Classical diffusional models

The model is based on the film theory and comprises the material and energy balances of a differential element of the two-phase volume in the packing. The classical film model shown in Fig. 10.2 is extended here to consider the catalyst phase (Fig. 10.6). A pseudohomogeneous approach is chosen for the catalyzed reaction (see also [89, 90]), and the correspondent overall reaction kinetics is determined by fixed-bed experiments [9]. This macroscopic kinetics includes the influence of the liquid distribution and mass-transfer resistances at the liquid-solid interface as well as diffusional transport phenomena inside the porous catalyst. 

The diffusional transport model for systems in which sorbed molecules can be divided in two populations, one formed by completely immobilized molecules and the other by molecules free to diffuse, has been developed by Vieth and Sladek 33) in a modified form of the Fick s second law. However, if linear isotherms are experimentally found, as in the case of the DGEBA-TETA system in Fig. 4, the diffusion of the penetrant may be described by the classical diffusion law with constant value of the effective diffusion coefficient,... 

The tortuosity term is intended to account for increases in diffusional path length due to windiness. Classical descriptions of the tortuosity predict a value of 1 to 3 for random porous media (.2.). Since the tortuosities inferred by these models are orders of magnitude greater than expected, other physical properties of the system must be important in determining release rates. Since continuum diffusion models provide an incomplete description of the release from these devices, the microscopic details of the system must be considered explicitly. 

An integration constant has been voluntarily added for allowing this relation to be inverted, as explained earlier in the classical approach, in order to retrieve Equation G7.5. This integration constant is the unperturbed concentration far from the place where the diffusional process occurs, meaning that this model applies to infinite (or semi-infinite) transient diffusion. 

Before complex thermodynamic models including explicit kinetics (here the diffusional transport of reactive elementary or molecular species) are employed, it is most useful to obtain, with the aid of classical thermochemical calculations, a picture of the momentary situation, i.e. of the frozen-in state at a certain moment in time. For that purpose the databank system FactSage provides two modules which are particidarly suited Equilib and Phase Diagram. 

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