Diffusion in ternary systems

Let us now turn our attention to n-component mixtures. Exact analytical solutions of the Maxwell-Stefan equations for a film model can be obtained for a mixture of ideal gases for which the binary diffusion coefficients are independent of composition and identical to the diffusivity of the binary gas i-k pair. Solutions of the Maxwell-Stefan equations for certain special cases involving diffusion in ternary systems have been known for a long time (Gilliland (1937) = 0) Pratt (1950) (TV, = 0) Cichelli et al. (1951) Toor (1957),... 

Semen V. Kornienko PhD (1999). Chair of Theoretical Physics. Having graduated from Cherkassy National University with the degree in physics, he defended his PhD thesis at Kharkov National University. His field of expertise includes nucleation, inter- and reactive diffusion in ternary systems, phase growth under electromigration, diffusion with nonequilibrium vacancies. 

Diffusive dissolution in ternary systems analysis with applications to... 

Polymer transport in ternary systems including an analysis of the cross diffusion coefficients and component distribution within the systems. 

In earlier chapters we examined systems with one or two types of diffusing chemical species. For binary solutions, a single interdiffusivity, D, suffices to describe composition evolution. In this chapter we treat diffusion in ternary and larger multicomponent systems that have two or more independent composition variables. Analysis of such diffusion is complex because multiple cross terms and particle-particle chemical interaction terms appear. The cross terms result in TV2 independent interdiffusivities for a solution with TV independent components. The increased complexity of multicomponent diffusion produces a wide variety of diffusional phenomena. 

There are extensive reviews of the many measurements of the Ay, particularly in ternary systems [1]. Numerous systems exhibit uphill diffusion, due to strong particle-particle interactions, and efforts have been made to interpret the diffusivity behavior in terms of thermodynamic activity data and particle-particle interaction models. In many cases the diffusion behavior has been explained, and more details and discussion are found in Kirkaldy and Young s text [1]. 

Estimations for nonideal mixtures need six diffusivities at infinite dilution and three diffusivities of the type D kl x. Negative diffusion coefficients can exist in ternary systems and are consistent with the nonequilibrium thermodynamics approach. 

Figure 5.2. The diffusion flux as a function of the composition gradient for (a) binary and (h) ternary systems. Note the diffusion barrier, the osmotic diffusion point and the region of reverse diffusion that are possible in ternary systems.

Show that the effective diffusivity method leads to composition profiles in ternary systems that are straight lines when plotted on triangular diagrams. 

Then, there is the very serious difficulty that empirical extension of Tick s law to systems with more than two components leads to logical inconsistencies and major calculation difficulties tTaylor and Krishna. 1993 Wesselingh and Krishna. 2QQQ1 For example, in ternary systems, the Fickian diffusion coefficient is not symmetrical, Dy Djy, which means that additional constants are required. In addition, the values of... 

PROBLEM 6.10 Steady-state diffusion path in ternary system. 

The consequence of Eq. (1.2.42) is very significant in the sense that for a multi-component system, mutual diffusivities of all the components vanish at the spinodal curve. This has been clearly shown in binary (Caneba and Saxena, 1992) and even in ternary systems (Morral and Cahn, 1971) in the past. 

I 9 Diffusion Phase Competition in Ternary Systems rule,... 

At reaction-diffusion processes in ternary systems, the phase spectram of the diffusion zone, even for small annealing times, depends on the initial composition of the diffusion couple and on the set of diffusion parameters [28- 33]. Furthermore, the choice of the diffusion path may appear to be ambiguous [34, 35). In such a case, the stage of nucleation becomes a decisive one. 

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