Driving force of diffusion

The ionic mobilities Uj depend on the retarding factor 0 valid for a particular medium [Eq. (1.8)]. It is evident that this factor also influences the diffusion coefficients. To find the connection, we shall assume that the driving force of diffusion is the chemical potential gradient that is, in an ideal solution,... 

The driving force of diffusion is the gradient of the chemical potential. In the case of singlecomponent diffusion in a zeolite, the chemical potential can be related to the concentration by considering the equilibrium vapor phase [12,20]... 

The most important tfansport phenomenon—diffusion [76]—then remains. Using expression (4.511), we obtain for the driving force of diffusion (4.512)... 

Permeation is a function of two variables one relating to diffusion between molecular chains and the other to the solubility of the permeant in the polymer. The driving force of diffusion is the partial pressure of gases and the concentration gradient of liquids. Solubility is a function of the affinity of the permeant for the pol)uner. 

DRIVING FORCE OF DIFFUSION-INDUCED INTERFACE MIGRATION (DIIM)... 

Diffusion in micropore is assumed to be driven by the chemical potential gradient of the adsorbed species, instead of the concentration gradient. This is not a general rule, but it has been shown in many systems (Ruthven, 1984) that the chemical potential gradient is the proper description for the driving force of diffusion in zeolite, especially zeolites A, X, Y. Diffusion in other zeolites, and molecular sieve particles, there are still some discrepancies in the description of the diffusion. Solid structure and properties of the diffusing molecule may all contribute to these discrepancies. 

For the driving force of diffusion redistribution close to the front R, we put down... 

The process can be broadly classified as bulk diffusion, Knudsen diffusion, and surface diffusion. The molecular driving force of diffusion is the chemical potential difference created by a local population of a chemical species. Molecules tend to distribute uniformly across the space while migrating among like or unlike molecules. Bulk diffusion is the predominant mechanism when the pressures are high and pore sizes are large. On the other hand, at lower pressures, Knudsen diffusion prevails, when the mean free path of the molecules are larger than the pore size. When the molecules are adsorbed strongly on the pores or the pore sizes are too small, the mechanism of diffusion becomes surface diffusivity. 

Diffusion of an adsorbate molecule in the adsorbent particle occurs when there is concentration distribution in the particle. Since the mechanism of diffusion and the real driving force of diffusion may not... 

The effective surface diffusion coefficient is defined by taking the gradient of the amount adsorbed as the driving force of diffusion. 

Diffusion of molecules which are similar in size to the size of the pores is very restricted because of the effect of potential field of the wall atoms. Diffusion in molecular sieve materials is often of this type. Diffusion in this case is accompanied by relatively large activation energy and can be correlated by assuming that the driving force of diffusion is the chemical potential gradient. Ordinarily, diffusion coefficient is defined in terms of amount adsorbed, q, similar to the case of surface diffusion. 

When the driving force of diffusion is taken as the slope of the chemical potential, then by using mobility, B, flux can be described as... 

In order to continue the reaction, the diffusion must be carried out in reduction products, and the diffusion is only carried out at marginal layers (outer layer) of the metal products or low-valence oxide can influence the overall reduction rates. The diffusion in the inner layer does not have a direct impact on the reduction rate. The driving force of diffusion is the concentration gradient of the iron among each border of the different phases. The iron activity can be established on both sides of oxides. Therefore, the reduction rate is related with internal layer thickness of oxide. The opposite side is the thickness of the outer layer of products, which increases with the degree of reduction. 

The dynamics of the system is controlled by the rate rn(4), which is directly related to the static stmcture factor Sn(driving force of diffusion as well as stability of the fluctuations. When rii(0)>0, where rn(thermodynamically stable region, and we can take the limit of t=infinitely large in the dynamic stmcture factor and obtain... 

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