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DOE OSTI2019

Bulk viscosity of baryonic matter with trapped neutrinos

Here, we study bulk viscosity arising from weak current Urca processes in dense baryonic matter at and beyond nuclear saturation density. We consider the temperature regime where neutrinos are trapped and therefore have nonzero chemical potential. We model the nuclear matter in a relativistic density functional approach, taking into account the trapped neutrino component. We find that the resonant maximum of the bulk viscosity would occur at or below the neutrino trapping temperature, so in the neutrino trapped regime the bulk viscosity decreases with temperature as $T^{–2}$, this decrease being interrupted by a drop to zero at a special temperature where the proton fraction becomes density-independent and the material scale-invariant. The bulk viscosity is larger for matter with lower lepton fraction, i.e., larger isospin asymmetry. We find that bulk viscosity in the neutrino-trapped regime is smaller by several orders of magnitude than in the neutrino-transparent regime, which implies that bulk viscosity in neutrino-trapped matter is probably not strong enough to affect significantly the evolution of neutron star mergers. This also implies weak damping of gravitational waves emitted by the oscillations of the post-merger remnant in the high-temperature, neutrino-trapped phase of evolution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Bulk viscosity from Urca processes: n p e μ matter in the neutrino-transparent regime

We study the bulk viscosity of moderately hot and dense, neutrino-transparent relativistic npeμ matter arising from weak-interaction direct Urca processes. This work parallels our recent study of the bulk viscosity of npeμ matter with a trapped neutrino component. The nuclear matter is modeled in a relativistic density functional approach with two different parametrizations—DDME2 (which does not allow for the low-temperature direct-Urca process at any density) and NL3 (which allows for low-temperature direct-Urca process above a low-density threshold). Here, we compute the equilibration rates of Urca processes of neutron decay and lepton capture, as well as the rate of the muon decay, and find that the muon decay process is subdominant to the Urca processes at temperatures T ≥ 3 MeV in the case of DDME2 model and T ≥ 1 MeV in the case of NL3 model. Thus, the Urca-process-driven bulk viscosity is computed with the assumption that pure leptonic reactions are frozen. As a result the electronic and muonic Urca channels contribute to the bulk viscosity independently and at certain densities the bulk viscosity of npeμ matter shows a double-peak structure as a function of temperature instead of the standard one-peak (resonant) form. In the final step, we estimate the damping timescales of density oscillations by the bulk viscosity. We find that, e.g., at a typical oscillation frequency f = 1~kHz, the damping of oscillation is most efficient at temperatures 3 ≤ T ≤ 5~MeV and densities n B ≤ 2n 0 where they can affect the evolution of the post-merger object.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Viscosity of the magnetized strongly coupled one-component plasma

The viscosity tensor of the magnetized one-component plasma, consisting of five independent shear viscosity coefficients, a bulk viscosity coefficient, and a cross coefficient, is computed using equilibrium molecular dynamics simulations and the Green-Kubo relations. A broad range of Coulomb coupling and magnetization strength conditions are studied. Magnetization is found to strongly influence the shear viscosity coefficients when the gyrofrequency exceeds the Coulomb collision frequency. Three regimes are identified as the Coulomb coupling strength and magnetization strength are varied. Here, the Green-Kubo relations are used to separate kinetic and potential energy contributions to each viscosity coefficient, showing how each contribution depends upon the magnetization strength. The shear viscosity coefficient associated with the component of the pressure tensor parallel to the magnetic field, and the two coefficients associated with the component perpendicular to the magnetic field, are all found to merge to a common value at strong Coulomb coupling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Magnetic Eddy Viscosity of Mean Sheared Flows in Two-Dimensional Magnetohydrodynamics

