Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “liquid”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Towards nanoscale electrical measurements in liquid by advanced KPFM techniques: a review

Fundamental mechanisms of energy storage, corrosion, sensing, and multiple biological functionalities are directly coupled to electrical processes and ionic dynamics at solid–liquid interfaces. In many cases, these processes are spatially inhomogeneous taking place at grain boundaries, step edges, point defects, ion channels, etc and possess complex time and voltage dependent dynamics. This necessitates time-resolved and real-space probing of these phenomena. In this review, we discuss the applications of force-sensitive voltage modulated scanning probe microscopy (SPM) for probing electrical phenomena at solid–liquid interfaces. We first describe the working principles behind electrostatic and Kelvin probe force microscopies (EFM & KPFM) at the gas–solid interface, review the state of the art in advanced KPFM methods and developments to (i) overcome limitations of classical KPFM, (ii) expand the information accessible from KPFM, and (iii) extend KPFM operation to liquid environments. We briefly discuss the theoretical framework of electrical double layer (EDL) forces and dynamics, the implications and breakdown of classical EDL models for highly charged interfaces or under high ion concentrations, and describe recent modifications of the classical EDL theory relevant for understanding nanoscale electrical measurements at the solid–liquid interface. We further review the latest achievements in mapping surface charge, dielectric constants, and electrodynamic and electrochemical processes in liquids. Lastly, we outline the key challenges and opportunities that exist in the field of nanoscale electrical measurements in liquid as well as providing a roadmap for the future development of liquid KPFM.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Conference Report on the 7th International Symposium on Liquid metals Applications for fusion (ISLA-7)

Supported by the world magnetic fusion research community, a series of International Symposia on Liquid metals Applications for fusion (ISLA) have been held biannually since 2010. The 7th edition (ISLA-7) was held for the period from 12 December through 16 December 2022, at Chubu University located in Kasugai, Aichi, Japan. For the first time in the history of this series of symposia, ISLA-7 was held in a hybrid fashion, due to the COVID-19 situation. The total number of the participants was 60, 34 out of whom attended the symposium in person, and the rest participated online. As to the presentation statistics, 29 papers were presented in person, whereas 21 presentations were delivered online but real-time by the presenters in China, Spain, the UK, and the USA. Both of the presentations delivered in person and online were recorded, and the video has been shared by all participants. These participants represent 11 countries: China, Czech, Italy, Japan, Latvia, Netherlands, Russia, Thailand, the UK, and the USA. All these numbers are among the largest in this series of symposia. Covered by these presentations are; in session-2, program overviews and liquid metal research review; in session-3, liquid metal flows, and MHD issues; in session-4, liquid metal facilities; in sessions-5 and 6, liquid metal experiments and modeling; in session-7, divertor physics and heat flux mitigation; in session-8, plasma and liquid metals interactions; in session-9 liquid metal plasma-facing components, erosion, and wettability. In addition, there were an opening session whereby several opening addresses were delivered and also a closing session where all technical session summaries were presented by the respective session chairs.

divertor↗
DOE OSTI2021

Bose-Luttinger liquids

In this report we study systems of bosons whose low-energy excitations are located along a spherical submanifold of momentum space. We argue for the existence of gapless phases which we dub “Bose-Luttinger liquids,” which in some respects can be regarded as bosonic versions of Fermi liquids, while in other respects they exhibit striking differences. These phases have bosonic analogues of Fermi surfaces, and like Fermi liquids they possess a large number of emergent conservation laws. Unlike Fermi liquids, however, these phases lack quasiparticles, possess different RG flows, and have correlation functions controlled by a continuously varying exponent η, which characterizes the anomalous dimension of the bosonic field. We show that when η > 1, these phases are stable with respect to all symmetric perturbations. These theories may be of relevance to several physical situations, including frustrated quantum magnets, rotons in superfluid He, and superconductors with finite-momentum pairing. As a concrete application, we show that coupling a Bose-Luttinger liquid to a conventional Fermi liquid produces a resistivity scaling with temperature as T η . We argue that this may provide an explanation for the non-Fermi liquid resistivity observed in the paramagnetic phase of MnSi.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Perspective: Ferromagnetic Liquids

