Partial melting of a Pb‐Sn mushy layer due to heating from above, and implications for regional melting of Earth's directionally solidified inner core

Yu, James; Bergman, Michael; Huguet, Ludovic; Alboussière, Thierry

doi:10.1002/2015gl064908

Cited by 7 publications

(6 citation statements)

References 49 publications

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“…Beyond the application of geological carbon storage, solute-driven convection in porous media occurs in many geophysical processes. These include the formation of sea ice (Feltham et al, 2006;Wettlaufer et al, 1997), coastal and volcano hydrogeology (Cigolini et al, 2001;Greskowiak, 2014;Van Dam et al, 2009), evaporation from soil (Norouzi Rad & Shokri, 2012), and the solidification of metallic cores (Yu et al, 2015). In all these diverse applications, our results potentially affect both the interpretation of the observed patterns and the inferred solute fluxes.…”

Section: Discussionmentioning

confidence: 99%

Effect of Dispersion on Solutal Convection in Porous Media

Liang

Wen

Hesse

et al. 2018

Geophysical Research Letters

109

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Solutal convection in porous media is thought to be controlled by the molecular Rayleigh number, Ra m , the ratio of the buoyant driving force over diffusive dissipation. The mass flux should increase linearly with Ra m and the finger spacing should decrease as Ra −1∕2 m. Instead, our experiments find that flux levels off at large Ra m and finger spacing increases with Ra m . Here we show that the convective pattern is controlled by a dispersive Rayleigh number, Ra d , balancing buoyancy and dispersion. Increasing the bead size of the porous medium increases Ra m but decreases Ra d and hence coarsens the pattern. While the flux is predominantly controlled by Ra m , the anisotropy of mechanical dispersion leads to an asymmetry in the pattern that limits the flux at large bead sizes.Plain Language Summary Pattern formation in simple physical systems is intriguing, and convection in porous media is an example that was thought to be well understood. Convection is controlled by the balance between buoyant driving forces and dissipative mechanisms such as diffusion that smear out the concentration and hence density differences. Here we use simple laboratory experiments to show that the convective pattern is controlled by a different process than previously thought. A Rayleigh number based on mechanical dispersion, which is independent of fluid properties, predicts the flow pattern of solutal convection in bead packs.

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Section: Discussionmentioning

confidence: 99%

Effect of Dispersion on Solutal Convection in Porous Media

Liang

Wen

Hesse

et al. 2018

Geophysical Research Letters

109

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“…No single model of a transition layer explains all our data, implying that the characteristics of the transition must be spatially varying. An irregular transition (a patchy inner core boundary) whose characteristics vary, as inferred here, appears to favor nonlinear solidification models, where inner core growth is locally modulated by thermal perturbations at the ICB (Bergman et al, ; Bergman & Fearn, ; Calkins et al, ; Ren et al, ; Yu et al, ). Based on our observations, the hypothesis of isothermal, and therefore, uniform growth leading to an inner core void of a mushy region can be rejected (Morse, ).…”

Section: Discussionmentioning

confidence: 60%

“…Fine-scale structural features of this nature are important for understanding the geodynamics of inner core growth. The most plausible explanation for the presence of an irregular transition layer having variable rigidity is nonlinear solidification driven by small-scale 10.1029/2018GC007562 convection in the bottommost outer core that produces short-scale thermal perturbations along the inner core boundary (e.g., Calkins et al, 2012;Yu et al, 2015). EAR-1261681) (Stammler, 1993) and SAC (Goldstein et al, 2003) were used to process seismograms.…”

Section: Discussionmentioning

confidence: 99%

“…interface (Spetzler & Anderson, 1968;Yu et al, 2015). Models having an additional discontinuity, however, can explain anomalously high spatially localized PKIIKP/PKIKP energy ratios if the velocity and density profiles are uniform (i.e., no gradient) between the ICB and the additional discontinuity (e.g., see Figures 9c and S4).…”

Section: Geochemistry Geophysics Geosystemsmentioning

confidence: 99%

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Irregular Transition Layer Beneath the Earth's Inner Core Boundary From Observations of Antipodal PKIKP and PKIIKP Waves

