Molecular diffusion in gases

2 MOLECULAR DIFFUSION IN GASES 6.2A Equimolar Counterdiffusion in Gases 

In Fig. 6.2-1 a diagram is given of two gases A and B at constant total pressure P in two large chambers connected by a tube where molecular diffusion at steady state is oc- 

The subscript z is often dropped when the direction is obvious. Writing Pick s law for B for constant c. 

This shows that for a binary gas mixture of A and B the diffusivity coefficient for A diffusing in B is the same as Dg for B diffusing into A. 

The negative value for JJ means the flux goes from point 2 to 1. 

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For liquids, the mean free path is commonly a few angstroms, so the Knudsen number is almost always very small and diffusion inside the pores is usually only by ordinary molecular diffusion. In gases, the mean free path can be estimated from the following (Cussler, 1997) ... 

Figure 6.2-1. Equimolar counterdiffusion of gases A and B. Sec. 6.2 Molecular Diffusion in Gases...

Interestingly, there are three different cases of steady-state molecular diffusion in gases. ... 

The Chapman-Enskog equation (see Chapman and Cowling, 1970) is semi-empirical because it uses equation (3.11) and adjusts it for errors in the observations of diffusivity in gases. It also includes a parameter, S2, to account for the elasticity of molecular collisions ... 

Explain qualitatively the semiempirical relation of Fuller et al. (1966) for molecular diffusivity in air (Eq. 18-44). How is this expression related to the molecular theory of gases ... 

Typical values for p are between 0.3 and 0.6, and for tp between 2 and 5. So, a reasonable assumption for the effective diffusion De is that it is Vio of the diffusivity I). This diffusivity D can be calculated from the Knudsen (corresponding to collisions with the wall) and molecular diffusivity (intramolecular collisions). The molecular diffusivity was estimated at 10 5 m2/s, which is reasonable for the diffusion in gases. The Knudsen diffusivity depends on the pore diameter. The exact formulas for the molecular and Knudsen diffusion are given by Moulijn et at1. For zeolites, the determination of the diffusivity is more complicated. The microporous nature of zeolites strongly influences the diffusivity. Therefore, the diffusion... 

Equations describing molecular diffusion in liquids are similar to those applied to gases. The rate of diffusion of material A in a liquid is given by Eq. (40). 

Rates of mass transfer to the catalyst surface and pore diffusion can be calculated by the methods of Section 2.2.2 if the diffusion coefficients are known. However, the molecular theory of diffusion in liquids is relatively undeveloped and it is not yet possible to treat diffusion in liquids with the same rigour as diffusion in gases. The complicating factors are that the diffusion coefficient varies with concentration and that the mass density is usually more constant than the molar density of the solution. An empirical equation, due to Wilke and Chang, which applies in dilute solution, gives... 

The third mechanistic model of gas transfer at the air-water interface, the surface renewal model, is of intermediate complexity. There are several versions of the surface renewal model (Dankwertz, 1970) but the basic assumptions are the same. One envisions the surface of the liquid as a location that is repeatedly replaced by pristine parcels of water from below with the bulk gas concentration (Fig. 10.3). While the water parcel is at the interface it exchanges gases as though it is infinitely deep and stagnant. The equations of molecular diffusion in a semi-infinite space can thus be used to characterize the transfer process. The parameter that characterizes the rate of gas... 

Denbigh has provided useful guidelines for deciding when deviations (in conversion) from ideal tubular-flow performance are significant. In laminar flow, molecular diffusion in the axial direction causes little deviation if the reactor is reasonably long with respect to its diameter. Molecular diffusion in the radial direction may be important, particularly for gases, but it serves to offset the deviation from ideal performance caused by the velocity distribution. That is, radial diffusion tends to make the reactor... 

This is the usual boundary condition for molecular diffusion to surfaces in gases and liquids for a perfectly ab.sorbing surface. Hence the results of experiment and theory for molecular diffusion in the absence of a force field can often be directly applied to particle diffusion. However, the effect of finite particle size is very imporiaiU when diffusion boundary layers are present as discussed in the next chapter. 

For R —> 0 ( point particles), theories of particle and molecular diffusion are equivalent. Schmidt numbers for particle diffusion are much larger than unity, often of the same order of magnitude as for molecular diffusion in liquids. The principle of dimensional similitude tells us that the results of diflusion experiments with liquids can be used to predict rates of diffusion of point particles in gases, at the same Reynolds number. 

In the dry removal of trace gases turbulent diffusion, followed by molecular diffusion in the laminar layer, plays an important role, provided that the soil, vegetation or water surface chemically adsorbs or absorbs the gas considered. 

Calculate molar fluxes during steady-state molecular, one-dimensional diffusion in gases. 

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