Factor binary diffusion

Multicomponent Diffusion. In multicomponent systems, the binary diffusion coefficient has to be replaced by an effective or mean diffusivity Although its rigorous computation from the binary coefficients is difficult, it may be estimated by one of several methods (27—29). Any degree of counterdiffusion, including the two special cases "equimolar counterdiffusion" and "no counterdiffusion" treated above, may arise in multicomponent gas absorption. The influence of bulk flow of material through the films is corrected for by the film factor concept (28). It is based on a slightly different form of equation 13 ... 

For diffusion coefficients in systems under high pressure, the method of Dawson-Khoury-Kobayashi (see Ref. [52]) suggests a relevant pressure correction factor. To estimate the molar volumes, some reliable equations of state should be applied, whereas the necessary binary diffusivities at 1 atm can be determined with one of the methods described above. 

Catchpote and King [6] examined binary diffusion data of near-critical fluids in the reduced density range of 1 to 2.5 and found that their data correlated with average deviations of 10 percent and a maximum deviation of 60 percent. They observed two classes of behavior. For the first, no correction factor was required (R = 1). That class was comprised of alcohols as solvents with aromatic or aliphatic solutes, or... 

Based on a binary diffusion coefficient for N2/He of 0.687 cmVs and an assumed tortuosity factor T of 2. 

S Correction factor for porosity (binary diffusion coefficient). 

Therefore, any column that is packed well for ultrahlgh resolution LC separations does not lose its maximum efficiency in SFC separations. However, the linear velocity (u) must be significantly higher, by a factor of at least three, to obtain the most efficient operation. Again, this is expected since the optimum linear velocity is inversely proportional to the particle diameter and directly proportional to the mobile phase/solute binary diffusivity (D12) and the solute capacity factor (k ) ... 

Catalyst particles size -35 -i-48 Tyler mesh were used in all tests. Porosity was measured using a mercury porosimeter. A 0.1356 pm pore mean diameter was determined. The Satterfield and Sherwood (7) methodology was used to verify that reaction occurs without any diSusional limitation (internal or external). The effective diffusivity was estimated from the porosity measurements and binary diffusion coefficient and pore tortuosity pubhshed in the hterature, leading to an estimated value of 10 for the generahzed Thiele Modvdus based on the reaction rate. The efi ectiveness factor was then considered as 1.0. 

Vignes30 correlated the composition dependence of binary diffusion coefficients in terms of their infinite-dilution values and this thermodyxamic correction factor. 

The deviation of the pore geometry from the ideal cylindrical form is taken into account by the labyrinth factor which often Ues on the order of magnitude of 1/2 to 1 /6. Thus, the effective diffusion coefficient in pores is is obtained from the binary diffusion coefficient according to Equation (2.1-26). 

The porosity and tortuosity factor can be brought into the diffusion coefficients [51] by scaling the standard binary diffusion coefficients using the porosity t and tortuosity factor A according to... 

For example, the experimental conditions can be adjusted such that the molecular diffusion is the dominating mechanism (high pressure). This can be experimentally confirmed by the validation of the independence of the steady state flux with respect to the total pressure because the total molar concentration c is proportional to the total pressure while the molecular diffusivity is inversely proportional to pressure (eq. 13.2-12). In this regime, eq. (13.2-12) can be used to determine the tortuosity factor if the binary diffusion coefficient D b is known. 

Diffusion. A variety of correlations exist for diffusivities in dilute binary nonelectrolytic solutions (33), as well as electrolytic solutions (34). The most well-known correlation is the Wilke-Chang equation, where i is the solute, j is the solvent, 4> is an association factor, MW is the molecular weight, fi is the viscosity, and V is the molar volume (35). Tabulations of binary diffusivities exist (36). 

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. 

In Section 5.2, phenomenological models of the first intermediate phase nucle-ation at reactive diffusion in a binary diffusion couple are presented, and methods of thermodynamic analysis of the process, based on the theory of nucleation in a concentration gradient field, are given. We have pioneered the explanation of experimental results using thermodynamic suppression of nucleation rather than kinetic factors [1]. 

FIGURE 5.1 Golay plots for air, hydrogen, and helium as carrier gases using a 10-m-long, 0.25-mm-i.d. thin-film colnmn. Literature values of gas viscosity and binary diffusion coefficients for benzene at 50°C are used. A retention factor of 2.0 is assumed. 

FIGURE 5.2 Golay plots for 10-m-long, thin-film columns of various diameters using hydrogen as carrier gas. A binary diffusion coefficient of 0.4 cm /s and a retention factor of 2.0 are assumed. 

FIGURE 5.4 Golay plots for atmospheric outlet pressure (dotted lines) and 0.01 atmosphere outlet pressure (solid hues) using 5.0-m-long columns with hydrogen carrier gas and i.d. values of 0.10 mm (a), 0.25 mm (b), and 0.53 mm (c). A binary diffusion coefficient of 0.4 cm /s and a retention factor of 2.0 are assumed. 

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