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DOE OSTI2025

Reference Correlations for the Density and Viscosity of Molten Alkali and Alkaline Earth Fluoride Salts

While there is a significant body of literature pertaining to thermophysical property measurements of molten salts, there is often a wide degree of variability among independent measurements of the same compounds. As such, the scientific community benefits greatly from an unbiased, independent assessment of duplicate datasets, so that reference correlations which describe these thermophysical properties as functions of temperature can be determined and then commonly used by researchers, scientists, and engineers. With regard to molten fluoride compounds, a significant time has elapsed since density and viscosity reference correlations have been determined; Janz conducted the most recent effort, in 1988, to provide reference correlations for the densities and viscosities of molten fluoride compounds via the National Standard Reference Data System coordinated by the National Bureau of Standards. Since then, new data have been published for molten fluoride compounds, and a new precedent has surfaced for putting forth reference correlations that involve fitting to multiple primary datasets. In this work, reference correlations are put forth for molten alkali and alkaline earth fluoride compounds in an effort to provide updated, improved correlations for general use. For molten alkali fluoride densities, estimated uncertainties with a 95% confidence interval are summarized as follows: LiF (0.63%), NaF (0.48%), KF (0.76%), RbF (0.93%), and CsF (0.75%). For molten alkaline earth fluoride densities, an estimated uncertainty was not able to be quantified for BeF 2 because of limited data; however, estimated uncertainties with a 95% confidence interval are summarized as follows for the remaining alkaline earth fluorides: MgF 2 (1.5%), CaF 2 (0.92%), SrF 2 (1.6%), and BaF 2 (0.23%). For molten alkali fluoride viscosities, uncertainty was not able to be quantified for RbF and CsF because of limited data; however, estimated uncertainties with a 95% confidence interval are summarized as follows for the remaining alkali fluorides: LiF (4.4%), NaF (3.0%), and KF (4.0%). For molten alkaline earth fluoride viscosities, limited consistent data resulted in the recommendation of single datasets (from literature) that are deemed to be the most trustworthy based on the quality of the underlying experimental studies.

Birri, A. [Oak Ridge National Laboratory (ORNL), O↗

DOE OSTI2025

Investigation of resonant layer response in electron viscosity regime

We present a supplementary study of previous work in Waybright and Park [Phys. Plasmas 31, 022502 (2024)] which demonstrates a substantial effect of electron viscosity on the resonant layer response to non-axisymmetric magnetic perturbations. A main refinement is to include a curl element of electron viscosity in the generalized Ohm's law. The refinement reveals a resonant layer response in the electron viscosity regime corresponding to slowly rotating and highly viscous plasmas.

Asymptotic analysis↗

DOE OSTI2024

Classical and quantum computing of shear viscosity for ( 2 + 1 ) D SU(2) gauge theory

We perform a nonperturbative calculation of the shear viscosity for ( 2 + 1 )-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green’s function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density η s is consistent with a well-known holographic result 1 4 π at several temperatures on a 4 × 4 honeycomb lattice with the local electric representation truncated at j max = 1 2 . We also find the ratio of the spectral function and frequency ρ x y ( ω ) ω exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond j max = 1 2 on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation including j max truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Sedimentation and shear-induced dynamics of spheroids in fluids with spatial viscosity variations

A generalized reciprocal theorem is used to relate the force and torque induced on a particle in an inertia-less fluid with small variation in viscosity to integrals involving Stokes flow fields and the spatial dependence of viscosity. These resistivity expressions are analytically evaluated using spheroidal harmonics and then used to obtain the mobility of the spheroid during sedimentation, and in linear flows, of a fluid with linear viscosity stratification. The coupling between the rotational and translational motion induced by stratification rotates the spheroid’s centerline, creating a variety of rotational and translational dynamics dependent upon the particle’s aspect ratio, κ, and the component of the stratification unit vector in the gravity direction, d g . Spheroids with 0.55 ⪅ κ ⪅ 2.0 exhibit the largest variety of settling behaviors. Interestingly, this range covers most microplastics and typical microorganisms. One of the modes include a stable orientation dependent only on κ and d g , but independent of initial orientation, thus allowing for the potential control of settling angles and sedimentation rates. In a simple shear flow, cross-streamline migration occurs due to the stratification-induced force generated on the particle. Similarly, a particle no longer stays at the stagnation point of a uniaxial extensional flow. While fully analytical results are obtained for spheroids, numerical simulations provide a source of validation. These simulations also provide additional insights into the stratification-induced force- and torque-producing mechanisms through the stratification-induced stress, which is not accessed in the reciprocal theorem-based analytical calculations.

