Mass transfer models film theory

This simple mass transfer model based on simplified film theory has been proposed to describe the process of facilitated transport of penicillin-G across a SLM system [53]. In the authors laboratory, CPC transport using Aliquat-336 as the carrier was studied [56] using microporous hydrophobic polypropylene membrane (Celgard 2400) support and the permeation rate was found to be controlled by diffusion across the membrane. 

In this investigation we carried out experiments with simultaneous absorption of H2S and CO2 into aqueous 2.0 M diisopropanol-amine (DIPA) solutions at 25 °C. The results are evaluated by means of our mathematical mass transfer model both in penetration and film theory form. The latter version has been derived from the penetration theory mass transfer model [5],... 

The mass transfer model. In our previous work [6] the mass transfer model equations and their mathematical treatment have been described extensively. The relevant differential equations, describing the process of liquid-phase diffusion and simultaneous reactions of the species according to the penetration theory, are summarized in table 1. Recently we derived from this penetration theory description a film model version, which is incorporated in the evaluation of the experimental results. Details on the film model version are given elsewhere [5]. 

The fundamental principles of the gas-to-liquid mass transfer were concisely presented. The basic mass transfer mechanisms described in the three major mass transfer models the film theory, the penetration theory, and the surface renewal theory are of help in explaining the mass transport process between the gas phase and the liquid phase. Using these theories, the controlling factors of the mass transfer process can be identified and manipulated to improve the performance of the unit operations utilizing the gas-to-liquid mass transfer process. The relevant unit operations, namely gas absorption column, three-phase fluidized bed reactor, airlift reactor, liquid-gas bubble reactor, and trickled bed reactor were reviewed in this entry. 

In Chapter 7 we define mass transfer coefficients for binary and multicomponent systems. In subsequent chapters we develop mass transfer models to determine these coefficients. Many different models have been proposed over the years. The oldest and simplest model is the film model this is the most useful model for describing multicomponent mass transfer (Chapter 8). Empirical methods are also considered. Following our discussions of film theory, we describe the so-called surface renewal or penetration models of mass transfer (Chapter 9) and go on to develop turbulent eddy diffusivity based models (Chapter 10). Simultaneous mass and energy transport is considered in Chapter 11. 

An apparent weakness of the film model is that it suggests that the mass transfer coefficient is directly proportional to the diffusion coefficient raised to the first power. This result is in conflict with most experimental data, as well as with more elaborate models of mass transfer [surface renewal theory considered in the next chapter, e.g., or boundary layer theory (Bird et al., I960)]. However, if we substitute the film theory expression for the mass transfer coefficient (Eq. 8.2.12) into Eq. 8.8.1 for the Sherwood number we find... 

A number of investigators used the wetted-wall column data of Modine to test multicomponent mass transfer models (Krishna, 1979, 1981 Furno et al., 1986 Bandrowski and Kubaczka, 1991). Krishna (1979b, 1981a) tested the Krishna-Standart (1976) multicomponent film model and also the linearized theory of Toor (1964) and Stewart and Prober (1964). Furno et al. (1986) used the same data to evaluate the turbulent eddy diffusion model of Chapter 10 (see Example 11.5.3) as well as the explicit methods of Section 8.5. Bandrowski and Kubaczka (1991) evaluated a more complicated method based on the development in Section 8.3.5. The results shown here are from Furno et al. (1986). 

For heat transfer the film theory is the most commonly used model, and the physical picture of a laminar film in which the whole temperature difference is situated leads to a result analogous to the mass transfer coefficient model [5]. After integrating Fourier s law over the film, a comparison with the heat transfer coefficient model (5.126) yields ... 

Huang and Kuo also solved two equations for a rapid first-order reversible reaction (i.e., equilibrium in the bulk liquid). The solutions are extremely lengthy and will not be given here. From a comparison of the film, surface renewal, and intermediate film-penetration theories it was found that for irreversible and reversible reactions with equal diffusivities of reactant and product, the enhancement factor was insensitive to the mass transfer model. For reversible reactions with product diffusivity smaller than that of the reactant, the enhancement factor can differ by a factor of two between the extremes of film and surface renewal theory. To conclude, it would seem that the choice of the model matters little for design calculations the predicted differences are negligible with respect to the uncertainties of prediction of some of the model or operation parameters. 

In this chapter, fluid-fluid flow patterns and mass transfer in microstructured devices are discussed. The first part is a brief discussion of conventionai fluid-fluid reactors with their advantages and disadvantages. Further, the ciassi-flcation of fluid-fluid microstructured reactors is presented. In order to obtain generic understanding of hydrodynamics, mass transfer, and chemical reaction, dimensionless parameters and design criteria are proposed. The conventional mass transfer models such as penetration and film theory as well as empirical correlations are then discussed. Finally, literature data on mass transfer efficiency at different flow regimes and proposed empirical correlations as well as important hydrodynamic design parameters are presented. 

