Film concept

Fig. 3. The two-film concept and x are the concentrations in the bulk of the phases jy and x are the actual interfacial concentrations at equiHbrium ...

At high velocities where turbulence dominates, the main body of flowing fluid is well mixed in the direction normal to the flow, minor differences in temperature and concentration can be neglected, and the film concept can be applied. This describes the flow as if all gradients for temperature and concentration are in a narrow film along the interface with the solid (Nernst 1904), and inside the film conduction and diffusion are the transfer mechanisms. This film concept greatly simplifies the engineering calculation of heat and mass transfer. 

Hydrogen Storage in Organic Chemical Hydrides on the Basis of Superheated Liquid-Film Concept... 

Thermodynamic Backgrounds of the Superheated Liquid-Film Concept.468... 

Although the suspended catalysts under boiling and refluxing conditions were active for dehydrogeno-aromatization of alkyl-substituted cyclohexanes, the levels of reaction rates were unsatisfactorily low. A breakthrough toward low catalytic activities was accomplished by our introduction of "superheated liquid-film concept" (vide infra) [30]. 

Our "superheated liquid-film concept" stands on the thermodynamic basis of (1) equilibrium shifts due to reactive separation under boiling and refluxing conditions and (2) irreversible processes of heat flows through the catalyst layer as well as bubble formation from the catalyst surface. 

Another theoretical basis of the superheated liquid-film concept lies on the irreversible thermodynamics developed by Prigogine [43]. According to this theory, irreversible chemical processes would be described (Equation 13.17) by extending the equation of De Donder, provided that simultaneous reactions were coupled in a certain thermodynamic model, as follows ... 

The characteristics of equilibrium shifts and the irreversible nature in the superheated liquid-film concept are summarized in Figure 13.28. 

The use of organic chemical hydrides on the basis of superheated liquid-film concept would, thus, make it possible to combine electrolysis hydrogen produced from renewable energy and by-product hydrogen recovered from various industrial processes, with the hydrogen demand practically for stationary fuel cells and hydrogen vehicles. 

Two-equivalent couplers, 19 250, 255 Two-film concept, in absorption, 1 37, 46 Two-film theory... 

This equation expresses the two-film concept of Whitman (40), the numerator being a concentration driving force and the denominator being the sum of two mass transfer resistances in series. Analogous expressions may be written for two liquid film resistances in series. Figure 1 illustrates qualitatively the concentration profiles through two liquid films. 

This expression is based on Hatta s film concept. Similar expressions result from penetration theory. Figure 3 illustrates the concentration profiles for A and B in and around the fluid film for Regime II. 

For model comparisons with the dynamic flow-through chamber system, Aneja et al., (200Id) developed a mass transport model based on the quiescent thin film concept (Danckwerts,... 

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. 

FIGURE 6.3 1 Diagram of two-film concept. Cj and p, represent equitibriion conditions at the interface. 

The two-film concept is convenient in describing transfer phenomena. However, use of this general concept, applicable even to agitated fluids near the interface, should not be taken as support for the classical stagnant film... 

If potential flow and constant surface temperature are assumed, an equation analogous to Eq. (18) is obtained for the internal Nusselt number. Note, however, that the reference velocity in the internal Peclet number is the drop velocity. Similar results will be obtained from the penetration theory, according to which the film is assumed infinite with respect to the depth of heat penetration during the short contact time of a fluid element sliding over the interface. Licht and Pansing (L13) report West s equation, based on the transient film concept, for the case of mass transfer through the combined film resistance. In terms of the overall heat-transfer resistance, l/U (= l//jj + I/he) and if the contact time is that required for the drop to traverse a distance equal to its diameter. West s equations yield... 

Due to slow kinetics, the conventional heterogeneous catalysis of the dehydrogenation of decalin in the solid-gas phase is performed at temperatures of more than 400 °C, which might result in the formation of by-products or carbonaceous deposit on the catalyst in addition to thermal energy loss. In a recent study, an attempt was made to apply the so-called liquid-film concept to hydrogen evolution from decalin with carbon-supported platinum-based catalysts under reactive distillation conditions in order to obtain high electric power suflficient for PEMFC vehicle operations in the temperature range 200-300°C [236]. 

Figure 6.2-1 Two-film concept for mass transfer between a gas and a liquid. 

