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FY24 Progress Report on Viscosity and Thermal Conductivity Measurements of Nuclear Industry Relevant Chloride Salts: An Experimental and Computational Study

As presented in this report, experimental and computational techniques were performed to assess the viscosity and thermal conductivity of key alkali and actinide chloride mixtures for molten salt reactor developers. These mixtures were pure LiCl, NaCl-KCl, LiCl-NaCl, LiCl-KCl, LiCl-NaCl-KCl, and NaCl-UCl 3 . Experimental measurements of viscosity were performed with a rolling ball viscometer, whereas experimental measurements of thermal conductivity were performed with a variable gap apparatus. Additional benchmarking work was performed using both property measurement systems to prepare for x-ray radiography in stainless-steel crucibles for viscosity and to ensure that calibration methods were accurate for thermal conductivity before assessing the NaCl-UCl 3 system. Validation data for the NaCl-UCl 3 in literature are minimal. Details on the calibration methods, salt measurement processes, and sources of error and uncertainty are discussed in detail for both property measurements. The computational methods described herein involved ab-initio molecular dynamics (AIMD) calculations using CP2K. The calculations were performed for the LiCl-KCl-NaCl and NaCl-UCl 3 systems. These calculations not only provided thermophysical property estimations for comparison to experimental data, but they also allowed for the determination of diffusion coefficients, coordination numbers, and radial distribution functions to provide insight into ion mobility and local coordination environments, which is linked to macroscopic property trends.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Bulk viscosity of two-flavor color superconducting quark matter in neutron star mergers

This work investigates the bulk viscosity of warm, dense, neutrino-transparent, color-superconducting quark matter, where damping of density oscillations in the kHz frequency range arises from weak-interaction-driven direct Urca processes involving quarks. We study the two-flavor red-green paired color-superconducting (2SC) phase, while allowing for the presence of unpaired strange quarks and blue color light quarks of all flavors. Our calculations are based on the SU(3) Nambu–Jona–Lasinio model, extended to include both vector interactions and the ‘t Hooft determinant term. The primary focus is on how variations in the NJL Lagrangian parameters—specifically, the diquark and vector coupling strengths—affect both the static properties of quark matter, such as its equation of state and composition, and its dynamical behavior, including bulk viscosity and associated damping timescales. We find that the bulk viscosity and corresponding damping timescale can change by more than an order of magnitude upon varying the vector coupling by a factor of two at high densities and by a lesser degree at lower densities. This sensitivity primarily arises from the susceptibility of 2SC matter, with a smaller contribution from modifications to the weak interaction rates. In comparison, changes in the diquark coupling have a more limited impact. The damping of density oscillations in 2SC matter is similar quantitatively to nucleonic matter and can be a leading mechanism of dissipation in merging hybrid stars containing color superconducting cores.

Gravitational Waves

Viscoseal performance with rarefied-gas sealant

A fundamental study of viscoseals having a rarefied gas as the sealant has been conducted. Both experimental and analytical investigations are reported. Three different analytical models have been formulated and are described in detail. An experimental investigation has been conducted on multiple grooved two-inch diameter viscoseals over a wide range of gas densities and shaft speeds up to 30,000 rpm. Comparisons are presented between actual viscoseal performance and the theoretical predictions for both sealing coefficient and net leakage parameters as functions of the degree of gas rarefication. Recommendations are presented for the use of the analytical models.

Milligan, M. W.

Performance of continuum gas viscoseals.

Viscoseals performance as predicted by three different analytical models is compared with experimental data for air as the continuum gas sealant. An experimental investigation has been conducted on two multiple-grooved two-inch diameter viscoseals up to shaft speeds of 35,000 rpm. The two seal geometries considered differ significantly insofar as groove aspect ratio is concerned. The results of this continuum investigation of sealing coefficient for the gas viscoseals suggest that the Boon and Tal model is a good design tool for the laminar continuum regime provided it is restricted to high aspect ratio groove applications.

Wilkerson, H. J.

Viscosity of the earth's core.

Calculation of the viscosity of the core at the boundary of the inner and outer core. It is assumed that this boundary is a melting transition and the viscosity limits of the Andrade (1934,1952) hypothesis (3.7 to 18.5 cp) are adopted. The corresponding kinematic viscosities are such that the precessional system explored by Malkus (1968) would be unstable. Whether it would be sufficiently unstable to overcome a severely subadiabatic temperature gradient cannot be determined.

Gans, R. F.

Viscosity and thermal conductivity of moderately dense gas mixtures.

