Diffusion surface resistance

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.

The relative importance of gas-phase and surface resistances depends on the nature of the pollutant and the surface as well as the meteorology (Shaw, 1984 Unsworth et al., 1984 Chameides, 1987 Wesely and Hicks, 1999). The gas-phase resistance (rgas) is determined by the vertical eddy diffusivity, which depends on the evenness of the surface and the meteorology, for example, wind speed, solar surface heating, and so on. The surface resistance (rsur[) depends on the detailed characteristics of the surface (e.g., type, whether... 

Figure 50 shows three examples for (different) kinetic situations in which bulk diffusion, surface reaction, and transport across a grain boundary are the sluggish steps. Nonetheless, the other parameters can also be evaluated. This becomes especially clear from the top figure, where the nonunity intercepts reveal surface effects. Similarly, the nonzero bending of the profiles in the other two figures indicates transport resistances. 

The flux of trace gases and particles from the atmosphere to the surface is calculated by multiplying concentrations in the lowest model layer by the spatially and temporally varying deposition velocity, which is proportional to the sum of three characteristic resistances (aerodynamic resistance, sublayer resistance, and surface resistance). The surface resistance parametrization developed by Wesely (1989) is used. In this parametrization, the surface resistance is derived from the resistances of the surfaces of the soil and the plants. The properties of the plants are determined using land-use data and the season. The surface resistance also depends on the diffusion coefficient, the reactivity, and water solubility of the reactive trace gas. 

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... 

Here, the first term represents the resistance due to eddy transport, and the second term that of molecular diffusion. The term B = 0.1 m/s depends on the type of surface, but it is only mildly dependent on u (Chamberlain, 1966 Garland, 1977). In this manner, rg(z) becomes amenable to calculation, and Table 1-11 presents some numerical values that were given by Garland (1979). The results are maximal velocities, as they do not yet include the effect of the surface resistance rs. For the uptake of gases by soils and vegetation, rs must be considered an empirical quantity to be determined by experiments. 

Microfluidics handles and analyzes fluids in structures of micrometer scale. At the microscale, different forces become dominant over those experienced in everyday life [161], Inertia means nothing on these small sizes the viscosity rears its head and becomes a very important player. The random and chaotic behavior of flows is reduced to much more smooth (laminar) flow in the smaller device. Typically, a fluid can be defined as a material that deforms continuously under shear stress. In other words, a fluid flows without three-dimensional structure. Three important parameters characterizing a fluid are its density, p, the pressure, P, and its viscosity, r. Since the pressure in a fluid is dependent only on the depth, pressure difference of a few pm to a few hundred pm in a microsystem can be neglected. However, any pressure difference induced externally at the openings of a microsystem is transmitted to every point in the fluid. Generally, the effects that become dominant in microfluidics include laminar flow, diffusion, fluidic resistance, surface area to volume ratio, and surface tension [162]. 

Measurements by interference microscopy are, under favorable conditions, capable of yielding both internal diffusivities and apparent diffusivities based on overall sorption rates. The former tend to approach the values obtained from microscopic measurements while the latter yield values similar to those obtained by other macroscopic methods. Of necessity these studies have been carried out in large zeolite crystals. One may expect that smaller crystals may be less defective, although the influence of surface resistance may be expected to be greater. The extent to which these conclusions are applicable to the small zeolite crystals generally used in commercial zeolite catalysts and adsorbents remains an open question. 

Fig. 17 Transient profile for desorption of isobutane from a surface-etched silicalite. The observation direction was perpendicular to the x-y plane in (a) and (c) and perpendicular to the z-x plane in (b), (d), and (f). The form of the profiles suggests that the desorption rate is controlled by the combined effects of internal diffusion and surface resistance. The effect of a crack in the crystal is evident in (c) and (e). From Kortunov et al. [103]...

In the frequency response method, first applied to the study of zeolitic diffusion by Yasuda [29] and further developed by Rees and coworkers [2,30-33], the volume of a system containing a widely dispersed sample of adsorbent, under a known pressure of sorbate, is subjected to a periodic (usually sinusoidal) perturbation. If there is no mass transfer or if mass transfer is infinitely rapid so that gas-solid mass-transfer equilibrium is always maintained, the pressure in the system should follow the volume perturbation with no phase difference. The effect of a finite resistance to mass transfer is to cause a phase shift so that the pressure response lags behind the volume perturbation. Measuring the in-phase and out-of-phase responses over a range of frequencies yields the characteristic frequency response spectrum, which may be matched to the spectrum derived from the theoretical model in order to determine the time constant of the mass-transfer process. As with other methods the response may be influenced by heat-transfer resistance, so to obtain reliable results, it is essential to carry out sufficient experimental checks to eliminate such effects or to allow for them in the theoretical model. The form of the frequency response spectrum depends on the nature of the dominant mass-transfer resistance and can therefore be helpful in distinguishing between diffusion-controlled and surface-resistance-controlled processes. 

Fig. 17 Transient concentration profiles in y-direction (i.e., along 8-ring channels) measured by interference microscopy for a adsorption and b desorption of methanol in a large crystal of ferrierite for pressure steps 5 -> 10 and 10 5 mbar. The form of the profiles shows that both surface resistance and internal diffusion (along the 8-ring chan-...

If we abandon the very unlikely case of anisotropic diffusion with principal tensor axes which are not perpendicular to the crystal faces normal, molecular fluxes may quite generally be assumed to be directed perpendicular to the crystal surfaces. Hence, molecular uptake and release may be considered to proceed via one-dimensional diffusion quite generally, as long as the fluxes stemming from different crystal faces do not superimpose upon each other. This includes in particular the initial phases of uptake and release. We shall see that due to this reason, by measuring surface permeabilities, interference microscopy is in general able to quantify the intensity of surface resistances. 

Fig. 56 Correlation between the actual boundary concentration (Csurf) and the relative uptake (m) at the corresponding instant of time. Three different cases are shown the mass transport is essentially limited by intracrystalline diffusion (la/D = 100), by surface barriers la/D = 0.01), and both by intracrystalline diffusion and surface resistance la/D = 1)...

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

Abstract Theoretical, experimental principles and the applications of the frequency response (FR) method for determining the diffusivities in microporous and bidispersed porous solid materials have been reviewed. Diffusivities of hydrocarbons and some other sorbates in microporous crystals and related pellets measured using the FR technique are presented, and the FR data are analysed to demonstrate the identification of the FR spectra. These results display the ability of the FR method to discriminate multi-kinetic mechanisms, including a surface resistance or surface barrier occurring simultaneously in the systems, which are difficult to be determined using other microscopic or macroscopic methods. The FR measurements also showed that the diffusivity of a system depends significantly on the subtle differences in molecular shape and size of sorbates in various... 

---