Mathematics
Scientific paper
Jul 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994e%26psl.125....1i&link_type=abstract
Earth and Planetary Science Letters (ISSN 0012-821X), vol. 125, no. 1-4, p. 1-16
Mathematics
34
Channel Flow, Earth Mantle, Fusion (Melting), Geochemistry, Mathematical Models, Melts (Crystal Growth), Nonequilibrium Conditions, Porosity, Protactinium Isotopes, Radioactive Decay, Radium 226, Thallium Isotopes, Transport Properties, Uranium 235, Uranium 238, Garnets, Mid-Ocean Ridges, Percolation, Peridotite, Spinel
Scientific paper
A one-dimensional melting model for radioactive decay series is presented, incorporating melt transport by porous flow, with diffusive chemical interaction between melt and solid matrix, and instantaneous melt ascent through chemically isolated channels. If melt transport through the channels is dominant, the melting is essentially similar to fractional melting. A significant radioactive disequilibrium can be produced near the bottom of the melting column if mantle upwelling velocity is 10(exp -10) m/s or less, although the time available for producing radioactive disequilibrium is limited, due to efficient element extraction from the solid. Fast melt transport through channels can retain the disequilibrium up to the surface. In this case a small amount of melting (approximately 0.5%) of garnet peridotite can account for an activity ratio (Th-230)/(U-238) of much greater than 1, despite a successively larger amount of melting of spinel peridotite. If porous flow is dominant, compositions of melt and solid are similar to those produced by batch melting because the melt can re-equilibrate with the solid. The time available for producing radioactive disequilibrium is longer than that for melting with channel flow. However, the slow melt percolation and continuous chemical reaction with spinel peridotites buffer the (Th-230)/(U-238) of the percolating melt around unity. For realistic melting conditions, local chemical disequilibrium probably has an insignificant effect on the activity ratios, except that (Ra-226)/(Th-230) can be greatly decreased by a small degree of chemical disequilibrium. Comparisons between model predictions and observed activity ratios suggest that fast melt transport through chemically isolated channels is dominant beneath mid-ocean ridges, whereas melt transport within the Hawaiian plume is not constrained: the full range of models from porous to channel flow is possible.
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