Multicomponent film factor

Multicomponent Diffusion. In multicomponent systems, the binary diffusion coefficient has to be replaced by an effective or mean diffusivity Although its rigorous computation from the binary coefficients is difficult, it may be estimated by one of several methods (27—29). Any degree of counterdiffusion, including the two special cases "equimolar counterdiffusion" and "no counterdiffusion" treated above, may arise in multicomponent gas absorption. The influence of bulk flow of material through the films is corrected for by the film factor concept (28). It is based on a slightly different form of equation 13 ... 

Numerous investigators have attempted to control the precursor structure and related solution chemistry effects with varying degrees of success, to influence subsequent processing behavior, such as crystallization tempera-ture.40-42,78,109 110 Particular attention has been given to precursor characteristics such as structural similarity to the desired product and the chemical homogeneity of the precursor species. For multicomponent films, this latter factor is believed to influence the interdiffusional distances associated with the formation of complex crystal structures, such as perovskite compounds. Synthetic approaches have been geared toward the preparation of multimetal species with cation stoichiometry identical to that of the desired crystalline phase.40 42 83 84... 

Multicomponent polymers systems such as polyblends, and block copolymers often exhibit phase separation in the solid state which results in one polymer component dispersed in a continuous phase of a second component. The morphological properties of these systems depend upon a number of factors such as the molar ratios of the components, the molecular weights, the thermal history of the system and, for solvent cast films, the solvent and drying conditions. 

These values are within 5% of the values calculated with the penetration theory correction factor matrix and support our earlier suggestion that it is sufficient to use the simpler film model correction factor matrix in multicomponent mass transfer calculations at high mass transfer rates. ... 

The mass transfer outside catalyst particles was modelled with rigorous Maxwell-Ste n equations, along with simultaneous heat transfer [9]. The multicomponent mass transfer coefficient matrix was calculated by assuming a film model for mass transfer and estimating the jo factor for the packed bed [10], The mass transfer coefficient correlations were extended into multicomponent systems by approximate matrix function calculations [11]. 

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