Resistance-model hollow

Figure 3. Cross-section of a resistance-model hollow-fiber and electrical circuit analog...

The history of the membrane developments for reverse osmosis and gas permeation shows that because of inherent differences, it is not possible to simply apply the techniques and materials from one separation technology to the other. The success of the resistance-model hollow-fiber technology which is based on the glassy-fiber technology invented for reverse osmosis, demonstrates the necessity to search for advanced techniques to prepare more selective membranes free of imperfections, rather than to look for new, unavailable materials. 

Henis, J.M.S. Tripodi, M.K. Composite hollow fiber membranes for gas separation resistance model approach. J. Membr. Sci. 1981, 8, 233-246. 

Resistance model for transport in composite hollow fibre membranes based on polysul-fone with siloxane coating has been described in a classical work by Henis and Tripody [51], The resistance in series model assumes that the gas molecules encounter constrictions at certain positions throughout the pore which control the rate of diffusion [20,27,33]. For this scenario the total permeability is inversely related to the total resistance, thus... 

Since the Henis and Tripodi s resistance model led to the development of the Prism hollow fiber, their model is examined in detail in the following example. 

In the patents and papers whieh deseribe the resistance model, it is shown that permeation through composite hollow fibre membranes is analogous to electrical resistance. The symbols used to denote flux or permeation rate are the ones used by Henis and Tripodi. The permeation rate or flux Qi is given by Eq.(11.3) ... 

TABLE 4.22 Impact resistance of GeoDeck 2X6 hollow deck boards filled with fiy ash. Specimen size 102 X 102 mm. GRC Dynatup Model 8200 Series 930-V1.16, tnp diameter 12.7 mm. The specimens did not exhibit any cracking. Average data of the five tests are shown... 

An obvious conclusion is that although mathematical modeling has shown a clear benefit of the modified composite hollow board over the conventional one in flexural modulus and impact resistance, a direct experiment showed that these properties are about the same for both the boards Furthermore, the mathematical modeling showed that flexural strength should be the same for both the boards, a direct experiment showed that the modified board is 13-17% weaker, fhaf is, practically parallel with the weight reduction of 14%. 

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. 

Various parameters in Equation 31.17 have been defined earlier. Danesi et al. [92] described a simple correlation between permeability coefficient in FSSLM and HFSLM configuration. At very large values of ( ) (as compared to 1), Equation 31.17 is transformed into the one used for FSSLM by Danesi et al. [92]. Hence, the smaller the value of ( ), the higher will be the negative value of the left-hand side of Equation 31.17, which suggests the higher rate of mass transfer. Later on, D Elia et al. [93] considered the resistance in series model where they have studied the mass transport across hollow-fiber contactors in NDSX mode. They showed that the overall mass transfer resistance is equal to the sum of individual mass transfer resistances across the aqueous boundary layer and membrane phase. Mathematically, it can be written as follows ... 

Polydopamine and polydopamine- -PEG coatings increase hydrophdicity of the membrane surfaces and have previously been shown to improve fouling resistance toward model od/water emulsions in laboratory studies. Polyacrylonitrde hollow fibre UF and polyamide spiral wound RO membrane modules were surface-modified with an aqueous solution containing dopamine to deposit polydopamine on the membrane surfaces and other wetted parts inside the modules [76]. UF modules were further... 

Abstract. The context of this work is the enhancement of the thermal conductivity of polymer by adding conductive particles. It will be shown how we can use effective thermal conductivity models to investigate effect of various factors such as the volume fraction of filler, matrix thermal conductivity, thermal contact resistance, and inner diameter for hollow particles. Analytical models for lower bounds and finite element models will be discussed. It is shown that one can get some insights from effective thermal conductivity models for the tailoring of conductive composite, therefore reducing the amount of experimental work. 

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