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Dependence of Perpendicular Viscosity on Magnetic Fluctuations in a Stochastic Topology
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A Composition-Based Approach for Predicting Hanford Tank Waste Liquid Viscosity
Liquid viscosity is an important Hanford waste physical property that governs, in part, the performance of key Hanford flowsheet unit operations and processes, including waste filtration, ion exchange, pumping and transport, and mixing. Evaluation and optimization of these processes rely on liquid viscosity correlations subject to substantial error (at least ±60%) that can lead to overly conservative, and sometimes physically unachievable, limits for validation and operation of these unit operations. The current liquid viscosity correlations used for the Hanford flowsheet attempt to capture the effects of specific waste chemistry (namely, the speciation of various salts) on liquid viscosity using liquid density alone. It is postulated that the ±60% or greater error associated with these “density-based” liquid viscosity predictions is driven in part by the inability of waste density to capture the full impact of waste chemistry on liquid viscosity, and that improved prediction accuracy could be achieved by implementing a composition-based approach to evaluating liquid viscosity for Hanford wastes. Recent publications, namely those of Lencka et al. (1998), Hu (2004), and Laliberté (2007a), provide correlations and comprehensive, consolidated databases of single-salt solution viscosity that enable composition-based predictions for Hanford-type liquids (i.e., concentrated multi-component aqueous electrolyte solutions). In the current study, the viscosities of Hanford wastes and waste simulants were predicted using a composition-based model developed by Laliberté (2007a) (hereafter referred to as the “Laliberté viscosity model”) to evaluate its accuracy relative to the current density-based models used to predict waste viscosity for engineering applications at the Hanford Site. A viscosity database that captured the composition and viscosity of wastes and waste simulants was developed to support this evaluation. To facilitate application of the Laliberté viscosity model, waste and waste simulant compositions were converted to an equivalent salt recipe composed of salts with known viscosity coefficients using a number of simplifying assumptions that have the potential to impact the fidelity of the model prediction. Despite these simplifications, the Laliberté viscosity model was able to predict viscosity more accurately than the density-based correlations currently available for Hanford flowsheet use, such as that proposed in RPP-RPT- 51652. The use of composition-based viscosity models, like that proposed by Laliberté (2007a), shows promise for leading to improved prediction of liquid waste viscosity. As implemented in this study, application of the Laliberté viscosity model could lead to a decrease in the uncertainty associated with liquid viscosity prediction by as much as a factor of two, allowing for reduction in unit operation design conservatism and for the more realistic selection of test simulants for flowsheet process evaluation and optimization, all of which could potentially reduce flowsheet design margins, lower costs and reduce duration of the Hanford mission, and reduce Hanford flowsheet risks.
Effective viscosities in a hydrodynamically expanding boost-invariant QCD plasma
Background: The near-equilibrium properties of a QCD plasma can be encoded into transport coefficients such as bulk and shear viscosity. In QCD, the ratio of these transport coefficients to entropy density, ζ/$\textit{s}$ and η/$\textit{s}$, depends nontrivially on the plasma's temperature. This is unlike in conformal systems where they take constant values such as η/$\textit{s}$ = 1/(4π). Purpose: In this work, we show that in a (0 + 1)D boost-invariant fluid with no transverse expansion, a temperature-dependent ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ can be described by an equivalent effective viscosity $\langleζ/s\rangle_{\text{eff}}$ or $\langleη/s\rangle_{\text{eff}}$. This effective viscosity combines the actual temperature-dependent ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ with the temperature profile of the fluid. Further, we extend the concept of effective viscosity in systems with transverse expansion and discuss how effective viscosities can be used to identify families of ζ/$\textit{s(T)}$ and η /$\textit{s(T)}$ that lead to similar hydrodynamic evolution. Methods: The Navier-Stokes relativistic hydrodynamic equations are used to provide a first definition of effective viscosity, in (0 + 1)D and (1 + 1)D. In the (0 + 1)D case, the analysis is extended to Israel-Stewart-type second-order hydrodynamics to clarify the effect of higher-order hydrodynamics corrections on the effective viscosity. Results: In a boost-invariant fluid with no transverse expansion [(0 + 1)D], the effective viscosity is expressed as a simple integral of ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ over temperature, with a weight determined by the speed of sound of the fluid. The result is general for any equation of state with a moderate temperature dependence of the speed of sound, including the QCD equation of state. This definition of effective