Mechanical jamming of nanoparticles at liquid–liquid interfaces has evolved into a versatile approach to structure liquids with solid-state properties. Ferromagnetic liquids obtain their physical and magnetic properties, including a remanent magnetization that distinguishes them from ferrofluids, from the jamming of magnetic nanoparticles assembled at the interface between two distinct liquids to minimize surface tension. This perspective provides an overview of recent progress and discusses future directions, challenges and potential applications of jamming magnetic nanoparticles with regard to 3D nano-magnetism. We address the formation and characterization of curved magnetic geometries, and spin frustration between dipole-coupled nanostructures, and advance our understanding of particle jamming at liquid–liquid interfaces.

36 MATERIALS SCIENCE↗
NASA NTRS2013

Liquid Water Cloud Measurements Using the Raman Lidar Technique: Current Understanding and Future Research Needs

This paper describes recent work in the Raman lidar liquid water cloud measurement technique. The range-resolved spectral measurements at the National Aeronautics and Space Administration Goddard Space Flight Center indicate that the Raman backscattering spectra measured in and below low clouds agree well with theoretical spectra for vapor and liquid water. The calibration coefficients of the liquid water measurement for the Raman lidar at the Atmospheric Radiation Measurement Program Southern Great Plains site of the U.S. Department of Energy were determined by comparison with the liquid water path (LWP) obtained with Atmospheric Emitted Radiance Interferometer (AERI) and the liquid water content (LWC) obtained with the millimeter wavelength cloud radar and water vapor radiometer (MMCR-WVR) together. These comparisons were used to estimate the Raman liquid water cross-sectional value. The results indicate a bias consistent with an effective liquid water Raman cross-sectional value that is 28%-46% lower than published, which may be explained by the fact that the difference in the detectors' sensitivity has not been accounted for. The LWP of a thin altostratus cloud showed good qualitative agreement between lidar retrievals and AERI. However, the overall ensemble of comparisons of LWP showed considerable scatter, possibly because of the different fields of view of the instruments, the 350-m distance between the instruments, and the horizontal inhomogeneity of the clouds. The LWC profiles for a thick stratus cloud showed agreement between lidar retrievals andMMCR-WVR between the cloud base and 150m above that where the optical depth was less than 3. Areas requiring further research in this technique are discussed.

vapor and liquid water↗
DOE OSTI2024

Unusual dynamics of tetrahedral liquids caused by the competition between dynamic heterogeneity and structural heterogeneity

Tetrahedral liquids exhibit intriguing thermodynamic and transport properties because of the various ways tetrahedra can be packed and connected. Recently, an unusual temperature dependence of the stretching exponent β in a model tetrahedral liquid ZnCl 2 from T m + 85 K to T m + 35 K has been reported using neutron-spin echo spectroscopy. This discovery stands in sharp contrast to other glass-forming liquids. In this study, we conducted neural network force field driven molecular dynamic simulations of ZnCl 2 . We found a non-monotonic temperature dependence of β from liquid to supercooled liquid temperatures. Further structural decomposition and dynamic analysis suggest that this unusual dynamic behavior is a result of the competition between the decrease in the diversity of tetrahedra motifs (structural heterogeneity) and the increase in glassy dynamic heterogeneity. Furthermore, this result may contribute to new understandings of the structural relaxation of other network liquids.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Atomic Cluster Aggregates in Nucleation of Solid Alumina Inclusion in the Aluminum Deoxidation for Liquid Iron

