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 UFN, 2009, Volume 179, Number 1, Pages 91–105 (Mi ufn691)

This article is cited in 21 scientific papers (total in 21 papers)

METHODOLOGICAL NOTES

Direct observations of the viscosity of the outer core and extrapolation of measurements of the viscosity of liquid iron

D. E. Smyliea, V. V. Brazhkinb, A. Palmerc

a Department of Earth and Space Science and Engineering, York University, Toronto, Ontario, Canada
b Institute for High Pressure Physics, Russian Academy of Sciences
c Sander Geophysics Ltd., Ottawa, Ontario, Canada

Abstract: Estimates vary widely as to the viscosity of Earth's outer fluid core. Directly observed viscosity is usually orders of magnitude higher than the values extrapolated from high-pressure high-temperature laboratory experiments, which are close to those for liquid iron at atmospheric pressure. It turns out that this discrepancy can be removed by extrapolating via the widely known Arrhenius activation model modified by lifting the commonly used assumption of pressure-independent activation volume (which is possible due to the discovery that at high pressures the activation volume increases strongly with pressure, resulting in $10^2$ Pa s at the top of the fluid core and in $10^{11}$ Pa s at the bottom). There are of course many uncertainties affecting this extrapolation process. This paper reviews two viscosity determination methods, one for the top and the other for the bottom of the outer core, the former of which relies on the decay of free core nutations and yields $2.371\pm 1.530$ Pa s; and the other relies on the reduction in the rotational splitting of the two equatorial translational oscillation modes of the solid inner core and yields an average $1.247\pm 0.035\times 10^{11}$ Pa s. Encouraged by the good performance of the Arrhenius extrapolation, a differential form of the Arrhenius activation model is used to interpolate along the melting temperature curve and to find the viscosity profile across the entire outer core. The variation is found to be nearly log-linear between the measured boundary values.

DOI: https://doi.org/10.3367/UFNr.0179.200901d.0091

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English version:
Physics–Uspekhi, 2009, 52:1, 79–92

Bibliographic databases:

PACS: 66.20.-d, 91.35.-x, 93.85.-q
Received: January 16, 2008
Revised: August 4, 2008

Citation: D. E. Smylie, V. V. Brazhkin, A. Palmer, “Direct observations of the viscosity of the outer core and extrapolation of measurements of the viscosity of liquid iron”, UFN, 179:1 (2009), 91–105; Phys. Usp., 52:1 (2009), 79–92

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This publication is cited in the following articles:
1. Xian J.-W., Sun T., Tsuchiya T., “Viscoelasticity of Liquid Iron At Conditions of the Earth'S Outer Core”, J. Geophys. Res.-Solid Earth
2. Zhang Y., Nelson P., Dygert N., Lin J.-F., “FE Alloy Slurry and a Compacting Cumulate Pile Across Earth'S Inner-Core Boundary”, J. Geophys. Res.-Solid Earth
3. V. N. Zharkov, “On estimating the molecular viscosity of the Earth's outer core”, Phys. Usp., 52:1 (2009), 93–95
4. Vernon F. Cormier, “A glassy lowermost outer core”, Geophys J Int, 2009
5. Zuberi M., Smylie D.E., “Spectral analysis of the VLBI pole path”, Journal of Geodynamics, 48:3–5 (2009), 230–234
6. V. M. Ovtchinnikov, P. B. Kaazik, D. N. Krasnoshchekov, “Weak velocity anomaly in the Earth’s outer core from seismic data”, Izv., Phys. Solid Earth, 48:3 (2012), 211
7. Ovchinnikov V.M., Kaazik P.B., Krasnoschekov D.N., “Slabaya anomaliya skorosti vo vneshnem yadre zemli iz seismicheskikh dannykh”, Fizika zemli, 2012, no. 3, 34–34
8. Yu.D. Fomin, V.N. Ryzhov, V.V. Brazhkin, “Properties of liquid iron along the melting line up to Earth-core pressures”, J. Phys.: Condens. Matter, 25:28 (2013), 285104
9. Behnam Seyed-Mahmoud, Ali Moradi, “Inertial modes of the elliptical core: implementation of a Clairaut coordinate system”, Physics of the Earth and Planetary Interiors, 2013
10. S.J.. Peale, Jean-Luc Margot, S.A.. Hauck, S.C.. Solomon, “Effect of core-mantle and tidal torques on Mercury’s spin axis orientation”, Icarus, 2013
11. D. K. Belashchenko, “Computer simulation of liquid metals”, Phys. Usp., 56:12 (2013), 1176–1216
12. Qi-Long Cao, Pan-Pan Wang, Duo-Hui Huang, Jun-Sheng Yang, Ming-Jie Wan, “Transport coefficients and entropy-scaling law in liquid iron up to Earth-core pressures”, J. Chem. Phys, 140:11 (2014), 114505
13. N. A. Zarkevich, D. D. Johnson, “Coexistence pressure for a martensitic transformation from theory and experiment: Revisiting the bcc-hcp transition of iron under pressure”, Phys. Rev. B, 91:17 (2015)
14. Pirooz Mohazzabi, J.D.. Skalbeck, “Superrotation of Earth’s Inner Core, Extraterrestrial Impacts, and the Effective Viscosity of Outer Core”, International Journal of Geophysics, 2015 (2015), 1
15. Ding H., Chao B.F., “the Slichter Mode of the Earth: Revisit With Optimal Stacking and Autoregressive Methods on Full Superconducting Gravimeter Data Set”, J. Geophys. Res.-Solid Earth, 120:10 (2015), 7261–7272
16. Shen Wen-Bin, Luan Wei, “Detection of the Slichter Mode Triplet Using Superconducting Gravimetric Observations”, Chinese J. Geophys.-Chinese Ed., 59:3 (2016), 840–851
17. Meyer N., Xu H., Wax J.-F., “Temperature and density dependence of the shear viscosity of liquid sodium”, Phys. Rev. B, 93:21 (2016), 214203
18. G. I. Kanel', A. S. Savinykh, G. V. Garkushin, S. V. Razorenov, “Evaluation of glycerol viscosity through the width of a weak shock wave”, High Temperature, 55:3 (2017), 365–369
19. Adushkin V.V., Spivak A.A., Ryabova S.A., Kharlamov V.A., “Tidal Effects in Geomagnetic Variations”, Dokl. Earth Sci., 474:1 (2017), 579–582
20. A. S. Savinykh, G. V. Garkushin, G. I. Kanel', S. V. Razorenov, “Evaluation of viscosity of $Bi$–$\rm Pb$ melt $(56.5%$$43.5%)$ by the width of a weak shock wave”, High Temperature, 56:5 (2018), 685–688
21. Luan W., Shen W., Ding H., Zhang T., “Potential Slichter Triplet Detection Using Global Superconducting Gravimeter Data”, Surv. Geophys., 40:5 (2019), 1129–1150
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