Infinite-dilution diffusivity

Example 39 Estimate the Infinite Dilution Diffusivity of Propane... 

Hayduk-Laudie They presented a simple correlation for the infinite dilution diffusion coefficients of nonelectrolytes in water. It has about the same accuracy as the Wilke-Chang equation (about 5.9 percent). There is no explicit temperature dependence, but the 1.14 exponent on I compensates for the absence of T in the numerator. That exponent was misprinted (as 1.4) in the original article and has been reproduced elsewhere erroneously. 

Matthews, M.A. and Akgerman, A. Infinite dilution diffusion coefficients of methanol and 2-propanol in water. J. Chem. Eng. Data, 33(2) 122-123, 1988. 

Here D() is the infinite dilution diffusion coefficient, kd is the concentration coefficient and c is the concentration. A plot illustrating this behaviour is shown in Fig. 3.32. The concentration coefficient is given by (Vink 1985). 

Thus generally, for liquids D°AB D°BA. Different techniques with which to estimate the infinite dilution diffusion coefficient are described by Reid et al. [31]. Various correlation s (valid for an arbitrary composition of a binary mixture and for electrolytes) are also given. In the Wilke-Chang correlation for D°AB the effect of temperature has been accounted for by assuming D°AB — T. Although this approximation may be valid over small temperature ranges, it is usually preferable to assume that... 

This theory also gives good quantitative agreement with available experimental data for these properties. For example, for the non-LC backbone polymer polyisoprene [see Figure 3(a)] at infinite dilution in hexane [CHj-(Cl -CHj] in the I liquid phase at T - 293 K, the infinite dilution diffusion coefficient D g (in units of... 

As the mole fraction of either component in a binary mixture approaches unity, the thermodynamic factor E approaches unity and the Fick D and the Maxwell-Stefan D are equal. This result is shown clearly in Figures 4.1-4.3. The diffusion coefficients obtained under these conditions are the infinite dilution diffusion coefficients and given the symbol )°. 

TABLE 4.3 Infinite Dilution Diffusion Coefficients of Methanol and 2-Propanol in Water"... 

SOLUTION The Wilke-Chang equation is selected to illustrate the calculation of the infinite dilution diffusivities. The association factor for water is 2.26... 

The infinite dilution diffusivities computed from all four correlations are given in Table... 

SOLUTION We will use the Vignes method to estimate the MS diffusivity. Substituting the numerical values for the infinite dilution diffusivities and the mole fraction into Eq. 

DATA The infinite dilution diffusivities are (Tyn and Calus, 1975b)... 

Ideally one would like to be able to predict the elements of [D] from a knowledge of the infinite dilution diffusion coefficients f)°y. A comparison of the generalized Fick s law (Eq. 3.2.5), with the Maxwell-Stefan equations (Eq. 2.2.10) shows that, for a nonideal system, the... 

The infinite dilution diffusivities, )°y, are positive definite (cf. Eq. 2.3.21) and, consequently, Eq. 4.2.18 leads us to conclude that the >,y are positive definite everywhere in the composition space. 

M7L4 The infinite dilution diffusion coefficients >°y have been estimated as follows [10-" mVs] ... 

The infinite dilution diffusivities in the liquid phase [units are 10 m /s]... 

Carry out a review of methods for estimating infinite dilution diffusion coefficients in binary liquid mixtures. Your review should include calculations to test the accuracy of the methods that have been proposed. Fundamental data for computing the coefficients should be obtained from a single source as far as is possible we recommend the compilation by Daubert and Danner (1985). 

From the experimental data the infinite dilution diffusion coefficients can be determined as follows... 

Solution Although the liquids are somewhat viscous, fust estimate the infinite-dilution diffusivities using the Wilke-Chang correlation. Eq. (2.3-17). The molar volumes at the boiling point are estimated hy Shroeder s method10 as... 

In contrast to the case for gases, where an advanced kinetic theory to explain molecular motion is available, theories of the structure of liquids and their transport characteristics are still inadequate to allow a rigorous treatment. Liquid diffusion coefficients are several orders of magnitude smaller than gas diffiisivities, and depend on concentration due to the changes in viscosity with concentration and changes in the degree of ideality of the solution. As the mole fraction of either component in a binary mixture approaches unity, the thermodynamic factor T approaches unity and the Fick diffusivity and the MS diffusivity are equal. The diffusion coefficients obtained under these conditions are the infinite dilution diffusion coefficients and are given the symbol TP. 

Most methods for predicting D in concentrated liquid solutions attempt to combine the infinite dilution diffusion coefficients (D12)° and (D2,)° in a single function of composition. The Vignes formula is recommended by Reid et al. (1987) ... 

Estimate the MS and Fick diffusion coefficients for an acetone(l)-benzene(2) mixture of composition xx = 0.7808 at 298 K. The infinite dilution diffusivities are... 

These, and all other equations for concentration-dependent diffusion, consist of an infinite dilution diffusivity and a thermodynamic correction term. The thermodynamie correction term in all cases is equivalent to the derivative dGildx. The definition of the thermodynamic metastable limit (the spinodal curve) is the locus of points where dG2ldx = 0. This means that concentration-dependent diffusion theory predicts a diffusivity of zero at the spinodal. Thermodynamics tells us that the diffusivity goes from some finite value at saturation to zero at the spinodal. Unfortunately, it does not tell us how the diffusion coefficient declines. In addition, lack of thermodynamic data makes prediction of the spinodal difficult. We are, therefore, left with only the fact that as the concentration is increased in the supersaturated region, the diffusivity should decline towards zero but we do not know at what concentration the diffusivity becomes zero. 

T) 2 = infinite dilution diffusivity T) = self-diffusion coefficient of the solvent Ps = viscosity of the solution pi = viscosity of the solvent... 

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