Inflated membranes

The operating principle of a DAC is elegantly simple (Figure 15). A gasket of metal foil (usually steel, W or Re) is placed between the diamond anvils. A hole drilled in the center of the gasket contains the sample immersed in a hydrostatic liquid. The anvils are mounted on beryllium (for X-ray transparency) back-plates, to which force is apphed by an inflatable membrane, a level-arm mechanism or just by tightening screw-bolts. Thus a hydrostatic compression is achieved. Such cells can be operated also at high and low temperature, and are also suitable for spectroscopic studies, since diamond is an ideal transmitter of heat and of all types of radiation. 

An inflatable diaphragm or membrane has been used in membrane plate presses which are closely related to the conventional plate and frame presses. A pressure filtration period is followed by compression with the hydraulically operated membrane or by a hydraulically operated ram if flexible rim seals are fitted. This principle is also used in vertical presses that use either one or two endless cloth belts indexing between plates. Inflatable membrane is also used on a cylindrical filtration surface with or without a preceding pressure filtration stage, in the so-called tube presses. 

The driving force for filtration in pressure filters is usually the liquid pressure developed by pumping or by the force of gas pressure in the suspension feed vessel. Alternatively, or in addition, the liquid may be squeezed through and out of the cake by the mechanical action of an inflatable membrane, a piston or a porous medium pressed on top of the cake. Pressure filtration is, therefore, defined here as any means of surface filtration where the liquid is driven through the medium by either hydraulic or mechanical pressure, greater than atmospheric. The solids are deposited on top of the filter medium (as in all surface filters), with the possible exception of some cartridge filters which also use a certain amount of depth filtration. In this chapter, the suspension is assumed to approach the medium at 90° and this excludes the so-called dynamic fUter/thickeners or cross-flow filters (also driven by pressure) which are dealt with in a separate chapter (11). 

Membrane filter presses are modified filter presses with the introduction of inflatable membrane systems. 

Figure 15a shows a sample of data captured from the inflating membrane experiment, for a natural rubber membrane as the dielectric (Kaltseis et al. 2014). The figure shows data capture for the sixth cycle of operation. The reason for discarding the first five cycles is to allow the Mullin s effect to elapse, so that the... 

Karamanou et al. [65] have performed finite element analyses to large strains to simulate the thermoforming process, in which thin sheets of polymer are inflated using gas pressure. They adopted a model comprising hyperelastic components and a linear viscous element. Applying a thin shell analysis enabled them to produce realistic predictions of the inflating membrane. 

Note that the relationship between load and deflection is again a cubic one for small deflections of an inflated membrane, Eq. (28), even though the overlying layer has been assumed to be linearly-elastic. As a result, Eq. (29) for the failure pressure has an unusual three-fourths power dependence upon fracture energy, as in Eq. (25). And, again, if we measure simultaneously the failure pressure II and the deflection y of the blister, then we obtain a particularly simple relationship for the fracture eneigy G ... 

Figure 3. AFM images of inflated membranes (nanobubbles) of A) poly(vinyl acetate) at 40 °C and a pressure of 48 kPa. Film thickness=150 nm. B) polystyrene at 100 °C and a pressure of 27 kPa. Film thickness=65 nm. (After reference 23).

If we then introduce a flaw into the system, by poking a pin into the inflated balloon, the balloon will explode, and all this energy will be released. The membrane fails by fast fracture, even though well below its yield strength. But if we introduce a flaw of the same dimensions into a system with less energy in it, as when we poke our pin into a partially inflated balloon, the flaw is stable and fast fracture does not occur. Finally, if we blow up the punctured balloon progressively, we eventually reach a pressure at which it suddenly bursts. In other words, we have arrived at a critical balloon pressure at which our pin-sized flaw is just unstable, and fast fracture just occurs. Why is this ... 

As yet, models for fluid membranes have mostly been used to investigate the conformations and shapes of single, isolated membranes, or vesicles [237,239-244], In vesicles, a pressure increment p between the vesicle s interior and exterior is often introduced as an additional relevant variable. An impressive variety of different shapes has been found, including branched polymer-like conformations, inflated vesicles, dumbbell-shaped vesicles, and even stomatocytes. Fig. 15 shows some typical configuration snapshots, and Fig. 16 the phase diagram for vesicles of size N = 247, as calculated by Gompper and Kroll [243]. 

The inner liner forms the vital internal membrane which holds the inflation medium at an elevated pressure within the structure of the tire. In early days the liner was a separate tube of natural or butyl, or more particularly, XIIR compound as an integral part of the tire structure. Adhesion levels of butyl compounds can be critically low requiring an insulating or barrier layer of an NR compound to act as an interface between the liner and the casing. 

The Wavebag (50 L volume) was placed on the temperature-controlled tray and completely inflated with air using a membrane pump. The airflow was adjusted to 2250 mL using a thermal mass flow meter. 

