Diffusion effects, surface

Equations 6.38 and 6.39 represent volume diffusion effects. Surface diffusion and grain-boundary diffusion may also be important, under certain circumstances. Grain boundaries are less dense than the grains themselves and so are easy diffusion paths. 

We also assume that the rate of consumption of (05 - 5+) on the catalyst surface (due to desorption or reaction) is first order in 0j (or C ) and denote by Ds the effective surface diffusivity (m2/s) of the backspillover species on the catalyst surface. 

SPAN module. It was mentioned at the beginning that the special polyacrylonitrile fibers of SPAN have a wall thickness of 30 gm, which is considerably thicker than the 8 gm wall thickness of the SMC modules [19]. As a consequence, the presence of stronger capillary effects from the special porous fiber material of the SPAN module would be a reasonable conclusion. Furthermore, the texture of the special polyacrylonitrile fibers is expected to have better surface properties, supporting the permeation of molecules as compared with synthetically modified cellulose. In conclusion, both convection and diffusion effectively contribute to the filtration efficiency in a SPAN module, whereas for the SMC membrane, diffusion is the driving force for molecular exchange, the efficiency of which is also considerable and benefits from the large surface-to-volume ratio. 

D = diffusion coefficient of drug S = effective surface area of drug particles h = stationary layer thickness Cs = concentration of solution at saturation C = concentration of solute at time t... 

In this equation the entire exterior surface of the catalyst is assumed to be uniformly accessible. Because equimolar counterdiffusion takes place for stoichiometry of the form of equation 12.4.18, there is no net molar transport normal to the surface. Hence there is no convective transport contribution to equation 12.4.21. Let us now consider two limiting conditions for steady-state operation. First, suppose that the intrinsic reaction as modified by intraparticle diffusion effects is extremely rapid. In this case PA ES will approach zero, and equation 12.4.21 indicates that the observed rate per unit mass of catalyst becomes... 

Usually for applications to combustors or room fires, diffusion effects can be ignored at surfaces where transport of fluid occurs, but within diffusion flames these effects are at the heart of its transport mechanism. 

It is seen that the intracrystalline MgO induces pore blockage in a fraction of the pore system and alters the porosity as well as D0, and/or r with the latter factors contributing most to the reduced diffusivity. In contrast, the coke modifier appears to affect mainly the surface-to-volume ratio and suggests that the effective surface area, number of available entrance ports, is reduced by two orders of magnitude. 

Figure 7 shows that PS thickness increases linearly with time up to certain thickness.16,17 Such constant growth rate at a constant current density means that the PS formed is uniform in thickness (Effective surface area remains constant assuming reaction kinetics is the same). At a large thickness the growth may deviate from linearity due to the effect of diffusion in the electrolyte within the pores.19,25 It has been found that for a very thick PS layer (150 pm) there is about 20% difference in HF concentration between that at the tips of pores and that in the bulk solution.19... 

When the pore bottom is covered by an oxide, the change of applied potential occurs almost completely in the oxide due to the very high resistance of the oxide. The rate of reactions is now limited by the chemical dissolution of the oxide on the oxide covered area. When the entire pore bottom is covered with an oxide the rate of reaction is the same on the entire surface of the pore bottom. As a result, the bottom flattens and the condition for PS formation disappears. The change of oxide coverage on the pore bottom can also occur when diffusion of the electrolyte inside deep pores becomes the rate limiting process. Since the current at which formation of an oxide occurs increases with HF concentration, a decreased HF concentration at pore bottom due to the diffusion effect can result in the formation of an oxide on the pore bottom of a deep pore at a condition that does not occur in shallow pores. 

Each diffuse swarm ion contributes to oq the effective surface charge of an individual ion i can be apportioned according to... 

Gilliland, E., R. F. Baddour and G. P. Perkinson. 1974. Diffusion on surfaces. Effect of concentration on the diffusivity of physically adsorbed gases. Ind. Eng. Fundam. 13 95-100. 

The Gouy-Chapman model describes the properties of the diffuse region of the double-layer. This intuitive model assumes that counterions are point charges that obey a Boltzmann distribution, with highest concentration nearest the oppositely charged fiat surface. The polar solvent is assumed to have the same dielectric constant within the diffuse region. The effective surface... 

When the steps become bigger, or p-xylene concentration is lower, the corner in the steps forms a groove. In this tage, the diffusion effect is increasing in rate determining factors instead of the surface Integration. 

I learned about chemical reactors at the knees of Rutherford Aris and Neal Amundson, when, as a surface chemist, I taught recitation sections and then lectures in the Reaction Engineering undergraduate course at Minnesota. The text was Aris Elementary Chemical Reaction Analysis, a book that was obviously elegant but at first did not seem at all elementary. It described porous pellet diffusion effects in chemical reactors and the intricacies of nonisothermal reactors in a very logical way, but to many students it seemed to be an exercise in applied mathematics with dimensionless variables rather than a description of chemical reactors. 

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