Coefficients of diffusion

Fuller s equation, applied for the estimation of the coefficient of diffusion of a binary gas mixture, at a pressure greater than 10 bar, predicts values that are too high. As a first approximation, the value of the coefficient of diffusion can be corrected by multiplying it by the compressibility of the gas /... 

Z) g = mutual coefficient of diffusion AB = mutual coefficient of diffusion calculated by Fuller s method... 

The coefficient of diffusion for one-dimensional motion of particles is given by... 

From experimentally measured sensor signals as functions of distance X we estimated the coefficients of diffusion for protium and deuterium. At T = 345 K they are equal to 1.56-10 and I.OO-IO" m/s, respectively. 

Ceria shows the highest coefficient of diffusion in the range of 10 15-10 l6m2s, which is coherent with the high OSC values obtained with this oxide. 

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. 

By determining the water vapour and oxygen permeability of the free films as well as the water solubility in the coatings, the coefficients of diffusion of water could be established. 

The experimental permeability Is the product of the coefficient of diffusion and solubility (P D x S). When the measured solubilities are taken Into consideration It appears that the differences In permeability observed can mainly be attributed to this factor. The calculated diffusion coefficients differ at most a factor of three. However, If It Is realized that this coefficient Is derived from two experimentally observed variables and that the... 

Using simple arguments, show that the coefficient of diffusion D (the net number of particles that flow in unit time through a unit plane perpendicular to a unit... 

The transport coefficients of diffusion, heat conductivity, and viscosity can all be computed by the method of correlation functions. 

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

The Chapman-Enskog theory was developed for dilute, monatomic gases for pure substances and for binary mixtures. The extension to multicomponent gas mixtures was performed by Curtiss and Hirschfelder (C12, Hll), who in addition have shown that the Chapman-Enskog results may also be obtained by means of an alternate variational method. Recently Kihara (K3) has shown how expressions for the higher approximations to the transport coefficients may be obtained, which are considerably simpler than those previously proposed by Chapman and Cowling these simpler formulas are particularly advantageous for calculating the coefficients of diffusion and thermal diffusion (M3, M4). 

An expression for the coefficient of diffusion identical with that given in Chapman and Cowling (C3) has also been obtained by considering diffusion as a random-walk process (F12). 

Two special applications of Eq. (86) should be mentioned, namely the calculation of isotopic diffusion and the calculation of the coefficient of diffusion for polar-nonpolar mixtures. For mixtures of heavy isotopes, Ma = MB = M, aK = = [Pg.188]

The Lennard-Jones (6-12) potential has served very well as an inter-molecular potential and has been widely used for statistical mechanics and kinetic-theory calculations. It suffers, however, from having only two adjustable constants, and there is no reason why it should not gradually be replaced by more flexible and more realistic functions. Recently a number of applications have been made of the Buckingham (6-exp) potential [Eq. (82)], which has three adjustable parameters. For this potential the first approximation to the coefficient of diffusion is written by Mason (M3) in the form... 

The studies of Hasinoff [53] on the recombination rate of carbon monoxide and the heme units after photodissociation of carboxy ferrous microperioxidase come close to satisfying the requirements for observing the effects of anisotropic reactivity and rotational diffusion on the rate of a translational diffusion-limited reaction. In Chap. 2, Sect. 5.6, the details of this study were briefly mentioned. Hasinoff found that the rate of recombination was substantially diffusion-limited in all three aqueous solvents used at 260 K, but at higher temperatures, the rate of reaction of the encounter pair, feact, was a significant factor in determining the overall rate of recombination (see Fig. 9). The observed rate coefficient of recombination, feobs, was separated into the rate coefficient of diffusive formation of encounter pairs, feD, and the rate coefficient of reaction of encounter pairs, fcact, with the Collins and Kimball expression, eqn. (26)... 

Molecular exclusion chromatography. The stationary phase in molecular exclusion chromatography is a material containing pores, the dimensions of which are chosen to separate the solutes present in the sample based on their molecular size. This can be perceived as a molecular sieve allowing selective permeation. This technique is known as gel filtration or gel permeation, depending on the nature of the mobile phase, which is either aqueous or organic. The distribution coefficient in this technique is called the coefficient of diffusion. 

This relationship, which can be very accurate when the film thickness is negligible compared to the diameter of the column, does not contain an A term, contrary to van Deemter s equation (cf. 1.11). The coefficients CG and CL are related to the coefficients of diffusion of the solute in the gaseous and liquid phases. Equation (1.17) is obtained from this equation. 

Figure 10. Velocity of Penetration (i) and Mean Coefficient of Diffusion (D) of Phthalates in the Polymer, PVC -PVC (87 13)...

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