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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Self-consistent hopping theory of activated relaxation and diffusion of dilute penetrants in dense crosslinked polymer networks

We generalize a microscopic statistical mechanical theory of the activated dynamics of dilute spherical penetrants in glass-forming liquids to study the influence of crosslinking in polymer networks on the penetrant relaxation time and diffusivity over a wide range of temperature and crosslink fraction (f n ). Our calculations are relevant to recent experimental studies of a nm-sized molecule diffusing in poly-(n-butyl methacrylate) networks. The theory predicts the penetrant relaxation time increases exponentially with the glass transition temperature, T g (f n ), which grows roughly linearly with the square root of fn due to the coupling of local hopping to longer-range collective elasticity. Moreover, T g is also found to be proportional to a geometric confinement parameter defined as the ratio of the penetrant diameter to the mean network mesh size. The decoupling ratio of the penetrant and Kuhn segment alpha times displays a complex non-monotonic dependence on f n and temperature that is well collapsed based on the variable T g (f n )/T. A model for the penetrant diffusion constant that combines activated relaxation and entropic mesh confinement is proposed, which results in a significantly stronger suppression of mass transport with degree of effective supercooling than predicted for the penetrant alpha time. Furthermore, this behavior corresponds to a new network-based type of “decoupling” of diffusion and relaxation. In contrast to the diffusion of larger nanoparticles in high temperature rubbery networks, our analysis in the supercooled regime suggests that for the penetrants studied the mesh confinement effects are of secondary importance relative to the consequences of crosslink-induced slowing down of activated hopping of glassy physics origin.

Chemistry↗
DOE OSTI2026

A New Theoretical Framework for Parameterizing Nonequilibrium Fractionation During Evaporation From the Ocean

The evaporation model for water isotopes proposed by Craig and Gordon (1965, https://books.google.co.in/books?id=6wIKAQAAIAAJ) is used in most isotope-enabled atmospheric models for the parameterization of nonequilibrium fractionation during evaporation from the ocean. In this model, one of the most uncertain parameters is the nonequilibrium fractionation factor 𝛼 𝑘 . Many isotope models use the formulation of Merlivat and Jouzel (1979, https://doi.org/10.1029/jc084ic08p05029), which parameterizes 𝛼 𝑘 as a function of wind speed and distinguishes between a smooth and a rough regime to account for the effect of ocean waves. The resulting discontinuity in 𝛼 𝑘 between smooth and rough regimes has been disputed by several empirical studies. Here, we present a new approach to parameterizing 𝛼𝑘 by explicitly accounting for the influence of wave drag on the momentum flux near the surface. Following Cifuentes-Lorenzen et al. (2018, https://doi.org/10.1007/s10546-018-0376-0), we add a third wave-induced component to the total momentum flux, in addition to the viscous and turbulent components, and extend the definition of the eddy viscosity to account for the momentum flux due to waves and turbulent dissipation near the surface. The new scheme predicts a slight decrease of 𝛼 𝑘 with wind speed, similar to the smooth-regime parameterization of Merlivat and Jouzel (1979, https://doi.org/10.1029/jc084ic08p05029). This new parameterization is incorporated into the isotope-enabled Community Atmosphere Model, where it improves the correlation of simulated and measured vapor deuterium excess relative to the default version and a version with constant 𝛼 𝑘 , suggesting that it may be used as a valid representation of fractionation during evaporation from the ocean in future isotope models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Investigation of countercurrent flow profile and liquid holdup in random packed column with local CFD data

