Fibers hexagonal array

It is worth noting that ideal arrangements of fibers of circular cross section with the highest packing, hexagonal arrays with the fibers touching, would lead to a theoretical volume fiber fraction of 0.9. This value is never... 

Hartwick (17) aligned uniformly sized fibers into a densely packed hexagonal array. The interstices between the fibers represented the flow channels. There was no transport between the channels. The performance of the device was low relative to its permeability. This is not unexpected A key property of a packed bed is the radial mass transfer, which evens out flow nonuniformities. Tto is not possible in a device consisting of parallel independent flow paths. In an array of circular parallel channels, the breakthrough time for an unretained sample is inversely proportional to the square of the diameter of the channel. To obtain a plate count of 10,000 plates, it would be necessary that the relative standard deviation of the channel diameter is under 0.5% (see also the footnote in Section 2.1.4). This is clearly a tall order. For retained peaks, similar demands would need to be placed on the uniformity of the stationary phase from channel to channel. 

Figure 2. Schematic of the myofilament lattice of the long tonic fibers of crayfish leg muscle. The large circles represent the myosin filaments which are arranged in a hexagonal array, forming lattice planes (1, O ) with the distance between the lattice planes indicated (di o)> The small circles represent the actin filaments, twelve of which are arranged equidistant around each myosin filament, providing a 6 1 unit cell (---). There appear to be no struc-...

Fig. 19 Example of a mesoporous silica nanofiber containing hexagonal arrays of meso-pores winding about the fiber axis. Reproduced from [177]. (2005) American Chemical...

Figure 17.33 Distance between individual 7 xm diameter carbon fiber filaments in a regular hexagonal array at different packing fractions.

An orthotropic material is called transversely isotropic when one of its principal planes is a plane of isotropy, i.e. at every point there is a plane on which the mechanical properties are the same in all directions [2]. Unidirectional carbon fibers packed in a hexagonal array with a relatively high volume fraction can be considered transversely isotropic, with the 2-3 plane normal to the fibers as the plane of isotropy (Figure 22.2). For a transversely isotropic material, it should be noted that the subscripts 2 and 3 (for a 2-3 plane of symmetry) in the material constants are interchangeable. Hence... 

Fig. 7.18. Source of shrinkage stresses (a) rigid inclusion embedded in a matrix (b) resin pockets surrounded by fibers in hexagonal and square arrays. After Hull (1981).

Fig. 2-8 presents a schematic of the model on which various analytical methods are based. A longitudinal section of the composite having a hexagonal fiber array is shown, and all the pertinent elements are identified. 

Fig. 29-3 Sections of infinite arrays of fibers illuminated alternatively with power + and —. The arrays are (a) one-dimensional, (b) columnar, (c) hexagonal and (d) chess board.

Fig. 29-4 (a) Infinite, one-dimensional array of fibers labelled by n and with center-to-center separation d. (b) and (c) are finite polygonal arrays for the triangular (n = 3) and hexagonal (n = 6) cores. The central fiber is not necessarily identical to the surrounding fibers, and the center-to-center separation between the central and surrounding fibers is d. 

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