Nucleation plays a decisive role in determining the structure and size distribution of a solid inclusion particle in liquid iron. The literature does not yet provide a clear picture about the pathway leading to solid alumina inclusion from liquid iron. The main confusion surrounds the little-known structures and thermodynamic properties of metastable alumina phase (MAP) that appear in the nucleation of alumina inclusion. In this work, it is suggested that MAP could appear in the Al-deoxidation reaction, based on the summaries and analysis in terms of various equilibrium experimental results and thermodynamic modeling of the Al deoxidation in liquid iron since the 1950s. The structures and thermodynamic properties of a species of MAP, alumina atomic cluster aggregates (AACAs), are calculated by density functional theory (DFT) methods. The thermodynamics on formation and transformation of AACAs shows that AACAs are in equilibrium with Al and O with various contents measured in the Al-deoxidation equilibrium experiments for liquid iron. It is suggested that the residual Al and O, which cannot nucleate, appear in the form of AACAs in Al-deoxidized liquid iron. It can be concluded that AACAs are the metastable intermediates and structural units for alumina inclusion nucleating from liquid iron. Thus, the behaviors of AACAs are important to the control of the nucleation rate of alumina inclusions in the Al deoxidation for liquid iron.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Transport of coexisting Ni-Cu sulfide liquid and silicate melt in partially molten peridotite

Transport of coexisting sulfide and silicate melts in partially molten peridotite contributes to the redistribution of chalcophile elements within the upper mantle as well as the genesis of magmatic Ni-Cu sulfide deposits, but has not been investigated systematically. Using laboratory experiments, theoretical calculations, and X-ray synchrotron microtomography, this study documents the topology and considers controls on the extraction of two immiscible liquids during partial melting of mantle peridotite. Under hydrostatic conditions, the measured dihedral angle at silicate melt-mineral-mineral junctions is 13.7–21.3°. Silicate melt is distributed along grain edges forming incompletely interconnected melt channels that disconnected by some dead ends at melt fractions ~7–9 vol%. Application of theoretically predicted permeability (k ~10 -14 -10 -16 m 2 ) permits estimation of the extraction velocity of silicate melt of 0.7-11.1 μm/day within a single interconnected melt channel. In the absence of silicate melt, isolated sulfide droplets (3.77 vol%) show a sulfide-olivine-olivine dihedral angle of 91.5–101.3°. However, in the presence of silicate melt, sulfide droplets (average size ~2.53±2.14μm, 1σ) are partially surrounded by silicate melt and stranded in triple junctions or melt pockets due to the limitation of the smallest dimension (0.3μm) of melt channels. Thus, the extraction of sulfide liquid is highly restricted by these dead ends and the smallest dimension of melt channels during porous flow of silicate melt. In contrast, during large-strain shear deformation (strain ~1.6–2.5), initially stranded sulfide droplets were elongated and extracted with silicate melt into liquid-rich sheets with a length of several hundred microns, constantly oriented at 14.3±4.5°to the shear plane and antithetic to the shear direction. The angle is lower than that (18-30°) of those sheets containing sulfide liquid only, indicating that silicate melt dominates liquid-rich sheets. Driven by stress, silicate melt-dominated liquid-rich sheets open the appropriately oriented grain boundaries between silicate minerals, thus providing an efficient pathway for the extraction of sulfide liquid during deformation. When such sheet-like channels remain open, sulfide droplets (> millimeter-scale) can be potentially mobile through high strain domains of the upper mantle, contributing to the addition of chalcophile elements and the fertilization of the lithospheric mantle.

high P-T experiment↗
DOE OSTI2025

Dehumidification energy storage using a stratified liquid desiccant tank

Liquid desiccants can play an important role in reducing dehumidification energy requirements in the built environment. Because they are in a liquid state, the desiccant can be easily stored and then used to dehumidify buildings during peak energy consumption periods. By maintaining stratification between concentrated and diluted desiccant solutions, a single tank can be used to store liquid desiccant for energy storage purposes. Using a stratified tank instead of separate tanks for dilute and concentrated solutions will reduce storage costs and increase energy storage densities for liquid desiccant systems. This paper describes the experimental validation and one-dimensional modeling of a stratified liquid desiccant tank. The stratified tank prototype developed achieved 80 % of the theoretical energy storage density based on an imposed desiccant concentration change. Here, the stratified tank model was able to reasonably reproduce the experimental results. Using this model, the impact of varying operational conditions on the energy density of the stratified liquid desiccant energy storage was evaluated. Depending on the operating conditions, stratified liquid desiccant energy storage using aqueous LiCl up to 40 wt% can achieve energy storage densities in excess of 330 kWh/m 3 .

