Stretched membrane

Toffoli and Margolus [tofF86] point out that what appears on the macroscopic scale is a good simulation of surface tension, in which the boundaries behave as though they are stretched membranes exerting a pull proportional to their curvature. Vichniac adds that the behavior of such twisted majority rules actually simulates the Allen-Cahn equation of surface tension rather accurately ... 

The surface tension, y, and the mechanical equilibrium at interfaces have been described in the literature in detail (Adamson and Gast, 1997 Chattoraj and Birdi, 1984 Birdi, 1989, 2002, 2008). The surface has been considered as a hypothetical stretched membrane, which is termed as the surface tension. In a real system undergoing an infinitesimal process, it can be written that... 

Iversen et al. [6] found that for a polymer strucmre similar to the interstices between closely packed spheres (phase inversion membrane), Equation 38.4 is able to well describe the tortuosity-porosity relationship whereas for a polymer structure similar to random spheres or clusters (stretched membrane), Equation 38.5 has to be used. 

Pilot plant smdied have also been performed by Larsen et al. [37], who obtained stable operation and more than 95% SO2 removal from flue gas streams with a gas-side pressure drop of less than 1000 Pa. The importance of the membrane structure on the SO2 removal has been studied by Iversen et al. [6], who calculated the influence of the membrane resistance on the estimated membrane area required for 95% SO2 removal from a coal-fired power plant. Authors performed experiments on different hydrophobic membranes with sodium sulfite as absorbent to measure the SO2 flux and the overall mass-transfer coefficient. The gas mixture contained 1000 ppm of SO2 in N2. For the same thickness, porosity, and pore size, membranes with a structure similar to random spheres (typical of stretched membranes) showed a better performance than those with a closely packed spheres stmcture. 

Other techniques for membrane formation include stretching the polymeric film, commonly polytetra-fluoroethylene (PTFE), while it is still in a flexible state and then annealing the membrane to lock in and strengthen the pores in the stretched membrane. The stretching process results into a distinctive membrane structure of PTFE nodes, which are interconnected by fibrils (Fig. 5). 

To obtain a static stress (stretched membrane), the face area of the glass cups was made lOX larger than the face area of the rubber cups. 

The phenomenon of surface tension can be explained by assuming that the surface behaves like a stretched membrane, with 2l force of tension acting in the surface at right angles, which tends to pull the liquid surface away from this line in both directions (Figure 3.1). 

To employ this approach in the considered example, the membrane was described in a continuum limit through a surface, h(y,z), identified as the position of the bilayer midplane. The results of such an analysis for the cases of a tensionless and a 10% stretched membrane are shown in the main panel of Fig. 11 with red and black solid symbols, respectively. The solid lines are fits of the power spectrum It2 with (21). It can be seen that, indeed, Aa = 0.066/f2 g) (predicted by the free edge simulations) corresponds to the membrane tensionless state. The bending rigidity of the bilayer is 4.5kBT and seems to decrease with tension, presumably due to membrane thinning. 

Several authors have in the past stretched the term surface tension to imply that liquids have a saturated film in their surfaces, some mechanism such as a stretched membrane or contractile skin. However we should be careful since this view can lead to great problems when the structure of the so-called skin is considered in terms of molecules. Some writers propose that the surface molecules have their force-fields so deflected that they form a kind of linked skin in the surface, and the attractions between the surface molecules are directed along the surface instead of equally in all directions. This is wrong on two points ... 

The Catastrophe. Population increases are not effected without hazard. If the initial rate is too steep or if N is too high, the sigmoid gives way to a peaked curve whose residual level is some fraction of the maximum population. This behavior, observed in latexes, has been interpreted (51) in terms of the percentage of substrate that is occupied by polymer. Most films break away from the substrate in the form of discrete Islands, reflecting the domain character of the residual stresses (in contrast with the stretched membrane analogy). Both cohesive and adhesive failures are observed. 

