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At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Hydrodynamic description of an unmagnetized plasma with multiple ion species. I. General formulation

A generalization of the Braginskii ion fluid description [S. I. Braginskii, Sov. Phys. JETP 6, 358 (1958)] to the case of an unmagnetized collisional plasma with multiple ion species is presented. An asymptotic expansion in the ion Knudsen number is used to derive the individual ion species continuity, as well as the total ion mass density, momentum, and energy evolution equations accurate through the second order. Expressions for the individual ion species drift velocities with respect to the center of mass reference frame, as well as for the total ion heat flux and viscosity, which are required to close the fluid equations, are evaluated in terms of the first-order corrections to the lowest order Maxwellian ion velocity distribution functions. A variational formulation for evaluating such corrections and its relation to the plasma entropy are presented. Employing trial functions for the corrections, written in terms of expansions in generalized Laguerre polynomials, and maximizing the resulting functionals produces two systems of linear equations (for “vector” and “tensor” portions of the corrections) for the expansion coefficients. A general matrix formulation of the linear systems as well as expressions for the resulting transport fluxes are presented in forms convenient for numerical implementation. The general formulation is employed in the companion paper [A. N. Simakov and K. Molvig, Hydrodynamic description of an unmagnetized plasma with multiple ion species. II. Two and three ion species plasmas, submitted to Phys. Plasmas (2015)] to evaluate the individual ion drift velocities and the total ion heat flux and viscosity for specific cases of two and three ion species plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

The influence of different dispersion methods on the size of the aggregate of CNTs in epoxy resin for the manufacturing of carbon fiber reinforced composites

Different industrial mixing methods and some of their combinations (1) ultrasound; (2) stirring; (3) (4) by roller machine, (5) by gears machine (6) Ultrasound radiation + high stirring were investigated for incorporating Multi walled Carbon nanotubes (MWCNT) into a resin based on an aeronautical epoxy precursor, cured with 4,4′ diamine-dibenzylsulfone (DDS). The effect of different parameters, ultrasound intensity, number of cycles, type of blade, gears speed on the nanofiller dispersion were analyzed. The inclusion of the nanofiller in the resin causes a drastic increase in the viscosity, preventing the homogenization of the resin and a drastic increase in temperature in the zones closest to the ultrasound probe. To overcome these challenges, the application of high speed agitation simultaneously with the application of ultrasonic radiation was used. This allows on the one hand a homogeneous dispersion, on the other hand an improvement of the dissipation of heat generated by ultrasonic radiation. A comprehensive study with parameters like viscosity and temperature was performed. It is necessary a balance between viscosity and temperature. Viscosity must be low enough to facilitate the dispersion and homogenization of the nanofillers, whereas the temperature cannot be too high because of re-agglomerations.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2016

Tearing mode dynamics and locking in the presence of external magnetic perturbations

In normal operation, Madison Symmetric Torus (MST) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field pinch plasmas exhibit several rotating tearing modes (TMs). Application of a resonant magnetic perturbation (RMP) results in braking of mode rotation and, if the perturbation amplitude is sufficiently high, in a wall-locked state. The coils that produce the magnetic perturbation in MST give rise to RMPs with several toroidal harmonics. As a result, simultaneous deceleration of all modes is observed. In this paper, the measured TM dynamics is shown to be in qualitative agreement with a magnetohydrodynamical model of the RMP interaction with the TM [R. Fitzpatrick, Nucl. Fusion 33, 1049 (1993)] adapted to MST. To correctly model the TM dynamics, the electromagnetic torque acting on several TMs is included. Quantitative agreement of the TM slowing-down time was obtained for a kinematic viscosity in the order of ν k i n ≈ 10 – 20 m 2 /s. Analysis of discharges with different plasma densities shows an increase of the locking threshold with increasing density. Modeling results show good agreement with the experimental trend, assuming a density-independent kinematic viscosity. Finally, comparison of the viscosity estimates in this paper to those made previously with other techniques in MST plasmas suggests the possibility that the RMP technique may allow for estimates of the viscosity over a broad range of plasmas in MST and other devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

