Fuller method

The determination of diffusion properties can also be carried out by static observation at a particular point on the surface and by following the change in concentration with time, rather than by the fuller method of profile analysis. Such methods have been used by Renard and Deloche [261] (equation given earlier) and Abramenkov et al. [260] these methods of analysis are detailed elsewhere [406, 410] and will not be discussed here. 

Av is the so-called diffusion volume, which can be evaluated from the group contributions given in Table 3.8. The average error of the Fuller method is reported to be 4% (6). 

Table 3.8 Structural groups for the evaluation of the diffusion volume using the Fuller method.

In this discussion. Dab represents the diffusion coefficient for solute A in solvent B. For ideal gases, however. Dab is independent of concentration, so that Dab = D a-Two empirical methods to estimate Dab for binary gas systems at low pressures are described by Reid et al (1987). These are the Wilke-Lee method (Wilke Lee 1955) and the Fuller method (Fuller et al. 1965,1966,1969). The Wilke-Lee method requires only the liquid volume of components A and B at their normal boiling points, the molar mass of A and B, temperature and pressure. 

Both the Wilke-Lee and Fuller methods are reliable, often giving errors of only a few percent occasionally, however, they can give errors as high as 10 to 20%. 

For a binary mixture of two components A and B in the gas phase, the mutual diffusion coefficient such as defined in 4.3.2.3, does not depend on composition. It can be calculated by the Fuller (1966) method ... 

Z) g = mutual coefficient of diffusion AB = mutual coefficient of diffusion calculated by Fuller s method... 

A procedure involving only the wall area and based on the cylindrical pore model was put forward by Pierce in 1953. Though simple in principle, it entails numerous arithmetical steps the nature of which will be gathered from Table 3.3 this table is an extract from a fuller work sheet based on the Pierce method as slightly recast by Orr and DallaValle, and applied to the desorption branch of the isotherm of a particular porous silica. 

The foremnner of the modern methods of asphalt fractionation was first described in 1916 (50) and the procedure was later modified by use of fuller s earth (attapulgite [1337-76-4]) to remove the resinous components (51). Further modifications and preferences led to the development of a variety of fractionation methods (52—58). Thus, because of the nature and varieties of fractions possible and the large number of precipitants or adsorbents, a great number of methods can be devised to determine the composition of asphalts (5,6,44,45). Fractions have also been separated by thermal diffusion (59), by dialysis (60), by electrolytic methods (61), and by repeated solvent fractionations (62,63). 

Methane, chlorine, and recycled chloromethanes are fed to a tubular reactor at a reactor temperature of 490—530°C to yield all four chlorinated methane derivatives (14). Similarly, chlorination of ethane produces ethyl chloride and higher chlorinated ethanes. The process is employed commercially to produce l,l,l-trichloroethane. l,l,l-Trichloroethane is also produced via chlorination of 1,1-dichloroethane with l,l,2-trichloroethane as a coproduct (15). Hexachlorocyclopentadiene is formed by a complex series of chlorination, cyclization, and dechlorination reactions. First, substitutive chlorination of pentanes is carried out by either photochemical or thermal methods to give a product with 6—7 atoms of chlorine per mole of pentane. The polychloropentane product mixed with excess chlorine is then passed through a porous bed of Fuller s earth or silica at 350—500°C to give hexachlorocyclopentadiene. Cyclopentadiene is another possible feedstock for the production of hexachlorocyclopentadiene. 

For prediction of the gas diffusivity of binary air-hydrocarbon or nonhydrocarbon gas mixtures at low pressures, the method of Fuller et al. given by Eq. (2-152) is recommended. 

TABLE 5-16 Atomic Diffusion Volumes for Use in Estimating Oab by the Method of Fuller/ Schettler/ and Giddings... 

X-ray studies indicate that the vinyl chloride polymer as normally prepared in commercial processes is substantially amorphous although some small amount of crystallinity (about 5% as measured by X-ray diffraction methods) is present. It has been reported by Fuller d in 1940 and Natta and Carradini in 1956 that examination of the crystalline zones indicates a repeat distance of 5.1 A which is consistent with a syndiotactic (i.e. alternating) structure. Later studies using NMR techniques indicate that conventional PVC is about 55% syndiotactic and the rest largely atactic in structure. 

The.se two approaches may be shown to be thermodynamically equivalent and, given the same assumptions, will lead to identical results for the state downstream of a cooled row (if the input conditions are the same—see the published discussion of Ref. 7 ). But the Young and Wilcock method gives a fuller understanding of the details of the cooling process. 

A fuller review of the AL law together with an illustration of the method is given by Mullin (2001). 

Cocking has shown that the compound with o-cresol melts, not at 50° but at 55-2°, and has prepared a method for the determination of cineol based on the preparation of this compound (vide infra). This method was criticised adversely in Volume I of this work. Further examination of the method has shown that this criticism is not altogether justified, and should be deleted, a fuller review of the method given on p. 282 taking its place. 

A method, proposed more recently by FULLER, SCHETTLER and GlDDlNGSf8 . is claimed to give an improved correlation. In this approach the values of the diffusion volume have been modified to give a better correspondence with experimental values, and have then been adjusted arbitrarily to make the coefficient in the equation equal to unity. The method does contain some anomalies, however, particularly in relation to the values of V for nitrogen, oxygen and air. Details of this method are given in Volume 6. 

Fuller details of the methods used for toxicity testing, the interpretation of the result and their use in setting standards for industrial hygiene are given in the more specialised texts on the subject see Carson and Mumford (1988) and Lees (1996). 

Coating Mass Uniformity and Distribution. Basically, there have been two approaches to model the accumulation of mass (coating material) on the surface of bed particles (i) the use of population balances and (ii) the probabilistic modelling of the spray-particle interaction. We will look at each of these approaches and see how it may be possible to combine these methods to give a fuller picture of coating performance. 

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