Magnetic induction in magnetohydrodynamic fluids at magnetic Reynolds number (Rm) less than 1 has long been known to cause magnetic drag. Here we show that when Rm $\gg 1$ and the fluid is in a hydrodynamic-dominated regime in which the magnetic energy is much smaller than the kinetic energy, induction due to a mean shear flow leads to a magnetic eddy viscosity. The magnetic viscosity is derived from simple physical arguments, where a coherent response due to shear flow builds up in the magnetic field until decorrelated by turbulent motion. The dynamic viscosity coefficient is approximately $(B^2_p/2_{μ_0}) τ_{corr}$, the poloidal magnetic energy density multiplied by the correlation time. We confirm the magnetic eddy viscosity through numerical simulations of two-dimensional incompressible magnetohydrodynamics. We also consider the three-dimensional case, and in cylindrical or spherical geometry, theoretical considerations similarly point to a nonzero viscosity whenever there is differential rotation. Hence, these results serve as a dynamical generalization of Ferraro's law of isorotation. The magnetic eddy viscosity leads to transport of angular momentum and may be of importance to zonal flows in astrophysical domains such as the interior of some gas giants.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

The effect of blood viscosity on shear‐induced hemolysis using a magnetically levitated shearing device

Abstract Introduction Blood contacting medical devices, including rotary blood pumps, can cause shear‐induced blood damage that may lead to adverse effects in patients. Due in part to an inadequate understanding of how cell‐scale fluid mechanics impact red blood cell membrane deformation and damage, there is currently not a uniformly accepted engineering model for predicting blood damage caused by complex flow fields within ventricular assist devices (VADs). Methods We empirically investigated hemolysis in a magnetically levitated axial Couette flow device typical of a rotary VAD. The device is able to accurately control the shear rate and exposure time experienced by blood and to minimize the effects of other uncharacterized stresses. Using this device, we explored the effects of both hematocrit and plasma viscosity on shear‐induced hemolysis to characterize blood damage based on the viscosity‐independent shear rate, rather than on shear stress. Results Over a shear rate range of 20 000 – 80 000 1/s, the Index of Hemolysis (IH) was found to be dependent upon and well‐predicted by the shear rate alone. IH was independent of hematocrit, bulk viscosity, or the suspension media viscosity and less correlated to shear stress (MSE = 0.46–0.75) than to shear rate (MSE = 0.06–0.09). Conclusion This study recommends that future investigations of shear‐induced blood damage report findings with respect to the viscosity‐neutral term of shear rate, in addition to the bulk whole blood viscosity measured at an appropriate shear rate relevant to the flow conditions of the device.

Krisher, James A.↗

DOE OSTI2023

FY23 Progress Report on Viscosity and Thermal Conductivity Measurements of Molten Salts

As presented in this report, thermal conductivity and viscosity measurements were performed on key chloride pseudo-binary molten salt systems of relevance to molten salt reactor developers. Thermal conductivity measurements were conducted with a variable gap technique, in which a known heat flux is driven across a molten salt specimen and the temperature difference is measured, allowing calculation of the thermal conductivity. This is achieved by establishing a small gap between the bottom of a cylindrical inner containment, which houses electrical heating elements, and an outer containment, which houses cooling channels; the gap size can be varied by compression of a formed bellows. A new calibration scheme was developed herein, involving a correction factor to the heat flux based on He measurements at various temperatures. Furthermore, the data processing methodology was improved to minimize the impact of radiative heat transfer in the calculation of salt specimen thermal conductivity from the temperature difference measurements. Viscosity measurements were conducted with a rolling ball viscometer, in which a ball rolls some known distance in an angled tubular crucible, and the terminal velocity can be used to calculate the viscosity of the salt. The measurement can be performed in a quartz crucible, with which a standard camera can be used to track the ball, or in a metal crucible, with which x-ray radiography is required to track the ball. A new custom x-ray system was made and dedicated to the rolling ball viscometer to enable high throughput automated measurements with salts which require containment with metal. Both systems have been integrated with a ventilation stack which allows for off-gassing of radioactive material, enabling future measurements with U-bearing salts. The thermal conductivity measurements performed herein were with NaCl-KCl (44 mol% NaCl). This salt system was measured in the previous fiscal year, however the thermal conductivity values obtained were comparatively low, and so the system was remeasured with the aforementioned calibration scheme and improved post-processing techniques. The newly obtained thermal conductivity values for NaCl-KCl (44 mol% NaCl) indicate good agreement with kinetic theory and ab-initio models (within 5–10 %). The viscosity measurements performed herein were with three different compositions of NaCl-KCl: 75, 50, and 25 mol% NaCl; a new calibration scheme was applied to account for variable flow effects in the laminar regime. The results show reasonable agreement with literature (5–20 %, depending on the temperature, composition, and study); however, literature values are likely higher than true values based on pure end-member measurements performed in the comparative studies. The measurements conducted herein do show a trend such that viscosity increases with increasing NaCl concentration, which agrees well with one of two comparative studies. In general, the measurements conducted herein gives confidence in the capability to use these systems to accurately measure thermal conductivity and viscosity of actinide-bearing salts within the next fiscal year.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