SATURATION OF THE MAGNETO-ROTATIONAL INSTABILITY IN STRONGLY RADIATION-DOMINATED ACCRETION DISKS

The saturation level of the magneto-rotational instability (MRI) in a strongly radiation-dominated accretion disk is studied using a new Godunov radiation MHD code in the unstratified shearing box approximation. Since vertical gravity is neglected in this work, our focus is on how the MRI saturates in the optically thick mid-plane of the disk. We confirm that turbulence generated by the MRI is very compressible in the radiation-dominated regime, as found by previous calculations using the flux-limited diffusion approximation. We also find little difference in the saturation properties in calculations that use a larger horizontal domain (up to four times the vertical scale height in the radial direction). However, in strongly radiation pressure dominated disks (one in which the radiation energy density reaches {approx}1% of the rest mass energy density of the gas), we find that Maxwell stress from the MRI turbulence is larger than the value produced when radiation pressure is replaced with the same amount of gas pressure. At the same time, the ratio between Maxwell stress and Reynolds stress is increased by almost a factor of eight compared with the gas pressure dominated case. We suggest that this effect is caused by radiation drag, which acts like bulk viscosity and changes the effective magnetic Prandtl number of the fluid. Radiation viscosity significantly exceeds both the microscopic plasma viscosity and resistivity, ensuring that radiation-dominated systems occupy the high magnetic Prandtl number regime. Nevertheless, we find that radiative shear viscosity is negligible compared to the Maxwell stress and Reynolds stress in the flow. This may have important implications for the structure of radiation-dominated accretion disks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

THE KOZAI–LIDOV MECHANISM IN HYDRODYNAMICAL DISKS. II. EFFECTS OF BINARY AND DISK PARAMETERS

Martin et al. showed that a substantially misaligned accretion disk around one component of a binary system can undergo global damped Kozai–Lidov (KL) oscillations. During these oscillations, the inclination and eccentricity of the disk are periodically exchanged. However, the robustness of this mechanism and its dependence on the system parameters were unexplored. In this paper, we use three-dimensional hydrodynamical simulations to analyze how various binary and disk parameters affect the KL mechanism in hydrodynamical disks. The simulations include the effect of gas pressure and viscosity, but ignore the effects of disk self-gravity. We describe results for different numerical resolutions, binary mass ratios and orbital eccentricities, initial disk sizes, initial disk surface density profiles, disk sound speeds, and disk viscosities. We show that the KL mechanism can operate for a wide range of binary-disk parameters. We discuss the applications of our results to astrophysical disks in various accreting systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Renormalizing a viscous fluid model for large scale structure formation

Using the Stochastic Adhesion Model (SAM) as a simple toy model for cosmic structure formation, we study renormalization and the removal of the cutoff dependence from loop integrals in perturbative calculations. SAM shares the same symmetry with the full system of continuity+Euler equations and includes a viscosity term and a stochastic noise term, similar to the effective theories recently put forward to model CDM clustering. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, they are necessarily non-local in time. To ensure Galilean Invariance higher order vertices related to the viscosity and the noise must then be added and we explicitly show at one-loop that these terms act as counter terms for vertex diagrams. The Ward Identities ensure that the non-local-in-time theory can be renormalized consistently. Another possibility is to include the viscosity in the linear propagator, resulting in exponential damping at high wavenumber. The resulting local-in-time theory is then renormalizable to one loop, requiring less free parameters for its renormalization.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Effect of thermal modification on rheological properties of polyethylene blends

