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The local temperature solution near the triple-phase line of a solidifying front, its melt, and a surrounding inert phase was obtained analytically including all three phases and solidification kinetics. This analytical solution was validated using a three-phase numerical model of the horizontal ribbon growth of silicon and compared to a two-phase analysis that models the effect of the third phase (e.g. the gas) as an applied heat flux. Although the three-phase solutions have additional modes to represent the gas behavior, for many conditions the two-phase and three-phase models predicted consistent behaviors. However, introduction of a non-zero growth angle causes the gas phase heat fluxes to have strong gradients near the triple-phase line. Even with zero growth angle, there are conditions in which the two-phase and three-phase solutions are very different; one predicting infinite heat fluxes while the other predicts finite fluxes. This depended on the ratios of thermal conductivities, and the angle at which the solid-melt interface intersected the free surface. In particular, when the thermal conductivity of the inert phase was comparable to the melt or solid phases there were significant differences.
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The dispersive velocity of compressional waves in magmatic suspensions
SUMMARY The geophysical detection of magma bodies and the estimation of the dimensions, physical properties and the volume fraction of each phase composing the magma is required to improve the forecasting of volcanic hazards and to understand transcrustal magmatism. We develop an analytical model to calculate P waves velocity in a three-phase magma consisting of crystals and gas bubbles suspended in a viscous melt. We apply our model to calculate the speed of sound as a function of the temperature in three magmas with different chemical compositions, representative of the diversity that is encountered in arc magmatism. The model employs the coupled phase theory that explicitly accounts for the exchanges of momentum and heat between the phases. We show that the speed of sound varies nonlinearly with the frequency of an acoustic perturbation between two theoretical bounds. The dispersion of the sound in a magma results from the exchange of heat between the melt and the dispersed phases that affects the magnitude of their thermal expansions. The lower bound of the sound speed occurs at low frequencies for which all the constituents can be considered in thermal equilibrium, whereas the upper bound occurs at high frequencies for which the exchange of heat between the phases may be neglected. The presence of gas in a magma produces a sharp decrease in the velocity of compressional waves and generates conditions in which the dispersion of the sound is significant at the frequencies usually considered in geophysics. Finally, we compare the estimates of our model with the ones from published relationships. Differences are largest at higher frequencies and are <10 per cent for typical magma.
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- Award ID(s):
- 1950113
- PAR ID:
- 10555582
- Date Published:
- Journal Name:
- Geophysical Journal International
- Edition / Version:
- 1
- Volume:
- 228
- Issue:
- 3
- ISSN:
- 0956-540X
- Page Range / eLocation ID:
- 2122 to 2136
- Subject(s) / Keyword(s):
- none
- Format(s):
- Medium: X Size: 2MB
- Size(s):
- 2MB
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/gji/ggab432
