Pore tortuosity, porous membrane diffusion

With porous membrane DS devices of this geometry and for thin membranes with low-tortuosity pores (i.e., where the diffusion distance within the pores is very small compared to the radial diffusion distance in the DS), good predictions for the collection efficiencies can be obtained if the nominal X and dfd0 values are both multiplied by the fraction of the surface that is porous. For example, with a diffusion scrubber based on such a membrane tube (L = 40 cm, dQ = 0.5 cm, d = 0.045 cm, fractional porosity 0.4), the corrected X values for H20.2 as sample gas are 0.32, 0.16, 0.11, and 0.08, respectively for Q = 0.5, 1.0, 1.5, and 2.0 L/min, and the corrected djda value is 0.036. The collection efficiencies predicted from Figure 1 (interpolating between dfdQ values of 0.02 and 0.05) are in good agreement with... 

Porous Membrane DS Devices. The applicability of a simple tubular DS based on a porous hydrophobic PTFE membrane tube was demonstrated for the collection of S02 (dilute H202 was used as the scrubber liquid, and conductometric detection was used) (46). The parameters of available tubular membranes that are important in determining the overall behavior of such a device include the following First, the fractional surface porosity, which is typically between 0.4 and 0.7 and represents the probability of an analyte gas molecule entering a pore in the event of a collision with the wall. Second, wall thickness, which is typically between 25 and 1000 xm and determines, together with the pore tortuosity (a measure of how convoluted the path is from one side of the membrane to the other), the overall diffusion distance from one side of the wall to the other. If uptake probability at the air-liquid interface in the pore is not the controlling factor, then items 1 and 2 together determine the collection efficiency. The transport of the analyte gas molecule takes place within the pores, in the gas phase. This process is far faster than the situation with a hydrophilic membrane the relaxation time is well below 100 ms, and the overall response time may in fact be determined by liquid-phase diffusion in the boundary layer within the lumen of the membrane tube, by liquid-phase dispersion within the... 

The diffusion coefficient in the polymeric membrane is related to the free volume available within the membrane matrix. In the case of porous membranes, the diffusivity of the molecules can be directly related to the porosity (pore size and distribution) and tortuosity of the pathways available for the molecules, and a fine tuning of these two characteristics can help in increasing the flux without affecting the membrane selectivity [31,32]. On the other side, in nonporous membranes the fiee volume represents... 

Finally, it is important to notice the effect of the support in the pervaporation flux, analyzed by de Bruijn et al. [164] who proposed a model and evaluated the contribution of the support layer to the overall resistance for mass transfer in the selected literature data. They found that in many cases, the support is limiting the flux the permeation mechanism through the support corresponds to a Knudsen diffusion mechanism, which makes improvements in the porosity, tortuosity, pore diameter, and thickness necessary for an increase in the pervaporation flux. In fact, the researchers of Bussan Nanotech Research Institute Inc. (BNR), Sato et al. [165], designed and patented an appropriate asymmetric ceramic porous support to suppress pressure drop, and in this case, the water flux increased dramatically compared to previous reported results. Wang et al. [166] have clearly shown that the flux of the membranes increased with the porosity of the hollow fiber supports. In spite of the thin 1 pm zeolite layer, prepared by Zhou et al. [167], the flux enhancement compared to layers 10 times thicker [168] was not significant. 

Porous glasses in the shape of beads and ultrathin membranes with comparable texture properties are an ideal model system to investigate the transport characteristics of the mesopores inside the primary particles of silica supports. The hydrogenation of benzene over a nickel catalyst based on the porous glass beads is a suitable test reaction to estimate the effective diffusivities. The tortuosity factors can be obtcdned from measurements of the permeability of membranes with comparable texture properties. Now, the pore diffusivity of benzene under reaction conditions can be calculated. The low absolute values of the pore diffusivities obtained in this study indicate that interactions between the difiusing reactant and the surface of the support or pore roughness effects have to be considered. 

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