viscosity can be used to identify infinite families of ζ/$\textit{s(T)}$ or η/$\textit{s(T)}$ that produce essentially indistinguishable temperature profiles. In a boost-invariant cylindrical system [(1 + 1)D], a similar definition of effective viscosity is obtained in terms of characteristic trajectories in time and transverse direction. This leads to an infinite number of constraints on an infinite functional space for ζ/$\textit{s(T)}$ and η/$\textit{s(T)}$. Realistic examples are presented by using a finite number of constraints on a finite functional space. Conclusions: The definition of effective viscosity in a (0 + 1)D system clarifies how infinite families of ζ/$\textit{s(T)}$ and η/$\textit{s(T)}$ can result in nearly identical hydrodynamic temperature profiles. By extending the study to a boost-invariant cylindrical [(1 + 1)D] fluid, we identify an approximate but more general definition of effective viscosity that highlights the potential and limits of the concept of effective viscosity in fluids with limited symmetries.
Predictions of the glass transition temperature and viscosity of organic aerosols from volatility distributions
Abstract. Volatility and viscosity are important properties of organic aerosols (OA), affecting aerosol processes such as formation, evolution, and partitioning of OA. Volatility distributions of ambient OA particles have often been measured, while viscosity measurements are scarce. We have previously developed a method to estimate the glass transition temperature (Tg) of an organic compound containing carbon, hydrogen, and oxygen. Based on analysis of over 2400 organic compounds including oxygenated organic compounds, as well as nitrogen- and sulfur-containing organic compounds, we extend this method to include nitrogen- and sulfur-containing compounds based on elemental composition. In addition, parameterizations are developed to predict Tg as a function of volatility and the atomic oxygen-to-carbon ratio based on a negative correlation between Tg and volatility. This prediction method of Tg is applied to ambient observations of volatility distributions at 11 field sites. The predicted Tg values of OA under dry conditions vary mainly from 290 to 339 K and the predicted viscosities are consistent with the results of ambient particle-phase-state measurements in the southeastern US and the Amazonian rain forest. Reducing the uncertainties in measured volatility distributions would improve predictions of viscosity, especially at low relative humidity. We also predict the Tg of OA components identified via positive matrix factorization of aerosol mass spectrometer (AMS) data. The predicted viscosity of oxidized OA is consistent with previously reported viscosity of secondary organic aerosols (SOA) derived from α-pinene, toluene, isoprene epoxydiol (IEPOX), and diesel fuel. Comparison of the predicted viscosity based on the observed volatility distributions with the viscosity simulated by a chemical transport model implies that missing low volatility compounds in a global model can lead to underestimation of OA viscosity at some sites. The relation between volatility and viscosity can be applied in the molecular corridor or volatility basis set approaches to improve OA simulations in chemical transport models by consideration of effects of particle viscosity in OA formation and evolution.
Dynamical influences on the moment of inertia tensor from lateral viscosity variations inferred from seismic tomographic models
We have investigated the influences of lateral variations of viscosity on the moment of inertia tensor from viscous flows due to the density anomalies in the mantle inferred from seismic tomographic models. The scaling relations between the density and the seismic anomalies is taken as either a constant or a function increasing with depth in accord with the recent high-pressure experimental studies. The viscosity is taken as an exponential function of the 3D density anomaly. In models with an isoviscous background, the effects on the perturbed moment of inertia tensor from the lateral viscosity variations are smaller than those due to variations in the radial viscosity profiles. In mantle models with a background viscosity increasing with depth, the influences of the lateral viscosity variations are significant. The most striking feature in the latter case is that the two off-diagonal elements delta I(sub xz) and delta I(sub yz) in the inertia tensor exhibit greatest sensitivity to lateral variations of the viscosity. While the other elements of the inertia change by only about a few tens of percent in the range of lateral viscosity contrast considered (less than 300), delta I(sub xz) and delta I(sub yz) can vary up to 40 times even with a change in sign, depending on the radial viscosity stratification and the location of the strongest lateral variations. The increase in the velocity-density scaling relation with depth can reduce the influences of the lateral viscosity variations, but it does not change the overall sensitive nature of delta I(sub xz) and delta I(sub yz). This study demonstrates clearly that the lateral viscosity variations, especially in the upper mantle, must be considered in the determination of long-term polar wander, since the variations in the delta I(sub xz) and delta I(sub yz) terms are directly responsible for exciting rotational movements.
