Gases dilute, diffusion coefficients

The gas-phase diffusion coefficients are calculated using the equation given in Ref. [40]. The liquid-phase diffusion coefficients of components at infinite dilution in... 

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. 

Zhao, C. Li, J. Jiang, Z. Chen, C., Measurement of the Infinite Dilution Diffusion Coefficient of Small Molecule Solvents in Silicone Rubber by Inverse Gas Chromatography. Eur. Polym. J. 2006, 42, 615-624. 

BON Bonifaci, L. and Ravanetti, G.P., Measurement of infinite dilution diffusion coefficients of 8-caprolactam in nylon-6/solvent at elevated temperatures by inverse gas chromatography, J. Chromatogr., 607, 145, 1992. 

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. 

Generally, diffusion coefficients at infinite dilution are in the range 5xl(T10 and 3x10 m2 s 1 [29, 35, 36]. Since hydrogen is a very small molecule, it diffuses faster than most other dissolved gas. As a result, correlation-based estimates are often underestimated, as shown in Table 45.5. 

Chlorine (Cl), 6 130-211 9 280. See also Inorganic chlorine XeCl laser addition to fullerene, 12 240-241 analytical methods, 6 202 bleaching agent, 4 50 capacities of facilities, 6 193-198t catalyst poison, 5 257t chemical properties, 6 133-138 diffusion coefficient for dilute gas in water at 20° C, l 67t diffusion coefficient in air at 0° C, l 70t for disinfection, 8 605 economic aspects, 6 188-202 electrolytic preparation/production of, 12 759 16 40 end uses, 6 134-135 in fused quartz manufacture, 22 413 generating from hydrogen chloride, 13 833... 

Locate or calculate the binary-component diffusivity or self-diffusion coefficient for a gas, dilute solute, or melt. 

In this section, the basic theory required for the analysis and interpretation of adsorption and ion-exchange kinetics in batch systems is presented. For this analysis, we consider the transient adsorption of a single solute from a dilute solution in a constant volume, well-mixed batch system, or equivalently, adsorption of a pure gas. Moreover, uniform spherical particles and isothermal conditions are assumed. Finally, diffusion coefficients are considered to be constant. Heat transfer has not been taken into account in the following analysis, since adsorption and ion exchange are not chemical reactions and occur principally with little evolution or uptake of heat. Furthermore, in environmental applications,... 

A kinetic theory for dilute polyatomic gases has been developed by Wang-Chang and Uhlenbeck (W3, U3). No calculations have been made of the diffusion coefficients on the basis of this theory, however. For most polyatomic gases the results of the Chapman-Enskog monatomic gas theory seem to be adequate. 

The diffusion coefficient as defined by Fick s law, Eqn. (3.4-3), is a molecular parameter and is usually reported as an infinite-dilution, binary-diffusion coefficient. In mass-transfer work, it appears in the Schmidt- and in the Sherwood numbers. These two quantities, Sc and Sh, are strongly affected by pressure and whether the conditions are near the critical state of the solvent or not. As we saw before, the Schmidt and Prandtl numbers theoretically take large values as the critical point of the solvent is approached. Mass-transfer in high-pressure operations is done by extraction or leaching with a dense gas, neat or modified with an entrainer. In dense-gas extraction, the fluid of choice is carbon dioxide, hence many diffusional data relate to carbon dioxide at conditions above its critical point (73.8 bar, 31°C) In general, the order of magnitude of the diffusivity depends on the type of solvent in which diffusion occurs. Middleman [18] reports some of the following data for diffusion. 

These equations contain a number of assumptions. First of all, they are a result of a dilute gas approximation in which binary diffusion coefficients, which may be assumed independent of composition, are used. Secondly, thermal diffusion has been neglected although this assumption should be verified for the system under investigation. It appears that the flux due to thermal diffusion could be a substantial fraction of the ordinary diffusion flux for some systems (F6). 

Concentration of A Arrhenius constants Arrhenius constant Constant in equation 5.82 Surface area per unit volume Parameter in equation 5.218 Cross-sectional area Concentration of B Stoichiometric constants Parameter in equation 5.218 Concentration of gas in liquid phase Saturation concentration of gas in liquid Concentration of G-mass Concentration of D-mass Dilution rate DamkOhler number Critical dilution rate for wash-out Effective diffusion coefficient Dilution rate for maximum biomass production Dilution rate for CSTF 1 Dilution rate for CSTF 2 Activation energy Enzyme concentration Concentration of active enzyme Active enzyme concentration at time t Initial active enzyme concentration Concentration of inactive enzyme Total enzyme concentration Concentration of enzyme-substrate complex with substance A... 

In the case of combustion of a condensed substance, conservation of enthalpy and similarity occur only in the gas phase and only in part of the space. In the c-phase the diffusion coefficient is much smaller than the thermal diffusivity, and we have heating of the c-phase by heat conduction without dilution by diffusion. The enthalpy of the c-phase at the boundary, for x — 0 (from the side x < 0), is larger than the enthalpy of the c-phase far from the reaction zone and larger than the enthalpy of the combustion products. The advantage of the derivation given here is that the constancy of the enthalpy in the gas phase and its equality to H0 (H0 is the enthalpy of the c-phase far from the combustion zone, at x — —oo) are obtained without regard to the state of the intermediate layers of the c-phase. We should particularly emphasize that the constancy of the enthalpy in the combustion zone occurs only for a steady process. The presence of layers of the c-phase with increased enthalpy opens the possibility in a non-steady process of a temporary change in the enthalpy of the gas and the combustion temperature (on this see 5). 

Fick s law is derived only for a binary mixture and then accounts for the interaction only between two species (the solvent and the solute). When the concentration of one species is much higher than the others (dilute mixture), Fick s law can still describe the molecular diffusion if the binary diffusion coefficient is replaced with an appropriate diffusion coefficient describing the diffusion of species i in the gas mixture (ordinary and, eventually, Knudsen, see below). However, the concentration of the different species may be such that all the species in the solution interact each other. When the Maxwell-Stefan expression is used, the diffusion of... 

Dm denotes the molecular diffusion coefficient F denotes the interphase mass exchange rate between the dense and the dilute phases and Fc = — F, which can be directly calculated with EMMS/matrix model parameters if the reaction source term, Sk, is negligible compared to the bulk gas conservation. For vaporization of A, the source term reads... 

The method of Blanc [16] permits calculation of the gas-phase effective multicomponent diffusion coefficients based on binary diffusion coefficients. A conversion of binary diffusivities into effective diffusion coefficients can be also performed with the equation of Wilke [54]. The latter equation is frequently used in spite of the fact that it has been deduced only for the special case of an inert component. Furthermore, it is possible to estimate the effective diffusion coefficient of a multicomponent solution using a method of Burghardt and Krupiczka [55]. The Vignes approach [56] can be used in order to recalculate the binary diffusion coefficients at infinite dilution into the Maxwell-Stefan diffusion coefficients. An alternative method is suggested by Koijman and Taylor [57]. 

From a detailed analysis of molecular motion in dilute gases a much better prediction of diffusion coefficients results with the Chapman-Enskog equation. This equation, which describes a mixture of two solutes A and B (binary gas system) is ... 

It is assumed that component A is the component not in excess, thus /3g < 1, )8C < 1,... and that the numbersPb, 0. a do not depend on the temperature. They do not depend on the gas composition inside the catalyst pellet either, since the gas diluted. Notice the superscript + of the effective diffusion coefficient, which denotes that the catalyst pellet may be anisotropic. 

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