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** Mass Transfer at a Gas-Liquid Interface (Two-Film Theory) **

** Mass transfer coefficients overall in two-film theory **

Explain the basic concepts underlying the two-film theory for mass transfer across a phase boundary and obtain an expression for film thickness. [Pg.283]

The two-film theory supposes that the entire resistance to transfer is contained in two fictitious films on either side of the interface, in which transfer occurs by molecular diffusion. This model leads to the conclusion that the mass-transfer coefficient kL is proportional to the diffusivity DAB and inversely proportional to the film thickness Zy as [Pg.228]

The so-called Two Film Theory (Lewis and Whiteman, 1923-24) assumes the formation of laminar boundary layers on both sides of the interphase. Mass transfer through these boundary layers can only be effected by means of diffusion, while the phase transition is immeasurably fast, Fig. 86. Consequently, an equilibrium predominates in the interphase and the saturation concentration cG of the gas in the interphase ( ) obeys Henry s law [Pg.197]

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. [Pg.87]

Figure 23.1 Setting up the rate equation for straight mass transfer based on the two film theory. |

Point efficiency is usually discussed in terms of the two-film theory. The theory postulates resistances to mass transfer in both the vapor and liquid films near a vapor-liquid ihterface (Fig. 7.2a). The molar rate of diffusion, N (moles/s), is given by [Pg.367]

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 [Pg.641]

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. [Pg.81]

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 [Pg.35]

Several different mechanisms have been proposed to provide a basis for a theory of interphase mass transfer. The three best known are the two-film theory, the penetration theory, and the surface renewal theory. [Pg.228]

Note that the transfer rate equation is based on an overall concentration driving force, (X-X ) and overall mass transfer coefficient, Kl. The two-film theory for interfacial mass transfer shows that the overall mass transfer coefficient, Kl, based on the L-phase is related to the individual film coefficients for the L and G-phase films, kL and ko, respectively by the relationship [Pg.168]

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 [Pg.228]

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. [Pg.659]

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 [Pg.74]

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 [Pg.81]

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. [Pg.74]

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 [Pg.619]

Like their random-packing efficiency model (above), the Bravo, Fair et al. structured-packing model is based on the two-film theory. The HTU is calculated from the mass transfer coefficients and interfacial areas using Eqs. (9.23) and (9.24). The HETP can be calculated from the HTU using Eqs. (9.12) and (9.13). The mass transfer coefficients are evaluated from [Pg.529]

In rate-based multistage separation models, separate balance equations are written for each distinct phase, and mass and heat transfer resistances are considered according to the two-film theory with explicit calculation of interfacial fluxes and film discretization for non-homogeneous film layer. The film model equations are combined with relevant diffusion and reaction kinetics and account for the specific features of electrolyte solution chemistry, electrolyte thermodynamics, and electroneutrality in the liquid phase. [Pg.141]

All three of these proposals give the mass transfer rate N A directly proportional to the concentration difference (CAi — CAL) so that they do not directly enable a decision to be made between the theories. However, in the Higbie-Danckwerts theory N A a s/Dj whereas NA

In spite of all the effort that has been expended on this topic, the prediction of mass transfer efficiency still is not on a satisfactory basis. The relatively elaborate method of the AIChE Bubble-Tray Manual (AIChE, New York, 1958) is based on the two-film theory but has not had a distinguished career. A number of simpler correlations have been proposed and have some value as general guidance. That literature has been surveyed recently by Vital, Grossel, and Olsen [Hyd. Proc., 55-56 (Oct. 1984) 147-153 (Nov. 1984) 75-78 (Dec. 1984)]. [Pg.439]

Continuous changes in compositions of phases flowing in contact with each other are characteristic of packed towers, spray or wetted wall columns. 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 13.14(a). [Pg.423]

Another difficulty is related to the mass transfer by convection, as, by definition, the films are stagnant and hence, there should be no mass transport mechanism, except for molecular diffusion in the direction normal to the interface (Kenig, 2000). Nevertheless, convection in films is directly accounted for in correlations. Moreover, in case of reactive systems, the film thickness should depend on the reaction rate, which is beyond the two-film theory consideration. [Pg.17]

The system described forms the basis of the two-film theory. Because of the mutual solubility of acetone in water, the rate at which molecules of acetone move through the liquid film is large. Consequently, acetone molecules in the air that approach the liquid film are removed at such a fast rate that the concentration of acetone in the air film becomes less than it is in the main body of gas. This concentration gradient between the air film and main air body supplies the main driving force for the transfer of mass. [Pg.47]

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 [Pg.80]

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. [Pg.737]

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). [Pg.74]

Theoretical prediction methods for tray efficiency are based on the two-film theory and use the sequence of steps in Fig. 7.3. Almost ell evolved from the AIChE model (84,125,132,133). This model was developed over five years in the late 1950s in three universities. Over the last few decades, several aspects of the AIChE model have been examined, criticised, corrected, and modified. State-of-the-art reviews are given by Lockett (12) and Chan and Fair (134,136). A modified version of the AIChE model that alleviated several of ita shortcomings and updated ita hydraulic and mass transfer relationships was produced by Chan and Fair (134,135). [Pg.372]

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. [Pg.314]

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. [Pg.257]

See also in sourсe #XX -- [ Pg.674 ]

See also in sourсe #XX -- [ Pg.104 , Pg.412 , Pg.428 ]

See also in sourсe #XX -- [ Pg.104 , Pg.412 , Pg.428 ]

See also in sourсe #XX -- [ Pg.104 , Pg.412 , Pg.428 ]

** Mass Transfer at a Gas-Liquid Interface (Two-Film Theory) **

** Mass transfer coefficients overall in two-film theory **

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