Attanayake

Thomas

Cormier

et al. 2018

Geochem Geophys Geosyst

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Standard Earth models assume a simple uniform inner core boundary (ICB) separating the liquid iron outer core from the solid iron inner core. Metallurgical and geodynamic experiments, however, predict lateral variations along this boundary originating from thermochemical and geodynamic instabilities during solidification. We search for evidence of this lateral heterogeneity by exploiting the sensitivity of antipodal PKIIKP waveforms to the shear wave velocity structure of the uppermost inner core beneath their reflection points on the underside of the ICB. Measuring PKIIKP/PKIKP energy ratios from 33 rare antipodal seismograms in the 178o to 180o distance range, we find this ratio varying between 0.1 and 1.1. Synthetic seismograms demonstrate that a laterally homogeneous liquid‐solid ICB cannot account for this variability. Observations instead support a spatially variable ICB transition consisting of either (1) gradients in seismic velocities and density in which they smoothly increase from those at the outer core to those in the bulk of the inner core over a maximum depth of 10 km or (2) a layered transition with localized double discontinuities in velocities and densities separated by 4–10 km. A layered transition can generate a coda following PKIKP if shear velocity is small (<2 km/s) in the transition. Our results imply that the ICB is not uniform and might appear patchy with lateral rigidity variations. Nonuniform small‐scale structural features that we infer to be present at the ICB are consistent with nonlinear solidification mechanisms driven by small‐scale outer core convection in the lowermost outer core.

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“…Wettlaufer et al (1997) determined the time-evolution of the vertically-averaged solid fraction in an aqueuous sodium chloride mushy layer by measuring the volumetric change during solidification due to the density difference between water and ice. A variety of experimental systems have been used to show that the melting of a reactive mixed phase region can result in solidification deeper within that region as a result of convection, and investigated the evolution of the solid fraction (Hallworth & Huppert 2004;Hallworth et al 2005;Yu et al 2015;Huguet et al 2016). Several authors (Shirtcliffe et al 1991;Chiareli & Worster 1992;Notz et al 2005) developed methods to measure the electrical resistance in the melt, which varies with the local solid fraction and allows the evolution of φ(z) to be determined as it evolves during solidification.…”

Section: Introductionmentioning

confidence: 99%

Solidification of binary aqueous solutions under periodic cooling. Part 2. Distribution of solid fraction

2019

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We report an experimental study of the distributions of temperature and solid fraction of growing $\text{NH}_{4}\text{Cl}$–$\text{H}_{2}\text{O}$ mushy layers that are subjected to periodical cooling from below, focusing on late-time dynamics where the mushy layer oscillates about an approximate steady state. Temporal evolution of the local temperature $T(z,t)$ at various heights in the mush demonstrates that the temperature oscillations of the bottom cooling boundary propagate through the mushy layer with phase delays and substantial decay in the amplitude. As the initial concentration $C_{0}$ increases, we show that the decay rate of the thermal oscillation with height also decreases, and the propagation speed of the oscillation phase increases. We interpret this as a result of the solid fraction increasing with $C_{0}$, which enhances the thermal conductivity but reduces the specific heat of the mushy layer. We present a new methodology to determine the distribution of solid fraction $\unicode[STIX]{x1D719}(z)$ in mushy layers for various $C_{0}$, using only measurements of the temperature $T(z,t)$. The method is based on the phase behaviour during thermal modulation, and opens up a new approach for inferring mushy-layer properties in geophysical and engineering settings, where direct measurements are challenging. In our experiments, profiles of the solid fraction $\unicode[STIX]{x1D719}(z)$ exhibit a cliff–ramp–cliff structure with large vertical gradients of $\unicode[STIX]{x1D719}$ near the mush–liquid interface and also near the bottom boundary, but much more gradual variation in the interior of the mushy layer. Such a profile structure is more pronounced for higher initial concentration $C_{0}$. For very low concentration, the solid fraction appears to be linearly dependent on the height within the mush. The volume-average of the solid fraction, and the local fluctuations in $\unicode[STIX]{x1D719}(z)$ both increase as $C_{0}$ increases. We suggest that the fast increase of $\unicode[STIX]{x1D719}(z)$ near the bottom boundary is possibly due to diffusive transport of solute away from the bottom boundary and the depletion of solute content near the basal region.

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Partial melting of a Pb‐Sn mushy layer due to heating from above, and implications for regional melting of Earth's directionally solidified inner core

Cited by 7 publications

References 49 publications

Effect of Dispersion on Solutal Convection in Porous Media

Effect of Dispersion on Solutal Convection in Porous Media

Irregular Transition Layer Beneath the Earth's Inner Core Boundary From Observations of Antipodal PKIKP and PKIIKP Waves

Solidification of binary aqueous solutions under periodic cooling. Part 2. Distribution of solid fraction

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