Modified effective binary approach

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) 

Zhang (1993) used this approach successfully to model concentration profiles from crystal dissolution experiments. The applicability needs to be investigated further. To establish this method, a major effort is necessary to extract and compile V values for geological applications. 

A more rigorous way to generalize Pick s law is to use phenomenological equations based on linear irreversible thermodynamics. In this treatment of an N-component system, the diffusive flux of component i is (De Groot and Mazur, 

The entropy production during diffusion in a multicomponent system is (Appendix 1) 

Choosing an appropriate reference frame such as a = 1 for all k, the diffusivity matrix can be written as 

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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) ... 

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. 

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. 

A success/failure approach will be particularly effective if the endpoint is already binary, for example cured/not cured in a trial of an anti-infective. In the earlier discussion of modified ITT the CPMP (1997) Note for Guidance on the Evaluation of New Anti-bacterial Medicinal Products goes on to say Patients who have no measurements after baseline are included as failures in the analysis. ... 

Vetere " proposed combining the FH equation (empirically modified to account for free-volume effects) with the NRTL expression for the energetic effects. The two NRTL parameters were correlated with the solubility parameters of the components. The relative importance of the combinatorial and residual contributions was analyzed and satisfactory results (for both VLB and LLE) are obtained for some binary systems, including aqueous polymer solutions. This recent approach is under development. 

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