Ternary diffusion coefficients

Typical diffusion coefficients for gases are shown in Table 7.4-1. These values are not experimental, but are calculated from the Chapman-Enskog theory (see Section 5.1) and from Table 7.1-1. The first two rows in the table show how the values of D12 and 21 are larger as the solution becomes concentrated. The second and third rows refer to the same solution but with a different species chosen as the solute. The difference in the diffusion coefficients illustrates why ternary diffusion coefficients can be difficult to interpret. The final three rows are other characteristic situations. 

Note All coefficients have units of square centimeters per second and are calculated from the equations in Table 7.1-1. 

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Fig. 16. Graphically smoothed data for calculated ternary diffusion coefficients in a system with a uniform concentration of dextran T500 (Hw 500,000) with an imposed 5 kg m-3 concentration gradient of PVP 360 the dextran concentration is varied...

When all ternary diffusion coefficients are known, we can predict the concentration gradients of all components35 > and therefore density gradients in the system at any time. 

Lee] Lee, Byeong-Joo, Ternary Diffusion Coefficients and Phase Diagram in Fe-M-C Systems , J. Korean Inst. Metal Mater., 32(2), 214-223 (1994) (Calculation, Thermodyn., Kinetics, 33)... 

The theory of the Taylor dispersion technique is well described in the literature [11-20], and so the authors only indicate some relevant points concerning this method on the experimental determination of binary and ternary diffusion coefficients (Figure 2). 

Also, from the measurements of diffusion coefficients of the ternary systems already studied (e.g., y -cyclodextrin plus caffeine [15], 2-hydroxypropyl-p-cyclodextrin plus caffeine [16], CuCl (1) plus caffeine [10], and KCl plus theophylline (THP) [18]), it is possible to give a contribution to the understanding of the stmcture of electrolyte solutions and their thermodynamic behavior. For example, by using Equations (22) and (23), and through the experimental tracer ternary diffusion coefficients of KCl dissolved in supporting THP solutions, D (c/c = 0) and tracer ternary diffusion coefficients of THP dissolved in supporting KCl solutions, D°2 (c /Cj = 0) [18], it will be possible to estimate some parameters, such as the diffusion coefficient of the aggregate between KCl and THP [18] and the respective association constant. 

Table 1 Ternary diffusion coefficient from a single experiment (noise level...

The ternary diffusion coefficient strongly depends on the solution concentration. In order to calculate accurate mass transfer coefficients, experimental data of diffusion coefficients at the interest concentrations and temperatures are necessary. However, data are not available at concentrations and temperature used at the present study, it was assumed that the ternary diffusion coefficients were equal to the binary diffusion coefficients. The binary diffusion coefficients of the KDP-water pairs and the urea-water pairs were taken from literature (Mullin and Amatavivadhana, 1967 Cussler, 1997). The values were transformed into the Maxwell-Stefan diffiisivities using the thermodynamic correction factor. 

The main seope of our work shown here is to present the experimental studies eoneeming the transport properties of systems containing calcium ions and caffeine, and some ab initio calculations. On the other words, we present ternary diffusion coefficients D, and for the system containing calcium chloride and caffeine, for concentrations of each component between 0.0025 M and 0.05 M and at 25 C and 37 C, using a specially designed apparatus built for measuring diffusion coefficients based on the Taylor technique (studies already done and indicated in the literature [4]). In addition, for the same systems and for the same temperatures, we report new viscosity and densities measurements. To obtain a better understanding of the structure of the chemical species formed, we have complemented these studies with ab initio calculations. 

TABLE 2 Ternary diffusion coefficients, and for aqueous calcium... 

Nonetheless, some concentrated systems are best described using multicomponent diffusion equations. Examples of these systems, which commonly involve unusual chemical interactions, are listed in Table 7.0-1. They are best described using the equations derived in Section 7.1. These equations can be rationalized using the theory of irreversible thermodynamics, a synopsis of which is given Section 7.2. In most cases, the solution to multi-component diffusion problems is automatically available if the binary solution is available the reasons for this are given in Section 7.3. Some values of ternary diffusion coefficients are given in Section 7.4 as an indication of the magnitude of the effects involved. Finally, tracer diffusion is detailed as an example of ternary diffusion in Section 7.5. 

Table 7.1-1 Ternary diffusion coefficients known functions of binary values for ideal gases...

Ternary diffusion coefficients in liquids and solids cannot be found from binary values, but only from experiments. When experiments are not available, which is usually the case, one can make estimates by assuming that the Onsager phenomenological coefficients are a diagonal matrix that is. 

Experimental values of ternary diffusion coefficients characteristic of liquids are shown in Table 7.4-2. In cases like KCl NaCl water, KCl sucrose-water, and tolu-ene-chlorobenzene-bromobenzene, the cross-term diffusion coefficients are small, less than ten percent of the main diffusion coefficients. In these cases, we can safely treat the diffusion as a binary process. 

Because air is really a misture, the exact solution involves ternary diffusion coefficients that can be calculated from Table 7.1-1. Calculate the ternary concentration profile and compare it with the binary one (S. Gehrke). 

Use these data to calculate the four ternary diffusion coefficients, and compare them with the following values found with the Gouy interferometer Du = 0.497,7>i2 = 0.021,... 

A few experimental values of a are shown in Table 21.5-1. The values of a are frequently small, especially in dilute solution. They are largest for solutes of very different molecular weights or for highly nonideal solutions. They are more nearly constant for near-ideal solutions and are concentration-dependent in nonideal liquid mixtures. In short, they behave much like the ternary diffusion coefficients discussed in Chapter 7. They are usually of minor practical importance, even though they can be used to effect surprisingly good separations. 

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