Geophysical and Geological Flows: Stratified flows↗

DOE OSTI2025

Sustainable Shape Memory Elastomers with Reduced Melt Viscosity and Enhanced Stiffness

Melt reactive processing of lignin with nitrile rubber is a promising approach to synthesizing shape memory materials. The strong intramolecular interactions in lignin macromolecular structures, caused by π–π stacking in aromatic rings and hydrogen bonding, often result in large phase separation or low miscibility with rubbers. In this study, we investigated the chemical and molecular characteristics, as well as the stiffness and complex viscosity, of modified kraft lignin melt-reacted with an acrylonitrile/butadiene copolymer containing 41% acrylonitrile (NBR41). To enhance the macromolecular compatibility of kraft lignin with NBR41, kraft lignin was cross-linked with poly(propylene glycol) diglycidyl ether (PPDE) and trimethylolpropane triglycidyl ether (TTE), both rich in epoxy reactive groups capable of forming chemical bonds with hydroxyl and carboxyl groups. Here, our findings demonstrate that the modification of kraft lignin with PPDE and TTE resulted in significantly increased stiffness of the composites. The elastic modulus of NBR41-Kraft lignin-PPDE and NBR41-Kraft lignin-TTE increased by 82 and 162%, respectively. Both the yield strength and Young’s modulus of these two samples showed dramatic improvements. Specifically, the yield strength and Young’s modulus of NBR41-Kraft lignin-TTE increased nearly 4 and 3-fold, respectively, compared to the control sample. Interestingly, despite significant improvements in mechanical properties, the viscosity of NBR41-Kraft lignin-PPDE was substantially lower than that of the control sample. At 210 °C and an angular frequency of 1 rad/s, the complex viscosity of NBR41-Kraft lignin was approximately 100.25 ± 4.77 kPa·s, while that of NBR41-Kraft lignin-PPDE was significantly lower at 56 ± 0.93 kPa·s. These findings were validated through Fourier transform infrared spectroscopy, scanning electron microscopy, dynamic mechanical analysis, thermal characterization, rheological tests, and quasi-elastic neutron scattering techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

The ultralow viscosity of volatile-rich kimberlite magma: Implications for the water content of primitive kimberlite melts

The eruption of deeply sourced kimberlite magma offers the fastest route to bring deep-seated volatiles back to the Earth’s surface. However, the viscosity of kimberlite magma, a factor governing its migration and eruption dynamics within Earth, remains poorly constrained. We conducted synchrotron in situ falling sphere viscometry experiments to examine kimberlite magma with different volatile contents (0 to 5 wt % H 2 O and 2 to 8 wt % CO 2 ) under high pressure-temperature conditions. The results reveal that the viscosity of volatile-rich kimberlite magma is ~1 to 2 orders lower than that of mid-ocean ridge basalt (MORB) and comparable to the ultramobile pure carbonate melt. Using the measured viscosity values, we simulated the ascent and eruption process of kimberlite magma. We found that a minimum content of ~0.5 wt % water in the primitive magma is necessary to allow the ultrafast eruption process of kimberlite, thereby enabling the preservation of diamonds and high-pressure mineral inclusions transported by the magma.

58 GEOSCIENCES↗

DOE OSTI2024

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↗

DOE OSTI2025

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↗

DOE OSTI2025

pH-SWITCHABLE DYNAMIC BINARY COMPLEXES AS VISCOSITY MODIFYING AGENTS

The study of supramolecular structures has been gaining a lot of momentum in recent years due to their potential application in several interesting areas such as medicine, catalysis, energy, oil and gas, etc. Hydraulic fracturing is one area where the ongoing demand for novel viscosity modifiers has prompted researchers to explore various facets of chemistry. In this study, a dynamic binary complex (DBC) solution is presented, with the potential to be useful in the hydraulic fracturing domain. It has a supramolecular structure that is formed by the self-assembly of oleic acid and diethylenetriamine into an elongated network under alkaline conditions. With less than 2 wt% of constituents in aqueous solution, a viscous gel that exhibits high viscosities even under shear was formed. It was sensitive to pH and salinity, and its zero-shear viscosity could be tuned by a factor of ~280 by changing the pH. Furthermore, its viscous properties were pronounced in the presence of salt. Sand settling tests revealed its potential to hold up sand particles for extended periods of time, longer than 24 hours. In conclusion, this DBC solution system has potential to be utilized as a smart pH-switchable hydraulic fracturing fluid that can be prepared using seawater.