Ion Viscosity Mediated by Tangled Magnetic Fields: An Application to Black Hole Accretion Disks
We examine the viscosity associated with the shear stress exerted by ions in the presence of a tangled magnetic field. As an application, we consider the effect of this mechanism on the structure of black hole accretion disks. We do not attempt to include a self-consistent description of the magnetic field. Instead, we assume the existence of a tangled field with coherence length lambda(sub coh), which is the average distance between the magnetic 'kinks' that scatter the particles. For simplicity, we assume that the field is self-similar, and take lambda(sub coh) to be a fixed fraction zeta of the local disk height H. Ion viscosity in the presence of magnetic fields is generally taken to be the cross-field viscosity, wherein the effective mean free path is the ion Larmor radius lambda(sub L), which is much less than the ion-ion Coulomb mean free path A(sub ii) in hot accretion disks. However, we arrive at a formulation for a 'hybrid' viscosity in which the tangled magnetic field acts as an intermediary in the transfer of momentum between different layers in the shear flow. The hybrid viscosity greatly exceeds the standard cross-field viscosity when (lambda/lambda(sub L)) much greater than (lambda(sub L)/lambda(sub ii)), where lambda = ((lambda(sub ii)(sup -1) + lambda(sub (coh)(sup -1))(sup -1) is the effective mean free path for the ions. This inequality is well satisfied in hot accretion disks, which suggests that the ions may play a much larger role in the momentum transfer process in the presence of magnetic fields than was previously thought. The effect of the hybrid viscosity on the structure of a steady-state, two-temperature, quasi-Keplerian accretion disk is analyzed. The hybrid viscosity is influenced by the degree to which the magnetic field is tangled (represented by zeta = lambda(sub coh)), and also by the relative accretion rate M/M(sub E), where M(sub E) = L(sub E)/c(sup 2) and L(sub E) is the Eddington luminosity. We find that ion viscosity in the presence of magnetic fields (hybrid viscosity) can dominate over conventional magnetic viscosity for fields that are tangled on sufficiently small scales.
Source of Processable Vitrimer Viscosities: Swap Frequencies and Steric Factors
Vitrimers exhibit high, processable viscosities, where other polymers do not, and are among the most promising polymers for closed-loop material circularity. We sought to investigate the underlying chemical kinetic factors that result in high viscosities for vitrimers, which are crucial to designing vitrimers with tunable viscosity. To interrogate these factors, we achieved the first simulated predictions of real vitrimer viscosities, using a novel kinetic Monte Carlo molecular dynamics method, overcoming the time and length scale gaps to predict experimental bulk viscosities. The vitrimer architecture investigated is based on poly(dimethylsiloxane) chains and vinylogous urethane bond swaps. We probed the effects of the extent of free swapping groups, %F, the activation energy, E A , and the steric factor, ρ. The steric factor is related to the intrinsic reaction probability for molecules with sufficient energy. All three factors were found to be significant, but the role of ρ was found to be the biggest and also the most underappreciated. The results show that the inclusion of accurate ρ is of critical importance for viscosity predictions, with the evidence suggesting that the typical assumption of ρ = 1 is not valid for vitrimers and that, indeed, very low steric factors are present in bond-swap vitrimers such that values of ρ < 10 –10 may be typical. This greatly influences the bond exchange rates and, ultimately, the viscosities. Recognition of this result is necessary for the prediction of vitrimer viscosities from molecular simulations and to make vitrimers by design from molecular dynamics. We also investigated the effects that E A , ρ, and the number of free swapping groups have upon vitreous range temperatures, TV, with respect to achieving a specific viscosity (η V = 1 × 10 8 Pa·s), as well as for a commonly reported higher viscosity extrapolation (η V = 1 × 10 12 Pa·s). The evidence suggests that vitrimers may follow universal curves for E A vs T V , as a function of ρ. Finally, this study achieves the first of these comparisons of molecular simulations to experiments and reveals critical insights toward creating vitrimers by design, while providing a route for the prediction of T V from kinetic Monte Carlo molecular dynamics simulations.