Liquid holdup and mass transfer area are critical parameters used in packed column design and CO 2 capture efficiency prediction. Compared to experimental methods, 3D computational fluid dynamics (CFD) can provide high-resolution data for studying countercurrent flow hydrodynamics in a packed column. In this paper, a framework was established for modeling the liquid–gas countercurrent flow in a random packed column with pall rings. Besides the column-averaged information, the radial pall ring distribution, velocity, and liquid holdup profiles are obtained in the simulations. The radial two-phase velocity and liquid holdup profiles show significant fluctuations caused by the non-uniform pall ring distribution. The entrance effect and wall influence are also observed in the packed column. By using local countercurrent flow information, the packing specific area $a_p$ and liquid velocity $u_L$ range are significantly expanded for liquid holdup hL prediction. This enables us to develop the liquid holdup correlation with one packing size and six CFD runs only. The proposed power law of the liquid holdup correlation $h_L~u_L^{0.44}$ indicates the random packed column falls in a viscous to turbulent transition regime with a Reynolds Number range of [6.7–40.2]. The derived liquid holdup correlation is in good agreement with existing correlations that are developed using the column-averaged experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Optimal observables for the chiral magnetic effect from machine learning

The detection of the chiral magnetic effect (CME) in relativistic heavy-ion collisions remains challenging due to substantial background contributions that obscure the expected signal. In this Letter, we present a novel machine learning approach for constructing optimized observables that significantly enhance CME detection capabilities. By parametrizing generic observables constructed from flow harmonics and optimizing them to maximize the signal-to-background ratio, we systematically develop CME-sensitive measures that outperform conventional methods. Using simulated data from the anomalous viscous fluid dynamics framework, our machine learning observables demonstrate up to 90% higher sensitivity to CME signals compared to traditional 𝛾 and 𝛿 correlators, while maintaining minimal background contamination. The constructed observables provide physical insight into optimal CME detection strategies and offer a promising path forward for experimental searches of the CME at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Nonlinear dynamics and dissipation of a curvilinear vortex driven by a strong time-dependent Meissner current

Here, we report numerical simulations of large-amplitude oscillations of a trapped vortex line under a strong ac magnetic field $\textit{H(t) = H}$ sin$\textit{ωt}$ parallel to the surface. The power dissipated by an oscillating vortex segment driven by the surface ac Meissner currents was calculated by taking into account the nonlinear vortex line tension, vortex mass, and a nonlinear Larkin-Ovchinnikov (LO) viscous drag coefficient $\textit{η(v)}$. We show that the LO decrease of $\textit{η(v)}$ with the vortex velocity $\textit{v}$ can radically change the field dependence of the surface resistance R i ( H ) caused by trapped vortices. At low frequencies, $R_i(H)$ exhibits a conventional increase with $\textit{H}$, but as $\textit{ω}$ increases, the surface resistance becomes a nonmonotonic function of $\textit{H}$ which decreases with $\textit{H}$ at higher fields. The effects of frequency, pin spacing, and the mean-free path $l_i$ on the field dependence of $R_i(H)$ were calculated. It is shown that, as the surface gets dirtier and $l_i$ decreases, the anomalous drop of $R_i(H)$ with $\textit{H}$ shifts to lower fields which can be much smaller than the lower critical magnetic field. Our numerical simulations also show that the LO decrease of $\textit{η(v)}$ with $\textit{v}$ can cause a vortex bending instability at high field amplitudes and frequencies, giving rise to the formation of dynamic kinks along the vortex. Measurements of $R_i(H)$ caused by sparse vortices trapped perpendicular to the surface can offer opportunities to investigate an extreme nonlinear dynamics of vortices driven by strong current densities up to the depairing limit at low temperatures. The behavior of $R_i(H)$, which can be tuned by varying the rf frequency or concentration of nonmagnetic impurities, is not masked by strong heating effects characteristic of dc or pulse transport measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Combined Influence of Rotation and Scrape-Off Layer Drifts on Recycling Asymmetries in Tokamak Plasmas

Coupled 2D fluid-kinetic simulations of a DIII-D high confinement tokamak plasma show that plasma rotation coupled with drift effects near the plasma edge play a significant role in the creation of the observed poloidal distribution of neutrals. It is observed that including either drift or rotation effects enhances particle flux at the inner target in the case of ion 𝐵×∇𝐵 drift toward the 𝑋-point. However, the particle flux asymmetry is significantly higher with the combination of drifts and rotation than either effect alone. The heightened particle flux asymmetry allows for improved simulation of the strong in-out asymmetry of the Lyman-𝛼 brightness profiles measured in the experiment. Enhancement of radial transport of parallel momentum changes the upstream scrape-off layer flow pattern, increasing the fraction of deuterium flux that reaches the inboard divertor entrance while lowering that which arrives at the outboard. In conclusion, this Letter indicates that by combining drifts, rotation, and viscous coupling, existing boundary plasma models can achieve a satisfactory agreement with experimentally measured neutral asymmetries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Forward sensitivity analysis and mode dependent control for closure modeling of Galerkin systems

