Diffusivity in gases

The Morse function which is given above was obtained from a study of bonding in gaseous systems, and dris part of Swalin s derivation should probably be replaced with a Lennard-Jones potential as a better approximation. The general idea of a variable diffusion step in liquids which is more nearly akin to diffusion in gases than the earlier treatment, which was based on the notion of vacant sites as in solids, remains as a valuable suggestion. 

Grew, K.E. and Ibbs, T.L. Thermal Diffusion in Gases (Cambridge University Press, Cambridge, 1952). 

The diffusivity in gases is about 4 orders of magnitude higher than that in liquids, and in gas-liquid reactions the mass transfer resistance is almost exclusively on the liquid side. High solubility of the gas-phase component in the liquid or very fast chemical reaction at the interface can change that somewhat. The Sh-number does not change very much with reactor design, and the gas-liquid contact area determines the mass transfer rate, that is, bubble size and gas holdup will determine reactor efficiency. 

Let us consider the typical mechanisms of spontaneous processes that decrease /. The direction and driving force of such mechanisms are determined by the laws of equilibrium thermodynamics, and the rate is proportional to diffusion in gases, viscosity in liquids, and transfer of atoms, vacancies, and other defects in solids. 

Cunningham, R. E. and R. J. J. Williams. 1980. Diffusion in Gases and Porous Media. Plenum Press, New York. 

Marrero and Mason [45] have reviewed the subject of diffusion in gases and give a comprehensive list of data. Diffusion coefficients of gases are inversely proportional to the pressure and vary with temperature according to a power of T between 1.5 and 2. If experimental values are not available, the Wilke—Lee method [46] predicts the diffusion coefficients of non-polar mixtures to within about 4% of their true value. 

The dimensionless time, t, for Sh to come within 100x% of the steady value indicates the duration of the unsteady state for Pe = 0, Tq.i == 31.8, and — 2.35. Diffusivities in gases are of order 10" times diffusivities in liquids hence, for particles with equal size and equal exposure, transient effects in a stagnant medium are much more significant in liquids. 

The molecules are generally much farther apart in gases, so the diffusivity of a compound in a gas is significantly larger than in a liquid. We will return to this comparison of diffusion in gases and hquids in Chapter 3. 

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 ... 

Drickamer contributed much to the knowledge of diffusion in gases and liquids. As an example, recent studies of the effect of pressure upon material transport in several inorganic systems have been made available... 

Barber, "D if fusion in and through Solids , Cambridge Univ press, NY(1952), 477 pp 16) K.E, Grew T.L. Ibbs, Thermal Diffusion in Gases , Cambridge Univ press,... 

The constant of proportionality, D, is the diffusion coefficient, and the negative sign is necessary because the net flux is from the region of high concentration to the region of low concentration. Table 23-1 shows that diffusion in liquids is 104 times slower than diffusion in gases. Macromole-cules such as ribonuclease and albumin diffuse 10 to 100 times slower than small molecules. 

The main observation from Table 2.1 is the enormous range of values of diffusion coefficients—from 10 1 to 10 30 cm2/s. Diffusion in gases is well understood and is treated in standard textbooks dealing with the kinetic theory of gases [24,25], Diffusion in metals and crystals is a topic of considerable interest to the semiconductor industry but not to membrane permeation. This book focuses principally on diffusion in liquids and polymers in which the diffusion coefficient can vary from about 10 5 to about 10-10 cm2/s. 

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... 

For multicomponent diffusion in gases at low density, the Maxwell-Stefan equations provide satisfactory approximations when species / diffuses in a homogeneous mixture... 

Fig. V1IL5. Illuwstrating mass diffusion in gases in one dimension.

Equations for diffusion through a layer of stagnant liquid can also be developed. The applicability of these equations is, however, limited because diffusivity in a liquid varies with concentration. In addition, unless the solutions are very dilute, the total molar concentration varies from point to point. These complications do not arise with diffusion in gases. 

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... 

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