Thermophysical modeling of raw glaze liquidus temperature and viscosity
Raw glazes, which do not contain pre-melted glass frits, are widely used due to their low cost. The natural variability of the mineral compositions used in raw glazes affects their viscosity during firing. Molten glaze viscosity plays an important role in determining the final surface quality; therefore, it is important to determine how raw glaze composition and firing conditions affect viscosity. Thermophysical modeling provides a way to evaluate the liquidus temperature and viscosity of molten glazes as a function of composition and oxygen activity. Equilibrium phase volume fraction and composition of 242 raw glaze recipes were evaluated under oxidizing and reducing conditions. Undissolved or precipitation of solid phases explain the secondary flux transition from anti-fluxing to fluxing near the liquidus temperature. The liquidus temperature and viscosity of iron glazes decrease as a function of increasing iron content under a reducing atmosphere. The empirical probability distribution of molten glaze viscosity follows a lognormal distribution, with lead glazes having significantly lower viscosity compared with glazes without lead. Here, the peak firing temperature viscosity of lead-free glazes is near the working point of glass. Multiple linear regression analysis shows that the peak firing temperature viscosity and liquidus temperature significantly predict the viscosity factor.
Universal Solvent Viscosity Reduction via Hydrogen Bonding Disruptors
Liquid Ion Solutions LLC (DBA RoCo Global) in partnership with Carnegie Mellon University and Carbon Capture Scientific LLC, has performed lab-scale development and evaluation of novel additives that lower the viscosity of water-lean amine solvents for post-combustion carbon dioxide capture. This project focuses on developing additives that minimize the formation of long-range electrostatic and hydrogen bonding (HB) networks, decreasing the solvent viscosity, improving diffusion, and improving the process economics. The project objectives included: 1) performing computer simulation to understand the molecular interactions of the additive molecules in water-lean CO 2 capture solvents, 2) design and synthesis of HB disruptors additives, 3) performance testing with additive molecules on model amine solvents, and 4) demonstration of the effectiveness of the optimized additives in the presence of synthetic flue gas. To meet the abovementioned objectives, the project team utilized a holistic approach that combines molecular simulation, experimental testing, and economic analysis studies. The project team developed ab initio molecular model and then perform computer simulation to develop relationship between hydrogen bonding, viscosity, and performed quantitative analysis of additive on the viscosity of the solvent. The team completed computational comparative study on a range of organic functional groups such as ethers, esters, cyclic carbonates, alkanes, and ammonium salts for their effect on viscosity gaining key insights into molecular interactions and the impact of various functional groups and molecular shapes on viscosity. Assisted with molecular simulation insights, the project team conducted additive synthesis and testing, including a proof-of-concept study, additive screening, optimization, and synthetic flue gas testing. The experimental proof-of-concept study proved that the hydrogen bonding acceptors result in significant decrease of viscosities. Detailed additive screening (exploring various functionalities and molecular structures) has been performed. Several promising additives showed excellent reduction in viscosity (30-41%) at 5% additive loading, and over 50% viscosity reduction at 10% additive loading for the model solvents. The team also performed complex screening studies on additive loadings and mixing effect among additives using the design of experiments. Based on multiple screening experiments, one additive-solvent candidate was down-selected for synthetic flue gas testing. A 100-hour continuous absorption/desorption study was conducted under simulated flue gas using a lab-scale continuous capture and separation system. No degradation (for both solvent and additive) was observed based on the GC results of the solvent samples collected from the continuous study. The team conducted preliminary engineering analyses and cost-benefit analyses to quantify the potential economic benefits of the additive approach for solvent viscosity reduction. Based on the experimental data, CO 2 capture cost savings from the capital and operating cost savings are estimated at $\$$4.7/tonne and $\$$0.3/tonne CO 2 captured, respectively. Considering the additive cost, the net benefit is estimated to be between $\$$4.32~$\$$4.86/tonne CO 2 captured.
