Cylindrical filament

Quantitative Relationship of Conductivity and Antistatic Action. Assuming that an antistatic finish forms a continuous layer, the conductance it contributes to the fiber is proportional to the volume or weight and specific conductance of the finish. As long as the assumption of continuity is fulfilled it does not matter whether the finish surrounds fine or coarse fibers. Assuming a cylindrical filament of length 1 cm and radius r, denoting the thickness of the finish layer as Ar and the specific conductance of the finish k, the conductance R of the finish layer is given by the equation (84) ... 

Cylindrical Filaments. If cylindrical filaments are studied, the last-mentioned assumption is not be fulfilled. In this case it is more suitable to cross an elongated24 primary beam and the fiber in such a way that the irradiated height of the beam, Bgo, is constant. Then the irradiated volume becomes V = Bbo nrj, with /y being the radius of the fiber. In many practical applications the studied fiber is very thin, and the effective absorption coefficient can be approximated by exp (—fiteff) 1. If this approximation is not feasible, the absorption factor exp (—ji ) must be integrated for the chord length distribution gc ( ) of a circle with radius ry (cf. p 168) in order to yield the effective absorption. 

The most common morphology observed in current mesophase carbon fibers of moderate modulus (55 to 75 Mpsi, 379 to 517 GPa) is a cylindrical filament with a random-structured core and a radial rim (12) Given the fracture section of Figure 3, with its scroll-like features, the core appears to be an array of +2ir and -ir disclinations. The radial rim of heavily wrinkled layers usually constitutes half or more of the cross section. 

Figure 1.12 Rotating clamp device used by Meissner to impose a uniaxial extensional strain on a cylindrical filament of polymer of length Lq. Leaf springs in one of the sets of rotating clamps allow the extensional stress to be measured. (From Meissner 1971, reprinted with permission from Steinkopff Publishers.)...

The test can be applied to cylindrical filaments of a very small diameter (=100 o.m) but appreciable corrections have to be made. This case was treated by Rueda et al. (1982) and an appropriate equation was derived in the following way. 

A general solution for the hysteresis loss for arbitrarily shaped filaments with transport current in full penetration transverse fields has been provided by Walker and Murphy [ ]. For the case of cylindrical filaments, dynamic resistivity increases with transport current. Dynamic resistance has been observed in several experiments conducted to examine the effect of transport current on losses... 

The loss is the sum of the losses which result from the contributing current distributions. The first term describes the eddy current loss. The second term treats the total loss that occurs in the filaments and includes losses which, from a continuum point of view, result from the dynamic resistivity of the continuum and the intrinsic magnetization hysteresis of the continuum. The current dependence, g(///c), for cylindrical filaments is given in Fig. 2. The derivation and experimental support for these equations and associated conditions of applicability is contained elsewhere [2 5,7,i5-2ij metallic sheath surrounding the filament-filled redon of the conductor may have an appreciable effect on the eddy current loss if it... 

A spontaneous columnar or cylindrical filament, which rarely branches, of monocrystalline tin emanating from the surface of a plating finish. Furthermore, tin whiskers may have the following characteristics ... 

In order to discover the part played by adhesion in the filtration process, let us consider the deposition of particles on a single cylindrical filament placed in a... 

As diameters of fibers decrease, surface-to-volume ratios SIV increase rapidly. When choosing a specific volume, V (1 cc) of a continuous cylindrical filament, it can be derived that ... 

This idea, not easily acceptable a priori, is, moreover, in dissension with what the experiments of 400 show, when the ratio between the spacing and the diameter of the solid bases equals or exceeds very little the limit of stability, so that the transformation is carried out with enough slowness so that one can observe the changes of the meridian line well, this last form always has a perfectly continuous curve, until the middle of narrowing has only a small thickness only then one sees the cylindrical filament developing with speed. Also Beer, to whom 1 had announced my remark, recognized his eiror ... 

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