Derivation of a simple, semitheoretical expression for the initial density dependence of the viscosity and thermal conductivity of gaseous mixtures in terms of the appropriate properties of the pure components and of their interaction quantities. The derivation is based on Enskog's theory of dense gases and yields an equation in which the composition dependence of the linear factor in the density expansion is explicit. The interaction quantities are directly related to those of the mixture extrapolated to zero density and to a universal function valid for all gases. The reliability of the formulation is assessed with respect to the viscosity of several binary mixtures. It is found that the calculated viscosities of binary mixtures agree with the experimental data with a precision which is comparable to that of the most precise measurements.

Wakeham, W. A.

Effects of additives on volume change on melting, surface tension, and viscosity of liquid aluminum oxide

The effects of various oxide additives on the volume change on melting, the surface tension, and the viscosity of liquid Al2O3 were studied. Additives of Sm2O3, MgO, and Y2O3 which form solid solutions, compounds, and multiphase solids with Al2O3 were studied. A review of the property data for Al2O3 and Al2O3 containing oxide additives is presented. Oxide additives to Al2O3 reduce the volume change on melting and with the exception of SiO2 lower the viscosity; surface tensions change with oxide additives, but changes vary with different container material. Viscosity and volume change on melting appeared to be significantly more important for studying the properties of liquid oxides than surface tension. Supercooling of 270 K of yttrium aluminum garnet was observed.

Bates, J. L.

Viscoseal performance with rarefied-gas sealant

A fundamental study of viscoseals having a rarefied gas as the sealant was conducted. Both experimental and analytical investigations are reported. Three different analytical models were formulated and are described in detail. An experimental investigation was conducted on multiple grooved two-inch diameter viscoseals over a wide range of gas densities and shaft speeds up to 30,000 rpm. Comparisons are presented between actual viscoseal performance and the theoretical predictions for both sealing coefficient and net leakage parameters as functions of the degree of gas rarefication. Recommendations are presented for the use of the analytical models.

Milligan, M. W.

A kinematic eddy viscosity model including the influence of density variations and preturbulence

A model for the kinematic eddy viscosity was developed which accounts for the turbulence produced as a result of jet interactions between adjacent streams as well as the turbulence initially present in the streams. In order to describe the turbulence contribution from jet interaction, the eddy viscosity suggested by Prandtl was adopted, and a modification was introduced to account for the effect of density variation through the mixing layer. The form of the modification was ascertained from a study of the compressible turbulent boundary layer on a flat plate. A kinematic eddy viscosity relation which corresponds to the initial turbulence contribution was derived by employing arguments used by Prandtl in his mixing length hypothesis. The resulting expression for self-preserving flow is similar to that which describes the mixing of a submerged jet. Application of the model has led to analytical predictions which are in good agreement with available turbulent mixing experimental data.

Cohen, L. S.

Viscosity of liquid anorthite.

The viscosity of liquid anorthite has been determined over the temperature ranges between 1450 to 1620 C and 820 to 950 C. The high-temperature data agree well with previous experimental data and with predictions of the Bottinga and Weill model. The overall log (viscosity) versus 1/T relation exhibits pronounced and rather continuous curvature. The viscosity of anorthite is higher at any given temperature and more strongly temperature-dependent than that of the anorthite-rich lunar compositions 14259, 14310, and 15418. The room-temperature density of glassy anorthite (2.64 gm/cu cm) and the thermal expansion coefficients of glassy and liquid anorthite have also been determined. The volume expansion coefficient for the glass is about 0.000018 per deg C, and that for the liquid is about 0.000048 per deg C. These values are used to relate the high-temperature flow data to the predictions of free-volume theories.

Cukierman, M.

Convection in the moon - Effect of variable viscosity

This work determines criteria for stability of the lunar interior to thermal convection in the case of variable viscosity. The conditions necessary for solid convection to play an important role in the moon's revolution are determined by application of the calculated stability criteria to a variety of thermal history models. Most thermal history temperature profiles would be unstable to solid convection at the present time, if currently used estimates of the viscosity function are applicable. A possible explanation of lunar seismic data is that temperatures near the melting point of silicates exist at depths greater than 800 km. If this is the case, either the lunar interior is stable, or solid convection is occurring at a rate insufficient to cool the lunar interior substantially. If the former is true, the viscosity of lunar material is higher than that usually assumed.

Cassen, P.

A spin-orbit constraint on the viscosity of a Mercurian liquid core

The escape of Mercury from the stable spin-orbit resonance in which the spin angular velocity is twice the orbital mean motion (2n) requires that the kinematic viscosity of a molten core with a laminar boundary layer be comparable to that of water (0.01 sq cm/s) and the tidal Q be less than about 100. If the boundary layer is turbulent, escape from the resonance is only consistent with a liquid core of low viscosity if the critical Reynolds number for the onset of turbulence is above about 500, the moment difference (B - A)/C is below about 0.00001, and the tidal dissipation factor Q is less than about 40. These conclusions depend on the assumptions that Mercury's obliquity was near 0 deg at the time of resonance passage, that the liquid core was not stably stratified at the time at which Mercury passed through the resonance, that a turbulent boundary layer can be characterized by a turbulent or eddy viscosity coefficient, and that the most important coupling between core and mantle is a viscous coupling at a smooth spherical boundary.