Reduced viscosity steadily weakens oceanic currents
The viscosity of both air and water is temperature dependent. A rising temperature leads to an increased viscosity for air but a decreased viscosity for water. As climate becomes warmer, this increased air viscosity can partly inhibit the reduction of wind stress over the ocean, and the reduced water viscosity causes less downward momentum and heat transport. As these opposing effects of warming on air and water viscosity are not included in the state-of-the-art climate models, the understanding of their potential impacts on the response of the climate system to the anthropogenic warming is lacking. Here, via analyzing the Simple Ocean Data Assimilation oceanic reanalysis dataset, we show that the ocean heat content increases at a rate of ~1.3 × 10 22 J/yr over 35 years, which leads to a continuous reduction of oceanic viscosity. As a result, the ocean vertical shear enhances with a shoaling of the mixed layer depth and a reduced vertical linkage in the ocean. Our calculations show a reduction of the oceanic kinetic energy at a rate of ~2.4 × 10 16 J/yr. Potentially, this could generate far-reaching impacts on the energy storage of the climate system and, hence, could pace the global warming. Thus, it is important to include the temperature-dependent viscosity in our climate models. Freshwater discharged from polar ice sheets and mountain glaciers also contributes to the reduction in oceanic viscosity but, at present, to a lesser extent than that in oceanic warming. Reduced oceanic viscosity, therefore, is an important, but hitherto overlooked, response to a warming climate and contributes to many recent weather extremes including heavier rainfall rates in hurricanes, slackening of the polar vortex, and oceanic heat waves.
Predicting the glass transition temperature and viscosity of secondary organic material using molecular composition
Secondary organic aerosol (SOA) accounts for a large fraction of submicron particles in the atmosphere. SOA can occur in amorphous solid or semi-solid phase states depending on chemical composition, relative humidity (RH), and temperature. The phase transition between amorphous solid and semi-solid states occurs at the glass transition temperature ( T g ). We have recently developed a method to estimate T g of pure compounds containing carbon, hydrogen, and oxygen atoms (CHO compounds) with molar mass less than 450 g mol -1 based on their molar mass and atomic O : C ratio. In this study, we refine and extend this method for CH and CHO compounds with molar mass up to ~1100 g mol -1 using the number of carbon, hydrogen, and oxygen atoms. We predict viscosity from the T g -scaled Arrhenius plot of fragility (viscosity vs. T g / T ) as a function of the fragility parameter D . We compiled D values of organic compounds from the literature and found that D approaches a lower limit of ~10 (±1.7) as the molar mass increases. We estimated the viscosity of α -pinene and isoprene SOA as a function of RH by accounting for the hygroscopic growth of SOA and applying the Gordon–Taylor mixing rule, reproducing previously published experimental measurements very well. Sensitivity studies were conducted to evaluate impacts of T g , D , the hygroscopicity parameter ( κ ), and the Gordon–Taylor constant on viscosity predictions. The viscosity of toluene SOA was predicted using the elemental composition obtained by high-resolution mass spectrometry (HRMS), resulting in a good agreement with the measured viscosity. We also estimated the viscosity of biomass burning particles using the chemical composition measured by HRMS with two different ionization techniques: electrospray ionization (ESI) and atmospheric pressure photoionization (APPI). Due to differences in detected organic compounds and signal intensity, predicted viscosities at low RH based on ESI and APPI measurements differ by 2–5 orders of magnitude. Complementary measurements of viscosity and chemical composition are desired to further constrain RH-dependent viscosity in future studies.