25 ENERGY STORAGE↗
DOE OSTI2025

Identifying High Ionic Conductivity Compositions of Ionic Liquid Electrolytes Using Features of the Solvation Environment

Binary mixtures of ionic liquids with molecular solvents are gaining interest in electrochemical applications due to the improvement in their performance over neat ionic liquids. Dilution with suitable molecular solvents can reduce the viscosity and facilitate faster diffusion of ions, thereby yielding substantially higher ionic conductivity than that for a pure ionic liquid. Although viscosity and diffusion coefficients typically behave as monotonic functions of concentration, ionic conductivity often passes through a peak value at an optimum molar ratio of the molecular solvent to the ionic liquid. The ionic conductivity maximum is generally explained in terms of a balance between the ease of charge transport and the concentration of the charge carriers. In this work, fluctuation in the local environment surrounding an ion is invoked as a plausible explanation for the ionic conductivity mechanism with a binary mixture of 1-ethyl-3-methylimidazolium tetrafluoroborate and ethylene glycol as an example. The magnitude of the dynamism in the local environment is captured by measuring the spatial and temporal features of the solvation environment. Standard deviation in the number of ions in the solvation environment serves as a spatial feature, while the cage correlation lifetimes for oppositely charged ions within the first solvation shell serve as a temporal feature. Large standard deviations in the cluster ion population and short cage correlation lifetimes are indicators of highly dynamic ionic environment at the molecular level and consequently yield high ionic conductivity. Such compositions were found to be in good agreement with the optimum ionic liquid mole fractions obtained through experimental measurement. Short cage correlation lifetimes enable the identification of optimum mixture compositions using simulation trajectories significantly shorter than those required to implement the Nernst–Einstein or Einstein formalisms for calculating ionic conductivity. We validated the applicability of this approach across force fields and in six ionic liquid-molecular solvent electrolytes formed with combination of cations, anions, and solvents. We offer a computationally efficient approach of screening ionic liquid-molecular solvent binary mixture electrolytes to identify molar ratios that yield high ionic conductivity.

25 ENERGY STORAGE↗
DOE OSTI2018

Thermally Responsive Hyperbranched Poly(ionic liquid)s: Assembly and Phase Transformations

Here, a library of linear and branched amphiphilic poly(ionic liquid)s based on hydrophobic cores and peripheral thermally sensitive shells was synthesized and studied with regard to their ability to form stimuli-responsive, organized assemblies in aqueous media. The thermally responsive derivatives of poly(ionic liquid)s were synthesized by neutralizing 32 terminal carboxyl groups of functionalized polyester cores by amine-terminated poly( N -isopropylacrylamide)s (PNIPAM) (50% and 100%). We observed that these hyperbranched poly(ionic liquid)s possessed a narrow low critical solution transition (LCST) window with LCST for hyperbranched compounds being consistently lower than that for linear PNIPAM containing counterparts. We found that the poly(ionic liquid)s form spherical micellar assemblies with diverse morphologies, such as micelles and their aggregates, depending on the terminal compositions with reduced sizes for hyperbranched poly(ionic liquid)s. Increasing temperature above LCST promoted formation of network-like aggregates, large vesicles, and spherical micelles. Moreover, all PNIPAM-terminated compounds exhibited distinct unimolecular prolate nanodomain morphology in contrast to common spherical domains of initial cores. We proposed a multilength scale organized morphology to describe the thermoresponsive poly(ionic liquid)s micellar assemblies and discussed their morphological transformations during phase transitions associated with changes in hydrophobic–hydrophilic balance of poly(ionic liquid)s with distinct hydrophobic cores and variable peripheral shells.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Logarithm Diameter Scaling and Carrier Density Independence of One-Dimensional Luttinger Liquid Plasmon

