Tortuosity effect

The >eff across the porous medium for this example is linearly related to the porosity of the path, which is in turn simply the ratio of the open cross-sectional area to the total cross-sectional area. There are no constriction or tortuosity effects in this example i.e., t = 1 and... 

In a more extensive development of the tortnons-path and barrier theories, Boyack and Giddings [45] considered the transport of solnte in a simple geometrical system similar to that used in the diffnsion analysis of Michaels [241] bnt with added tortuosity effects. The effective mobility in this system was found to be... 

Boyack and Giddings [45] considered the tortuosity effects to be separable from the constriction effects. In their derivation they assumed that the electric field in the constricted channel decreased proportionally to the decrease in cross-sectional area and changes in path length. The field was assumed not to penetrate the barrier. The effect of constriction can be written in terms of porosity and L as... 

H.J.C. le Hennepe, C.A. Smolders, D. Bargeman, and M.H.V. Mulder, Exclusion and tortuosity effects for alcohol/water. separation by zeolite filled PDMS membranes, Sep. Sci. Technol. 26(4) 585 (1991). 

The crystallites are impermeable to penetrants leading to a hindered diffusion (tortuosity effect). For a semicrystalline polymer, sorption of pure liquid is given by [36]... 

Here Cq = c(z = 0,t) and Dg is the effective diffusion coefficient (porosity and tortuosity effects are incorporated in Dg). If the upstream (high) pressure is constant and much larger than the downstream (low) pressure, the slope of the asymptote will correspond to the steady state and so it is possible to determine the diffusivity under both steady state and transient conditions from a single permeation experiment. With a narrow and unimodal pore size distribution both methods yield reasonable consistent values. Large discrepancies point to strong microstructural effects (bimodal broad distribution, many dead ends, many defects). 

Within a porous body the flow of a fluid is resisted by viscous and geometric (tortuosity) effects. A porous media friction term is therefore added to the right hand side of the momentum equation. The physical meaning of different terms in the equation is explained in sect 3.4.6. 

In practice, a solid catalyst is most conveniently modeled as a quasi-homo-geneous phase. Even if the catalyst particle is porous, visualize it as a homogeneous, but permeable solid. Mass transfer in its interior is retarded by two effects obstruction of part of the cross-sectional area by the solid material, and diffusion paths that are longer because molecules have to wind their way around the obstructions (tortuosity effect). In the quasi-homogeneous model, the retardation is accounted for by the use of appropriately smaller "effective mass-transfer or diffusion coefficients. 

In the work of Bixler and Sweeting5 it was assumed that chain restriction effects are negligible for the compact helium molecule, so dial only tortuosity (edded path length) contributes to the rednclion of the di (fusion coefficient for this penetrant. Furthermore, for the 30% ciystalliue polyethylene sample studied, these authors suggest thet the tortuosity effect is essentially nondiscriminating and causes about a 65% reduction in mobility compared to the hypothetical totally amorphous case. The transport properties of a hypothetical totally amorphous branched polyethylene were assumed by these authors co be equivalam io those of unvulcanized natural rubber. 

No change of the sorption properties of the amorphous phase is observed by thermal treatment. A low gas permeability measured at the biaxially stretched films is related to both a change of the free volume sizes distribution and a tortuosity effect. The barrier properties of biaxially stretched films are kept even after annealing the film at 250°C. 

The Nielsen model has been a popular theory, originally used to explain polymer lay nanocomposites. This model is used to describe the tortuosity effect of plate-like particulates of filled rubber polymer composite on the gas permeation. An increase in barrier properties of gas permeation of rubber polymer nanocomposites is a result of the impermeable nature of filler particles which creates a long path of penetrant molecule by directing them around the particle. 

Fishman, Z., and Bazylak, A., 2011, Heterogeneous through-plane distributions of tortuosity, effective diffusivity, and permeability for PEMFC GDLs , J. Electrochem. 5oc., 158 (2)pp. B247. 

In order to understand the phenomena behind resistance variations in the conductive polymer composites (CPCs) due to solvent diffiision. Feller et al. [71] have performed sorption exjjeriments with poly (ethylene-co-ethyl acrylate)-carbon black (EEA-CB) and EEA films in the presence of toluene. One main point here was to determine the influence of CB in the diffiision process. The first results showed that, whichever polymer was used, the diffiision coefificiem increased with toluene activity, which indicated plasticization of the material by the solvent. However, it was interesting to note that the plasticization phenomenon was reduced when fillers were introduced into the polymer matrix. It also appeared that the toluene diflfiisivity was about twofold lower in EEA-CB than in EEA, which was certainly due to a hindrance effect of the carbon black particles. In other words, the decrease in toluene solubility was the result of a tortuosity effect due to the morphology of CPC with a dispersion of CB particles, which acted as barrier components and increased the path for toluene molecules inside the composite. 

Crystalline domains require penetrant migration around them, which increases the average pathlength relative to the nominal dimensions of the sample (tortuosity effect). 

Carrera et al. [51] proposed that the increase in barrier properties which were found at low contents of clay were due to defects at the interface which had less resistance to permeation. At higher content of OMt, and since the crystallinity was maintained as that of the pure polymer, the barrier properties were increased as a result of the tortuous path created by the exfoliated structure of the OMt. Monsivais-Barro et al. [52], proposed that the tortuosity effect caused by the dispersed nanolayers in HDPE improve the gas barrier properties in some cases while in other cases the interfacial regions or the free... 

Okamoto et al. studied the proton conductivities for SPI/Si02 hybrid membranes at different humidification conditions at 60°C. They found that under 100% RH, the hybrid membrane showed a decrease in proton conductivity compared with that of pristine SPI (from 178 to 124 mS cm" ) however, the conductivity at low RHs of 30%-50% hardly changed. It is considered that in the highly swollen hybrid membranes, the doped silica particles act as an insulating filler to reduce the conductivity by the tortuosity effect. On the other hand, under the low humidification of 30%-50% RH, the silica particles may act as water adsorbate to compensate the conductivity. 

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