Stretched Membranes. Another relatively simple procedure for preparing microporous membranes is the stretching of a homogeneous polymer film of partial crystallinity. This technique is mainly employed with films of polyethylene or polytetrafluoroethylene which have been extruded from a polymer powder and then stretched perpendicular to the direction of extrusion.10 11 This leads to a partial fracture of the film and relatively uniform pores with diameters of 1 to 20jum. A typical stretched membrane prepared from tetrafluoroethylene is shown in the scanning electron micrograph of Figure 1.2. 

Lucassen (1968) and Lucassen-Reynders (1969) worked out the theory for longitudinal surface waves, which appear at elasticity modules higher than 30 mN/m and behaves like a stretched membrane. The related dispersion equation has the form... 

The above argument cannot hold, for example, at a liquid-gas interface since although the molecules are free to move in the liquid, their motion is far more restricted than in a gas where there is little attraction between the molecules. The attraction between the liquid molecules will prevent but a small fraction of them from escaping (vaporizing) into the gas. Therefore, the liquid molecules at the interface are attracted inward and to the side, but there is no outward attraction to balance the pull because, by comparison, there are not many liquid molecules outside in the gas (see Fig. 10.1.1). As a result, the liquid molecules at the surface are attracted inward and normal to the liquid-gas interface, which is equivalent to the tendency of the surface to contract (shrink). The surface of the liquid thus behaves as if it were in tension like a stretched membrane. We emphasize, however, that there really is not a macroscopic smooth meniscus-type surface at which the molecular concentration changes discontinuously from that of the liquid phase to that of the gaseous phase. Rather, this change between the two phases takes place continuously over a small distance of about 100 nm or less. 

Stretched membranes are prepared by stretching an extruded partially crystalline polymer film perpendicular to the direction of extrusion (Fig. 3.6-5). This process creates small ruptures between the crystalline regions in the film that constitute the actual pores. Thermally and chemically very stable PTFE, PP and PE membranes can thus be prepared with pore sizes between 0.1 and 3 pm and porosities up to 90%. 

Fig. 3.6-5 Schematic presentation of the preparation of a stretched membranes (left).

C. Li, J. Liu, R. Guan, P. Zhang, and Q. Zhang. Effect of heating and stretching membrane on ionic conductivity of sulfonated poly(phenylene oxide). J. Membr. ScL, 287(2) 180-186, January 2007. 

Selectivity coefficient Semicondiictor industry Semi-crystalline Separation - factor - gaseous mixtures - liquid mixtures 9 302.481 38.193,259 9 39,308,472,493 332 Stress Stretched membranes Sublayer Sucrose Surface analysis -energy tension 44 73.289.353 13319J33 221 201 367 368... 

A liquid flows readily yet it can adopt extremely stable shapes. A drop of oil in water or a soap bubble forms a perfect sphere that is smooth on an atomic scale and is hardly deformable (Figure 1.1). The fluctuations of the surface thickness are of the order of a mere Angstrom. A liquid surface can be thought of as a stretched membrane characterized by a surface tension that opposes its distortion. 

A liquid-gas interface behaves somewhat like a stretched membrane. The upper and lower surfaces of the liquid film in the device depicted in Fig. 5.1 exert a force F on the sliding rod, tending to pull it in the direction that reduces the surface area. We can measure the force by determining the opposing force Fext needed to prevent the rod from moving. This force is found to be proportional to the length of the rod and independent of the surface area. The force also depends on the temperature and pressure. 

The equilibrium shape of a small liquid droplet surrounded by vapor of the same substance, when the effects of gravity and other external forces are negligible, is spherical. This is the result of the surface tension of the liquid-gas interface which acts to minimize the ratio of surface to volume. The interface acts somewhat like the stretched membrane of an inflated balloon, resulting in a greater pressure inside the droplet than the pressure of the vapor in equilibrium with it. 

A uniformly stretched rubber membrane is similar in many respects to a soap film, or the interface between two fluids. It has a uniform tension and the thickness of the membrane is small compared with the dimensions of the surface area. The analysis of section 5.2, which derives the Laplace-Young equation for a fluid interface or soap film, applies equally to a uniformly stretched membrane with a transverse pressure load that is perpendicular to the surface. So the Laplace-Young equation for the membrane is... 

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