Quantum-confined electrons in one-dimensional (1D) metals are described by a Luttinger liquid. The collective charge excitations (i.e., plasmons) in a Luttinger liquid can behave qualitatively different from their conventional counterparts. For example, the Luttinger liquid plasmon velocity is uniquely determined by the electron–electron interaction, which scales logarithmly with the diameter of the 1D material. In addition, the Luttinger liquid plasmon is predicted to be independent of the carrier concentration. Here in this paper, we report the observation of such unusual Luttinger liquid plasmon behaviors in metallic single-walled carbon nanotubes, a model system featuring strong electron quantum confinement. We systematically investigate the plasmon propagation in over 30 metallic carbon nanotubes of different diameters using infrared nanoscopy. We establish that the plasmon velocity has a weak logarithm dependence on the nanotube diameter, as predicted by the Luttinger liquid theory. We further study the plasmon excitation as a function of the carrier density in electrostatically gated metallic carbon nanotubes and demonstrate that the plasmon velocity is completely independent of the carrier density. These behaviors are in striking contrast to conventional plasmons in 1D metallic shells, where the plasmon dispersion changes dramatically with the metal electron density and the 1D diameter. The unusual behaviors of Luttinger liquid plasmon may enable novel nanophotonic applications based on carbon nanotubes.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Morphology Evolution in Self-Healing Liquid-Gallium-Based Mg-Ion Battery Anode

Conventional solid battery anodes suffer from dendrite growth and volume changes, resulting in poor cycling performances. Self-healing electrodes made of liquid metals and alloys can overcome these issues by reversibly undergoing liquid–solid phase transformations during (dis)charging. Just recently, we achieved 1000 cycles in Mg-ion battery anodes using liquid Ga as the active material, which reversibly transformed into solid Mg 2 Ga 5 during (de)magnesiation. However, the fundamental mechanism behind this liquid–solid phase transformation remains unclear. In this follow-up work, cryogenic focused ion beam electron microscopy is used to elucidate the morphology evolution when liquid Ga embedded in a carbon-binder matrix transforms into solid Mg 2 Ga 5 during cycling. We found that liquid Ga gradually diffuses into the surrounding matrix, increasing the contact area between active material and electrolyte, facilitating the charge transfer process. These new insights will help understand the performance of alkali- and alkaline-earth-metal batteries based on liquid anodes.

25 ENERGY STORAGE↗
DOE OSTI2019

Colloidal Gelation in Liquid Metals Enables Functional Nanocomposites of 2D Metal Carbides (MXenes) and Lightweight Metals

Nanomaterials dispersed in different media, such as liquids or polymers, generate a variety of functional composites with synergistic properties. In this work, we discuss liquid metals as the nanomaterials' dispersion media. For example, 2D transition-metal carbides and nitrides (MXenes) can be efficiently dispersed in liquid Ga and lightweight alloys of Al, Mg, and Li. We show that the Lifshitz theory predicts strong van der Waals attraction between nanoscale objects interacting through liquid metals. However, a uniform distribution of MXenes in liquid metals can be achieved through colloidal gelation, where particles form self-supporting networks stable against macroscopic phase segregation. This network acts as a reinforcement boosting mechanical properties of the resulting metal-matrix composite. By choosing Mg-Li alloy as an example of ultralightweight metal matrix and Ti 3 C 2 T x MXene as a nanoscale reinforcement, we apply a liquid metal gelation technique to fabricate functional nanocomposites with an up to 57% increase in the specific yield strength without compromising the matrix alloy's plasticity. MXenes largely retain their phase and 2D morphology after processing in liquid Mg-Li alloy at 700 degrees C. The 2D morphology enables formation of a strong semicoherent interface between MXene and metal matrix, manifested by biaxial strain of the MXene lattice inside the metal matrix. Finally, this work expands applications for MXenes and shows the potential for developing MXene-reinforced metal matrix composites for structural alloys and other emerging applications with metal-MXene interfaces, such as batteries and supercapacitors.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Do Ionic Liquids Slow Down in Stages?

