Diffusion with surface resistance

Diffusion with Surface-Resistance or Surface-Barrier Model. 247... 

Fig. 5 Theoretical FR spectra for diffusion with surface resistance with f as a parameter for spherical crystal geometry when J = 0.15 and D/r = 0.1 s ...

Tables FR parameters of N2, CO, CO2 and propane diffusion in theta-1 the fits by using the single-diffusion with surface resistance model derived from...

Shen et al. measured the FR curves of O2 and N2 in different CMS pellets and analysed the data using the above procedures [64]. Micropore diffusion with surface resistance dominates in those CMS samples with a micropore... 

Fig. 9. Uptake curves for N2 in two samples of carbon molecular sieve showing conformity with diffusion model (eq. 24) for sample 1 (A), and with surface resistance model (eq. 26) for example 2 (0)j LDF = linear driving force. Data from ref. 18.

Fig. 12 FR experimental data ( , o) of CO2 diffusion in 0.4 g theta-1 (cf. [65]) at 2.0 Torr and temperatures of 273 (a), 298 (b), 323 (c) and 348 K (d) fitted by the single diffusion process with surface resistance model. Note 1 Torr = 133.33 Pa...

In either equation, /c is given by Eq. (16-84) for parallel pore and surface diffusion or by Eq. (16-85) for a bidispersed particle. For nearly linear isotherms (0.7 < R < 1.5), the same linear addition of resistance can be used as a good approximation to predict the adsorption behavior of packed beds, since solutions for all mechanisms are nearly identical. With a highly favorable isotherm (R 0), however, the rate at each point is controlled by the resistance that is locally greater, and the principle of additivity of resistances breaks down. For approximate calculations with intermediate values of R, an overall transport parameter for use with the LDF approximation can be calculated from the following relationship for sohd diffusion and film resistance in series... 

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

Pore Diffusion Resistance Combined with Surface Kinetics 381... 

PORE DIFFUSION RESISTANCE COMBINED WITH SURFACE KINETICS... 

Using the computer programs discussed above, it is possible to extract from these breakthrough curves the effective local mass transfer coefficients as a function of CO2 concentration within the stable portion of the wave. These mass transfer coefficients are shown in Figure 15, along with the predicted values with and without the inclusion of the surface diffusion model. It is seen that without the surface diffusion model, very little change in the local mass transfer coefficient is predicted, whereas with surface diffusion effects included, a more than six-fold increase in diffusion rates is predicted over the concentrations measured and the predictions correspond very closely to those actually encountered in the breakthrough runs. Further, the experimentally derived results indicate that, for these runs, the assumption that micropore (intracrystalline) resistances are small relative to overall mass transfer resistance is justified, since the effective mass transfer coefficients for the two (1/8" and 1/4" pellets) runs scale approximately to the inverse of the square of the particle diameter, as would be expected when diffusive resistances in the particle macropores predominate. 

Ma et al. [104] attributed a decrease in diffusivity with an increase in initial concentration to pore diffusion effects. Because zeolites are bi-dispersed sorbents, both surface and pore diffusions may dominate different regions. In micropores, surface diffusion may be dominant, while pore diffusion may be dominant in macropores. This, therefore, supports the use of a lumped parameter (De). To explore further the relative importance of external mass transfer vis-a-vis internal diffusion, Biot number (NBl — kf r0/De) was considered. Table 9 summarizes the NBi values for the four initial concentrations. The NBi values are significantly larger than 100 indicating that film diffusion resistance was negligible. 

At this stage of developments, most fixed-bed adsorption models assume that film mass transfer resistance is small compared with the other transport resistances in the system and that equilibrium is reached instantaneously between the solute in the pore liquid and at the surface of the sorbent. Even if it assumed that a homogeneous adsorptive HPLC sorbent is used, it can be readily shown, however, that both film and pore diffusion mass transfer resistances cannot be ignored393,394 and that the dynamic behavior of the adsorption stage is greatly dependent on the rate of the polypeptide- or protein-ligate interaction.8,357,395 Breakthrough of solute(s) may thus occur... 

For n = 1-e, where 0electrode surface roughness or distribution/accumulation of charge carriers. For n = 0.5 e, where 0< < 0.1, the CPE is related to diffusion, with deviations from Fick s second law. For n = 0 e, where 0inductive energy accumulation. Therefore, the CPE is a generalized element. Several factors can contribute to the CPE surface roughness, varying thickness or composition, non-uniform current distribution, and a distribution of reaction rates (non-homogeneous reaction rates on the electrode surface) [3],... 

The effects of dry deposition are included as a flux boundary condition in the vertical diffusion equation. Dry deposition velocities are calculated from a big leaf multiple resistance model (Wesely 1989 Zhang et al. 2002) with aerodynamic, quasi-laminar layer, and surface resistances acting in series. The process assumes 15 land-use types and takes snow cover into account. 

We now consider an enclosure consisting of three opaque, diffuse, and gray surfaces, as shown in Fig. 13-26. Surfaces 1, 2, and 3 have surface areas Aj, and A3 cmissivities C, e, and 3 and uniform temperatures T, T , and T 3. respective . The radiation network of this geometry is constructed by following the standard procedure draw a surface resistance associated with each of the three surfaces and connect these surface resistances with space resistances, as shown in the figtire. Relations for the surface and space resistances are given by Fqs. 13-26 and 13-31. The three endpoint potentials and... 

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