Melt extraction phase equilibrium

Phase equilibria of vaporization, sublimation, melting, extraction, adsorption, etc. can also be represented by the methods of this section within the accuracy of the expressions for the chemical potentials. One simply treats the phase transition as if it were an equilibrium reaction step and enlarges the list of species so that each member has a designated phase. Thus, if Ai and A2 denote liquid and gaseous species i, respectively, the vaporization of Ai can be represented stoichiometrically as —Aj + A2 = 0 then Eq. (2.3-17) provides a vapor pressure equation for species i. The same can be done for fusion and sublimation equilibria and for solubilities in ideal solutions. 

Phase Equilibrium and Melt Extraction Table 1 Model fertile upper-mantle compositions. 

Next, the MgO content is constrained from the observation that molar Mg/(Mg - - Fe ) (i.e., bulk-rock Mg ) ought not to be affected by modal segregation, since mineral Mg s are nearly the same in olivine and in pyroxenes (as shown by experimental phase equilibrium studies and empirical studies of coexisting phases in peridotites). Hence, (Mg )oi = (Mg )buik, to a very good approximation, in spinel Iherzolites. Extraction of partial melt causes an increase in Mg, so that the most primitive samples should have the lowest Mg. Histograms of olivine compositions in spinel Iherzolites from a wide variety of environments show that the most fertile samples that have not been grossly disturbed by metasomatism have Mg s from 0.888 to —0.896. Since the uncertainty with which olivine Mg s are determined in individual samples is typically —0.001, we interpret this distribution as implying an Mg for the primitive depleted mantle of 0.890, which value we adopt. Hence,... 

Osmium isotopes currently provide the strongest case for mineral-to-mineral disequilibrium, and for mineral-melt disequilibrium available from observations on natural rocks. Thus, both osmium alloys and sulfides from ophiolites and mantle xenoliths have yielded strongly heterogeneous osmium isotope ratios (Alard et al., 2002 Meibom et al., 2002). The most remarkable aspect of these results is that these ophiolites were emplaced in Phanerozoic times, yet they contain osmiumbearing phases that have retained model ages in excess of 2 Ga in some cases. The melts that were extracted from these ophiolitic peridotites contained almost certainly much more radiogenic osmium and could, in any case, not have been in osmium-isotopic equilibrium with all of these isotopically diverse residual phases. 

All sulfur rings from Se to S28 have been detected in liquid sulfur by high-pressure liquid chromatography of extracts of quenched sulfur melts which had been equilibrated before at temperatures of between 116 and 250 °C [13]. Raman spectra of hot sulfur melts also showed the presence of cyclo-Sj besides Ss [14]. In addition, the sulfur melt contains varying concentrations of polymeric insoluble sulfur [13-15]. Above 150 C trace amounts of sulfur radicals have been detected in hquid sulfur by ESR spectroscopy [16, 17] as well as by magnetic measurements [18]. It can be expected that the equilibrium sulfur vapor exhibits a similarly complex molecular composition as the melt although the smaller molecules will be enriched in the gas-phase, of course. 

Extraction—distribution between immiscible liquid phases Crystallization—melting point or solubility Adsorption—surface sorption Reverse osmosis—diflusivity and solubility Membrane gas separation—diflusivity and solubility Ultrafiltration—molecular size ion exchange—chemical reaction equilibrium Dwlysis—diflusivity... 

When polyesters are made using melt-phase polymerization, small amounts of cyclic oligomers (1.4—1.8 wt%) are produced, which are in equilibrium with the linear polymer chains [23]. These oligomers, which can migrate to the surface of molded products and interfere with their appearance, can be removed from solid polymer pellets using solvent extraction processes. Unfortunately, the oligomers quickly reappear (due to transesterification reactions) if the polymer is remelted for further processing. 

Extraction—distribution between immiscible liquid phases Crystallization-melting point or solubility Adsorption-surface sorption Reverse osmosis—diffiisivity and solubility Membrane gas separation—diffusivity and solubility Ultrafiltration—molecular size Ion exchange—chemical reaction equilibrium Dialysis—diffiisivity... 

We consider here the role of bulk flow parallel to the direction of the chemical potential gradient based force in phetse-equilibrium based open two-phase systems. Vapor-liquid systems of flash vaporization, flash devolatilization and batch distillation are considered first, followed by a liquid-liquid system for extraction. Solid-liquid systems for zone melting and normal freezing are studied thereafter to explore how bulk flow parallel to the force direction is essential to considerable purifleation of solid systems followed by solid-vapor systems as in drying. 

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