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of the original system and the truncated one. We put forth a framework to apply a continuous time control signal in the latent space of the reduced order model (ROM) to account for the effect of truncation. We set the control input using parameterized models by following energy transfer principles. Our methodology relies on observing the system behavior in the physical space and using the projection operator to restrict the feedback signal into the latent space. Then, we leverage the forward sensitivity method (FSM) to derive relationships between the feedback and the desired mode-dependent control. We test the performance of the proposed approach using two test cases, corresponding to viscous Burgers and vortex merger problems at high Reynolds number. Results show that the ROM trajectory with the applied FSM control closely matches its target values in both the data-dense and data-sparse regimes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Estimation of secondary organic aerosol viscosity from explicit modeling of gas-phase oxidation of isoprene and α -pinene

Abstract. Secondary organic aerosols (SOA) are major components of atmospheric fine particulate matter, affecting climate and air quality. Mounting evidence exists that SOA can adopt glassy and viscous semisolid states, impacting formation and partitioning of SOA. In this study, we apply the GECKO-A (Generator of Explicit Chemistry and Kinetics of Organics in the Atmosphere) model to conduct explicit chemical modeling of isoprene photooxidation and α-pinene ozonolysis and their subsequent SOA formation. The detailed gas-phase chemical schemes from GECKO-A are implemented into a box model and coupled to our recently developed glass transition temperature parameterizations, allowing us to predict SOA viscosity. The effects of chemical composition, relative humidity, mass loadings and mass accommodation on particle viscosity are investigated in comparison with measurements of SOA viscosity. The simulated viscosity of isoprene SOA agrees well with viscosity measurements as a function of relative humidity, while the model underestimates viscosity of α-pinene SOA by a few orders of magnitude. This difference may be due to missing processes in the model, including autoxidation and particle-phase reactions, leading to the formation of high-molar-mass compounds that would increase particle viscosity. Additional simulations imply that kinetic limitations of bulk diffusion and reduction in mass accommodation coefficient may play a role in enhancing particle viscosity by suppressing condensation of semi-volatile compounds. The developed model is a useful tool for analysis and investigation of the interplay among gas-phase reactions, particle chemical composition and SOA phase state.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Anion-dependent phase behavior of methylimidazolium-based ionic liquids mixed with water: Correlation between local molecular structure and mesoscale behaviors

The mesoscopic phase behavior of decylmethylimidazolium (C 10 mim) ionic liquids (ILs) bearing three monovalent anions—thiocyanate (SCN − ), nitrate (NO 3 − ), and chloride (Cl − )—mixed with water at relatively high IL contents (50–95 wt%) was investigated. Small-angle and wide-angle X-ray scattering (SAXS/WAXS) were employed to follow the evolution of both local and mesoscale structures across this composition range. In the absence of water, C 10 mimSCN and C 10 mimCl behaved as disordered liquids, whereas C 10 mimNO 3 spontaneously formed a hexagonally ordered cylindrical mesophase and displayed a sticky-solid macroscopic appearance. Upon addition of water, C 10 mimSCN remained a viscous liquid and only weakly ordered lamellar domains were observed. This limited ordering is attributed to the lack of hydrogen bonding and weak interaction energy between SCN − anions and C 10 mim + cations. In contrast, the trigonal-planar NO 3 − and point-like Cl − anions promoted the formation of well-defined hexagonal mesophases up to 35–45 wt% water. The formation of hydrogen bonding of the two anions with imidazolium ring protons likely enabled the creation of compact ion clusters that effectively exclude water molecules from the immediate vicinity of the IL aggregates. These findings demonstrate that the interaction energy between ion pairs dictate IL-water interactions and therefore control the transition from disordered liquids to ordered mesophases in IL/water mixtures with high IL contents. In conclusion, the combined SAXS/WAXS analysis reveals a correlation between local intermolecular structure and the emergence of mesoscopic order, providing a systematic framework for tailoring mesoscale structures in alkylimidazolium-based IL/water systems.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Quark flavor equilibration of the quark-gluon plasma

