Transport coefficients tortuosity factor

For hydrophilic and ionic solutes, diffusion mainly takes place via a pore mechanism in the solvent-filled pores. In a simplistic view, the polymer chains in a highly swollen gel can be viewed as obstacles to solute transport. Applying this obstruction model to the diffusion of small ions in a water-swollen resin, Mackie and Meares [56] considered that the effect of the obstruction is to increase the diffusion path length by a tortuosity factor, 0. The diffusion coefficient in the gel, )3,i2, normalized by the diffusivity in free water, DX1, is related to 0 by... 

Substrate transport through the film may be formally assimilated to membrane diffusion with a diffusion coefficient defined as12 Ds = Dch( 1 — 9)/pjort. In this equation, the effect of film structure on the transport process in taken into account in two ways. The factor 1—0 stands for the fact that in a plane parallel to the electrode surface and to the coating-solution interface, a fraction 9 of the surface area in made unavailable for linear diffusion (diffusion coefficient Dcj,) by the presence of the film. The tortuosity factor,, defined as the ratio between the average length of the channel and the film thickness, accounts for the fact that the substrate... 

The diffusion coefficients are listed in Table 31.8. Transport of the TBP HNO3 complex was also reported in another study on a similar system [87]. However, based on the calculations made using the Stokes-Einstein equation, species of the type 2TBP HNO3 is the more probable species diffusing through the organic layer. The difference between the experimentally observed and predicted values is attributed to the intermolecular interaction and tortuosity factors. 

Fig.3. Diffiision coefficients D as derived from a fit of the experimental data in Fig.2 with the solution of the diffusion equation for cylindrical sample (open circles) in addition, values corrected for the amount of gas to be transported (D d>pseudo, fuU circles) are depicted. For comparison the theoretical diffusion coefficients for gas phase diffusion in cylindrical pores are also included (dashed lines) hereby the value of the macroporosity (50%) and a tortuosity factor of 3 are taken into account. The macroporosity was calculate fix)m the bulk density of the sample and the micropore volume (macroporDsity=total porosity—microporosity= 86 % - 36%).

The thinness of the unfrozen liquid film at lower temperatures, tortuosity factor, and reduced diffusion coefficients bring the transport rate down into extremely low values. For temperature and soil grain size as discussed above. 

The equations used to calculate permeability coefficients depend on the design of the in vitro assay to measure the transport of molecules across membrane barriers. It is important to take into account factors such as pH conditions (e.g., pH gradients), buffer capacity, acceptor sink conditions (physical or chemical), any precipitate of the solute in the donor well, presence of cosolvent in the donor compartment, geometry of the compartments, stirring speeds, filter thickness, porosity, pore size, and tortuosity. 

A decrease of the solubility is expected in nanostructured polymer blends due to the reduced polymer matrix volume, as well as a decrease in diffusion due to a more tortuous pathway for the diffusing molecules. The reduction of the diffusion coefficient is higher than that of the solubility coefficient. Indeed, the volume fraction of nanoplatelets is low and, thus, the reduction of the matrix volume is small. The major factor, then, is the tortuosity, which is connected directly to the shape and the degree of dispersion of nanoplatelets. Better dispersed clay systems increase the tortuosity path of the diffusing molecules whereas larger aggregates decrease the aspect ratio of the nanoparticles and can act as a low-resistance pathway for the gas transport. 

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