The hard sphere view of the outer core
Abstract The hard sphere model for liquids attempts to capture the physical behavior of a real liquid in a simple conceptual model: a fluid of fixed size spheres that only interact repulsively when they come into contact. Is the model good enough to use for modeling internal planetary structure? To...
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SpringerOpen
2015-05-01
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| Series: | Earth, Planets and Space |
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| Online Access: | https://doi.org/10.1186/s40623-015-0238-7 |
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| author | George Helffrich |
| author_facet | George Helffrich |
| author_sort | George Helffrich |
| collection | DOAJ |
| description | Abstract The hard sphere model for liquids attempts to capture the physical behavior of a real liquid in a simple conceptual model: a fluid of fixed size spheres that only interact repulsively when they come into contact. Is the model good enough to use for modeling internal planetary structure? To answer this question, I survey variants of hard sphere liquid theory by applying them to the Earth’s outer core to determine which of them explains wavespeeds in the outer core best. The variants explored here are the Carnahan-Starling hard sphere model, the Mansoori-Carnahan-Starling-Leland extension to hard sphere mixtures, the transition metal hard sphere liquid, and the Lennard-Jones hard sphere liquid with attractive forces. With an empirical addition of a temperature dependence to the liquid’s hard sphere diameter, all of the variants explored can replicate wavespeeds in most of the radius range of the outer core. The hard sphere model for liquid transition metals explains the wavespeed best because it yields a mean liquid atomic weight of 48.8 g mol −1 at 10 wt% light element abundance in the core which is in good cosmochemical agreement with core light element models. Other variants also fit core wavespeeds but require implausibly low liquid mean atomic weight implying excessive incorporation of hydrogen or helium in the core. Applied to the detailed wavespeed structure of the Earth’s outermost outer core, the model suggests that the mean atomic weight could be reduced by up to 1.74% or the temperature could be increased by up to 400 K relative to an adiabatic profile, or there could be 8% fewer valence electrons in the liquid. |
| format | Article |
| id | doaj-art-e118ba69eac941c0b53000f1a2f15250 |
| institution | Kabale University |
| issn | 1880-5981 |
| language | English |
| publishDate | 2015-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Earth, Planets and Space |
| spelling | doaj-art-e118ba69eac941c0b53000f1a2f152502025-01-12T12:11:30ZengSpringerOpenEarth, Planets and Space1880-59812015-05-0167111110.1186/s40623-015-0238-7The hard sphere view of the outer coreGeorge Helffrich0Earth-Life Science Institute, Tokyo Institute of TechnologyAbstract The hard sphere model for liquids attempts to capture the physical behavior of a real liquid in a simple conceptual model: a fluid of fixed size spheres that only interact repulsively when they come into contact. Is the model good enough to use for modeling internal planetary structure? To answer this question, I survey variants of hard sphere liquid theory by applying them to the Earth’s outer core to determine which of them explains wavespeeds in the outer core best. The variants explored here are the Carnahan-Starling hard sphere model, the Mansoori-Carnahan-Starling-Leland extension to hard sphere mixtures, the transition metal hard sphere liquid, and the Lennard-Jones hard sphere liquid with attractive forces. With an empirical addition of a temperature dependence to the liquid’s hard sphere diameter, all of the variants explored can replicate wavespeeds in most of the radius range of the outer core. The hard sphere model for liquid transition metals explains the wavespeed best because it yields a mean liquid atomic weight of 48.8 g mol −1 at 10 wt% light element abundance in the core which is in good cosmochemical agreement with core light element models. Other variants also fit core wavespeeds but require implausibly low liquid mean atomic weight implying excessive incorporation of hydrogen or helium in the core. Applied to the detailed wavespeed structure of the Earth’s outermost outer core, the model suggests that the mean atomic weight could be reduced by up to 1.74% or the temperature could be increased by up to 400 K relative to an adiabatic profile, or there could be 8% fewer valence electrons in the liquid.https://doi.org/10.1186/s40623-015-0238-7CoreSeismologyPlanetologyHard sphere liquidsLiquid metal properties |
| spellingShingle | George Helffrich The hard sphere view of the outer core Earth, Planets and Space Core Seismology Planetology Hard sphere liquids Liquid metal properties |
| title | The hard sphere view of the outer core |
| title_full | The hard sphere view of the outer core |
| title_fullStr | The hard sphere view of the outer core |
| title_full_unstemmed | The hard sphere view of the outer core |
| title_short | The hard sphere view of the outer core |
| title_sort | hard sphere view of the outer core |
| topic | Core Seismology Planetology Hard sphere liquids Liquid metal properties |
| url | https://doi.org/10.1186/s40623-015-0238-7 |
| work_keys_str_mv | AT georgehelffrich thehardsphereviewoftheoutercore AT georgehelffrich hardsphereviewoftheoutercore |