Stagnant-film model

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 

The film model referred to in Chapters 2 and 5 provides, in fact, an oversimplified picture of what happens in the vicinity of the interface. Based on the film model 

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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. 

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-... 

This can be further integrated from the wall to the boundary layer thickness y = 8, where the component is at the bulk concentration Cj,. Substituting / = - o and k = D/o, the mass-transfer coefficient yields the stagnant film model [Brian, Desalination by Reverse Osmosis, Merten (ed.), M.I.T. Press, Cambridge, Mass., 1966, pp. 161-292] ... 

Figure 1 Stagnant film model for dissolution of acidic drug (HA) in solution with base (B). (From Ref. 2.)...

Figure 7 Stagnant film model (top) and reaction plane model (bottom) for micelle-facilitated dissolution.

The sea-to-air flux of DMS in the study area was calculated to be about 4.4 /imol m 2d 1 over the open ocean (Drake Passage) and about 1.2 /imol m d 1 from the inshore waters of Gerlache and Bransfield Strait (121. The calculations were based on a simple parameterization of the stagnant film model (22). The results are estimated to be uncertain by a factor of 2 (1). The difference between the open ocean and inshore area values can be attributed mainly to differences in wind velocities rather than sea surface temperatures or aqueous DMS concentrations between both regions. 

Figure 5.2 The most common kinetic model used to estimate rates of gas exchange across the atmosphere-water boundary is the Stagnant Film Model. This model essentially has the following three regions of importance (1) a well-mixed turbulent atmospheric zone (PG) (2) a well-mixed thin-film liquid zone (PG) and (3) a laminar zone (A-B) separating the two turbulent regions. The thin-film is considered permanent with a thickness defined as z- (From Broecker and Peng, 1974, with permission.)...

In situations where equilibrium conditions are not applicable, rates of gas exchange across the atmosphere-water boundary can be made using kinetic models such as the Stagnant Film Model. 

Stagnant film model kinetic model used to calculate rates of gas exchange across the... 

A stagnant film model is used for two-phase boundaries (1-2), which in effect, isolates the mass transfer process to a thin region at the interface stagnant film. Once the expressions for entropy production in terms of pressure, temperature, and composition are available a transformation is made to process variables such as reflux ratio, column height, packing or tray geometry, column diameter and column efficiency. Results of this design optimization model are compared with the results obtained via traditional methods. 

The stagnant-film model discussed previously assumes a steady state in which the local flux across each element of area is constant ... 

Figure 11-4 Concentration profile for EMCD in stagnant film model...

In this stagnant film model, we consider all the resistance to mass transfer to be lumped into the thickness 5. The reciprocal of the mass transfer coefficient can be thought of as this resistance... 

However, in a similar analysis based on the classical stagnant film model for a steady-state continuous flow membrane... 

Four of the simplest and best known of the theories of mass transfer from flowing streams are (1) the stagnant-film model, (2) the penetration model, (3) the surface-renewal model, and (4) the turbulent boundary-layer model... 

The stagnant-film model was proposed by Nernst28 in 1904. The model may be described by visualizing the passage of a gas stream containing components A... 

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