Cylindrical irregularity, effect

Colloidal suspensions are systems of small mesoscopic solid particles suspended in an atomic liquid [1,2]. We will use the term colloid a little loosely, in the sense of colloidal particle. The particles may be irregularly or regularly shaped (Fig. 1). Among the regular shapes are tiny spherical balls, but also cylindrical rods or flat platelets. As the particles are solid, fluctuations of their form do not occur as they do in micellar systems. Not all particles in a suspension will, in general, have the same form. This is an intrinsic effect of the mesoscopic physics. Of course in an atomic system, say silicon, all atoms are precisely similar. One is often interested in the con-... 

Particle Shape Effect. To this point, we have been dealing only with spherical particle suspensions. When the particles have irregular shapes, the rheological properties are expected to be very different from those of the spherical particle suspensions. Consider, for example, a simple system of cylindrical fibre suspensions. Because the particles are expected to align in the direction of the flow or shear, the viscosity needs to be treated as a second-order tensor, that is, the values of the viscosity under the same condition are different when different directions are referred. Only at the low (zero) shear limit may the particles be randomly distributed and have an isotropic rheological behavior. 

Tortuosity In porosimetry evaluations, experimental data tend to be interpreted in terms of a model in which the porous medium is taken to comprise a bundle of cylindrical pores having radius r. If the Young-Laplace equation is then applied to the data, an effective value of r can be calculated, even though this model ignores the real distribution of irregular channels. The calculated r value is sometimes considered to represent the radius of an equivalent cylinder or, alternatively, is termed the tortuosity. 

The symmetry of the chain shape influences both and the abihty to form crystallites. Polyethylene and poly(tetrafluoroethylene) are both sufficiently symmetrical to be considered smooth stiff cylindrical rods. In the crystal, these rods tend to roll over each other and change position when thermally agitated. This motion within the crystal lattice, called premelting, increases the entropy of the crystal and effectively stabilizes it. Consequently, more thermal energy is required before the crystal becomes unstable, and is increased. Flat or irregularly shaped polymers, with bends and bumps in the chain, cannot move in this way without disrupting the crystal lattice, and so have lower values. This is only one aspect. 

Then they choose numerical solution of continuum turbulent flow equations with effective viscosity coefficient p, = Pr + Pm (Pm - coefficient of molecular viscosity) by the use of K-e turbulence model with method of finite elements on irregular computational grid [274]. These equations in cylindrical co-ordinates are as following ... 

Fibers vary in cross-sectional shape, both naturally and by design. Wool fibers are essentially round and cotton fibers are elliptical. Synthetic fibers made by melt spinning can be of a desired shape. Artificial fibers that are spun from solvents in air or from an aqueous medium are usually irregular in shape because of the skin-core effect [2]. Rayon, for example, can have both regular and irregular cylindrical forms composed of hollow as well as solid fibers. 

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