Material dispersion approximation

Since their commercial introduction during the 1940s as components of proprietary detergents and laundry preparations, these products have found extensive usage in the whitening of paper and textile materials. Disperse FBAs are available for whitening hydrophobic fibres and solvent-soluble FBAs impart fluorescence to oils, paints, varnishes and waxes. Approximately 75% of commercially established FBAs are stilbene derivatives with inherent substantivity for paper and cellulosic textiles, but the remainder come from about twenty different chemical classes. These include aminocoumarins (6%), naphthalimides (3%), pyrazoles and pyrazolines (each about 2%), acenaphthenes, benzidine sulphones, stilbene-naphthotriazoles, thiazoles and xanthenes (each about 1%). FBAs of these and other chemical types are discussed in detail in Chapter 11 of Volume 2. 

Colloidal suspensions, emulsions and solid dispersions are produced by means of colloid mills or dispersion mills. Droplets or particles of sizes less than 1 (im may be formed, and solids suspensions consisting of discrete solid particles are obtainable with feed material of approximately 100-mesh or 50 p,m in size. 

A similar procedure was used to produce PPy-poly(ethylene-covinyl acetate) [PEVA] composites.47 The host polymer can be dissolved in a toluene solution with pyrrole. A concentrated dispersion is then formed by adding it to an aqueous solution containing a surfactant. An aqueous solution of the oxidant (FeCl3) is then introduced to form the polymer. The conductivity of the resultant materials is approximately 5 S cm-1. The PEVA-based composites can be processed into films and other shaped articles by hot pressing at approximately 100-150°C and 15-20 MPa pressure for 1 h. The mechanical properties are determined by the PEVA content. For example, for composites of PPy-PEVA containing 20% (w/w) PPy, soft flexible films that can be extended up to 600% were produced. For pure PPy films, elongations of less than 5% are achievable. 

An experimental setup for gaseous systems is shown in Fig. 7. The actual ZLC column consists of a thin layer of adsorbent material placed between two porous sinter discs. The individual particles (or crystals) are dispersed approximately as a monolayer across the area of the sinter. This minimizes the external resistances to heat and mass transfer, so that the adsorption cell can be considered as a perfectly mixed isothermal, continuous-flow cell. The validity of this assumption has been examined in detail [52]. The isothermal approximation is generally valid for studies of diffusion in zeoHte crystals, but it can break down for strongly adsorbed species in large composite particles under conditions of macropore diffusion control. 

It is well known that the dispersion in the optical fibers is divided into three parts, modal dispersion, material dispersion, and waveguide dispersion. In the case of the SI POF, the modal dispersion is so large that the other two dispersions can be approximated to be almost zero. However, the quadratic refractive-index distribution in the GI POF can dramatically decrease the modal dispersion. We have succeeded in controlling the refractive-index profile of the GI POF to be almost a quadratic distribution by the interfacial-gel polymerization technique (2). Therefore, in order to analyze the ultimate bandwidth characteristics of the GI POF in this paper the optimum refractive index profile is investigated by taking into account not only the modal dispersion but also the material dispersion. 

Refractive-Index Profile. The refractive-index profile was approximated by the conventional power law. The output pulse width from the GI POF was calculated by the Wentzel-Kramers-Brillouin (WKB) method (10) in which both modal and material dispersions were taken into account as shown in Equations (3), (4), and (5). Here, aintemodai cTintramodai, and CTtotai signify the root mean square pulse width due to the modal dispersion, intramodal (material) dispersion, and both dispersions, respectively. 

Some useful approximations for material dispersion are given in reference [6]. For the wavelength range, 800-1700 nm. Equation 11 is claimed to be accurate to better than 10%. 

Initially we assume that the waveguide is composed of materials which are nondispersive. We subsequently determine the modification due to material dispersion. Only bound rays are included in the present chapter, as they characterize the transmission properties of long fibers. The major conclusion of this chapter is that pulse spreading on fibers is minimized if the profile has an approximately parabolic profile. 

Thus, the ray transit time is independent of skewness and is identical to the corresponding planar waveguide expression within the linear-dispersion approximation to material dispersion. It is implicit that p is small in these expressions. 

A colloid is a material that exists ia a finely dispersed state. It is usually a solid particle, but it may be a Hquid droplet or a gas bubble. Typically, coUoids have high surface-area-to-volume ratios, characteristic of matter ia the submicrometer-size range. Matter of this size, from approximately 100 nm to 5 nm, just above atomic dimensions, exhibits physicochemical properties that differ from those of both the constituent atoms or molecules and the macroscopic material. The differences ia composition, stmcture, and iateractions between the surface atoms or molecules and those on the iaterior of the colloidal particle lead to the unique character of finely divided material, specifics of which can be quite diverse (see Flocculating agents). 

Filter aids should have low specific surface, since hydraulic resistance results from frictional losses incurred as liquid flows past particle surfaces. Specific surface is inversely proportional to particle size. The rate of particle dispersity and the subsequent difference in specific surface determines the deviations in filter aid quality from one material to another. For example, most of the diatomite species have approximately the same porosity however, the coarser materials experience a smaller hydraulic resistance and have much less specific surface than the finer particle sizes. 

Recovering the bitumen is not easy, and the deposits are either strip-mined if they are near the surface, or recovered in situ if they are in deeper beds. The bitumen could be extracted by using hot water and steam and adding some alkali to disperse it. The produced bitumen is a very thick material having a density of approximately 1.05 g/cm. It is then subjected to a cracking process to produce distillate fuels and coke. The distillates are hydrotreated to saturate olefinic components. Table 1-8 is a typical analysis of Athabasca bitumen. ... 

The existence of yield stress Y at shear strains seems to be the most typical feature of rheological properties of highly filled polymers. A formal meaing of this term is quite obvious. It means that at stresses lower than Y the material behaves like a solid, i.e. it deforms only elastically, while at stresses higher than Y, like a liquid, i.e. it can flow. At a first approximation it may be assumed that the material is not deformed at all, if stresses are lower than Y. In this sense, filled polymers behave as visco-plastic media with a low-molecular and low-viscosity dispersion medium. This analogy is not random as will be stressed below when the values of the yield stress are compared for the systems with different dispersion media. The existence of yield stress in its physical meaning must be correlated with the strength of a structure formed by the interaction between the particles of a filler. 

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