The early stage of a heavy-ion collision is marked by rapid entropy production and the transition from a gluon saturated initial condition to a plasma of quarks and gluons that evolves hydrodynamically. However, during the early times of the hydrodynamic evolution, the chemical composition of the QCD medium is still largely unknown. We present a study of quark chemical equilibration in the (Q)GP using a novel model of viscous hydrodynamic evolution in partial chemical equilibrium. Motivated by the success of gluon saturated initial condition models, we initialize the QCD medium as a completely gluon dominated state. Local quark production during the hydrodynamic phase is then simulated through the evolution of time-dependent fugacities for each independent quark flavor, with the timescales set as free parameters to compare different rates of equilibration. We present the results of complete heavy-ion collision simulations using this partial chemical equilibrium model, and show the effects on hadronic and electromagnetic observables. In particular, we show that the development of flow is sensitive to the equilibration timescale, providing an empirical way to probe the chemical equilibration of the QCD medium.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Identification of Kelvin-Helmholtz generated vortices in magnetised fluids

The Kelvin-Helmholtz Instability (KHI), arising from velocity shear across the magnetopause, plays a significant role in the viscous-like transfer of mass, momentum, and energy from the shocked solar wind into the magnetosphere. While the KHI leads to growth of surface waves and vortices, suitable detection methods for these applicable to magnetohydrodynamics (MHD) are currently lacking. A novel method is derived based on the well-established λ-family of hydrodynamic vortex identification techniques, which define a vortex as a local minimum in an adapted pressure field. The J × B Lorentz force is incorporated into this method by using an effective total pressure in MHD, including both magnetic pressure and a pressure-like part of the magnetic tension derived from a Helmholtz decomposition. The λ MHD method is shown to comprise of four physical effects: vortical momentum, density gradients, fluid compressibility, and the rotational part of the magnetic tension. A local three-dimensional MHD simulation representative of near-flank magnetopause conditions (plasma β’s 0.5 – 5 and convective Mach numbers M f ∼ 0.4) under northward interplanetary magnetic field (IMF) is used to validate λ MHD . Analysis shows it correlates well with hydrodynamic vortex definitions, though the level of correlation decreases with vortex evolution. Overall, vortical momentum dominates λ MHD at all times. During the linear growth phase, density gradients act to oppose vortex formation. By the highly nonlinear stage, the formation of small-scale structures leads to a rising importance of the magnetic tension. Compressibility was found to be insignificant throughout. Finally, a demonstration of this method adapted to tetrahedral spacecraft observations is performed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Investigation of Nonlinear Difference-Frequency Wave Excitation on a Semisubmersible Offshore-Wind Platform with Bichromatic-Wave CFD Simulations: Preprint

The natural surge and pitch frequencies of semisubmersible offshore wind platforms are typically designed to be below the wave frequencies to avoid direct excitation. However, surge or pitch resonance can be excited by the nonlinear low-frequency loads generated by irregular incident waves. Second-order potential-flow models with added Morison drag have been found to underpredict this low-frequency excitation and response. As part of the OC6 project, Computational Fluid Dynamics (CFD) simulations were performed to enable a better understanding of the low-frequency loads and the limitations of lower-fidelity models. The focus of the current paper is to set up a computationally cost-effective CFD simulation of a fixed semisubmersible platform to investigate nonlinear difference-frequency loads and establish the corresponding uncertainty in the results. Due to the high computing cost, CFD simulations of irregular waves can be challenging. Instead, simulations were performed with bichromatic waves having a shorter repeat period. A preliminary comparison with Quadratic Transfer Functions from second-order potential-flow theory shows that CFD models consistently predict higher nonlinear wave loads at the difference frequency, likely due to flow separation and viscous drag not accounted for in potential-flow theory.

