Correlation for diffusion coefficient

Wilke, C. R. and Chang, P. (1955) AIChE Jl 1, 264. Correlation for diffusion coefficients in dilute solutions. 

Wilke (W8) has developed a correlation for diffusion coefficients on the basis of the Stokes-Einstein equation. His results may be summarized by the approximate analyti-... 

Correlations for Diffusion Coefficient Viscosity and Density of C09 Naphthalene Mixture "... 

This equation also finds use as a correlation for diffusion coefficients in solids. Tabulations of Dq and the activation energy E for various species can be found in the pertinent literature. An example of their application appears in Practice Problem 3.10. 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

Witherspoon, P.A. and Bonoli, L. Correlation of diffusion coefficients for paraffin, aromatic, and cycloparaffin hydrocarbons in water, Ind. Eng. Chem. Fundam., 8(3) 589 591, 1969. 

In spite of the high ionic conductivity, there is no guarantee that the IL can transport the desired ions such as metal ions or protons. It is therefore important to analyze the ion transport properties in ILs. The ion conduction mechanism in ILs is different from that in molecular solvents. The ionic conductivity is generally coupled to carrier ion migration and ionic conductivity (a) correlates to diffusion coefficient (D) according to the Nernst-Einstein equation (see Eq. (3.10)) where n and q imply the number of carrier ions and electric charge, respectively. R, T, and F stand for the gas constant, the temperature in K, and the Faraday constant, respectively. 

Having mentioned the correlative capabilities of this model, one can consider its semi-predictive abilities. It was mentioned that a number of diffusion data taken from a limited range of penetrant concentrations are required to calculate two of the parameters of the model. Once these parameters have been determined, one can make theoretical predictions for diffusion coefficients over a wider range of penetrant concentration or temperature variation. This is a critical test for any theoretical model,... 

In this respect one solution for the estimation of a Dp-value is to correlate the diffusion coefficient with the relative molecular mass, Mr, of the migrant and with matrix specific parameters at a given temperature T in Kelvin. This approach has already been successfully used (Piringer 1993,1994 Limm and Hollifield 1996). The estimation of the diffusion coefficient can be achieved for example using the following heuristic correlation (Piringer 1994 Baner et al. 1996) ... 

R and T are the gas constant and temperature in Kelvin respectively. For any one temperature it can be shown that the diffusion coefficient for the noble gases are well correlated with the square roots of their masses (Fig. 11). Although Ar has not been experimentally determined in this study, this clear relationship enables the values of A and Ea for Ar to be readily interpolated from the other noble gas values. The interpolated values for Ar are also shown in Table 5. The correlation of diffusion coefficient with the square root of their masses also allows the relative mass fractionation of noble gases to be calculated using Equations (27) and (28). 

It is further possible to relate the hydrodynamic radius of a particle to its partial specific volume, V, which in turn allows one to correlate the diffusion coefficient of the particle with its molecular weight, M. Thus, for the case of a spherical particle the following relationship holds [30] ... 

Capone [219] has summarized more recent analysis of the diffusion behavior, and an example is the work by Baojin et al. [249]. The rate of diffusion is modeled from cylindrical coordinates again based on Pick s law. The composition of actual filaments from the spin bath was analyzed, and the coagulant was a DMP water system. Correlations are presented for diffusion coefficients and flux ratios as functions of jet stretch, polymer solution concentration, and coagulation temperature. The flux ratios, they reported, are similar to those reported in Paul s data, 20 years earlier. The diffusion coefficients are in the same range of 4-10 X lO cm /s that Paul found for DMAC-H2O systems. 

It is known that glassy polymer membranes can have a considerable size-sieving character, reflected mainly in the diffusive term of the transport equation. Many studies have therefore attempted to correlate the diffusion coefficient and the membrane permeability with the size of the penetrant molecules, for instance expressed in terms of the kinetic diameter, Lennard-Jones diameter or critical volume [40]. Since the transport takes place through the available free volume in the material, a correlation between the free volume fraction and transport properties should also exist. Through the years, authors have proposed different equations to correlate transport and FFV, starting with the historical model of Cohen and Turnbull for self diffusion [41], later adapted by Fujita for polymer systans [42]. Park and Paul adopted a somewhat simpler form of this equation to correlate the permeability coefficient with fractional free volume [43] ... 

The Stokes-Einstein formula for diffusion coefficients is limited to cases in which the solute is larger than the solvent. Predictions for liquids are not as accurate as for gases. The Wilke and Chang [16] correlation for diffusion in liquids is an empirical correlation and is given by... 

Figures 3 and 4 present correlations between diffusion coefficients, log(D), and calculated CED. For all polyimides examined, including the polyimides in this study, good correlations between log(D) and CED were observed for each gas in spite of differences in measurement temperature.

Values of diffusion coefficients are frequently needed in many separation calculations. Readers should refer to Reid et al. (1987) and Cussler (1997) for diffusion coefficients in liquids and gases. For immediate use, the following correlations may be used. 

Albert Einstein (1879-1955) was a German-bom American theoretical physicist. He was awarded the Nobel Prize in Physics in 1921. In electrochemical science, a number of equations bear Einstein s name, for example, Nemst-Einstein equation showing the relationship between conductivity and diffusion coefficient or the correlation between diffusion coefficient and viscosity, which is known as the Stokes-Einstein equation. 

We call the correlation time it is equal to 1/6 Dj, where Dj is the rotational diffusion coefficient. The correlation time increases with increasing molecular size and with increasing solvent viscosity, equation Bl.13.11 and equation B 1.13.12 describe the rotational Brownian motion of a rigid sphere in a continuous and isotropic medium. With the Lorentzian spectral densities of equation B 1.13.12. it is simple to calculate the relevant transition probabilities. In this way, we can use e.g. equation B 1.13.5 to obtain for a carbon-13... 

Reasonable prediction can be made of the permeabiUties of low molecular weight gases such as oxygen, nitrogen, and carbon dioxide in many polymers. The diffusion coefficients are not compHcated by the shape of the permeant, and the solubiUty coefficients of each of these molecules do not vary much from polymer to polymer. Hence, all that is required is some correlation of the permeant size and the size of holes in the polymer matrix. Reasonable predictions of the permeabiUties of larger molecules such as flavors, aromas, and solvents are not easily made. The diffusion coefficients are complicated by the shape of the permeant, and the solubiUty coefficients for a specific permeant can vary widely from polymer to polymer. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Fuller-Schettler-Giddings The parameters and constants for this correlation were determined by regression analysis of 340 experimental diffusion coefficient values of 153 binary systems. Values of X Vj used in this equation are in Table 5-16. 

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. 

It is important to recognize that the effects of temperature on the liquid-phase diffusion coefficients and viscosities can be veiy large and therefore must be carefully accounted for when using /cl or data. For liquids the mass-transfer coefficient /cl is correlated in terms of design variables by relations of the form... 

The value of 0/ is calculated from Eq. (14-142). The term Dg is an eddy-diffusion coefficient that is obtained from experimental measurements. For sieve plates, Barker and Self [Chem. E/ig. Sci., 17,, 541 (1962)] obtained the Following correlation ... 

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