Concentration surface permeabilities

Figure 6 provides a comparison between measured spectra and theoretical spectra calculated under the assumption that the adsorption/desorption process is controlled by either intracrystalline diffusion (Fig. 6a) or external transport resistances such as surface barriers (Fig. 6b). For simplicity in the calculations, the crystallites have been assumed to be of nearly spherical shape with a concentration-independent transport diffusivity Dj or surface permeability a, respectively. Values of the intracrystalline mean lifetime are therefore given by...

Eq. (2)], (2) from the penetration through the crystallite surface [x harr R,J(3a), with a denoting the surface permeability with respect to the intracrystalline concentration, Eq. (12)], and (3) from long-range diffusion [Xp. iig, = / , /(15Du,ng range) Eq. (2)], where both the crystallites and pellets have been assumed to be of nearly spherical shape with radii R, and / , respectively. 

The surface permeability a is defined as the factor of proportionahty between the particle flux through the surface, , and the difference Ceq - Csurf(f) between the intracrystalhne concentration estabhshed in equilibrium with the surrounding atmosphere and the actual concentration in the layer close to the crystal surface... 

Fig. 44 Surface permeability of the MOF-type crystal under study during methanol uptake as a function of the boundary concentration (mean value during the considered time step) via Eqs. 7 and 8, with the boundary concentration Csurf(t) taken from the margins of the measured concentrations. The polynomial fit to these data is given by the broken line. The full line shows the dependence of the permeability on concentration, which leads to the best fit of the recalculated concentration profiles to the experimental ones (Fig. 45)...

Fig. 45 Comparison of the transient concentration profiles during methanol uptake by the MOF-type crystal as recorded by interference microscopy (symbols) with the corresponding profiles recalculated from the measured diffusivities with surface permeabilities (full line in Fig. 44) which lead to the best fit to the experimental points...

Fig. 48 Comparison of simulated and experimental profiles for pressure steps 0 to 5 mbar (a), 5 to 0 mbar (b), 0 to 10 mbar (c), 10 to 0 mbar (d), 0 to 40 mbar (e), 40 to 0 mbar (f), 0 to 80 mbar (g), and 80 to 0 mbar (h). Tbe points refer to experimental measurements. Tbe lines are simulated from tbe 2-D finite difference solution with the same concentration dependence of transport diffusivities as determined from Fig. 47 (full line) and the surface permeabilities determined from the use of Eqs. 7 and 8. For the simulations it is implied that Dz > Dy...

Fig. 52 Surface permeabilities determined from the calculated concentration profiles. The solid line (uy) and the dotted line (Uz) represent the analytical dependence of the surface permeabilities which yields excellent agreement with the measmed concentration integrals (standard deviation a = 0.006)...

In fact, this behavior can be shown to hold quite generally. With the simplifying assumption of constant diffusivities and surface permeabilities, the normahzed concentration profiles during molecular uptake by a plate of thickness 2l are given by the relation... 

Permeation of gas, vapor, or liquid through a polymer film consists of three steps (1) a solution of permeating molecules in the polymer, (2) diffusion through the polymer due to concentration gradient, and (3) emergence of permeating molecules at the outer surface. Permeability is therefore the product of solubility and diffusion so where the solubility obeys Henry s law one may write... 

The anode and cathode chambers are separated by a cation-permeable fluoropolymer-based membrane (see Membrane technology). Platinum-electroplated high surface area electrodes sold under the trade name of TySAR (Olin) (85,86) were used as the anode the cathode was formed from a two-layer HasteUoy (Cabot Corp.) C-22-mesh stmcture having a fine outer 60-mesh stmcture supported on a coarse inner mesh layer welded to a backplate. The cell voltage was 3.3 V at 8 kA/m, resulting ia a 40% current efficiency. The steady-state perchloric acid concentration was about 21% by weight. 

Of particular interest in the usage of polymers is the permeability of a gas, vapour or liquid through a film. Permeation is a three-part process and involves solution of small molecules in polymer, migration or diffusion through the polymer according to the concentration gradient, and emergence of the small particle at the outer surface. Hence permeability is the product of solubility and diffusion and it is possible to write, where the solubility obeys Henry s law,... 

Too high a concentration of formaldehyde will cause rapid curing of the surface of the section, thus reducing its permeability to formaldehyde, and as a result it is extremely difficult to cure adequately the centre of the casein. Too low a concentration will unnecessarily prolong the time of cure. 

Prepared saltwater completion fluids are made of fresh surface water, with sufficient salts added to produce the proper salt concentration. Usually, the addition of 5 to 10% NaCl, 2% CaClj, or 2% KCl is considered satisfactory for clay inhibition in most formations. Sodium chloride solutions have been extensively used for many years as completion fluids these brines have densities up to 10 Ib/gal. Calcium chloride solutions may have densities up to 11.7 lb/ gal. The limitations of CaClj solutions are (1) flocculation of certain clays, causing permeability reduction, and (2) high pH (10 to 10.5) that may accelerate formation clays dispersion. In such cases, CaC12-based completion fluids should be replaced with potassium chloride solutions. Other clear brines can be formulated using various salts over wide range of densities, as shown in Figure 4-123 [28]. 

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