Diffusion coefficient absorption effect

Multicomponent Diffusion. In multicomponent systems, the binary diffusion coefficient has to be replaced by an effective or mean diffusivity Although its rigorous computation from the binary coefficients is difficult, it may be estimated by one of several methods (27—29). Any degree of counterdiffusion, including the two special cases "equimolar counterdiffusion" and "no counterdiffusion" treated above, may arise in multicomponent gas absorption. The influence of bulk flow of material through the films is corrected for by the film factor concept (28). It is based on a slightly different form of equation 13 ... 

According to Maxwell s law, the partial pressure gradient in a gas which is diffusing in a two-component mixture is proportional to the product of the molar concentrations of the two components multiplied by its mass transfer velocity relative to that of the second component. Show how this relationship can be adapted to apply to the absorption of a soluble gas from a multicomponent mixture in which the other gases are insoluble and obtain an effective diffusivity for the multicomponent system in terms of the binary diffusion coefficients. 

Although long-time Debye relaxation proceeds exponentially, short-time deviations are detectable which represent inertial effects (free rotation between collisions) as well as interparticle interaction during collisions. In Debye s limit the spectra have already collapsed and their Lorentzian centre has a width proportional to the rotational diffusion coefficient. In fact this result is model-independent. Only shape analysis of the far wings can discriminate between different models of molecular reorientation and explain the high-frequency pecularities of IR and FIR spectra (like Poley absorption). In the conclusion of Chapter 2 we attract the readers attention to the solution of the inverse problem which is the extraction of the angular momentum correlation function from optical spectra of liquids. 

When the regular motion is simply uniform rotation of the absorption and emission dipoles with angular velocity to around the helix axis, one has p(t) - p(0) = cot. For the corresponding random motion, one might have m)2> = 2Dt, where D is the effective diffusion coefficient for Brownian rotation of the transition dipole around the helix axis. When these expressions are incorporated in Eqs. (4.31) and (4.24), the latter becomes a generalization of a relation recently derived using a more cumbersome approach/104-1... 

The presence of folds and villi structures on the surface area is not taken into account for the in vivo effective intestinal membrane permeability (Pefr when extrapolated from a perfusion experiment, a smooth tube is usually assumed). In humans, the fold expansion (FE) of the surface area is about threefold, and villi expansion (VE) is about 10-fold [7]. In the case of high epithelial membrane permeability (Pep) absorption occurs at the top of the villi before diffusing down the villi channels, whereas low Pep compound may diffuse down the villi channels to the crypts (Figure 6.1). Therefore, accessibility (Acc) to the surface depends on Pep and diffusion coefficient [7, 8]. The effective membrane permeability can be expressed as ... 

K. They noted a decay over timescales 95 and < 35 ns, respectively, which was attributed to geminate ion-pair recombination (see Fig. 33). The decay of the optical absorption is independent of the dose of radiation received and continues for about lps. Rather than displaying a dependence on time as eqn. (153), i.e. at f 3/2, the experimental results are more nearly represented by either at f 1 decay to an optical density about one tenth of the maximum or by a decay as t 1/2 to zero absorption. These effects may be the recombination of ions within a spur (or cluster of ion-pairs), which is more nearly like a homogeneous reaction. The range of electrons in propane at 100 K is 10 nm [334] and the extrapolated diffusion coefficient is 10 11 m2 s 1 [320]. The timescale of recombination is 10 ps. The locally greater concentration of ions within a spur probably leads to a faster rate of reaction and is consistent with the time-scale of the reaction observed. Baxendale et al. [395] observed the decay of the infrared optical absorption of the solvated electron in methylcyclo-hexane at 160 K. They noted that the faster decay occurring over < 50 ns was independent of dose and depended on time as t 1/2, i.e. the reaction rate decays as t 3/2, see eqn. (153). It was attributed to recombination of... 

The following effective diffusion coefficients D may be defined on the basis of standard sorption and permeation experiments 149 151 (when absorption or desorption conditions need to be specified, superscripts a or d respectively are again used) ... 

As the filler concentration increases so does the initial slope of Wt = f(j/x), see Fig. 12. According to Eq. (5) this may be due either to an increase of the diffusion coefficient or to the increased effective thickness of the specimen due to the addition of the filler that does not absorb water. Initially, there are small increments of the relative content of absorbed water, but the absolute quantity (referred to the binder) is almost independent of the filler concentration however in the next stages the absolute quantity of absorbed water becomes proportional to the microsphere concentration. Thus there are different absorption mechanisms effective in the course of time. 

Since reactive absorption systems often contain electrolyte species, the calculation of relevant diffusion coefficients is crucial. The effective diffusion coefficients for electrolyte components can be obtained from the Nernst-Hartley equation (see... 

According to the thermodynamics of irreversible processes, the mutual diffusion coefficient D may be a function of penetrant concentration ct, position x, and time t. In the present chapter we shall discuss sorption behavior of systems in which D varies with cx only, and shall use the notation D (cx) to indicate this condition. It is assumed that the sample film is so thin that diffusion takes place effectively in the direction of its thickness. At the beginning of an absorption or a desorption experiment the film is conditioned so that Cj is uniform everywhere in it. This initial concentration is denoted by cf. Then we have... 

If absorption measurements are made on samples, which initially contain no water, by immersing them in salt solutions of different concentrations, the effective absorption diffusion coefficient can be calculated. These measurements are followed by desorption experiments in which the samples are dried by blowing air across both major surfaces and the effective desorption coefficient is calculated. The diffusion coefficients obtained from such absorption and desorption measurements are shown in Table II. It is evident that the ratio of the diffusion coefficient obtained from desorption to that from absorption measurements increases as the concentration of water in the rubber, C, Increases. The diffusion coefficient obtained from a desorption experiment can only be expected to be greater than that from an absorption experiment if D decreases with increasing liquid concentration (3). 

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