Fiber shape cross-sectional area

Although human hair fibers vary in cross-sectional shape, from nearly circular to elliptical, normalizing most elastic and other properties to fiber thickness can significantly reduce experimental scatter. Thickness is usually characterized as fiber diameter or cross-sectional area. Corrections to diameter for ellipticity are generally not employed. Hair fiber dimensions are also necessary to calculate fundamental elastic properties, and dimensional changes are often employed to follow the course of chemical reactions with hair. 

The fiber cross-section frequently has a shape other than circular, such as the racetrack or dogbone contours. Although this causes no particular complication for measurements in extension, where th sample coefficient is determined directly by the cross-section area, it makes difficult the calculation of absolute values of viscoelastic properties from measurements in torsion or flexure, which involve higher... 

Tensile strength versus cross-sectional area for SiOj fibers prepared from viscous sols and heated at 500, 800, and 1000"C compared to conventional fused silica fibers. From Sakka [205], in Sol-Gel Technology for Thin Films, Preforms, Electronics, and Speciality Shapes, ed. L.C. Klein (Noyes Publications, Park Ridge, New Jersey, 1988). 

Fibers of noncircular cross section can modify and change both functional and aesthetic properties in textile structures. The triangular cross section is typical in those respects its shape leads to a stifler fiber than circular fiber of the same cross-sectional area, and in a fabric this results in less drapability and a crisper surface feel. Also, the flat surfaces reflect light in a different way than do curved surfaces and can create desirable lustrous... 

One frequent observation is the formation of band-shaped fibers characterized by a flat rectangular cross-sectional area [45]. An example of such a fiber shape is shown in Fig. lb. It results, for instance, in a very limited range of polymer concentrations in the case of polyamide 6 spim from acetic acid solutions, while fibers with spherical cross-sectional shape are formed outside this concentration range. Band-shaped fibers have also been reported for polymers such as polycarbonate and many more. 

The concept of tensile stress is simple and straightforward. However, the cross-sectional areas of mar r fibers are not well-defined due to their tmique cross-sectional shapes. One useful parameter to describe the fiber cross-sectional fineness is the linear density (ji), i.e., mass per unit length. For fibers with comparable bulk densities, their cross-sectional area is proportional to the fiber linear density. Hence, the term specific stress (ct) often is used, especially in the textile conununity ... 

The torsional rigidity of a fiber contains a material term (G) and a geometric term (h RV2). The geometric term contains the fiber radius to the fourth power, and hence the radius or diameter of a fiber has a significant effect on its torsional rigidity. Equation 15.33 can only be used for calculating the torsional rigidities of circular fibers, i.e., those with circular cross-sections. When a non-circular fiber is studied, the shape factor (A. ), i.e., the ratio of the perimeter of the non-circular fiber to that of a circular fiber of the same cross-sectional area, should be used ... 

The cross sections of plain and modified PP fibers were imaged by SEM. There was no significant change to the cross-sectional shape or the cross-sectional area upon... 

If a spinal cord is cross-sectioned, the gray matter appears as a roughly H-shaped area in its middle which is, divided into dorsal (posterior), lateral, and ventral (anterior) horns. The horns are interconnected by a crossbar, the gray commissure. The rest of the spinal cord is the white matter, made up largely of tracts of myelinated nerve fibers (axons). Ascending tracts carry afferent sensory impulses towards the brain, descending tracts transmit motor impulses from the brain to the motor neurons in the ventral or lateral horns of the gray matter. 

With ionizing radiation (consecutive steps procedure) with saturated aqueous ZnCl2 as solvent and a monomer concentration of 32%, the cross section of the fiber retained its natural shape, and polymer was distributed from the outer edge of the fiber towards the lumen area (33), as shown in Figure 11A. If more dilute aqueous ZnCl2 and a lower concentration of monomer were used, the cross section of the fiber was rounded, and the polymer was more concentrated in the outer layers of the fiber (31, 36), as shown in Figure 11C. When N,N-dimethylforma-... 

High Absorbency Rayons. Over the past years, disposable products have become commonplace, especially in the United States and Europe. Cellulosic fibers, particularly rayons, have served the needs of the disposables industry because of their absorbent qualities. The most useful fibers for disposable/ absorbent applications are the rayons with crenulations, crimp, and hollow regions, all of which add to the absorbency of the fiber. These characteristics are achieved in varying degrees by physical and chemical alterations in the spinning process. Crenulations, or random irregularities in the shape of the cross-section, typical for most rayon fibers, are caused by the rapid formation of skin before the dehydration is complete. As the fiber interior loses solvent, it collapses in certain areas and produces the crenulated shape. Furthermore, fabricators have learned how to... 

This pattern is more pronounced in fibers of low maturity. Even in mature fibers, the lumen cross section assumes an elongated shape on drying, thus giving the fiber cross section a long and a short axes. This asymmetric structure indicates that there may be differences in fibrillar packing densities around the perimeter of the fiber. Such zones would present different areas of accessibility in the fiber. It is not known whether these zones of variations in fibrillar density are due to inherent differences in fibrillar structure at different areas of the cross section, or whether physical forces during drying compress the structure in some areas and expand it in others [279,280]. Dried fibers with relatively thick secondary walls produce... 

Membrane materials are available in various shapes, such as flat sheets, tubular, hollow fiber, and monolithic. Flat sheets have typical dimensions of 1 m by 1 m by 200 pm thickness. Tubular membranes are typically 0.5 to 5.0 cm in diameter and up to 6 m in length. The thin, dense layer is on either the inside or the outside of the tube. Very small-diameter hollow fibers are typically 42 pm i.d. by 85 pm o.d. by 1.2 m long. They provide a very large surface area per unit volume. Honeycomb, monolithic elements of inorganic oxide membranes are available in hexagonal or circular cross section. The circular flow channels are typically 0.3 to 0.6 cm in diameter (Seader and Henley, 2006). 

The area so calculated is independent of cross-sectional shape. The fiber diameter (D) may then be calculated, assuming circularity. 

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