02 PETROLEUM↗

DOE OSTI2025

Viscosity-Controlled Thiol–Ene Reaction and Its Impact on Mechanical Response of Dynamic Networks

The impact of curing conditions on the final properties of thioester-thiol-based dynamic polymer networks was systematically investigated. Despite identical monomer and cross-linker compositions, networks synthesized in the absence of solvent exhibited significantly higher shear moduli and longer relaxation times compared to those cured in solvent. These differences arise from viscosity-controlled photoinitiated thiol–ene reactions, where reduced chain mobility under solvent-free conditions suppresses termination between two polymer radicals, leading to higher reaction conversion. Fourier Transform Infrared (FTIR) spectroscopy and solid-state NMR (ssNMR) spectroscopy confirmed a greater degree of “click” reaction completion in higher viscosity environments. Control experiments revealed that prolonged radical lifetimes and suppressed termination reactions under solvent-free curing conditions contribute to these variations. Here, this study highlights the crucial role of processing conditions in determining cross-link density and, consequently, the dynamic mechanical behavior of polymer networks. It demonstrates that, beyond polymer chemistry, dynamic cross-linker design, and phase separation, curing conditions serve as a key design parameter for tailoring material performance to specific applications.

polymers↗

DOE OSTI2025

Effect of Viscosity of a Deep Eutectic Solvent on CO 2 Capture Performance in an Energy-Efficient Membrane Contactor-Based Process

Greenhouse gas contributions to climate change have driven intense interest in the separation of CO 2 from wet flue gas streams. Deep eutectic solvents (DESs) are an emerging class of highly selective CO 2 absorbents. A prototypical DES, reline, is a mixture of choline chloride and urea. Reline is a thermally stable, nontoxic, and biodegradable solvent with negligible volatility and is inexpensive. We demonstrate a scalable and energy-efficient hollow fiber membrane contactor (HFMC)-based process using a green solvent for CO 2 capture. This process uses reline in HFMC to provide close interfacial interactions and contact between DES and CO 2 . This approach overcomes the disadvantages associated with direct absorption in DES and could potentially be applied to a variety of solvent-based CO 2 capture methods. Commercial, low-cost polymer hollow fiber membranes were evaluated for the capture of CO 2 with reline. From a mixed gas containing N 2 and CO 2 , the DES-based HFMC separated CO 2 with a purity of 97 mol %. The effect of the viscosity of reline on the CO 2 capture performance was investigated by adding water to the reline. The addition of water to reline significantly reduced its viscosity, which led to a permeate flux of 170 mmol/(m 2 ·h) at 35 °C, 4 bar, and 60 wt % water in solvent, which was approximately 8 times higher than that of the pure reline in the membrane contactor system. In situ Fourier transform infrared spectroscopy and nuclear magnetic resonance (NMR) revealed that reline absorbs CO 2 by physical absorption without forming new chemical compounds and that CO 2 separation by reline occurs via the pressure swing mechanism. This research provides fundamental insights about green physical solvent-based separation processes and a pathway toward industrial deployment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Measuring the density, viscosity, and surface tension of molten titanates using electrostatic levitation in microgravity

Rare earth and barium titanates are useful as ferroelectric, dielectric, and optical materials. Measurements of their thermophysical properties in the liquid state can help guide melt processing technologies for their manufacture and advance understanding of fragile liquids' behavior and glass formation. Here, we report the density, thermal expansion, viscosity, and surface tension of molten BaTi 2 O 5 , BaTi 4 O 9 , and 83TiO 2 -17RE 2 O 3 (RE = La or Nd). Measurements were made using electrostatic levitation and droplet oscillation techniques in microgravity, which provide access to quiescent liquid droplets and deep supercooling of 510–815 K below the equilibrium melting points. Densities were measured over 900–2400 K. Viscosities were similar for all four compositions, increasing from ~10 mPa s near 2100 K to ~30 mPa s near 1750 K. Surface tensions were 450–490 dyn cm -1 for the rare earth titanates and 383–395 dyn cm -1 for the barium titanates; surface tensions of all compositions had small or negligible temperature dependence over 1700–2200 K. In conclusion, for solids recovered after melt quenching, x-ray microtomography revealed the fracture mechanics in crystalline products and minimal internal porosity in glass products, likely arising from entrapped gas bubbles. Internal microstructures were generally similar for products processed either in microgravity or in a terrestrial aerodynamic levitator.

42 ENGINEERING↗

DOE OSTI2025

Multipolar Fermi Surface Deformations in Sr 2 ⁢RuO 4 Probed by Resistivity and Sound Attenuation: A Window into Electron Viscosity and the Collision Operator

Recent developments in electron hydrodynamics have demonstrated the importance of considering the full structure of the electron-electron scattering operator, which encodes a sequence of lifetimes, one for each component of the Fermi surface deformation in a multipolar expansion. In this context, the dipolar lifetime is measured by resistivity, whereas the quadrupolar component probes the viscosity and can be measured in the bulk via sound attenuation. We introduce a framework to extract the collision operator of an arbitrary metal by combining resistivity and sound attenuation measurements with a realistic calculation of the scattering operator that includes multiband and umklapp effects. The collision operator allows for the prediction of a plethora of properties, including the nonlocal conductivity, and can be used to predict hydrodynamic behavior for bulk metals. As a first application, we apply this framework to Sr 2 ⁢RuO 4 in a temperature range where electron-electron scattering is dominant. Furthermore, we find quantitative agreement between our model and the temperature dependence of both the resistivity and the sound attenuation, we find the quadrupolar (𝐵 1⁢𝑔 ) relaxation rate to be 30% higher than the dipolar one due to the presence of hot spots on the 𝛾 band, and we predict a strongly anisotropic viscosity arising from the 𝛼 and 𝛽 bands.