A theoretical/computational framework to measure SiO2 and MgO viscosity at high pressure

The convection of the mantle of Earth and super-Earths is important for many terrestrial phenomena, from plate tectonics to outgassing. Rheological properties, such as viscosity, regulate the transport of thermal energy and mass. However, the viscosity of mantle-relevant materials, such as MgO, at relevant pressures (>120 GPa) are not well constrained. The objective of this work was to develop a computational platform to simulate novel experiments aiming to measure the viscosity of MgO at high pressures. Experiments performed by our collaborators at Johns Hopkins University and Lawrence Livermore National Laboratory use the OMEGA EP laser facility to shock a corrugated MgO interface to 170 GPa, with resulting velocity evolution governed by the viscous Richtmyer-Meshkov instability. We used an in-house hydrocode to simulate this process and thus provide a bound on viscosity by comparing our simulations results to these experiments, as well as to examine the physical processes at play. We simulated the experiments with different values of MgO viscosity (from inviscid to 10,000 Pa∙s) while taking into account the unsteady laser pulse, the material's equation of state, and the rate-dependent constitutive relation for MgO, and the materials' equations of state. Our results suggest that MgO at these conditions has a viscosity within an order of magnitude of 5000 Pa∙s.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

A spline-based method to obtain spatially dependent viscosity in confined flows

Coupling chemical physics to continuum theories is a critical step to understanding multi-scale phenomena. This paper will connect non-equilibrium molecular dynamics simulations to a continuum-based Navier-Stokes equation that has relaxed the assumption of spatial uniformity in viscosity. Using a form for viscosity based on spline interpolation, viscosity as a function of position is obtained from the least squares fit of the velocity profile measured from molecular simulations of flow in a nanochannel. Viscosity can vary widely, particularly near the channel boundaries, indicating that uniform viscosity is no longer appropriate. Variations of the viscosity near the channel surfaces imply that considering solution and surface chemistry could be necessary to rigorously understand molecular-scale flows in nanochannels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Relative humidity-dependent viscosity of secondary organic material from toluene photo-oxidation and possible implications for organic particulate matter over megacities

