Membrane modulus

Figure 2. Schematic of UF equipment B, capillary membrane modulus S, must reservoir M, manometers.

Ways to increase membrane durability have been examined by various researchers across the country. Maurtiz et al. examined the use of metal-oxide metal particles to increase the properties of the membrane. A titanium isopropoxide (Figure 11.4) addition to Nation membranes generates quasi-network particles this improves membrane modulus and dimensional stability [17], In addition, the titanium matrix reduces fuel crossover and minimizes chemical degradation. Table 11.2 shows the increase in modulus along with stress and strain and stress changes after the addition of the titanium matrix [17], With a 20% load of the titanium matrix, performance criteria remain comparable. Acid functionality remains intact however, water uptake is reduced as volume inside clusters is occupied. Conductivity is reduced due to chain mobility [17],... 

Inert membranes are by far the most widely used in polymeric membrane reactors. Since in PIMRs the catalytic function is absent from the membrane, in comparison with PCMRs this type of membrane reactor represents a lower level in process integration. However, because of this and because the membrane modulus can be separated from the vessel where the chemical reaction takes place, PIMRs allow a much wider range of reactor configurations than PCMRs. 

For most hydrardic pressure-driven processes (eg, reverse osmosis), dense membranes in hoUow-fiber configuration can be employed only if the internal diameters of the fibers are kept within the order of magnitude of the fiber-wall thickness. The asymmetric hoUow fiber has to have a high elastic modulus to prevent catastrophic coUapse of the filament. The yield-stress CJy of the fiber material, operating under hydrardic pressure, can be related to the fiber coUapse pressure to yield a more reaUstic estimate of plastic coUapse ... 

Microindentation anisotropy 143, 145 Microspherulitic structure 139 Microvoiding 193 Microvoids 194, 205 Model membranes 49, 53, 55 Modulus 135 Moisture sensitivity 199... 

The assumption of membrane softness is supported by a theoretical argument of Nelson et al., who showed that a flexible membrane cannot have crystalline order in thermal equilibrium at nonzero temperature, because thermal fluctuations induce dislocations, which destroy this order on long length scales.188 189 The assumption is also supported by two types of experimental evidence for diacetylenic lipid tubules. First, Treanor and Pace found a distinct fluid character in NMR and electron spin resonance experiments on lipid tubules.190 Second, Brandow et al. found that tubule membranes can flow to seal up cuts from an atomic force microscope tip, suggesting that the membrane has no shear modulus on experimental time scales.191 However, conflicting evidence comes from X-ray and electron diffraction experiments on diacetylenic lipid tubules. These experiments found sharp diffraction peaks, which indicate crystalline order in tubule membranes, at least over the length scales probed by the diffraction techniques.123,192 193... 

It is believed that the Gaussian bending modulus k controls the membrane topology. In particular, a negative value of this constant is needed for stable bilayers. A positive value will induce nonlamellar topologies, such as bicontinuous cubic phases. Therefore, it is believed that k is negative for membranes. 

Figure 20. (a) The (dimensionless) lateral compressibility (dilatational modulus, elastic area expansion modulus) (left ordinate) and the dimensionless area per molecule (right ordinate) as a function of the tail length (t) of the PC lipids in equilibrium bilayer membranes. The conversion to real compressibilities and areas per molecule is discussed in the text, (b) The (dimensionless) surface tension and the (dimensionless) lateral compressibility as a function of the relative expansion for the C PC lipid... 

Again, using a lateral dimension of a site, d = 0.2 nm, and the lattice site area as = 3d2, means that y 1 corresponds with about 33mNm 1 lateral tension. In other words, one needs to apply a lateral tension of order 40mNm 1 to double the membrane area. This prediction seems to be a factor of about six lower than estimates that were recently reported by Evans and co-workers [107], These authors use micropipettes to pressurise giant vesicles and obtain values of the order Ka = 8y/Sinn = 230mNm. There are also some data on the compressibility modulus, as found by MD simulations on primitive surfactants [62] Ka = 400 mN m 1. In a molecular detailed simulation study on DPPC lipids, Feller and Pastor [40] report a KA value of about 140 mNm 1. 

Member properties are determined in accordance with Chapter 5, Required dynamic properties usually include unit weight, modulus of elasticity, elastic yield strength, and allowable deformations. Additional properties include post-yield strength or membrane resistance. 

The thermodynamic approach does not make explicit the effects of concentration at the membrane. A good deal of the analysis of concentration polarisation given for ultrafiltration also applies to reverse osmosis. The control of the boundary layer is just as important. The main effects of concentration polarisation in this case are, however, a reduced value of solvent permeation rate as a result of an increased osmotic pressure at the membrane surface given in equation 8.37, and a decrease in solute rejection given in equation 8.38. In many applications it is usual to pretreat feeds in order to remove colloidal material before reverse osmosis. The components which must then be retained by reverse osmosis have higher diffusion coefficients than those encountered in ultrafiltration. Hence, the polarisation modulus given in equation 8.14 is lower, and the concentration of solutes at the membrane seldom results in the formation of a gel. For the case of turbulent flow the Dittus-Boelter correlation may be used, as was the case for ultrafiltration giving a polarisation modulus of ... 

Bauer, Denneler, and Wilert-Porada also studied the influence of temperature (30-120°C) and humidity (0 - 100%) on the mechanical properties of Nation 117 membrane via dynamic mechanical analysis (DMA). The mechanical behavior of Nation membranes in a humid atmosphere was observed to differ significantly from that in dry atmosphere, and the influence of water on the mechanical properties of the acid form of Nation was found to be complex. The maximum of the storage modulus ( ) as a function of humidity was shifted to higher humidity values with increasing temperature. 

Srinivasan and Tien (18) have made an analytical study on the mass-transfer characteristics of reverse osmosis in curved tubular membranes. The increase in mass-transfer due to secondary flow resulted in a substantial reduction in the wall concentration (the polarization modulus) for Np =100 and a/R=0.01 (see Figure 39). Further, the production capacity (permeation rate) was markedly increased (see Figure 40). 

Figure 11.21 Normalized overall rate as a function of the dimensionless bulk substrate concentration for different values of the substrate modulus for internal diffusion in a membrane. Adapted from C.Horvath and J.M.Engasser. Biotechnol. Bioeng., 16, 909 (1974).

The value of Thiele modulus in biological membrane was evaluated by Professor Horvath of Yale. The value is not at all negligible. Because of the distances involved the Thiele modulus is still more important in lateral diffusion. 

When dealing with two-dimensional formation of patterns in lipidic-proteic membranes (fluid membranes), not only does the coupling between the chemical reaction in the membrane and the surface diffusion have to be considered (i.e., the Thiele modulus), but one must also consider the coupling with the onset of convection (Navier-Stokes equa-... 

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