The results of interfacial tension measurements on BLM formed from five different lipid solutions are given in Table I. One of the immediate questions is whether the measured values represent the true bifacial tension of BLM. It is implicitly assumed in order to apply equation 3 that yb is a characteristic property of BLM and should be independent of the extension of the BLM area. It is generally recognized that if the BLM also possessed elastic properties, the measured yb would be different when it is stretched. To answer this question, yb was measured during both expansion and contraction of the membrane. A typical trace of pressure difference vs. time in which the membrane was being expanded and contracted is shown in Figure 3. The symmetric nature of the curve indicates that little hysteresis was present during inflation and deflation of the BLM. Therefore, it seems safe to conclude that for BLM formed from lipid materials alone the membrane does not appear to possess appreciable elastic properties. 

In order to improve volume efficiency and reduce payload weight for earth-orbital remote-sensing applications, low-mass membrane-based synthetic aperture radar array concepts are being developed. One such system is an inflatable deployable SAR consisting of thin fabrics or membranes that are deployed for L-band operation with dual polarisation. The entire assembly is flexible before employment and is rolled up onto the spacecraft bus. The antenna comprises three membranes positioned vertically over one another the ground plane, the radiation patch, and the microstrip transmission line membranes74. 

The technology to fabricate ultrathin high-performance membranes into high-surface-area membrane modules has steadily improved during the modem membrane era. As a result the inflation-adjusted cost of membrane separation processes has decreased dramatically over the years. The first anisotropic membranes made by Loeb-Sourirajan processes had an effective thickness of 0.2-0.4 xm. Currently, various techniques are used to produce commercial membranes with a thickness of 0.1 i m or less. The permeability and selectivity of membrane materials have also increased two to three fold during the same period. As a result, today s membranes have 5 to 10 times the flux and better selectivity than membranes available 30 years ago. These trends are continuing. Membranes with an effective thickness of less than 0.05 xm have been made in the laboratory using advanced composite membrane preparation techniques or surface treatment methods. 

The approximate operating costs for brackish and seawater reverse osmosis plants are given in Table 5.3. These numbers are old, but improvements in membrane technology have kept pace with inflation so the costs remain reasonably current. 

The operating pressure of brackish water reverse osmosis systems has gradually fallen over the past 20 years as the permeability and rejections of membranes have steadily improved. The first plants operated at pressures of 800 psi, but typical brackish water plants now operate at pressures in the 200- to 300-psi range. Capital costs of brackish water plants have stayed remarkably constant for almost 20 years the rule of thumb of US 1.00 per gal/day capacity is still true. Accounting for inflation, this reflects a very large reduction in real costs resulting from the better performance of today s membranes. 

The industry is extremely competitive, with the manufacturers producing similar products and competing mostly on price. Many incremental improvements have been made to membrane and module performance over the past 20 years, resulting in steadily decreasing water desalination costs in inflation-adjusted dollars. Some performance values taken from a paper by Furukawa are shown in Table 5.5. Since 1980, just after the introduction of the first interfacial composite membranes, the cost of spiral-wound membrane modules on a per square meter basis has decreased seven-fold. At the same time the water flux has doubled, and the salt permeability has decreased seven-fold. Taking these improvements into account, today s membranes are almost 100 times better than those of the 1980s. This type of incremental improvement is likely to continue for some time. 

Figure 6.20 Purchase price in 2003 US dollars for ultrafiltration plants as a function of plant capacity. Data of Rogers corrected for inflation [20]. Reprinted from Synthetic Membrane Processes, A.N. Rogers, Economics of the Application of Membrane Processes, p. 454, G. Belfort (ed.), Copyright 1984, with permission from Elsevier...

An analytical elastic membrane model was developed by Feng and Yang (1973) to model the compression of an inflated, non-linear elastic, spherical membrane between two parallel surfaces where the internal contents of the cell were taken to be a gas. This model was extended by Lardner and Pujara (1980) to represent the interior of the cell as an incompressible liquid. This latter assumption obviously makes the model more representative of biological cells. Importantly, this model also does not assume that the cell wall tensions are isotropic. The model is based on a choice of cell wall material constitutive relationships (e.g., linear-elastic, Mooney-Rivlin) and governing equations, which link the constitutive equations to the geometry of the cell during compression. 

The parison is inflated fast, within seconds or less, at a predetermined rate such that it does not burst while expanding. It is a complex process that involves expansion of a nonuniform membrane-like element. Because the extension ratio is high (above 10), it is difficult to calculate the final thickness distribution. Naturally, much of the recent theoretical research on parison stretching and inflation (as in the case with thermoforming) focuses on FEM methods and the selection of the appropriate rheological constitutive models to predict parison shape, thickness, and temperature distribution during the inflation. 

FEM is the only practical tool to handle the problem. Not surprisingly, this method was first applied to membranes or thin shells in the field of structural analysis, a field where, in fact, FEM was pioneered, with a much later penetration to fluid mechanics and polymer processing. Indeed, Oden and Sato (81) were the first to apply FEM to examine the three-dimensional membrane inflation problem. Two other engineering fields that apply a similar FEM approach are metal sheet forming and glass bottle blowing (82). 

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