. The figure illustrates a concept that concentration gradients in both phases exist and that the total resistance for mass transfer is the sum of the resistance in each phase. 

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. 

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... 

This chapter will first provide some basics on ozone mass transfer, including theoretical background on the (two-) film theory of gas absorption and the definition of over-all mass transfer coefficients KLa (Section B 3.1) as well as an overview of the main parameters of influence (Section B 3.2). Empirical correction factors for mass transfer coefficients will also be presented in Section B 3.2. These basics will be followed by a description of the common methods for the determination of ozone mass transfer coefficients (Section B 3.3) including practical advice for the performance of the appropriate experiments. Emphasis is laid on the design of the experiments so that true mass transfer coefficients are obtained. 

Continuous changes in compositions of phases flowing in contact with each other are characteristic of packed towers, spray or wetted wall columns, and some novel equipment such as the FHGEE contactor (Fig. 13.14). The theory of mass transfer between phases and separation of mixtures under such conditions is based on a two-film theory. The concept is illustrated in Figure 13.15(a). 

The absorption of a gas by a liquid with simultaneous reaction in the liquid phase is the most important case. There are several theories of mass transfer between two fluid phases (see Volume 1, Chapter 10 Volume 2, Chapter 12), but for the purpose of illustration the film theory will be used here. Results from the possibly more realistic penetration theory are similar numerically, although more complicated in their mathematical form0,4. ... 

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 ... 

Differentiate two-film theory, penetration theory, and surface renewal theory of mass transfer across interfaces. 

Wang [69] employed the penetration theory of mass transfer instead of two-film theory to solve Eq. (3.38) mathematically to yield the following results ... 

The mathematics of mass diffusion within a single phase has thus been well estab-Ushed. Diffusion between phases such as air and water was not fully understood until 1923 when Whitman proposed the two-film theory in which transfer is expressed using two mass transfer coefficients in series, one for each phase (Whitman, 1923). This concept has been rediscovered in pharmacology and probably in other areas and is now more correctly termed the two-resistance theory. ... 

F = Function of the molecular volume of the solute. Correlations for this parameter are given in Figure 7 as a function of the parameter (j), which is an empirical constant that depends on the solvent characteristics. As points of reference for water, (j) = 1.0 for methanol, (j) = 0.82 and for benzene, (j) = 0.70. The two-film theory is convenient for describing gas-liquid mass transfer where the pollutant solute is considered to be continuously diffusing through the gas and liquid films. 

When the film theory is applicable to each phase (the two-film theory), the process is steady state throughout and the interface composition does not then vary with time. For this case the two film coefficients can readily be combined. Because material does not accumulate at the interface, the mass transfer rate on each side of the phase boundary will be the same and for two phases it follows that ... 

The experiments were conducted at four different temperatures for each gas. At each temperature experiments were performed at different pressures. A total of 14 and 11 experiments were performed for methane and ethane respectively. Based on crystallization theory, and the two film theory for gas-liquid mass transfer Englezos et al. (1987) formulated five differential equations to describe the kinetics of hydrate formation in the vessel and the associate mass transfer rates. The governing ODEs are given next. 

The two-film theory considering molecular diffusion through stagnant liquid and gas films is the traditional way of understanding mass transfer across the air-water boundary. As briefly described, other theories exist. However, the two-film theory gives an understanding of fundamental phenomena that may lead to simple empirical expressions for use in practice. 

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). 

According to the two-film theory, it is appropriate to consider the transport of volatile components between the water phase and the air phase in two steps from the bulk water phase to the interface and from the interface to the air, or vice versa. The driving force for the transfer of mass per unit surface area from the water phase to the interface and from the interface to the air phase is determined from the difference between the actual molar fractions, xA and yA, and the corresponding equilibrium values, xA and yA ... 

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