2nd order↗
DOE OSTI2026

Insights into mixing of non-isothermal multi-polymer melts for complex plastics recycling

Catalytic recycling or upcycling of plastics is often limited not by catalyst performance, but by transport, arising from highly viscous, non-Newtonian polymer melts. In this work, we develop a reactor-scale framework that integrates rheological measurements, constitutive modeling, computational fluid dynamics (CFD), and experiments to quantify mixing, heat transfer, and dispersion in surrogate hydrocarbon melts representing mixed plastics systems. Temperature- and shear rate-dependent viscosity of low-density polyethylene (LDPE) and high-density polyethylene (HDPE) is measured to create two surrogate polymers (PLD and PHD) that capture the dominant shear-thinning flow behavior while neglecting strong elastic effects, enabling tractable simulation of non-isothermal, polymer-melt mixing using a Carreau-Arrhenius generalized Newtonian framework. Three-dimensional CFD simulations are employed to evaluate impeller performance in PLD using mixing time, cavern volume, thermal uniformity, and interfacial area for regimes in which viscoelastic effects are not dominant. We show that magnetic stir bars commonly used in lab-scale studies produce large thermal gradients (~60 °C) and poor mixing, even under idealized power delivery and polymer flow conditions. In contrast, close-clearance anchor impellers achieve near-isothermal operation, reduce mixing times by up to 5×, and provide >90% active circulation volume. We further demonstrate that, at low pseudo-Deborah number (De*), motor power requirements can be predicted directly from shear rate-dependent rheology using the Carreau-Arrhenius framework, enabling rational selection of operating conditions. Extension to surrogate immiscible multi-polymer systems based on PLD and PHD shows that interfacial area is highly sensitive to operating conditions and impeller design, with coaxial anchor-turbine configurations enhancing dispersion by up to 4 × .

Close-clearance impellers↗
DOE OSTI2024

Ion‐Specific Interactions Engender Dynamic and Tailorable Properties in Biomimetic Cationic Polyelectrolytes

Abstract Biomaterials such as spider silk and mussel byssi are fabricated by the dynamic manipulation of intra‐ and intermolecular biopolymer interactions. Organisms modulate solution parameters, such as pH and ion co‐solute concentration, to effect these processes. These biofabrication schemes provide a conceptual framework to develop new dynamic and responsive abiotic soft material systems. Towards these ends, the chemical diversity of readily available ionic compounds offers a broad palette to manipulate the physicochemical properties of polyelectrolytes via ion‐specific interactions. In this study, we show for the first time that the ion‐specific interactions of biomimetic polyelectrolytes engenders a variety of phase separation behaviors, creating dynamic thermal‐ and ion‐responsive soft matter that exhibits a spectrum of physical properties, spanning viscous fluids to viscoelastic and viscoplastic solids. These ion‐dependent characteristics are further rendered general by the merger of lysine and phenylalanine into a single, amphiphilic vinyl monomer. The unprecedented breadth, precision, and dynamicity in the reported ion‐dependent phase behaviors thus introduce a broad array of opportunities for the future development of responsive soft matter; properties that are poised to drive developments in critical areas such as chemical sensing, soft robotics, and additive manufacturing.

Aubrecht, Filip J.↗
DOE OSTI2022

Modelling general-relativistic plasmas with collisionless moments and dissipative two-fluid magnetohydrodynamics