Scientific Objectives of the Critical Viscosity Experiment
In microgravity, the Critical Viscosity Experiment will measure the viscosity of xenon 15 times closer to the critical point than is possible on earth. The results are expected to include the first direct observation of the predicted power-law divergence of viscosity in a pure fluid and they will test calculations of the value of the exponent associated with the divergence. The results, when combined with Zeno's decay-rate data, will strengthen the test of mode coupling theory. Without microgravity viscosity data, the Zeno test will require an extrapolation of existing 1-g viscosity data by as much as factor of 100 in reduced temperature. By necessity, the extrapolation would use an incompletely verified theory of viscosity crossover. With the microgravity viscosity data, the reliance on crossover models will be negligible allowing a more reliable extrapolation. During the past year, new theoretical calculations for the viscosity exponent finally achieved consistency with the best experimental data for pure fluids. This report gives the justification for the proposed microgravity Critical Viscosity Experiment in this new context. This report also combines for the first time the best available light scattering data with our recent viscosity data to demonstrate the current status of tests of mode coupling theory.
Measurements and Model Estimations of Viscosities of the MnO-CaO-SiO{sub 2}-MgO-Al{sub 2}O{sub 3} Melts
The viscosities of the MnO (0 to 55 mass pct)-CaO-SiO{sub 2}-MgO (5 mass pct)-Al{sub 2}O{sub 3} (20 mass pct) melts were measured by rotating cylinder method in the temperature range from 1573 K to 1873 K (1300 °C to 1600 °C). The measurements were carried out in the atmosphere of flowing CO/CO{sub 2} gas mixture with a volume ratio of 99/1, and molybdenum crucible and spindle were adopted. The results reveal that MnO is a viscosity reducing component, and the effect of MnO is more notable in the melts with higher ratio of CaO to SiO{sub 2}. For example, in the melts with the mass ratio of CaO to SiO{sub 2} equal to 0.6, the addition of 5 mass pct MnO only slightly reduced the viscosities. Comparatively, the addition of 5 mass pct MnO made the viscosities of the melts with the mass ratio of CaO to SiO{sub 2} equal to 1.0 and 1.5 decrease remarkably. Based on the measured data, the viscosities estimation model proposed in our previous study was extended to the system containing MnO, and the model parameters were determined. The model can estimate and predict the viscosities of the aluminosilicate melts containing MnO well, and then some iso-viscosity contours of this system were calculated. From the iso-viscosity contours, it can be seen that MnO is almost equivalent to CaO in reducing the viscosities in the melt with high SiO{sub 2} content, while with the decrease of the SiO{sub 2} content MnO becomes more effective than CaO.
The effect of artificial bulk viscosity in simulations of forced compressible turbulence
The use of an artificial bulk viscosity for shock stabilization is a common approach employed in turbulence simulations with high-order numerics. The effect of the artificial bulk viscosity is analyzed in the context of large eddy simulations by using as a test case simulations of linearly-forced compressible homogeneous turbulence (Petersen and Livescu, 2010 [12]). This case is unique in that it allows for the specification of a priori target values for total dissipation and ratio of solenoidal to dilatational dissipation. A comparison between these target values and the true predicted levels of dissipation is thus used to investigate the performance of the artificial bulk viscosity. Results show that the artificial bulk viscosity is effective at achieving stable solutions, but also leads to large values of artificial dissipation that outweigh the physical dissipation caused by fluid viscosity. An alternate approach, which employs the artificial thermal conductivity only, shows that the dissipation of dilatational modes is entirely due to the fluid viscosity. However, this method leads to unwanted Gibbs oscillations around the shocklets. The use of shock sensors that further localize the artificial bulk viscosity did not reduce the amount of artificial dissipation introduced by the artificial bulk viscosity. Finally, an improved forcing function that explicitly accounts for the role of the artificial bulk viscosity in the budget of turbulent kinetic energy was explored.