To improve predictions of air quality, visibility, and climate change, knowledge of the viscosities and diffusion rates within organic particulate matter consisting of secondary organic material (SOM) is required. Most qualitative and quantitative measurements of viscosity and diffusion rates within organic particulate matter have focused on SOM particles generated from biogenic volatile organic compounds (VOCs) such as α -pinene and isoprene. In this study, we quantify the relative humidity (RH)-dependent viscosities at 295±1K of SOM produced by photo-oxidation of toluene, an anthropogenic VOC. The viscosities of toluene-derived SOM were 2 × 10 ₋1 to ~6 ×10 6 Pa s from 30 to 90%RH, and greater than ~2 × 10 8 Pa s (similar to or greater than the viscosity of tar pitch) for RH ≤ 17%. These viscosities correspond to Stokes–Einstein-equivalent diffusion coefficients for large organic molecules of ~2 ×10 ₋15 cm 2 s ₋1 for 30 % RH, and lower than ~3 × 10 ₋17 cm 2 s ₋1 for RH ≤ 17 %. Based on these estimated diffusion coefficients, the mixing time of large organic molecules within 200 nm toluene-derived SOM particles is 0.1–5 h for 30% RH, and higher than ~100 h for RH ≤ 17%. As a starting point for understanding the mixing times of large organic molecules in organic particulate matter over cities, we applied the mixing times determined for toluene-derived SOM particles to the world's top 15 most populous megacities. If the organic particulate matter in these megacities is similar to the toluene-derived SOM in this study, in Istanbul, Tokyo, Shanghai, and São Paulo, mixing times in organic particulate matter during certain periods of the year may be very short, and the particles may be well-mixed. On the other hand, the mixing times of large organic molecules in organic particulate matter in Beijing, Mexico City, Cairo, and Karachi may be long and the particles may not be well-mixed in the afternoon (15:00–17:00 LT) during certain times of the year.

Song, Mijung↗

NASA NTRS1980

The vagaries of variable viscosity convection

The wavelength dependence of convection with a temperature-dependent viscosity is studied using two-dimensional finite difference models. A steady-state solution with a horizontal wavelength of eight times the depth is found to transport heat more efficiently than a solution with exactly the same parameters but with a wavelength of twice the depth. Only at the longer wavelengths is it possible for the top high viscosity boundary layer to participate more fully in the flow. Using models with a constant heat flux resulted in a decrease in the interior temperature of approximately 30% for the longer wavelength. It is also demonstrated that a parameterization using only a constant viscosity thermal structure and an interior viscosity is inadequate to parameterize the variable viscosity calculations described. This suggests that parameterized convection schemes may not accurately resolve the thermal evolution of planetary interior unless they can correctly include the effects of vertical viscosity structure.

Daly, S. F.↗

NASA NTRS1984

The effect of viscosity on impact cratering and possible application to the icy satellites of Saturn and Jupiter

Impact experiments in Newtonian fluids with a range of viscosities of 0.001 to 60 Pa s demonstrate that transient crater volume and shape depend on target viscosity as well as on gravity. Volume is reduced, and depth-to-diameter ratio is increased for cratering events in which viscosity plays a dominant role. In addition to being affected by target kinematic viscosity, viscous scaling is most strongly influenced by projectile diameter, less strongly by projectile velocity, and least strongly by gravity. In a planetary context, viscous effects can occur for craters formed by small or slow moving impacting bodies, low planetary surface densities, high surface viscosities, and low gravity values; conditions all likely for certain impacts into the icy satellites of Saturn and Jupiter, especially if liquid mantles were still present beneath solid crusts. Age dating based on crater counts and size-frequency distributions for these icy bodies may have to be modified to account for the possibility that viscosity-dominated craters were initially smaller and deeper than their gravity-controlled counterparts.

Fink, J.↗

NASA NTRS1989

On the role of artificial viscosity in Navier-Stokes solvers

A method is proposed to determine directly the amount of artificial viscosity needed for stability using an eigenvalue analysis for a finite difference representation of the Navier-Stokes equations. The stability and growth of small perturbations about a steady flow over the airfoils are analyzed for various amounts of artificial viscosity. The eigenvalues were determined for a small perturbation about a steady inviscid flow over a NACA 0012 airfoil at a Mach number of 0.8 and angle of attack of 0 degrees. The movement of the eigenvalue constellation with respect to the amount of artificial viscosity is studied. The stability boundries as a function of the amount of artificial viscosity from both the eigenvalue analysis and the time marching scheme are also presented. This procedure not only allows for determining the effect of varying amounts of artificial viscosity, but also for the effects of different forms of terms for artificial viscosity.