High impact recent articles have reported on the existence of a liquid–liquid (L–L) phase transition as a function of both pressure and temperature in ionic liquids (ILs) containing the popular trihexyltetradecylphosphonium cation (P 666,14 + ), sometimes referred to as the “universal liquifier”. The work presented here reports on the structural-dynamic pathway from liquid to glass of the most well-studied IL comprising the P 666,14 + cation. We present experimental and computational evidence that, on cooling, the path from the room-temperature liquid to the glass state is one of separate structural-dynamic changes. The first stage involves the slowdown of the charge network, while the apolar subcomponent is fully mobile. A second, separate stage entails the slowdown of the apolar domain. Whereas it is possible that these processes may be related to the liquid–liquid and glass transitions, more research is needed to establish this conclusively.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Real-time observation of dynamic structure of liquid-vapor interface at nanometer resolution in electron irradiated sodium chloride crystals

The dynamics and structure of the liquid and vapor interface has remained elusive for decades due to the lack of an effective tool for directly visualization beyond micrometer resolution. Here, we designed a simple liquid-cell for encapsulating the liquid state of sodium for transmission electron microscopic (TEM) observation. The real-time dynamic structure of the liquid-vapor interface was imaged and videoed by TEM on the sample of electron irradiated sodium chloride (NaCl) crystals, a well-studied sample with low melting temperature and quantum super-shells of clusters. The nanometer resolution images exhibit the fine structures of the capillary waves, composed of first-time observed three zones of structures and features, i.e. flexible nanoscale fibers, nanoparticles/clusters, and a low-pressure area that sucks the nanoparticles from the liquid to the interface. Although the phenomenons were observed based on irradiated NaCl crystals, the similarities of the phenomenons to predictions suggest our real-time ovserved dynamic structure might be useful in validating long-debated theoretical models of the liquid-vapor interface, and enhancing our knowledge in understanding the non-equilibrium thermodynamics of the liquid-vapor interface to benefit future engineering designs in microfluidics.

36 MATERIALS SCIENCE↗
DOE OSTI2013

On the spatial stability of a liquid jet in the presence of vapor cavities

A dispersion equation describing the effect of temperature differences on the stability of three-dimensional cylindrical liquid jets in the presence of vapor cavities is presented by the use of linear stability analysis. The mathematical model and its solving method are verified by comparing them with the data in the literature, and then the effect of temperature differences between jet and surrounding gas on the spatial stability of liquid jet is investigated. Some conclusions can be drawn from the results of this investigation: (1) the temperature difference destabilizes the liquid jet when the jet liquid is cooler than the surrounding gas, (2) the smallest atomized droplet without taking into account the effect of temperature differences is significantly larger than that when the effect of temperature differences is taken into account, (3) the effect of temperature differences on the stability of liquid jet has little relationship with azimuthal wave modes, (4) cavitation destabilizes the liquid jet when the value of the bubble volume fraction is not greater than 0.1 (0 ≤ α ≤ 0.1), and the temperature difference can weaken this effect of cavitation on the stability of liquid jet, and (5) cavitation is responsible for generating smaller droplets, the effect of cavitation on the critical wave number with and without taking into account the effect of temperature differences is quite different, and temperature difference is likely to fully restrain the effect of cavitation on the critical wave number; however, cavitation is again responsible for generating smaller droplets despite the effect of temperature differences when the bubble volume fraction α = 0.1. These findings may explain some observations of practical atomizer performance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Liquid structure and temperature invariance of sound velocity in supercooled Bi melt

Structural rearrangement of liquid Bi in the vicinity of the melting point has been proposed due to the unique temperature invariant sound velocity observed above the melting temperature, the low symmetry of Bi in the solid phase and the necessity of overheating to achieve supercooling. The existence of this structural rearrangement is examined by measurements on supercooled Bi. The sound velocity of liquid Bi was measured into the supercooled region to high accuracy and it was found to be invariant over a temperature range of ∼60°, from 35° above the melting point to ∼25° into the supercooled region. The structural origin of this phenomenon was explored by neutron diffraction structural measurements in the supercooled temperature range. These measurements indicate a continuous modification of the short range order in the melt. The structure of the liquid is analyzed within a quasi-crystalline model and is found to evolve continuously, similar to other known liquid pnictide systems. The results are discussed in the context of two competing hypotheses proposed to explain properties of liquid Bi near the melting: (i) liquid bismuth undergoes a structural rearrangement slightly above melting and (ii) liquid Bi exhibits a broad maximum in the sound velocity located incidentally at the melting temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