Fibre packing

The twist of these aggregates determines the resulting structure. When ribbons stack into fibrils, and fibrils into fibres, packing considerations cause these twisted aggregates to bend and modify their twist with an elastic energy penalty8eiast- For fibrils, it can be shown that the afibrii per peptide in a fibril is ... 

As it will be shown below, it is difficult to match the correct iy-FVF using a simple representation of yam geometry. In general practice, a certain freedom for an interplay of o-FVF and iy-FVF is deemed acceptable yam volume is generally taken lower to allow for simpler yam cross-section shapes, and the iy-FVF is then increased to compensate for discrepancy in the o-FVF. There is a natural constraint to this approach yams have a fibre packing limit. 

To classify geometric features, we select two thresholds for FVF. The values above 75% of iy-FVF are called high or excessive. Models with such iy-FVF do not necessarily exaggerate the actual fibre packing. The 75% boundary shows the models created at their geometrical limits. Likewise, moderate and low iy-FVF does not mean a better quality or a higher precision of the models. Relatively low o-FVF of... 

Although there are a number of materials with the desired pore structure, for instance silicone rubbers, hydrocarbon rubbers, polyesters, polycarbonates and others, their use for industrial applications is limited to polysulfones and cellulose acetates. While the latt have been used with good success for dehydration, technical gas separation relies exclusively on polysulfones which can be used up to approximately 70 °C (their melting point is around 200 °C) and at pressures between IS and 140 bar. The lowest pressure differential between the feed gas side and the permeate gas side is 3 1 and this differential pressure determines the wall thickness of the membranes. Figure 2.8 shows the design of a membrane element developed by Monsanto Company, USA and marketed by the name of Prism separator. Each of these elements or modules contains thousands of hollow fibres packed to a density of approximately 1(X) per cm. ... 

The fibres usually have a log-normal distribution in length, with a mean value of the order of a few mm, depending on the type of pulp. The width of the fibres shows a normal distribution around a mean value of typically tens of microns. Apart from the dimensions of the fibres, the flexibility plays an important role in the formation characteristics. Increasing the wet fibre flexibility will affect both the fibre packing and bonding, and the more flexible the fibres are in a system, then the lower the tendency to flocculate. Despite the high aspect ratio of the fibres, typically 20-50, each fibre in the sheet only penetrates one or two fibre thicknesses and the structure of the paper sheet should therefore be characterized as layered rather than felted. 

Effect of Fibre Packing Variation Along Case... 

Reduced fibre packing at the bundle/case boundary is detrimental to performance. However, characterization of fibre packing in actual modules is required to determine the appropriate value for a and the impact of race tracking on performance. 

Figure 16.15 Effect of variable fibre packing near the module case on dry gas flow rate as a function of dew point. The symbols correspond to different values of a diamond - 0, square - 200, triangle - 400, circle - 600. The upper solid line corresponds to uniform sweep distribution. The lower solid line is provided as a guide for the reader...

If fibre packing is allowed to decrease at the interface between the fibre bundle and the enclosing case, preferential flow will occur along the interface relative to the centre of the bundle. Such flow is detrimental to performance for sufficiently large variation in hydraulic permeability. To determine the magnitude of this effect in commercial modules, fibre packing variations need to be characterized. 

The fibre volume fraction depends heavily on the method of manufacture. A uni directional composite may have a fibre volume fraction as high as 75%. However, this can only be achieved if all the fibres are highly aligned and closely packed. A more typical fibre volume fraction for uni directional composites is 65%. If the fibre configuration is changed to put fibres in other directions, then the maximum fibre packing is reduced further. A typical fibre volume fraction for bi-directional reinforcement (woven fibre) is 40% and a typical volume fraction for random in-plane reinforcement (chopped strand mat) is 20%. 

The complexity of geometrical models of semi-regular structures, e.g. yarns and random fibrous assembhes such as non-wovens,can be explained by a high level of randomness in their structure and a large number of elements, usually individual fibres that have to be considered. Furthermore, it is necessary to consider that fibres do not overlap one another, yet at the same time provide the required fibre orientation distribution and fibre packing density. 

The strength of materials approach provides fonr of the five elastic properties of transversely isotropic nnidirectional composites. Two properties Ey, V12) are well predicted by this simple approach, i.e. nsing the law of mixtures. The other two ( , G 2) require more accurate micromechanics models. The main reason for this is that E i and V12 are independent of fibre packing while d E and G i2 depend strongly on fibre arrangement. 

The maximum volume fraction of fibres to incorporate in a composite has both theoretical and practical limitations. The possible fibre arrangements lead to these limitations. Some examples of fibre packing geometry are shown in Fig. 11.13. 

Geometry of fibre packing for two cases square array and close packing. 

Spencer [17] also suggested that Fean be given for a large variety of fibre packing geometries and respective volume fractions Vf by... 

Nowadays mist eliminators are employed (Table 3.13) to cut out mist. They are made of glass fibre packed between stainless-steel screens which are rectangular or cylindrical in shape. 

Even for dyes of moderate and low strike, the objective of imiform dyeing of the fibre mass is rarely achieved ditring the initial stages of the operation. This is because of irregularities in the material s constraction, in the fibre packing and in the distribution of residital impirrities, as well as differences in temperatirre and flow rate of the solution in contact with the fibres. 

The value / /rdepends upon the fibre packing and the fibre volume content of the composite. The following equations for long fibres of circular cross section have been derived [3] ... 

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