Diffusion modified effective binary

Below, the effective binary approach and the concentration-based diffusivity matrix are introduced. The modified effective binary approach (Zhang, 1993) has not been followed up. The approach using the activity-based diffusivity matrix, similar to activity-based diffusivity T> (Equations 3-61 and 3-62), is probably the best approach, but such diffusivities require systematic effort to obtain. 

Despite the various drawbacks, the effective binary approach is still widely used and will be widely applied to natural systems in the near future because of the difficulties of better approaches. For major components in a silicate melt, it is possible that multicomponent diffusivity matrices will be obtained as a function of temperature and melt composition in the not too distant future. For trace components, the effective binary approach (or the modified effective binary approach in the next section) will likely continue for a long time. The effective binary diffusion approach may be used under the following conditions (but is not limited to these conditions) with consistent and reliable results (Cooper, 1968) ... 

Zhang (1993) proposed the modified effective binary approach (also called activity-based effective binary approach). In this approach, the diffusive flux of a component is related to its activity gradient and all other components are treated as one combined component. The diffusive flux for any component i is expressed as (by analogy with Equation 3-61)... 

In principle, the diffusion matrix approach can be extended to trace elements. My assessment, however, is that in the near future diffusion matrix involving 50 diffusing components will not be possible. Hence, simple treatment will still have to be used to roughly understand the diffusion behavior of trace elements the effective binary diffusion model to handle monotonic profiles, the modified effective binary diffusion model to handle uphill diffusion, or some combination of the diffusion matrix and effective binary diffusion model. 

To quantify the diffusion profiles is a difficult multicomponent problem. The activity-based effective binary diffusion approach (i.e. modified effective binary approach) has been adopted to roughly treat the problem. In this approach. 

A modified effective binary diffusion model. /. Geophys. Res. 98, 11901-... 

Above we have stated that over a substantial range of gas densities, essential parts of the profiles of collision-induced absorption spectra are invariant if normalized by density squared, a/q2, in pure gases, or by the product of densities, cl/q Q2, in mixed gases. Induced spectra that show this density-squared dependence may be considered to be of a binary origin. Above, we have seen examples that at very low frequencies many-body effects may cause deviations from the density-squared behavior at any pressure, over a limited frequency band near zero frequency (intercol-lisional effect). Furthermore, with increasing densities, a diffuse N-body effect with N > 2 more or less affects most parts of the observable spectra. It is interesting to study in some detail how the three-body (and perhaps higher-order) interactions modify the binary profiles. 

C.2. Modify the program of problem 6.C. 1 to account for external mass transfer resistance, given the effective binary diffusivities Djf of each species in the external fluid, the Sherwood number Sh, and the bulk concentrations cjh- Report yonr resnlts for the parameter values of problem 6.C. 1, replacing the known snrface concentrations with those computed by external mass transfer with... 

A modified Cahn-Hilliard (CH) model [114] is used for the theoretical analysis of the impact of thermal diffusion on phase separation by taking into account an inhomogeneous temperature distribution, which couples to a concentration variation via the Soret effect. The Flory-Huggins model is used for the free energy of binary polymer-mixtures. The composition is naturally measured in terms of volume fraction 0 of a component A, which can be related to the weight fraction c by... 

An interesting technique for the measurement of intraparticle diffusivity as well as longitudinal diffusion in the particle bed has been described by Deisler and Wilhelm (21). It deviates from all other techniques mentioned in that it is based on a dynamic flow study, analyzing the effect of the particles on the propagation of a sinusoidal variation of composition of a binary gas mixture passed through the catalyst bed. The authors have demonstrated the versatility of their general technique for determination of diffusion properties, as well as adsorption equilibria between the solids and the gas composition employed. If this general technique were modified to measure specifically the particle diffusivity, a very convenient and accurate method may result. 

The analysis of macropore diffusion in binary or multicomponent systenis presents no particular problems since the transport properties of one compos nent are not directly affected by changes ini the concentration of the bther components. In an adsorbed phase the situation is more complex since ih addition to any possible direct effect on thei mobility, the driving force for each component (chemical potential gradient is modified, through the multi-component equilibrium isotherm, by the coiicentration levels of all components in the system. The diffusion equations for each component are therefore directly coupled through the equilibrium relationship. Because of the complexity of the problem, diffusion in a mixed adscjrbed phase has been studied tjs only a limited extent. 

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