We examined the effects of thermal modification under flow field on the rheological properties of linear low-density polyethylene (LLDPE) with high molecular weight, low-density polyethylene (LDPE), and their blends, without thermal stabilizer. Although structural changes during processing are not detected by size extrusion chromatography or nuclear magnetic resonance spectroscopy, linear viscoelastic properties changed greatly, especially for the LLDPE. A cross-linking reaction took place, leading to, presumably, star-shaped long-chain branches. Consequently, the modified LLDPE, having high zero-shear viscosity, became a thermorheologically complex melt. Moreover, it should be noted that the drawdown force, defined as the uniaxial elongational force at a constant draw ratio, was significantly enhanced for the blends. Enhancement of elongational viscosity was also detected. The drawdown force and elongational viscosity are marked for the thermally modified blend as compared with those for the blend of thermally modified pure components. Intermolecular cross-linking reactions between LDPE and LLDPE, yielding polymers with more than two branch points per chain, result in marked strain-hardening in the elongational viscosity behavior even at small strain. The recovery curve of the oscillatory modulus after the shear modification is further evidence of a branched structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Rheological properties of corn stover slurries during fermentation by Clostridium thermocellum

Background: Milling during fermentation, termed cotreatment, has recently been proposed as an alternative to thermochemical pretreatment as a means to increase the accessibility of lignocellulosic biomass to biological attack. A central premise of this approach is that partial solubilization of biomass changes the slurry’s physical properties such that milling becomes more impactful and more feasible. A key uncertainty is the energy required to mill partially fermented biomass. To inform both of these issues, we report rheological characterization of small-particle, corn stover slurries undergoing fermentation by Clostridium thermocellum . Results: Fermented and unfermented corn stover slurries were found to be shear-thinning and well described by a power law model with an exponent of 0.10. Plastic viscosity of a slurry, initially at 16 wt.% insoluble solids, decreased as a result of fermentation by a factor of 2000, with the frst eightfold reduction occurring in the frst 10% of carbohydrate conversion. Large amplitude oscillatory shear experiments revealed only minor changes to the slurry’s rheological fngerprint as a result of fermentation, with the notable change being a reduction in the critical strain amplitude needed for the onset of nonlinearity. All slurries were found to be elastoviscoplastic, with the elastic/viscous crossover at roughly 100% strain amplitude. Conclusions: Whereas prior biomass rheology studies have involved pretreated feedstocks and solubilization mediated by fungal cellulase, we report results for feedstocks with no pretreatment other than autoclaving and for solubilization mediated by C. thermocellum . As observed in prior studies, C. thermocellum fermentation results in a dramatic decrease in viscosity. The magnitude of this decrease, however, is much larger starting with unpretreated feedstock than previously reported for pretreated feedstocks. LAOS measurements provide a detailed picture of the rheological fngerprint of the material. Viscosity measurements confrm the hypothesis that the physical character of corn stover slurries changes dramatically during fermentation by C. thermocellum , and indicate that the energy expended on overcoming slurry viscosity will be far less for partially fermented corn stover than for unfermented corn stover.

09 BIOMASS FUELS↗
DOE OSTI2016

THE CONVERGENCE OF PARTICLE-IN-CELL SCHEMES FOR COSMOLOGICAL DARK MATTER SIMULATIONS

Particle methods are a ubiquitous tool for solving the Vlasov–Poisson equation in comoving coordinates, which is used to model the gravitational evolution of dark matter (DM) in an expanding universe. However, these methods are known to produce poor results on idealized test problems, particularly at late times, after the particle trajectories have crossed. To investigate this, we have performed a series of one- and two-dimensional “Zel’dovich pancake” calculations using the popular particle-in-cell (PIC) method. We find that PIC can indeed converge on these problems provided that the following modifications are made. The first modification is to regularize the singular initial distribution function by introducing a small but finite artificial velocity dispersion. This process is analogous to artificial viscosity in compressible gas dynamics, and, as with artificial viscosity, the amount of regularization can be tailored so that its effect outside of a well-defined region—in this case, the high-density caustics—is small. The second modification is the introduction of a particle remapping procedure that periodically reexpresses the DM distribution function using a new set of particles. We describe a remapping algorithm that is third-order accurate and adaptive in phase space. This procedure prevents the accumulation of numerical errors in integrating the particle trajectories from growing large enough to significantly degrade the solution. Once both of these changes are made, PIC converges at second order on the Zel’dovich pancake problem, even at late times, after many caustics have formed. Furthermore, the resulting scheme does not suffer from the unphysical, small-scale “clumping” phenomenon known to occur on the pancake problem when the perturbation wavevector is not aligned with one of the Cartesian coordinate axes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