Unlike for gas- liquid systems, no efforts have been made to develop mass transfer models based on either film or penetration theory for liquid-liquid MSR. The... 

Van Baten and Krishna [41] performed a computational fluid dynamics (CFD) study of gas absorption in Taylor flow and found that in some of the experiments of Bercic and Pintar the contact time in the film was indeed long enough to saturate the liquid film fully. For shorter unit cells (or higher velocities), they formulated a mass transfer model of penetration theory for both the caps and the film... 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Other Models for Mass Transfer. In contrast to the film theory, other approaches assume that transfer of material does not occur by steady-state diffusion. Rather there are large fluid motions which constantiy bring fresh masses of bulk material into direct contact with the interface. According to the penetration theory (33), diffusion proceeds from the interface into the particular element of fluid in contact with the interface. This is an unsteady state, transient process where the rate decreases with time. After a while, the element is replaced by a fresh one brought to the interface by the relative movements of gas and Uquid, and the process is repeated. In order to evaluate a constant average contact time T for the individual fluid elements is assumed (33). This leads to relations such as... 

The simplest theory involved in mass transfer across an interface is film theory, as shown in Figure 3.10. In this model, the gas (CO) is transferred from the gas phase into the liquid phase and it must reach the surface of the growing cells. The rate equation for this case is similar to the slurry reactor as mentioned in Levenspiel.20... 

HARRIOTT 25 suggested that, as a result of the effects of interfaeial 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 thin 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 Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 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 C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

In a process where mass transfer takes place across a phase boundary, the same theoretical approach can be applied to each of the phases, though it does not follow that the same theory is best applied to both phases. For example, the film model might be applicable to one phase and the penetration model to the other. This problem is discussed in the previous section. 

Surface Renewal Theory. The film model for interphase mass transfer envisions a stagnant film of liquid adjacent to the interface. A similar film may also exist on the gas side. These h5q>othetical films act like membranes and cause diffu-sional resistances to mass transfer. The concentration on the gas side of the liquid film is a that on the bulk liquid side is af, and concentrations within the film are governed by one-dimensional, steady-state diffusion ... 

In Ref. 30, the transfer of tetraethylammonium (TEA ) across nonpolarizable DCE-water interface was used as a model experimental system. No attempt to measure kinetics of the rapid TEA+ transfer was made because of the lack of suitable quantitative theory for IT feedback mode. Such theory must take into account both finite quasirever-sible IT kinetics at the ITIES and a small RG value for the pipette tip. The mass transfer rate for IT experiments by SECM is similar to that for heterogeneous ET measurements, and the standard rate constants of the order of 1 cm/s should be accessible. This technique should be most useful for probing IT rates in biological systems and polymer films. 

Laubriet et al. [Ill] modelled the final stage of poly condensation by using the set of reactions and kinetic parameters published by Ravindranath and Mashelkar [112], They used a mass-transfer term in the material balances for EG, water and DEG adapted from film theory J = 0MMg — c ), with c being the interfacial equilibrium concentration of the volatile species i. 

On the basis of the simplified view of the flow patterns just described, a model for predicting mass transfer rates can be developed using penetration theory and the fact that mass is transferred simultaneously from both the nip and the wiped film. We can therefore write that the total molar mass transfer rate from an element of fluid over a length dk in the extruder is... 

The effects of mercury film electrode morphology in the anodic stripping SWV of electrochemically reversible and quasi-reversible processes were investigated experimentally [47-51], Mercury electroplated onto solid electrodes can take the form of either a uniform thin film or an assembly of microdroplets, which depends on the substrate [51 ]. At low sqtrare-wave frequencies the relationship between the net peak crrrrent and the frequency can be described by the theory developed for the thin-film electrode because the diffusion layers at the snrface of microdroplets are overlapped and the mass transfer can be approximated by the planar diffusion model [47,48],... 

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 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... 

The rate-based models usually use the two-film theory and comprise the material and energy balances of a differential element of the two-phase volume in the packing (148). The classical two-film model shown in Figure 13 is extended here to consider the catalyst phase (Figure 33). A pseudo-homogeneous approach is chosen for the catalyzed reaction (see also Section 2.1), and the corresponding overall reaction kinetics is determined by fixed-bed experiments (34). This macroscopic kinetics includes the influence of the liquid distribution and mass transfer resistances at the liquid-solid interface as well as dififusional transport phenomena inside the porous catalyst. 

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. 

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