Effective surface diffusivity

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. 

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. 

In conclusion, we can assert that the pyrolysis and activation process applied for the manufacture of activated carbons from nutshells resulted in good quality adsorbents. We have demonstrated the influence of both processes on the speed of the benzene adsorption from water solutions. The hypothesis that the effective surface diffusion is the slowest step of the global process was used and the estimation of the effective diffusion coefficient resulted in values ranging between 2 and 6 X 10-10 m /s. 

Equation 5.63 can also be derived assuming Langmuir kinetics for adsorption processes [59]. This equation shows that the effective surface diffusivities depend strongly both on the surface concentration and on the surface concentration gradient. In addition the effective surface diffusivity of each component is affected by the surface concentration gradient of the other component. 

Usually the pore volume diffusion flux is characterized by the use of a nonadsorbing gas. When an adsorbing gas is used the contribution of the surface diffusion can be obtained by subtracting the pore diffusion flux from the total flux. Knowing the surface diffusion flux, the effective surface diffusivity then can be calculated. 

Even fiuther ahead lies the region of ultrathin hlms. In general, they appear to be thick adsorbed hlms, the rate of movement of which is governed by an effective surface diffusion (Heslot et al., 1989 O Connor et al., 1996). If a very small soiuce is layered on a solid surface inihally and it spreads under surface diffusion, then the governing equahon (from Equarion 6.2) is... 

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

Several improvements of this equation were tried. Yang et at. (1973) considered the effect of residence time of the hopping molecule after landing on the occupied site and before starting the next hopping. Then the effective surface diffusion coefficient is described as... 

Fig. 4.9.(b) Comparison of effective surface diffusion coefficiems of butane, A,b for single-component system and D,th and Akr f f two-component system. 

Suzuki and Kawazoe (197S) measured the effective surface diffusion coefficients of various volatile organics during aqueous phase adsorption on activated carbon pellets and correlated the data using the boiling... 

Fig 4 11 Plots of the effective surface diffusion coefficient against Tb/ T for fifteen volatile organics. Tb boiling point of adsorbate (K), T adsorption temperature (K)... 

Z>to is related to characteristics of activated carbons if hopping distance, /, is considered to be in a two-dimensional direction and time constant of vibration, t, is considered to be 5X10 s. The effective surface diffusion coefficient also includes the tortuosity of diffusing path and = 2 is taken as a first approximate. Then the estimated Ao is given as... 

Micropore Diffusion. In very small pores in which the pore diameter is not much greater than the molecular diameter the diffusing molecule never escapes from the force field of the pore wall. Under these conditions steric effects and the effects of nonuniformity in the potential field become dominant and the Knudsen mechanism no longer appHes. Diffusion occurs by an activated process involving jumps from site to site, just as in surface diffusion, and the diffusivity becomes strongly dependent on both temperature and concentration. 

Ashby pointed out diat die sintering studies of copper particles of radius 3-15 microns showed clearly the effects of surface diffusion, and die activation energy for surface diffusion is close to the activation energy for volume diffusion, and hence it is not necessarily the volume diffusion process which predominates as a sintering mechanism at temperatures less than 800°C. 

We can include surface diffusion by adding to (90), neglecting again the effects of lateral interactions,... 

Access of air to the melt can be reduced by fitting a cover over it, or by floating a layer of powdered graphite on the melt surface. Diffusion rates in the melt can be reduced only by lowering the temperature, and this invariably reduces the amount of corrosion (except in certain cases in nitrate melts where passivity effects occur ). 

Kishinev ski/23 has developed a model for mass transfer across an interface in which molecular diffusion is assumed to play no part. In this, fresh material is continuously brought to the interface as a result of turbulence within the fluid and, after exposure to the second phase, the fluid element attains equilibrium with it and then becomes mixed again with the bulk of the phase. The model thus presupposes surface renewal without penetration by diffusion and therefore the effect of diffusivity should not be important. No reliable experimental results are available to test the theory adequately. 

Both questions have been recently addressed via a surface diffusion-reaction model developed and solved to describe the effect of electrochemical promotion on porous conductive catalyst films supported on solid electrolyte supports.23 The model accounts for the migration (backspillover) of promoting anionic, O5, species from the solid electrolyte onto the catalyst surface. The... 

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