Homogeneous source

When plotted in a In (Al203/Mg0) vs ln(FeO/MgO) (Figure 1.12), the clinopyroxene data define a unique trend which is reasonably linear, thereby supporting the hypothesis of fractional melting made by Johnson et al. (1990). In addition, the linear array supports a homogeneous source and rather constant 0MgoFeO = 0-3 and >MgoAl2° fractionation coefficients. 

Averaging of Results. The averaging of results can be a useful technique if the samples under study are derived from a uniform and homogeneous source. Averaging passing retest results and OOS results to make a release decision is not scientifically valid [17] however. The procedure is not valid since the OOS investigation will determine that the result it either (1) valid, in which case the product is rejected or reworked, if permitted) or (2) invalid, in which case it will be released on the basis of the retest results alone. 

This set is of the same algebraic form as eqns 5.16 for conversion of a single reactant to two products in parallel steps. Because quasi-equilibrium of isomerization is maintained, the reactant acts as a "homogeneous source" despite being split into two isomers, and the mathematics of product formation is the same as for the simpler reaction with network 5.15. Results from constant-volume batch plotted as lnx versus t for P, Q, and total A give identical straight lines with slope -k, as in Figure 5.6, where... 

Coupled parallel steps are an important combination not covered in any standard texts, and are therefore examined in more detail. Typical examples are isomerization in concert with conversion of the isomers to different products. If isomerization is very fast compared with conversion, the isomers are at quasi-equilibrium and act as "homogeneous source," producing a kinetic behavior like that of a single reactant. If isomerization is very slow compared with conversion, the reactions of the different isomers are essentially uncoupled. If the rates of isomerization and conversion are comparable, a more complex behavior ensues. Most interesting is the case with isomerization being somewhat faster than conversion. The isomer distribution then approaches a steady state (not necessarily close to equilibrium), and from then on the isomers act as homogeneous source. 

For most hydrocarbons burning in air, coo,oe/v is only about 0.07, and WF.eff is about 2, so that the pseudo-homogeneous source term in Equation 6 depends only weakly on wq. For this case, i/r plays the role of a zero-order Thiele modulus (13). Thus, the present continuum analysis clearly reveals that the dimensionless parameter which dictates the onset of incipient group combustion is simply a Damkohler niunber (Thiele modulus) which takes on a critical value (Equation 15) dependent only on the ambient oxidizer mass fraction, on the fuel vapor mass fraction at the droplet surface, and on the stoichiometric oxidizer/fuel mass ratio. 

Primary Lavas, melts, and liquids derived solely via melting of a specihc, homogeneous source. In practice, it is hard to recognize or even conceive of a truly primary melt. Strictly speaking, even mantle-derived MORBs may be mix-mres of primary melts derived from a variety of sources, including polybaric melts of variably depleted peridotites and/or basaltic veins. For brevity we have used the term primary in a few cases in this chapter. Where it is used without qualihcation, we refer to melts that are, or could be, in equilibrium with mantle olivine with Mg = 90-93. 

The above discussed the signature of individual particles. Powders, even from homogeneous sources, contain a variety of particle shapes. While a powder may have a variety of repeating particle shapes the composite of these different shapes cannot reproduce the typical particle shape of the powder. 

Here, too, only one straight-line reaction path can be found, namely, that for initial mixtures containing the isomers Ai and A2 in their steady-state ratio [i.e., as homogeneous source as defined in Section 5.3). This mixture is a pseudo-component. Unless isomerization is very fast compared with conversion, there is no unique equilibrium point because the relative amounts of P and Q at complete conversion depend on the initial isomer distribution. The single straight-line path and the rate of progress along that path are insufficient for determination of the four non-zero rate coefficients of the network. 

The FED and FED terms are not easy to describe mathematically, since thqr are not strictly speaking homogeneous sources, the reason being that particulate assemblies are not continua, but made up from discreet bodies. Nevertheless, dominance of co-TSEs in processing equipment is due to their capability of very rapid melting caused by repeated deformations imposed on compacted particulates by twin kneading elements. Eor extensive discussion, please refer to References [5, 45]. 

Schematic view of the transparent cell designed and constructed for observation of temperature non-homogeneities. (Source Maranzana et a ., 2008, with permission of Elsevier.)... 

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