Predicted viscosity of liquid HMX up to 40 GPa
Viscous flow serves as a significant heating mechanism during the formation of hot spots, but the shear viscosity which determines this response is poorly characterized for most high explosives. Most recently, a model was proposed for the shear viscosity of liquid HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane) that was fit to pressures reaching 5 GPa, but this work uncovered uncertainties in the viscosity at 0 GPa and remains untested at higher pressures. We use molecular dynamics (MD) simulations and the Green-Kubo formalism to predict the temperature- and pressure-dependent shear viscosity of HMX over the pressure interval 0 GPa≤P≤40 GPa. Reassessment of the viscosity at 0 GPa rules out several potential explanations for discrepancies between earlier reports; we attribute these differences to details of MD trajectory integration impacting molecular flexibility. The shear viscosity of HMX exhibits an Arrhenius temperature dependence at each pressure considered, with exponential prefactor and activation energy terms that are also strong functions of pressure. An analytic form for the viscosity is developed based on an extension of the well-known Andrade equation that simultaneously captures the temperature and pressure dependencies in the MD data up to 40 GPa. Comparison against a recently developed model for the viscosity of liquid RDX (1,3,5-trinitro-1,3,5-triazinane) shows that both materials exhibit similar functional dependencies with the viscosity of HMX being higher by roughly an order of magnitude at a given temperature-pressure state.
Arrhenian to non-Arrhenian crossover in glass melt viscosity
The activation energy for glass melt viscosity is a function of temperature, i.e., non-Arrhenian, within a middle range of viscosity values (typically, between 10 2 and 10 10 Pa s) and constant, i.e., Arrhenian, outside this range. At the low-viscosity end, the Arrhenian to non-Arrhenian transition (termed the crossover) falls within the glass processing range: glass melting and fining occur within the Arrhenian range while glass forming occurs within the non-Arrhenian range. By the Adam-Gibbs equation, the configuration entropy is nearly constant at high temperatures (low viscosities), where the glass melt turns into a simple liquid, and decreases with decreasing temperature (increasing viscosity) as the glass is increasingly polymerized. In the present study, the power-law function and hyperbolic tangent function are used to express the configuration entropy as a function of temperature. The viscosity crossover is defined as the point at which onset of structural grouping is causing the configuration entropy to deviate from its high-temperature value. In conclusion, it appears that the limited range of the configuration entropy of the fully depolymerized melt imposes a restriction on the crossover viscosity; for well-defined glass families, such as float glasses or nuclear waste glasses, the crossover point can be defined using a fixed, i.e., composition-independent, viscosity value.
Viscosity of 1-Alkyl-1-methylpyrrolidinium Bis(trifluoromethylsulfonyl)imide Ionic Liquids Saturated with Compressed CO 2
The viscosity of mixtures of pyrrolidinium-based ionic liquids saturated with compressed CO 2 was measured using a high-pressure viscometer at three different temperatures (298.15, 318.15 and 338.15 K). The high-pressure viscosity of 1-propyl-1-methyl-pyrrolidinium ([C 3 C 1 pyr]), 1-butyl-1-methyl-pyrrolidinium ([C 4 C 1 pyr]), and 1-hexyl-1-methyl-pyrrolidinium bis(trifluoromethylsulfonyl)amide ([C 6 C 1 pyr]) cations with common anion, bis(trifluoromethylsulfonyl)amide ([NTf 2 ]), was measured up to a maximum CO 2 pressure of 25 MPa. In the temperature range investigated, the viscosity of the ionic liquid/ CO 2 mixture dramatically decreases with increasing of CO 2 pressure up to approximately 7 MPa but the viscosity decrease becomes less significant at higher CO 2 pressures (from 7 to 25 MPa) because the CO 2 composition in ILs slightly increases with pressure. At lower CO 2 pressures (compositions), temperature has a higher impact on the CO 2 solubility in IL, thus the viscosity drops significantly for lower temperatures (e.g. 298.15 K). The effect of alkyl chain length of the cation on the viscosity of ionic liquid/ CO 2 mixture was also measured. Though the pure [C n C 1 pyr][NTf 2 ] viscosity increases significantly with the increasing alkyl chain length of the cation, the viscosity of every ionic liquid/ CO 2 mixture tested herein become quite similar at higher CO 2 pressures, for a fixed temperature.