Diffusion coefficient estimation methods

Diffusion Coefficient. The method of Reference 237 has been recommended for many low pressure binary gases (238). Other methods use solvent and solute parachors to calculate diffusion coefficients of dissolved organic gases in liquid solvents (239,240). Molar volume and viscosity are also required and may be estimated by the methods previously discussed. Caution should be exercised because errors are multiplicative by these methods. 

An estimate of the change in water permeability upon degradation can be combined with the estimate of solubility, as given above to obtain an estimate of the change in the diffusion coefficient. One method for the prediction of permeability constants which has been shown to be reasonably successful is the Perma-chor method as developed by Salame (6,7). For the case of water permeation (7), the expression is... 

The value of coefficient depends on the composition. As the mole fraction of component A approaches 0, approaches ZJ g the diffusion coefficient of component A in the solvent B at infinite dilution. The coefficient Z g can be estimated by the Wilke and Chang (1955) method ... 

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 ... 

Multicomponent Mixtures No simple, practical estimation methods have been developed for predicting multicomponent hquid-diffusion coefficients. Several theories have been developed, but the necessity for extensive activity data, pure component and mixture volumes, mixture viscosity data, and tracer and binaiy diffusion coefficients have significantly limited the utihty of the theories (see Reid et al.). 

Ruthven (gen. refs.) summarizes methods for the measurement of effective pore diffusivities that can be used to obtain tortuosity factors by comparison with the estimated pore diffusion coefficient of the adsorbate. Molecular diffusivities can be estimated with the methods in Sec. 6. 

The Gaussian diffusion equation is known as the Pasquill and Gifford model, and is used to develop methods for estimating the required diffusion coefficients. The basic equation, already presented in a slightly different form, is restated below ... 

With electrochemical methods such as chronoamperometry, cyclovoltammetry (CV), or conductivity measurements, the diffusion coefficients of charged chemical species can be estimated in highly dilute solutions [16, 17]. 

The above methods measure ion transport rates as ionic conductivities. By varying the parameters of the experiment, it is often possible to indirectly identify the mobile ion(s),173 and in some cases to estimate individual ion mobilities or diffusion coefficients.144 Because of the uncertainty in identifying and quantifying mobile ions in this way, EQCM studies that provide the (net) mass change accompanying an electrochemical process36 have played an important complementary role. 

The experimental results imply that the main reaction (eq. 1) is an equilibrium reaction and first order in nitrogen monoxide and iron chelate. The equilibrium constants at various temperatures were determined by modeling the experimental NO absorption profile using the penetration theory for mass transfer. Parameter estimation using well established numerical methods (Newton-Raphson) allowed detrxmination of the equilibrium constant (Fig. 1) as well as the ratio of the diffusion coefficients of Fe"(EDTA) andNO[3]. 

It is useful to be able to estimate diffusion coefficients either to supplement mass transport data or to compare with experimentally determined values. A theoretically based method to estimate the diffusion coefficient includes upper and lower bounds for small molecules and large diffusants, respectively [40], The equation... 

Sheikha H., Pooladi-Darvish M., et al. Development of graphical methods for estimating the diffusivity coefficient of gases in bitumen from pressure-decay data. 2005 Energy Fuels, 19, 2041- 2049. 

M. F. Blackwell, K. Gounaris, S. J. Zara, and J. Barber, A method for estimating lateral diffusion coefficients in membranes from steady-state fluorescence quenching studies, Biophys. J. 51, 735-744 (1987). 

Tucker, W.A. andNelken, L.H. 1982, Diffusion coefficients in nit andv/ater.hi Handbook cf Chemical Property Estimation Methods. Lyman, W.J., Reehl, W.F., Rosenblatt, D.H., Erls. McGraw-Hill New York, NY. 

The above experimental results largely relate to spectroscopic techniques, which do not give direct information about the spatial scale of the molecular motions. The size of the spatial heterogeneities is estimated by indirect methods such as sensitivity of the dynamics to the probe size or from the differences between translational and rotational diffusion coefficients (rotation-translation paradox). It might be expected that the additional spatial information provided by neutron scattering could help to discriminate between the two scenarios proposed. 

An improved gas-uptake model should incorporate the features of the DuBois and Rogers model and the McJilton et al. model. As shown in Figure 7-2 the model for gas uptake in the airways should include separate layers for mucous-serous fluid epithelial tissue and blood. Development of such a model awaits reliable data and methods for predicting the coefficient of diffusion of pollutant gases in tissue and information on the rates of local perfusion of blood and lymph in the bronchial epithelium. Experimental data from humans and animals on the rate of sulfur dioxide absorption in blood could be used to make improved estimates of the tissue-diffusion coefficients in vivo. 

Key material properties for SOFC, such as the ionic conductivity as a function of temperature, are available in refs 36—39. In addition, Todd and Young ° compiled extensive data and presented estimation methods for the calculation of diffusion coefficients, thermal conductivities, and viscosities for both pure components and mixtures of a wide variety of gases commonly encountered in SOFCs. Another excellent source of transport properties for gases and mixtures involved in a SOFC is the CHEMKIN thermodynamic database. ... 

Selected entries from Methods in Enzymology [vol, page(s)j Boundary analysis [baseline correction, 240, 479, 485-486, 492, 501 second moment, 240, 482-483 time derivative, 240, 479, 485-486, 492, 501 transport method, 240, 483-486] computation of sedimentation coefficient distribution functions, 240, 492-497 diffusion effects, correction [differential distribution functions, 240, 500-501 integral distribution functions, 240, 501] weight average sedimentation coefficient estimation, 240, 497, 499-500. 

The book by Reid et al. [9] is an excellent source of information on properties such as thermal conductivities, diffusion coefficients and viscosities of gases and liquids. Not only are there extensive tables of data, but many estimation methods and correlations are critically reviewed. 

Because the theory of the liquid state is not nearly so well developed as the kinetic theory of gases, estimation methods for liquid diffusion coefficients are not as reliable as those used for gases. For dilute solutions of non-electrolytes, one widely used correlation is that due to Wilke and Chang[48]... 

This section describes the experimental methods and focuses on the estimation of diffusivity after the experiment. The analytical methods are not described here. Estimation of diffusivity from homogeneous reaction kinetics (e.g., Ganguly and Tazzoli, 1994) is discussed in Chapter 2 and will not be covered here. Determination of diffusion coefficients is one kind of inverse problems in diffusion. This kind of inverse problem is relatively straightforward on the basis of solutions to forward diffusion problems. The second kind of inverse problem, inferring thermal history in thermochronology and geospeedometry, is discussed in Chapter 5. 

The model parameters q and ML can be estimated from experimental data for radius of gyration, intrinsic viscosity, sedimentation coefficient, diffusion coefficient and so on in dilute solutions. The typical methods are expounded in several recent articles and books [20-22], Here we refer only to the results of the application to representative liquid-crystalline polymers (See Table 1). 

Several other empirical relations for diffusion coefficients have been suggested Olson and Walton (01) have devised a means for estimating diffusion coefficients of organic liquids in water solution from surface-tension measurements. Hill (H5) has proposed a method based on Andrade s theory of liquids which allows for the concentration dependence of the diffusion coefficient in a binary liquid mixture. The formula of Arnold (A2, T6, p. 102) does not seem generally useful inasmuch as it contains two constants ( abnormality factors ) characteristic of the solute and of the solvent. 

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