ON THE GRAVITATIONAL STABILITY OF GRAVITO-TURBULENT ACCRETION DISKS

Low mass, self-gravitating accretion disks admit quasi-steady, “gravito-turbulent” states in which cooling balances turbulent viscous heating. However, numerical simulations show that gravito-turbulence cannot be sustained beyond dynamical timescales when the cooling rate or corresponding turbulent viscosity is too large. The result is disk fragmentation. We motivate and quantify an interpretation of disk fragmentation as the inability to maintain gravito-turbulence due to formal secondary instabilities driven by: (1) cooling, which reduces pressure support; and/or (2) viscosity, which reduces rotational support. We analyze the axisymmetric gravitational stability of viscous, non-adiabatic accretion disks with internal heating, external irradiation, and cooling in the shearing box approximation. We consider parameterized cooling functions in 2D and 3D disks, as well as radiative diffusion in 3D. We show that generally there is no critical cooling rate/viscosity below which the disk is formally stable, although interesting limits appear for unstable modes with lengthscales on the order of the disk thickness. We apply this new linear theory to protoplanetary disks subject to gravito-turbulence modeled as an effective viscosity, and cooling regulated by dust opacity. We find that viscosity renders the disk beyond ∼60 au dynamically unstable on radial lengthscales a few times the local disk thickness. This is coincident with the empirical condition for disk fragmentation based on a maximum sustainable stress. We suggest turbulent stresses can play an active role in realistic disk fragmentation by removing rotational stabilization against self-gravity, and that the observed transition in behavior from gravito-turbulent to fragmenting may reflect instability of the gravito-turbulent state itself.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Differentially rotating white dwarfs. I. Regimes of internal rotation

Most viable models of Type Ia supernovae (SNe Ia) require the thermonuclear explosion of a carbon/oxygen white dwarf that has evolved in a binary system. Rotation could be an important aspect of any model for SNe Ia, whether single or double degenerate, with the white dwarf mass at, below, or above the Chandrasekhar limit. Differential rotation is specifically invoked in attempts to account for the apparent excess mass in the super-Chandrasekhar events. Some earlier work has suggested that only uniform rotation is consistent with the expected mechanisms of angular momentum transport in white dwarfs, while others have found pronounced differential rotation. We show that if the baroclinic instability is active in degenerate matter and the effects of magnetic fields are neglected, both nearly uniform rotation and strongly differential rotation are possible. We classify rotation regimes in terms of the Richardson number, Ri. At small values of Ri ⩽ 0.1, we find both the low-viscosity Zahn regime with a nonmonotonic angular velocity profile and a new differential rotation regime for which the viscosity is high and scales linearly with the shear, σ. Employment of Kelvin–Helmholtz viscosity alone yields differential rotation. Large values of Ri ≫ 1 produce a regime of nearly uniform rotation for which the baroclinic viscosity is of intermediate value and scales as σ{sup 3}. We discuss the gap in understanding of the behavior at intermediate values of Ri and how observations may constrain the rotation regimes attained by nature.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Convergence of the Critical Cooling Rate for Protoplanetary Disk Fragmentation Achieved: The Key Role of Numerical Dissipation of Angular Momentum

We carry out simulations of gravitationally unstable disks using smoothed particle hydrodynamics (SPH) and the novel Lagrangian meshless finite mass (MFM) scheme in the GIZMO code. Our aim is to understand the cause of the nonconvergence of the cooling boundary for fragmentation reported in the literature. We run SPH simulations with two different artificial viscosity implementations and compare them with MFM, which does not employ any artificial viscosity. With MFM we demonstrate convergence of the critical cooling timescale for fragmentation at β{sub crit}≈3. Nonconvergence persists in SPH codes. We show how the nonconvergence problem is caused by artificial fragmentation triggered by excessive dissipation of angular momentum in domains with large velocity derivatives. With increased resolution, such domains become more prominent. Vorticity lags behind density, due to numerical viscous dissipation in these regions, promoting collapse with longer cooling times. Such effect is shown to be dominant over the competing tendency of artificial viscosity to diminish with increasing resolution. When the initial conditions are first relaxed for several orbits, the flow is more regular, with lower shear and vorticity in nonaxisymmetric regions, aiding convergence. Yet MFM is the only method that converges exactly. Our findings are of general interest, as numerical dissipation via artificial viscosity or advection errors can also occur in grid-based codes. Indeed, for the FARGO code values of β{sub crit} significantly higher than our converged estimate have been reported in the literature. Finally, we discuss implications for giant planet formation via disk instability.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Effect of Feed Composition on Cold-Cap Formation in Laboratory-Scale Melter