Boltzmann theory↗

DOE OSTI2025

Symmetry-Energy Dependence of the Bulk Viscosity of Nuclear Matter

We clarify how the weak-interaction-driven bulk viscosity ζ and the bulk relaxation time τ Π of neutrino-transparent n p e matter depend on the nuclear symmetry energy. We show that, at saturation density, the equation-of-state dependence of these transport quantities is fully determined by the experimentally constrained nuclear symmetry energy S and its slope L . Variations of L can change the bulk viscosity by orders of magnitude, which can affect both the dissipative and the conservative tidal response of neutron stars. Furthermore, this suggests that both conservative and dissipative effects encoded in the gravitational-wave signatures of binary neutron star inspirals may help constrain nuclear symmetry-energy properties.

Neutron stars & pulsars↗

DOE OSTI2025

Low viscosity of solid MgO at high pressures and strain rates measured using the laser-driven Richtmyer-Meshkov instability

Solids are often assumed to behave as viscous fluids under high-strain rates. This behavior has been studied experimentally in metals but largely unexplored in brittle ceramic materials. Here, in this study, we present a technique for measuring the viscosity of MgO using time-resolved velocimetry to track the growth rate of a perturbation caused by the Richtmyer-Meshkov instability at the OMEGA EP laser facility. To interpret the results, we use an in-house Eulerian hydrocode to simulate our experiments and model the plastic deformation of solid MgO as a viscous fluid. Results indicate that MgO has a surprisingly low upper bound to its effective viscosity of ∼10 2 ⁢ Pa s at 175 ± 15⁢ GPa, ∼3500⁢K, and 10 6 −10 7 s −1 strain rate.

Perez, Tyler M. [Johns Hopkins Univ., Baltimore, M↗

DOE OSTI2025

Viscosity Measurements in Extreme Conditions

Radiation-hydrodynamics simulations are critical to the NNSA complex for understanding high energy density physics and for addressing problems in national security science. However, current rad-hydro codes typically do not account for viscosity, which generally leads to large uncertainties in problems involving mixing of materials under shock loading. This report details progress made towards experimental measurements of fluid viscosity at high pressures and temperatures achieved by shock wave compression techniques, as well as complementary material model development and hydrodynamic simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Emergence of Microphysical Bulk Viscosity in Binary Neutron Star Postmerger Dynamics

Abstract In nuclear matter in isolated neutron stars, the flavor content (e.g., proton fraction) is subject to weak interactions, establishing flavor ( β -)equilibrium. However, there can be deviations from this equilibrium during the merger of two neutron stars. We study the resulting out-of-equilibrium dynamics during the collision by incorporating direct and modified Urca processes (in the neutrino-transparent regime) into general-relativistic hydrodynamics simulations with a simplified neutrino transport scheme. We demonstrate how weak-interaction-driven bulk viscosity in postmerger simulations can emerge and assess the bulk viscous dynamics of the resulting flow. We further place limits on the impact of the postmerger gravitational-wave strain. Our results show that weak-interaction-driven bulk viscosity can potentially lead to a phase shift of the postmerger gravitational-wave spectrum, although the effect is currently on the same level as the numerical errors of our simulation.

Astronomy & Astrophysics↗

DOE OSTI2024

Temperature and Composition Dependence Modeling of Viscosity and Electrical Conductivity of Low-Activity Waste Glass Melts

The development of models that accurately relate the properties of a glass melt to its temperature and composition is important for glass formulation, melter control, and modeling the melt flow, refractory corrosion, and production rate. Using a database consisting of more than 4,000 data points measured between 900 °C and 1250 °C for over 600 unique low-activity waste glass compositions, we developed models for the melt viscosity and electrical conductivity. Models based on the Gaussian process regression approach outperformed models based on the Vogel–Fulcher–Tammann equation according to four standard metrics and yielded reliable prediction intervals. The models found primarily linear effects between properties and individual components, except for the effect of the Na 2 O mass fraction on the electrical conductivity. The effects were found to be consistent with current theories on physical processes involved with those properties.

36 MATERIALS SCIENCE↗