ABSTRACT Relativistic plasmas are central to the study of black hole accretion, jet physics, neutron star mergers, and compact object magnetospheres. Despite the need to accurately capture the dynamics of these plasmas and the implications for relativistic transients, their fluid modelling is typically done using a number of (overly) simplifying assumptions, which do not hold in general. This is especially true when the mean free path in the plasma is large compared to the system size, and kinetic effects start to become important. Going beyond common approaches used in the literature, we describe a fully relativistic covariant 14-moment based two-fluid system appropriate for the study of electron–ion or electron–positron plasmas. This generalized Israel-Stewart-like system of equations of motion is obtained directly from the relativistic Boltzmann–Vlasov equation. This new formulation can account for non-ideal effects, such as anisotropic pressures and heat fluxes, not present in previous formulations of two-fluid magnetohydrodynamics. We show that a relativistic two-fluid plasma can be recast as a single fluid coupled to electromagnetic fields with (potentially large) out-of-equilibrium corrections. We keep all electron degrees of freedom, which provide self-consistent evolution equations for electron temperature and momentum. The out-of-equilibrium corrections take the form of a collisional 14-moment closure previously described in the context of viscous single fluids. The equations outlined in this paper are able to capture the full two-fluid character of collisionless plasmas found in black hole accretion and flaring processes around compact objects, as well Braginskii-like two-fluid magnetohydrodynamics applicable to weakly collisional plasmas inside accretion discs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Multi‐Layered Systems for Permanent Geologic Storage of CO 2 at the Gigatonne Scale

Abstract The effectiveness of Carbon Capture and Storage (CCS) as an imperative decarbonization technology relies on the sealing capacity of a fine‐grained caprock to permanently store CO 2 deep underground. Uncertainties in assessing the caprock sealing capacity increase with the spatial and temporal scales and may delay CCS deployment at the gigatonne scale. We have developed a computationally efficient transport model to capture the dynamics of basin‐wide upward CO 2 migration in a multi‐layered setting over geological time scales. We find that massive capillary breakthrough and viscous flow of CO 2 , even through pervasively fractured caprocks, are unlikely to occur and compromise the storage security. Potential leakage from the injection reservoir is hampered by repetitive layering of overlying caprocks. This finding agrees with geologic intuition and should be understandable by the public, contributing to the development of climate policies around this technology with increased confidence that CO 2 will be indefinitely contained in the subsurface.

58 GEOSCIENCES↗
DOE OSTI2020

Synergistic effect of dual Brønsted acidic deep eutectic solvents for oxidative desulfurization of diesel fuel

Deep eutectic solvents (DESs) are generally used as attractive solvents or extractants rather than catalysts in the field of synthesis and separation. Herein, dual Brønsted acidic DESs were prepared by mixing sulfonated quaternary ammonium and oxalic acid as extractants and catalysts for deep oxidative desulfurization. Compared to the DESs with single acidic group, the dual acidic DESs exhibited much higher catalytic activity likely due to the synergistic effect. The 1 H NMR study indicated that the weak interaction between DES and sulfur compounds led to a low extraction capacity. However, the sulfur removal could reach 97.7% under optimized reaction conditions. Density functional theory (DFT) calculations demonstrated that sulfonic group and carboxylic group are of equal importance to desulfurization performance. Further, the desulfurization efficiency was also strongly affected by the viscosity of DESs. Here, we put forward a new strategy that the reaction time could be sharply shortened to 40 min and 100 min by adding low viscous acetonitrile and polyethylene glycol into DES to form mixing reaction system, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Elucidating the Mechanism of Helium Evaporation from Liquid Water

Here, we investigate the evaporation of trace amounts of helium solvated in liquid water using molecular dynamics simulations and theory. Consistent with experimental observations, we find a super-Maxwellian distribution of kinetic energies of evaporated helium. This excess of kinetic energy over typical thermal expectations is explained by an effective continuum theory of evaporation based on a Fokker–Planck equation, parametrized molecularly by a potential of mean force and position-dependent friction. Using this description, we find that helium evaporation is strongly influenced by the friction near the interface, which is anomalously small near the Gibbs dividing surface due to the ability of the liquid–vapor interface to deform around the gas particle. Our reduced description provides a mechanistic interpretation of trace gas evaporation as the motion of an underdamped particle in a potential subject to a viscous environment that varies rapidly across the air–water interface. From it we predict the temperature dependence of the excess kinetic energy of evaporation, which is yet to be measured.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