Film models model

R. J. Pugh and E. Manev, The Study of Thin Aqueous Films as Models for Froths and Flotation," in Innovations in Flotation Technology, P. Mavros and K. A. Matis, eds., Kluwer, 1992, pp. 1-24. 

The Shei wood-number relation for gas-phase mass-transfer coefficients as represented by the film diffusion model in Eq. (5-286) can be rearrangecTas follows ... 

The stagnant-film model discussed previously assumes a steady state in which the local flux across each element of area is constant i.e., there is no accumulation of the diffusing species within the film. Higbie [Trans. Am. Jn.st. Chem. Eng., 31,365 (1935)] pointed out that industrial contactors often operate with repeated brief contacts between phases in which the contact times are too short for the steady state to be achieved. For example, Higbie advanced the theory that in a packed tower the liquid flows across each packing piece in laminar flow and is remixed at the points of discontinuity between the packing elements. Thus, a fresh liquid surface is formed at the top of each piece, and as it moves downward, it absorbs gas at a decreasing rate until it is mixed at the next discontinuity. This is the basis of penetration theoiy. 

The predictions of correlations based on the film model often are nearly identical to predictions based on the penetration and surface-renewal models. Thus, in view of its relative simphcity, the film model normally is preferred for purposes of discussion or calculation. It should be noted that none of these theoretical models has proved adequate for maldug a priori predictions of mass-transfer rates in packed towers, and therefore empirical correlations such as those outlined later in Table 5-28. must be employed. 

Effects of High Solute Concentrations on Ug and As discussed previously, the stagnant-film model indicates that fcc should be independent of ysM and/cc should be inversely proportional to The data of Vivian and Behrman [Am. Tn.st. Chem. Eng. J., 11, 656 (1965)] for the absorption of ammonia from an inert gas strongly suggest that the film model s predicted trend is correct. This is another indication that the most appropriate rate coefficient to use is fcc. nd the proper driving-force term is of the form (y — yd ysM-... 

On tbe basis of tbe two-film model for mass transfer, and relating all efficiencies to gas-pbase concentrations (for convenience only a similar development can be made on tbe basis of bquid concentrations), point efficiency can be expressed in terms of transfer units ... 

Although our simple oxide film model explains most of the experimental observations we have mentioned, it does not explain the linear laws. How, for example, can a material lose weight linearly when it oxidises as is sometimes observed (see Fig. 21.2) Well, some oxides (e.g. M0O3, WO3) are very volatile. During oxidation of Mo and W at high temperature, the oxides evaporate as soon as they are formed, and offer no barrier at all to oxidation. Oxidation, therefore, proceeds at a rate that is independent of time, and the material loses weight because the oxide is lost. This behaviour explains the catastrophically rapid section loss of Mo and W shown in Table 21.2. 

A more rigorous seheme of gas-liquid ehemieal reaetion and absorption followed by preeipitation is deseribed based on the film model (Englezos etai, 1987a,b Waehi and Jones, 1990 1991a Skovborg and Rasmussen, 1994). The eoneept is illustrated in Figure 8.13. 

Film-crystal model concentration profiles of A, B and C and particle number density distributions are shown in Figure 8.14(a). 

The data plotted in the figure clearly support the predicted positive dependence of crystal size on agitation rate. Precipitation in the crystal film both enhances mass transfer and depletes bulk solute concentration. Thus, in the clear film model plotted by broken lines, bulk crystal sizes are initially slightly smaller than those predicted by the crystal film model but quickly become much larger due to increased yield. Taken together, these data imply that while the initial mean crystal growth rate and mixing rate dependence of size are... 

Fig. 8.2 Strain-generated active path mechanisms, (a) Often referred to as the film rupture model and (b) the slip step dissolution model. In both cases growth is by dissolution film rupture is the rate controlling step, not the mechanism of crack growth...

Jss Flux obtained experimentally or from the film-model... 

D. Film-Penetration Model with Simultaneous Chemical Reaction. 341... 

A. Absorption in Agitated Liquid with Simultaneous Chemical Reaction—Film Model... 

Fig. 6. Film model for diffusion with simultaneous irreversible first-order chemical reaction [after Lightfoot (L5)].

The penetration theory holds for the region where t is much less than L2jD, the film theory for the region where t is much greater than L2/D. This comparison is shown in Fig. 8, which clearly shows that the film and penetration theories are asymptotes of the film-penetration model. 

Fig. 8. Comparison of film-penetration model with film and penetration models [after Toor and Marchello (T5)].

In 1963 and in 1965, Huang and Kuo (H18, H19) applied the film penetration model to the mechanism of simultaneous mass transfer and chemical reaction. 

In the film-penetration model (H19), it is assumed that the reactant A penetrates through the surface element by one-dimensional unsteady-state molecular diffusion. Convective transport is assumed to be insignificant. The diffusing stream of the reactant A is depleted along the path of diffusion by its reversible reaction with the reactant B, which is an existing component of the liquid surface element. If such a reaction can be represented as... 

For mass transfer with irreversible and reversible reactions, the film-penetration model is a more general concept than the film or surface renewal models which are its limiting cases. 

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. 

Using a steady-state film model, obtain an expression for the mass transfer rate across a laminar film of thickness /. in the vapour phase for the more volatile component in a binary distillation process ... 

The gas phase mass transfer coefficient for the absorption of ammonia into water from a mixture of composition NHj 20%, N2 73%, Hj 7% is found experimentally to be 0.030 m/s. What would you expect the transfer coefficient to be for a mixture of composition NH3 5%, N2 60%, Hj 35% All compositions are given on a molar basis. The total pressure and temperature are die same in both cases. The transfer coefficients are based on a steady-state film model and the effective film thickness may be assumed constant. Neglect the solubility of Ny and Hi in water. 

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 ... 

Zhu L, Susac D, Teo M, Wong KC, Wong PC, Parsons RR, Bizzotto D, Mitchell KAR, Campbell SA (2008) Investigation of CoSa-based thin films as model catalysts for the oxygen reduction reaction. J Catal 258 235-242... 

We have undertaken a series of experiments Involving thin film models of such powdered transition metal catalysts (13,14). In this paper we present a brief review of the results we have obtained to date Involving platinum and rhodium deposited on thin films of tltanla, the latter prepared by oxidation of a tltanliua single crystal. These systems are prepared and characterized under well-controlled conditions. We have used thermal desorption spectroscopy (TDS), Auger electron spectroscopy (AES) and static secondary Ion mass spectrometry (SSIMS). Our results Illustrate the power of SSIMS In understanding the processes that take place during thermal treatment of these thin films. Thermal desorption spectroscopy Is used to characterize the adsorption and desorption of small molecules, In particular, carbon monoxide. AES confirms the SSIMS results and was used to verify the surface cleanliness of the films as they were prepared. 

The tltanla-based thin film catalyst models were constructed by first oxidizing the titanium surface In 5 x 10 torr of O2 for approximately 30 minutes at 775 K. This produced an AES llneshape consistent with fully oxidized TIO2. The metal was then vapor deposited onto the oxide support with the latter held at 130 K. The thickness of the metal overlayer and Its cleanliness were verified by AES. After various annealing and adsorption procedures, these thin films were further characterized using SSIMS, AES and TDS. For comparison, some work was done with Pt on Al20s. In this case a Mo foil covered with AI2O3 replaced the Tl(OOOl) substrate. 

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