Diffusion through a Stagnant Film

Two modes of transport (a) equimolar counterdiffusion (b) diffusion through a stagnant film. 

Rate Laws and Transfer Coefficients for Equimolar Diffusion 

Conversion from Equimolal to Stagnant Film Coefficients 

We now introduce a clever device to reduce the nonlinear terms in Equation 1.18c to the product of a linear driving force in the diffusing species A, Pai Pah a constant mass transfer coefficient Icq. This is done by writing  

Using the definition of the log-mean pressure difference given by Equation 1.13 and setting Z2 - Zj = Zp as before, we obtain 

Two special cases of Equation 1.15a are to be noted equimolar counterdiffusion and diffusion through a stagnant film. 

Mass Transfer and Separation Processes Principles and Applications 

SO that Equation 1.15b, after solving for NJA, is reduced to the expression 

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Diffusion through a stagnant film, as in absorption or stripping processes involving the transfer of a single component between liquid and vapor phases. Since there is a concentration gradient... 

Figure 13.44. Factors in Eqs. (13.239) and (13.240) for HTUs of liquid and vapor films and slopes m and m" of the combining Eqs. (13.235) and (13.236) [Bolles and Fair, Inst. Chem. Eng. Symp. Ser. 56(2), 3.3/3.S, (1979)]. (a) Definitions of slopes m and m" in Eqs. (13.235) and (13.236) for combining liquid and gas film HTUs / = 1 for equimolal counter diffusion / = (jtB)mean for diffusion through a stagnant film, (b) Factor (j> of the liquid phase Eq. (13.239). (c) Factor C of the liquid phase, Eq. (13.239). (d) Factor ip of the gas phase, Eq. (13.240), for metal pall rings.

Differentiating Equation (6.2.6) (assuming constant diffusivity) and combining with Equation (6.2.7), yields the following differential equation that describes diffusion through a stagnant film ... 

The previous two sections describe separately the significant role that diffusion through a stagnant film surrounding a catalyst pellet and transport through the catalyst pores can play in a solid-catalyzed chemical reaction. However, these two dif-fusional resistances must be evaluated simultaneously in order to properly interpret the observed rate of a catalytic reaction. 

If we had assumed diffusion through a stagnant film (W, = 0 and B/ — yA A) rather than dilute concentration or equal molar counter diffusion (B z = 0), we could use the solution procedure discussed above (see the CD-ROM), starting with... 

We see that for the case of diffusion through a stagnant film the flux is greater. Why is this ... 

For diffusion through a stagnant film, the mole fraction profile is shown on the CD-ROM to be yAf>-... 

The film theory is the simplest model for interfacial mass transfer. In this case it is assumed that a stagnant film exists near the interface and that all resistance to the mass transfer resides in this film. The concentration differences occur in this film region only, whereas the rest of the bulk phase is perfectly mixed. The concentration at the depth I from the interface is equal to the bulk concentration. The mass transfer flux is thus assumed to be caused by molecular diffusion through a stagnant film essentially in the direction normal to the interface. It is further assumed that the interface has reached a state of thermodynamic equilibrium. 

The third condition, diffusion through a stagnant film, does not occur as often and is discussed in the summary notes and the solved problems on the CD. The fourth condition is the one we have been discussing up to now for plug flow and the PFR, that is. 

This problem is reworked for diffusion through a stagnant film in (he solved example problems on the CD-ROM/web solved problems. 

EFFECT OF ONE-WAY DIFFUSION. As shown previously, when only component A is diffusing through a stagnant film, the rate of mass transfer for a given concentration difference is greater than if component B is diffusing in the opposite direction. From Eqs. (21.19) and (21.24), the ratio of the fluxes is... 

In a multicomponent system, the diffusivity of A is estimated by assuming that it diffuses through a stagnant film of the other gases. Then the overall diffusivity, say, of component j can be calculated from the various constituent binary diffusivities using one of the following two equations (the second is slightly more accurate) ... 

The HTU-NTU analysis for concentrated absorbers and strippers with one solute is somewhat more conplex than for distillation because total flow rates are not constant and solute A is diffusing through a stagnant film with no counterdiffusion, Ng = 0. We will assume that the system is isothermal. For stagnant films with Ng = 0, Eqs. (15-32a-fl are the appropriate mass transfer equations. The flux equation is (repeat of Eqs. 15-32). 

In considering the transport of a species from a fluid in turbulent flow toward a solid surface, for example, an electrochemically active species to an electrode, Nemst assumed that the transport was governed by molecular diffusion through a stagnant film of fluid of thickness 6. This model, although having questionable physical relevance, is quite useful for correlating effects such as the influence of chemical reaction on mass transfer. A few simple examples of the use of film theoiy to describe mass transfer in the presence of chemical reaction are considered here. 

Rate Laws and Transfer Coefficients for Diffusion through a Stagnant Film... 

Equimolar Counterdiffusion and Diffusion through a Stagnant Film The Log-Mean Concentration Difference... 

Example 3.4-1 Fast diffusion through a stagnant film and into a semi-infinite slab Find differential equations describing these two situations from the general equations in Tables 3.4-1 to 3.4-3. Compare your results with the shell-balance results in the previous section. 

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