Peale, S. J.

Relating viscosity to polymer concentration

Equation developed by VanDijk and first applied to viscosity of Newtonian suspension of rigid particles by Eilers is rearranged to yield intrinsic viscosity as explicit function of polymer concentration in polymer solvent system. Experiments have shown relationship valid for polymer solutions having relative viscosities ranging from 1 to 100.

Fedors, R. F.

Release adiabat measurements on minerals: The effect of viscosity

The current inversion of pressure-particle velocity data for release from a high pressure shock state to a pressure-density path is analyzed. It is assumed that the release process is isentropic. It was shown that for geological materials below stresses of 150 GPa, the effective viscosity must be 1000 kg/m/s in order that the viscous (irreversible) work carried out on the material in the shock state remains small compared to the mechanical work recovered upon adiabatic rarefaction. The available data pertaining to the offset of the Rayleigh line from the Hugoniot for minerals, the magnitude of the shear stress in the high pressure shock state for minerals, and the direct measurements of the viscosities of several engineering materials shocked to pressures below 150 GPa yield effective viscosities of 1000 kg/m/s or less. An inferance that this indicates that the conditions for isentropic release of minerals from shock states are achieved, and a conclusion that the application of the Riemann integral to obtain pressure-density states along the release adiabats of minerals in shock experiments is valid are made.

Jeanloz, R.

Rapid viscosity measurements of powdered thermosetting resins

A rapid and inexpensive method of obtaining processing-related data on powdered thermosetting resins has been investigated. The method involved viscosity measurements obtained with a small specimen (less than 100 mg) parallel plate plastometer. A data acquisition and reduction system was developed which provided a value of viscosity and strain rate about 12-13 second intervals during a test. The effects of specimen compaction pressure and reduction of adhesion between specimen and parallel plates were examined. The plastometer was used to measure some processing-related viscosity changes of an addition polyimide resin, including changes caused by pre-test heat treatment, test temperature, and strain rate.

Price, H. L.

The double seismic zone in downgoing slabs and the viscosity of the mesosphere

The seismic zone beneath several island arcs between about 100 and 200 km depth consists of an upper zone having down-dip compression and a lower zone having down-dip tension. Several numerical models of the Aleutian arc were computed to test the hypothesis that these double seismic zones are due to sagging of the slab under its own weight. This sagging occurs because the asthenosphere (between about 100 and 200 km) provides little support or resistance to the slab, which is supported from below by the more viscous mesosphere and from above by the lithosphere. The viscosity of the mesosphere was constrained to the interval between 0.25 x 10 to the 22nd and 0.5 x 10 to the 22nd P by noting that the slab would have mainly down-dip compression at higher viscosities and mainly down-dip tension at lower viscosities. The deviatoric stress in the slab and the fault plane between the slab and the island arc is about 200-300 bars (expressed as shear stress). The models were calibrated to the observed depth and gravity anomalies in the trench.

Sleep, N. H.

Viscosity of multicomponent partially ionized gas mixtures

An approximate method is proposed for predicting the viscosity of partially ionized gas mixtures. This technique expresses the viscosity of a mixture in terms of the viscosities of the individual pure components, is simple in form, and does not require large computer run times or storage. Thus, the technique is suitable for use with complex flowfields and heat-transfer calculations. Results for gas mixtures which are representative of the atmospheres of Jupiter, Earth, and Venus, are presented and it is shown that the results compare favorably with detailed kinetic-theory analyses.

Armaly, B. F.

Viscous relaxation of impact craters on icy planetary surfaces - Determination of viscosity variation with depth

Spacecraft images show that the icy Galilean satellites have surfaces with very low topographic relief. Impact craters on Ganymede and Callisto are anomalously shallow and are characterized by sharp well-defined rims and domed floors. These morphological characteristics can be explained by viscous relaxation of topography on an icy crust in which the viscosity is uniform or decreases with depth. Under these conditions, large craters relax more rapidly than small craters, therefore explaining a possible underabundance of large craters. Viscous relaxation on an icy crust that is thin compared to the crater diameter or on a thick icy crust in which viscosity increases with depth could not produce this crater morphology and would result in the more rapid relaxation of small craters rather than large craters. The results of this study suggest that more detailed analysis of relaxing impact crater morphology may resolve the rate of viscosity decrease with depth and so provide evidence on the interior thermal evolution of icy planetary bodies.

Parmentier, E. M.