The development of advanced glass formulations are a part of the plan for reducing the cost and time for treatment and vitrification of the 210,000 m3 of nuclear waste at the Hanford Site in southeastern Washington State. One property of interest in this development is melt viscosity, which has a decisive influence on the rate of glass production. In an electric melter, the conversion process from feed-to-glass above the melt pool occurs in the cold cap. At the final stage of conversion when the glass-forming melt becomes connected, gas evolving reactions cause foaming. The melt viscosity affects foam stability. Three glasses were formulated with viscosities of 1.5, 3.5, and 9.5 Pa s at 1150°C by varying the SiO2 content at the expense of B2O3, Li2O, and Na2O kept at constant proportions. Cold caps were produced by charging simulated high-alumina, high-level waste feeds in a laboratory-scale melter (LSM). The spread of the feed on the cold cap during charging and the cross-sectional structure of the final cold caps were compared. The amount of the foam and the size of the bubbles increased as the viscosity increased.

Cold Cap↗
DOE OSTI2017

Effect of Silica Particle Size of Nuclear Waste-to-Glass Conversion - 17319

The process for converting nuclear waste-to-glass in an electric melter occurs in the cold cap, a crust of reacting solids floating on the glass pool. As the melter feed (a mixture of the nuclear waste and glass forming and modifying additives) heats up in the cold cap, glass-forming reactions ensue, causing the feed matrix to connect, trapping reaction gases to create a foam layer. The foam layer reduces the rate of melting by separating the reacting feed from the melt pool. The size of the silica particle additives in the melter feed affects melt viscosity and, hence, foam stability. To investigate this effect, seven nuclear waste simulant feeds of a high-level waste were batched as slurries and prepared with dissimilar ranges of silica particle size. Each slurry feed was charged into a laboratory-scale melter (LSM) to produce a cold cap and the propensity of feeds to foam was determined by pressing dried feeds into pellets and monitoring the change of pellet volume in response to heating. Two of these slurries were designed to have dissimilar glass viscosities at 1150°C. In the low temperature region of the cold cap, before the melter feed connects, the feeds without fine silica particles behaved similar to the high viscosity feed as their volume contracted while the feed with silica particles no larger than 5 µm reacted like the low viscosity feed. However, the feed volume similarities reversed as the feed connected and expanded through the foam region of the cold cap.

Cold Cap↗
DOE OSTI2017

Effect of Silica Particle Size on Nuclear Waste-to-Glass Conversion - 17319

The process for converting nuclear waste-to-glass in an electric melter occurs in the cold cap, a crust of reacting solids floating on the glass pool. As the melter feed (a mixture of the nuclear waste and glass forming and modifying additives) heats up in the cold cap, glass-forming reactions ensue, causing the feed matrix to connect, trapping reaction gases to create a foam layer. The foam layer reduces the rate of melting by separating the reacting feed from the melt pool. The size of the silica particle additives in the melter feed affects melt viscosity and, hence, foam stability. To investigate this effect, seven nuclear waste simulant feeds of a high-level waste were batched as slurries and prepared with dissimilar ranges of silica particle size. Each slurry feed was charged into a laboratory-scale melter (LSM) to produce a cold cap and the propensity of feeds to foam was determined by pressing dried feeds into pellets and monitoring the change of pellet volume in response to heating. Two of these slurries were designed to have dissimilar glass viscosities at 1150 deg. C. In the low temperature region of the cold cap, before the melter feed connects, the feeds without fine silica particles behaved similar to the high viscosity feed as their volume contracted while the feed with silica particles no larger than 5 μm reacted like the low viscosity feed. However, the feed volume similarities reversed as the feed connected and expanded through the foam region of the cold cap. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