Mahajan, Aparajit J.↗

NASA NTRS1991

Role of artificial viscosity in Euler and Navier-Stokes solvers

A method is proposed to determine directly the amount of artificial viscosity needed for stability using an eigenvalue analysis for a finite difference representation of the Navier-Stokes equations. The stability and growth of small perturbations about a steady flow over airfoils are analyzed for various amounts of artificial viscosity. The eigenvalues were determined for a small time-dependent perturbation about a steady inviscid flow over an NACA 0012 airfoil at a Mach number of 0.8 and angle of attack of 0 deg. The method has been applied to inviscid flows here, but as discussed is also applicable to viscous flows. The movement of the eigenvalue constellation with respect to the amount of artificial viscosity is studied. The stability boundaries as a function of the amount of artificial viscosity from both the eigenvalue analysis and the time-marching scheme are also presented. The eigenvalue procedure not only allows for determining the effect of varying amounts of artificial viscosity, but also for the effects of different forms of artificial viscosity.

Mahajan, Aparajit J.↗

NASA NTRS1993

The inference of mantle viscosity from an inversion of the Fennoscandian relaxation spectrum

The theory of Peltier (1976) for mantle viscosity is adopted, within the framework of nonlinear Bayesian Inference, to invert the Fennoscandian relaxation spectra derived by McConnell (1968). A set of rigorous constraints which all models for the viscosity variation beneath Fennoscandian must satisfy is derived. These constraints are used to test the plausibility of a wide class of viscosity models. It is shown that a model with a weak asthenosphere overlying an isoviscous 10 exp 21 Pa s deep mantle provides to good fit to the relaxation spectrum. This is also true of models with a thin sublithospheric low-viscosity zone overlying a two-layer deep mantle with a moderate jump in viscosity across 670 km depth, and models with a viscosity jump of between four and six across isoviscous upper and lower mantle regions.

Mitrovica, J. X.↗

NASA NTRS1994

New constitutive equation for the volume viscosity in fluids

The traditional volume viscosity, Stokes' hypothesis, and acoustical relaxation are reviewed. The lossy Navier-Stokes Equation is applied to periodic (acoustic) flow, and it is shown that the traditional volume viscosity leads to a result which contradicts that describing acoustical relaxation. It is demonstrated that the addition of a second volume viscosity term to the constitutive equation, to account for pressure relaxation, resolves the conflict, and leads to a direct correspondence between the volume viscosity parameters and the acoustical relaxation parameters. The representation of volume viscosity is formulated for the case of multiple relaxations, as occur in air. Finally, an application of the new constitutive equation to a simple convective compressible flow, namely a linearly accelerating flow, demonstrates the impact of volume viscosity upon the flow and the physical conditions for which it is important.

Zuckerwar, Allan J.↗

NASA NTRS1994

Coupled Marangoni-Benard/Rayleigh-Benard Instability with Temperature Dependent Viscosity

The onset of convection induced by coupled surface tension gradient and buoyancy forces is investigated with temperature dependent viscosity. Both surface tension and viscosity are assumed to vary linearly with temperature. The limiting case, Ma=0, is the buoyancy driven convection problem typically referred to as the Rayleigh-Benard stability problem. The other limiting case, Ra=0, is the surface tension (gradient) driven flow problem referred to as the Marangoni-Benard problem. The equations and boundary conditions obtained from the linear analysis are solved numerically as a generalized eigenvalue problem. Neutral stability curves for different viscosity slopes have been generated for the Marangoni-Benard and Rayleigh-Benard problems. It is shown that the curves can be collapsed to a single curve by appropriately scaling the results for each of the limiting cases. The critical Marangoni number is determined as a function of the slope of the viscosity temperature variation, epsilon, for different values of the Rayleigh number. When the viscosity decreases linearly with temperature, the coupled buoyancy-surface tension problem, including the limiting cases of Ra=0 and Ma=0, is found to be more stable than the constant viscosity case.

