A molecular dynamics study of bulk and shear viscosity of liquid iron using embedded-atom potential

On the interpretation of shear viscosity ultrasonic measurements

The thermodynamic properties of molten iron under Earth's outer core conditions are fundamental to understanding the core's structure, composition, and dynamics. However, experimental constraints under such extreme conditions remain scarce. Shock compression experiments can provide a viable means of reproducing the relevant thermodynamic regime of the outer core. Here, we report precise shock temperature measurements of molten iron up to ~364 GPa, approaching pressures at the core's center. By integrating these results with existing measurements of density and sound velocity in shock-compressed iron, we determine the thermal equation of state and compressional wave velocity (VP) of molten iron throughout outer core conditions. Compared with pure molten iron, Earth's outer core exhibits a depth-increasing density deficit and a depth-decreasing VP excess, reaching ~9.0% and ~1.3% at the inner-core boundary, respectively. Notably, the density deficit flattens while the VP excess steepens within the lowermost ~280 km of the outer core. These trends reveal a heterogeneous basal outer core, comprising a partially crystallized F-layer overlain by a gradient in light-element concentration. Our findings provide direct experimental constraints on the thermodynamic behavior of molten iron under outer core conditions, offering insights into the compositional stratification, thermal evolution, and long-term sustainability of the geodynamo.

Cavitation and thermal dilepton production in QGP

In this dissertation, we report the results of the first-principles molecular dynamics (FPMD) simulations and data analysis on the thermodynamic, structural, and transport properties of iron-rich metallic liquids considering several light and heavy elements under wide ranges of pressure and temperature that are relevant to the earth’s core. Our simulations of pure liquid iron cover the pressure range from 0 GPa at 2000 K to 380 GPa at 7000 K perhaps representing the most extensive computational study to date. We studied four molten iron-rich alloys corresponding to 2.67 atom% of Ni, Co, Mo, and W at pressures up to 380 GPa and at temperatures 4000 to 7000 K. We also simulated H- and C-bearing metallic systems at similar pressure-temperature conditions. The calculated pressure-temperature-volume (P-V-T) results of all liquid alloys can be accurately described with a three-term form of the equation of state consisting of the reference pressure-volume isotherm, the thermal pressure, and the impurity pressure. Moreover, pressure is corrected for the difference in calculation and recent experimental results by adding the fourth term to the equation of state. The resulting density-pressure profile of pure iron liquid along a geotherm shows that the outer core suffers from a density deficient of ~ 6.8%. Our results show that the addition of Mo and W in liquid iron in any amount widens the density gap whereas the addition of H and C reduces the gap. Both Ni and Co do not affect the liquid density significantly and they behave as host iron atoms showing similar bond distances and local coordination. The calculated mean iron coordination number of Mo and W is somewhat larger than that of Ni and Co and host iron atoms thus implying a substitutional incorporation mechanism, whereas both H and C are undercoordinated consistent with their interstitial incorporation. Our results from extended FPMD simulations for pure iron and FeW liquids show that the diffusion coefficient of Fe varies modestly over the outer core regime taking values of ~3 to 5 x 10-9 m2s-1. The heavy impurity (W) atoms tend to diffuse slower than host iron atoms by almost a factor of two, unlike highly mobile H atoms. The calculated viscosity of pure and alloyed iron liquids remains almost unchanged taking a low value of 12±2 mPa.s at the outer core conditions. It implies that outer core convection may involve small-scale turbulent circulation and barodiffusion possibly causing heavy elements to accumulate

The bulk properties of iron at the pressure and temperature conditions of Earth's core were determined by a method that combines first-principles and classical molecular dynamic simulations. The theory indicates that (i) the iron melting temperature at inner-core boundary (ICB) pressure (330 gigapascals) is 5400 (+/-400) kelvin; (ii) liquid iron at ICB conditions is about 6% denser than Earth's outer core; and (iii) the shear modulus of solid iron close to its melting line is 140 gigapascals, consistent with the seismic value for the inner core. These results reconcile melting temperature estimates based on sound velocity shock wave data with those based on diamond anvil cell experiments.

SUMMARY. - WE derive the Gruneisen's gamma as a function of temperature and pressure for liquid iron at the temperature and pressures of the Earth's outer core taking into account the anharmonic and electronic contributions in a self-consistent way. We obtain numerical values definetely different from those generally quoted in the geophysical literature, but in agreement with recent experimental determinations.

The effective shear and bulk viscosity, as well as dynamic viscosity, describe the rheological properties of the ceramic body during the liquid phase sintering process. The rheological parameters depend on the physical and thermo‐mechanical characteristics of the material such as relative density, temperature, grain size, diffusion coefficient, and activation energy. In this paper, the numerical‐experimental method has been developed to study both viscous and rheological behavior of hard porcelain ceramic body during liquid phase sintering. The other aim is to acquire a complete understanding of the response of an incompressible viscose material during sintering such as stress‐strain relations, sintering, and hydrostatic stress. Densification results confirmed that the bulk viscosity was well‐defined with relative density. The stress analysis proved that the sintering stress is more than the hydrostatic stress during the entire sintering time so, the sintering process occurs completely. Deflection results showed that the shear viscosity was a fair estimation of real ones. Dilatometry, SEM , XRD investigations as well as bulk viscosity simulation results confirmed that the “mullitisation plateau” was presented as a very little extraordinary expansion at the final sintering stage.

