Film-penetration theory

The penetration and film-penetration theories have been developed for conditions of equimolecular counterdiffusion only the equations are too complex to solve explicitly for transfer through a stationary carrier gas. For gas absorption, therefore, they apply only when the concentration of the material under going mass transfer is low. On the other hand, in the two-fihn theory the additional contribution to the mass transfer which is caused by bulk flow is easily calculated and hp (Section 10.23) is equal to (D/L)(Cr/Cum) instead of D/L. 

These relations between the various coefficients are valid provided that the transfer rate is linearly related to the driving force and that the equilibrium relationship is a straight line. They are therefore applicable for the two-film theory, and for any instant of time for the penetration and film-penetration theories. In general, application to time-averaged coefficients obtained from the penetration and film-penetration theories is not permissible because the condition at the interface will be time-dependent unless all of the resistance lies in one of the phases. 

As noted previously, for equimolecular counterdiffusion, the film transfer coefficients, and hence the corresponding HTUs, may be expressed in terms of the physical properties of the system and the assumed film thickness or exposure time, using the two-film, the penetration, or the film-penetration theories. For conditions where bulk flow is important, however, the transfer rate of constituent A is increased by the factor Cr/Cgm and the diffusion equations can be solved only on the basis of the two-film theory. In the design of equipment it is usual to work in terms of transfer coefficients or HTUs and not to endeavour to evaluate them in terms of properties of the system. 

What are the general principles underlying the two-film, penetration and film-penetration theories for mass transfer across a phase boundary Give the basic differential equations which have to be solved for these theories with the appropriate boundary conditions. 

Film-penetration theory, 1 47 Film processors, one-step, 19 276-278 Film production process, preservation of stoichiometry during, 24 739 Film properties... 

DeLancey GB. Multicomponent film-penetration theory with linearized kinetics— I. Linearization theory and flux expression. Chem Eng Sci 1974 29 2315-2323. 

An important variation of the model of Mickley and Fairbanks is the film penetration model developed by Yoshida et al. [48] by treating packets as a continuum with a finite thickness (8em). The film penetration theory includes two extremes of emulsion behavior. On one extreme, the packet contacts the heating surface for a short time so that all the heat entering the packet is used to heat up the packet (penetration theory) while none passes through it. On the other extreme, the packet stays at the surface long enough to achieve steady state and simply provides a resistance for heat conduction. 

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. 

Z[ thickness of laminar surface layer in the film-penetration theory... 

Thie film-penetration theory, presented by Toor and Marchello, represents a combination of the three earlier theories reviewed above. The entire transfer resistance is conside to lie in a laminar surface layer of thickness Zt, where is uniform at ca. for all z greater than Zl- Surface renewal occurs by eddies that penetrate the surface from the bulk of the phase. Thus, transfer through young elements of surface obeys the penetration theory (k transfer through old elements follows the film theory (k D), and transfer through elertients of intermediate age is characterized by bmh rrrechanisms. 

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