Combination film-surface renewal theory

Thefilm-penetraticn theory, presented by Toor and Marchello,23 represents a combination of the three earlier theories reviewed above. The entire transfer resistance is considered to lie in a laminar surface layer of thickness zL, where cA is uniform at cA for aft 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 otd elements follows the film theory k D), and transfer through elements of intermediate age is characterized by both rnechanisres. 

The surface renewal models only consider the liquid phase. In Sec. 6.3 on the film model the resistances of both gas and liquid phase were combined into one single expression like Eq. 6.3.b-5. The same can be done here Danckwerts [24] has shown that in most cases the surface renewal models combined with a gas side resistance lead to the same rules for the addition of resistances as the two-film theory. 

The main transport parameters to be estimated are the mass transfer coefficients (gas-liquid (liquid side) fc , gas-liquid (gas side) kg, and liquid-solid fc )). Coupled to that is the estimation of the interfacial area per unit volume a, and often it is the combination (i.e., kia or kgO) that is estimated in a certain experimental procedure. Thermodynamic parameters, such as Henry s law constant (fZ) can be estimated in a simpler manner since their estimation on the flow or on any time-dependent phenomenon. Mass transfer coefticients may be evaluated in well-defined geometries with known flow fields using classical theories like film theory, penetration theory, surface renewal... 

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