Compressional wave velocity Vp has been measured in liquid iron in the temperature range 1823–1883 K and in the frequency range 5.4–11.8 MHz for the first time using ultrasonic interferometry. The value of Vp at the melting temperature is 3820±3 ms−1 which is comparable to previous measurements all using time‐of‐flight methods. The temperature derivative of velocity, dVp/dT, in this temperature range (−0.72±0.07 m s−1 K−1 ) and the lack of dispersion observed in this frequency range are in agreement with previous studies. Our calculated value of the relaxed (adiabatic) bulk modulus K0 at the melting temperature is 102 GPa. Estimate of the average longitudinal relaxation time τl indicates that the liquid iron is in a relaxed state in the present frequency range. Accurate measurement of attenuation is not yet possible with our present apparatus, but typical interferograms indicate a very low attenuation, which is qualitatively consistent with the prediction from viscoelastic theory and seismological determinations of attenuation of Earth's outer core.

We have derived a set of equations to describe the thermal evolution of a neutron star which undergoes small-amplitude radial pulsations. We have taken into account, in the frame of the General Theory of Relativity, the pulsation damping due to the bulk and shear viscosity and the accompanying heating of the star. The neutrino emission of a pulsating non-superfluid star and its heating due to the bulk viscosity are calculated assuming that both processes are determined by the non-equilibrium modified Urca process. Analytical and numerical solutions to the set of equations of the stellar evolution are obtained for linear and strongly non-linear deviations from beta-equilibrium. It is shown that a pulsating star may be heated to very high temperatures, while the pulsations damp very slowly with time (a power law damping for 100-1000 years), as long as the damping is determined by the bulk viscosity. The contribution of the shear viscosity to the damping becomes important in a rather cool star with a low pulsation energy.

The bulk viscosities of two color‐superconducting phases, the color‐flavor locked (CFL) phase and the 2SC phase, are computed and compared to the result for unpaired quark matter. In the case of the CFL phase, processes involving kaons and the superfluid mode give the largest contribution to the bulk viscosity since all fermionic modes are gapped. In the case of the 2SC phase, ungapped fermionic modes are present and the process u+d↔u+s provides the dominant contribution. In both cases, the bulk viscosity can become larger than that of the unpaired phase for sufficiently large temperatures (T≳1 MeV for CFL, T≳0.1 MeV for 2SC). Bulk viscosity (as well as shear viscosity) is important for the damping of r‐modes in compact stars and thus can potentially be used as an indirect signal for the presence or absence of color‐superconducting quark matter.

Contributions of stochastic background fields to the shear and bulk viscosities of the gluon plasma

Introduction In this chapter we encounter measurements of a type demonstrating some of the unique capabilities of MD. Because the complete trajectories are available, it is no more difficult to measure time-dependent properties, both in and out of equilibrium, than it is to measure thermodynamic and structural properties at equilibrium. Here we concentrate on properties defined in terms of time-dependent correlation functions at the atomic level – the dynamic structure factor and transport coefficients such as the shear viscosity are examples. Most of the analysis is incorporated into the simulation program, but it would of course be possible (though extremely storage intensive) to store the required trajectory data for subsequent processing. Transport coefficients Background Transport coefficients describe the material properties of a fluid within the framework of continuum fluid dynamics. Discrete atoms play no role whatsoever in the continuum picture, but this does not seriously limit the enormous range of practical engineering applications of the continuum approach. The most familiar of the transport coefficients are those applicable to simple fluids; these are the diffusion coefficient, the shear and bulk viscosities and the thermal conductivity. Other transport coefficients appear when dealing with more complex fluids, such as those containing more than one species, or those with novel rheological behavior. In many problems the transport coefficients are assumed to be experimentally determined constants, depending only on the temperature and density of the fluid, which themselves are often assumed constant for a given problem, but in more complex situations transport coefficients can depend on local behavior, an example being the dependence of shear viscosity on the velocity gradient.

Transport properties in dense fluids and their binary mixtures

A lattice-Boltzmann scheme of the Navier–Stokes equation on a three-dimensional cuboid lattice

We consider how the five-dimensional Randall-Sundrum (one-brane) theory becomes modified when account is taken of the bulk viscosity of the cosmic fluid on the brane. We focus on the plasma era between $10^{12}$K (muon pair annihilation) to about $5\times 10^9$K (electron-positron annihilation), which includes the first order quark-hadron transition beginning at an energy density of about $5\times 10^9\rm MeV^4$. Various possibilities are examined for modeling the bulk viscosity, preference being at the end given to the results calculated from relativistic kinetic theory. According to this, the viscosity is negligible at the highest temperatures, but may amount to a few per cent corrections in the later stages of the plasma era. We also briefly consider anisotropic universes where the shear viscosity comes into play, and show that in the case of the Kasner model the influences from bulk viscosity and shear viscosity become comparable when the anisotropy parameter of the universe is of order $A \sim 10^{-11} $ in the beginning of the plasma era, and $A \sim 10^{-2}$ in its later region.