Gas diffusion coefficients

C = isobaric heat capacity per unit mass, gas D - diffusion coefficient, gas E = activation energy g = acceleration due to gravity... 

Gas-phase self-diffusion coefficient gas PFG NMR applied to the gas phase 3.4 X 10 m s ... 

Fig. 4.7 Scheme of the processes while phase transferring. Indices oo far from interface, 0 beginning of diffusion layer, ads outer surface, aq inner surface and aqueous phase, diss -dissolved, prot - protolyzed form, k reactions rate coefficients in gas phase (g), at surface ads) and in aqueous phase aq). Dg diffusion coefficient gas phase, sorption equilibrium coefficient, Dag diffusion coefficient aqueous phase, Kag equilibrium coefficient of protolysis, H Henry coefficent, Hgff effective Henry coefficient, a accommodation coefficient, /uptake coefficient. 

Diffusion coefficient, gas phase and liquid phase Height of clear liquid... 

Fuller, E. N. Giddings, J. C. (1965). A comparison of methods for predicting gaseous diffusion coefficients. Gas Chromatogr., 3,222-227. 

For a binary mixture of two components A and B in the gas phase, the mutual diffusion coefficient such as defined in 4.3.2.3, does not depend on composition. It can be calculated by the Fuller (1966) method ... 

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

Knudsen diffusion coefficient for the test gas in a micropore. represents the total void fraction and c that part of of the void fraction... 

As a particular case of this result, it follows that the stoichiometric relations are always satisfied in a binary mixture at the limit of bulk diffusion control and Infinite permeability (at least to the extent that the dusty gas equations are valid), since then all the binary pair bulk diffusion coefficients are necessarily equal, as there is only one of them. This special case was discussed by Hite and Jackson [77], and the reasoning set out here is a straightforward generalization of their treatment. 

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 ... 

The diffusion coefficient depends upon the characteristics of the absorption process. Reducing the thickness of the surface films increases the coefficient and correspondingly speeds up the absorption rate. Therefore, agitation of the Hquid increases diffusion through the Hquid film and a higher gas velocity past the Hquid surface could cause more rapid diffusion through the gas film. 

The effect of copolymer composition on gas permeability is shown in Table 9. The inherent barrier in VDC copolymers can best be exploited by using films containing Htde or no plasticizers and as much VDC as possible. However, the permeabiUty of even completely amorphous copolymers, for example, 60% VDC—40% AN or 50% VDC—50% VC, is low compared to that of other polymers. The primary reason is that diffusion coefficients of molecules in VDC copolymers are very low. This factor, together with the low solubiUty of many gases in VDC copolymers and the high crystallinity, results in very low permeabiUty. PermeabiUty is affected by the kind and amounts of comonomer as well as crystallinity. A change from PVDC to 50 wt °/ VC or 40 wt % AN increases permeabiUty 10-fold, but has Httle effect on the solubiUty coefficient. 

Water Transport. Two methods of measuring water-vapor transmission rates (WVTR) ate commonly used. The newer method uses a Permatran-W (Modem Controls, Inc.). In this method a film sample is clamped over a saturated salt solution, which generates the desired humidity. Dry air sweeps past the other side of the film and past an infrared detector, which measures the water concentration in the gas. For a caUbrated flow rate of air, the rate of water addition can be calculated from the observed concentration in the sweep gas. From the steady-state rate, the WVTR can be calculated. In principle, the diffusion coefficient could be deterrnined by the method outlined in the previous section. However, only the steady-state region of the response is serviceable. Many different salt solutions can be used to make measurements at selected humidity differences however, in practice,... 

In the former case, the rate is independent of the diffusion coefficient and is determined by the intrinsic chemical kinetics in the latter case, the rate is independent of the rate constant k and depends on the diffusion coefficient the reaction is then diffusion controlled. This is a different kind of mass transport influence than that characteristic of a reactant from a gas to ahquid phase. 

For prediction of gas phase diffusion coefficients in multicomponent hydi ocarbon/nonKydi ocai bon gas systems, the method of Wilke shown in Eq. (2-154) is used. 

In the late 1800s, the development of the kinetic theory of gases led to a method for calculating mmticomponent gas diffusion (e.g., the flux of each species in a mixture). The methods were developed simnlta-neonsly by Stefan and Maxwell. The problem is to determine the diffusion coefficient D, . The Stefan-Maxwell equations are simpler in principle since they employ binary diffnsivities ... 

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. 

The generalized Stefan-Maxwell equations using binary diffusion coefficients are not easily applicable to hquids since the coefficients are so dependent on conditions. That is, in hquids, each Dy can be strongly composition dependent in binary mixtures and, moreover, the binaiy is strongly affected in a multicomponent mixture. Thus, the convenience of writing multicomponent flux equations in terms of binary coefficients is lost. Conversely, they apply to gas mixtures because each is practically independent of composition by itself and in a multicomponent mixture (see Taylor and Krishna for details). 

The dimensionless numbers in tlris equation are the Reynolds, Schmidt and the Sherwood number, A/ sh. which is defined by this equation. Dy/g is the diffusion coefficient of the metal-transporting vapour species in the flowing gas. The Reynolds and Schmidt numbers are defined by tire equations... 

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