Skarda, J. Raymond Lee↗

NASA NTRS1999

Dynamic Nucleation of Supercooled Melts and Measurement of the Surface Tension and Viscosity

We investigate the phenomenon of acoustic pressure-induced nucleation by using a novel approach involving the large amplitude resonant radial oscillations and collapse of a single bubble intentionally injected into a supercooled liquid. Using a combination of previously developed and proven techniques, the bubble is suspended in a fluid host by an ultrasonic field which supplies both the levitation capability as well as the forcing of the radial oscillations. We observe the effects of an increase in pressure (due to bubble collapse) in a region no larger than 100 microns within the supercooled melt to rigorously probe the hypothesis of pressure-induced nucleation of the solid phase. The use of single bubbles operating in narrow temporal and spatial scales will allow the direct and unambiguous correlation between the origin and location of the generation of the disturbance and the location and timing of the nucleation event. In a companion research effort, we are developing novel techniques for the non-contact measurements of the surface tension and viscosity of highly viscous supercooled liquids. Currently used non-invasive methods of surface tension measurement for the case of undercooled liquids generally rely of the quantitative determination of the resonance frequencies of drop shape oscillations, of the dynamics of surface capillary waves, or of the velocity of streaming flows. These methods become quickly ineffective when the liquid viscosity rises to a significant value. An alternate and accurate method which would be applicable to liquids of significant viscosity is therefore needed. We plan to develop such a capability by measuring the equilibrium shape of levitated undercooled melt droplets as they undergo solid-body rotation. The experimental measurement of the characteristic point of transition (bifurcation point) between axisymmetric and two-lobed shapes will be used to calculate the surface tension of the liquid. Such an approach has already been validated through the experimental verification of numerical modeling results. The experimental approach involves levitation, melting, and solidification of undercooled droplets using a hybrid ultrasonic-electrostatic technique in both a gaseous as well as a vacuum environment. A shape relaxation method will be investigated in order to derive a reliable method to measure the viscosity of undercooled melts. The analysis of the monotonic relaxation to equilibrium shape of a drastically deformed and super-critically damped free drop has been used to derive interfacial tension of immiscible liquid combinations where one of the component has high viscosity. A standard approach uses the initial elongation of a droplet through shear flows, but an equivalent method could involve the initial deformation of a drop levitated in a gas by ultrasonic radiation pressure, electric stresses, or even solid body rotation. The dynamic behavior of the free drop relaxing back to equilibrium shape will be modeled, and its characteristic time dependence should provide a quantitative means to evaluate the liquid viscosity.

Trinh, E. H.↗

NASA NTRS1999

Viscosity Measurement of Highly Viscous Liquids Using Drop Coalescence in Low Gravity

The method of drop coalescence is being investigated for use as a method for determining the viscosity of highly viscous undercooled liquids. Low gravity environment is necessary in this case to minimize the undesirable effects of body forces and liquid motion in levitated drops. Also, the low gravity environment will allow for investigating large liquid volumes which can lead to much higher accuracy for the viscosity calculations than possible under 1 - g conditions. The drop coalescence method is preferred over the drop oscillation technique since the latter method can only be applied for liquids with vanishingly small viscosities. The technique developed relies on both the highly accurate solution of the Navier-Stokes equations as well as on data from experiments conducted in near zero gravity environment. In the analytical aspect of the method two liquid volumes are brought into contact which will coalesce under the action of surface tension alone. The free surface geometry development as well as its velocity during coalescence which are obtained from numerical computations are compared with an analogous experimental model. The viscosity in the numerical computations is then adjusted to bring into agreement of the experimental results with the calculations. The true liquid viscosity is the one which brings the experiment closest to the calculations. Results are presented for method validation experiments performed recently on board the NASA/KC-135 aircraft. The numerical solution for this validation case was produced using the Boundary Element Method. In these tests the viscosity of a highly viscous liquid, in this case glycerine at room temperature, was determined to high degree of accuracy using the liquid coalescence method. These experiments gave very encouraging results which will be discussed together with plans for implementing the method in a shuttle flight experiment.

Antar, Basil N.↗