Effect of Feed Composition on Cold-Cap Formation in Laboratory-Scale Melter - 16336

The development of advanced glass formulations is part of the plan for reducing the cost and time for treatment and vitrification of the 210,000 m{sup 3} of nuclear waste at the Hanford Site in southeastern Washington State. One property of interest in this development is melt viscosity, which has a decisive influence on the rate of glass production. In an electric melter, the conversion process from feed-to-glass above the melt pool occurs in the cold cap. At the final stage of conversion, when the glass-forming melt becomes connected, gas-evolving reactions cause foaming. The transient melt viscosity affects foam stability. Three glasses were formulated with viscosities of 1.5, 3.5, and 9.5 Pa s at 1150 deg. C by varying the SiO{sub 2} content at the expense of B{sub 2}O{sub 3}, Li{sub 2}O, and Na{sub 2}O kept at constant proportions. Cold caps were produced by charging simulated high-alumina, high-level waste feeds in a laboratory-scale melter. The spread of the feed on the cold cap during charging and the cross-sectional structure of the final cold caps were compared. The amount of the foam and the size of the bubbles increased as the viscosity increased. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2015

Impact of viscous fingering and permeability heterogeneity on fluid mixing in porous media

Fluid mixing plays a fundamental role in many natural and engineered processes, including groundwater flows in porous media, enhanced oil recovery, and microfluidic lab-on-a-chip systems. Recent developments have explored the effect of viscosity contrast on mixing, suggesting that the unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism to increase fluid-fluid interfacial area and enhance mixing. However, existing studies have not incorporated the effect of medium heterogeneity on the mixing rate. Here, we characterize the evolution of mixing between two fluids of different viscosity in heterogeneous porous media. We focus on a practical scenario of divergent-convergent flow in a quarter five spot geometry prototypical of well-driven groundwater flows. We study by means of numerical simulations the impact of permeability heterogeneity and viscosity contrast on the breakthrough curves and mixing efficiency, and we rationalize the nontrivial mixing behavior that emerges from the competition between the creation of fluid-fluid interfacial area and channeling.

58 GEOSCIENCES↗
DOE OSTI2017

Dominant Controls of Downdip Afterslip and Viscous Relaxation on the Postseismic Displacements Following the M w 7.9 Gorkha, Nepal, Earthquake

Here, we analyze three-dimensional GPS coordinate time series from continuously operating stations in Nepal and South Tibet and calculate the initial 1 year postseismic displacements. We first investigate models of poroelastic rebound, afterslip, and viscoelastic relaxation individually and then attempt to resolve the trade-offs between their contributions by evaluating the misfit between observed and simulated displacements. We compare kinematic inversions for distributed afterslip with stress-driven afterslip models. The modeling results show that no single mechanism satisfactorily explains near- and far-field postseismic deformation following the Gorkha earthquake. When considering contributions from all three mechanisms, we favor a combination of viscoelastic relaxation and afterslip alone, as poroelastic rebound always worsens the misfit. The combined model does not improve the data misfit significantly, but the inverted afterslip distribution is more physically plausible. The inverted afterslip favors slip within the brittle-ductile transition zone downdip of the coseismic rupture and fills the small gap between the mainshock and largest aftershock slip zone, releasing only 7% of the coseismic moment. Our preferred model also illuminates the laterally heterogeneous rheological structure between India and the South Tibet. The transient and steady state viscosities of the upper mantle beneath Tibet are constrained to be greater than 10 18 Pa s and 10 19 Pa s, whereas the Indian upper mantle has a high viscosity ≥10 20 Pa s. The viscosity in the lower crust of southern Tibet shows a clear trade-off with its southward extent and thickness, suggesting an upper bound value of ~8 × 10 19 Pa s for its steady state viscosity.

58 GEOSCIENCES↗