The diffusion theory states that matter is deposited in a continuous way on the surface of a crystal at a rate proportional to the difference in concentration between the bulk and the surface of the crystal. The mathematical analysis is then the same as for other diffusion and mass transfer processes and makes use of the film concept. Sometimes, the film theory is considered to be an oversimplification for crystallization and is replaced by a random surface removal theory (20-23). For both theories the rate of crystal growth (dm/dt) is given by equation XVII, where m, is the mass of solid deposited in time t k, the mass transfer coefficient by diffusion. A, the surface area of the crystal, c, the concentration in the supersaturated solution and Cj, the concentration at the crystal-solution interface (3). For the stagnant film and random surface removal model, equations XVIII and XIX can be used, respectively (3,4) D is the diffusion coefficient, x, the film thickness and f, the fractionai rate of surface renewal. 

Since the earlier treatments of this problem by Ramachandran and Sharma(4) and Uchida et.al.(7).several experimental studies and verifications of predictions of enhancement factors have been reported(7,15,16) several detailed models based on film concept have also been proposed(7-12).Recently a penetration model for an instantaneous irreversible chemical reaction has also been presented.which however differs numerically only negligibly than the film model(13).The most important modification of Ramachandran and Sharma s treatment is due to Uchida et. al.(7-9) who consider that the rate of solid dissolution may be accelerated by the absorption of gas as discussed above.They have also considered the case where the concentration of solid component in the bulk liquid phase may not be maintained at the saturation solubility(that is,"finite" slurry) which occurs of course when the rate of solid dissolution is relatively slow compared with gas absorption rate(8).The case where the solid dissolution is finite was further considered by Sada et.al.(12) both theoretically and experimentally.Uchida et.al.(8) could also explain the data of Takeda et.al.(14) by their modified model.Analytical solutions presented above are for instantaneous reactions ... 

Two-film Concept. Let us now apply this concept to a typical transfer of a solute from one liquid to another nonconsolute liquid in contact with it, under steady-state conditions. Assuming both liquids to be in motion in a general direction parallel to the interface between them, there will exist concentration gradients in both phases which act as driving forces for the transfer, and the resistance to diffusion can be represented by an effective film thickness for each phase. This picture of the complete mass-transfer process was first introduced by Whitman (16, 31), who also postulated that at the interface itself equilibrium would be established. The concentrations in each phase on either side of the interface and immediately in contact with it would be such that they correspond to an indefinitely long time of contact. There is no direct evidence to prove the latter concept indeed there have been a few experiments reported indicating the contrary (12). Nevertheless the general conclusions based on the assumption appear to be valid. 

In two-phase downflow and upflow fixed-bed reactors, gas-liquid mass transfer resistance can be detrimental to the overall reactor performance [14, 32]. Therefore, accurate estimation of gas-liquid mass transfer parameters is important for achieving successful reactor design or scale-up. The overall gas-liquid mass transfer coefficient may be expressed, according to the two-film concept, in terms of the liquid-side and the gas-side mass transfer coefficients ... 

Figure4.4.1 Two-film concept (stagnant film model) for gas-liquid mass transfer of component A.

Figure 4.4.3 Two-film concept for a gas-liquid reaction with a relatively slow rate of chemical reaction (thus the reaction mainly takes place in the bulk phase of the liquid).

The cast film process was developed in the late 1940s primarily by scientists at ICI, DuPont and Union Carbide. An early description of the cast film process was published in British Patents 474,426 (ICI) and 561,373 (DuPont).The cast film concept filed on June 26, 1948, and published as U.S. Patent 2,586,820, issued on February 26,1952, to WE Hemperly ef a/, and assigned to Union Carbide is shown in Figure 6.18. 

Transport Driven by a Potential Difference The Film Concept and the Mass Transfer Coefficient... 

We have thus reduced a complex nonlinear situation to one that fits the linear driving force and film concepts and agrees with the tabulations of Table 1.3. 

The two-film concept (a) mass transfer (b) heat transfer. 

The two-film concept can also be applied to heat transfer operations, as shown in Figure 1.7b. The process is similar to that of mass transport, but differs from it in two important aspects. Eirst, the two fluids (hot and cold) are usually, but not always, separated by a solid partition. This is in contrast to mass transfer operations where direct contact of the phases is the norm. Second, no phase-equilibrium relation needs to be invoked at the interface. Instead, convergence of the two temperature profiles on either side of an interface leads to one and the same temperature at this point. No jiunp-discontinuities in temperature occur at any location along an interface. We... 

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