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Keywords = liquid–vapor critical point

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33 pages, 13813 KiB  
Review
Advances in Thermal Management for Liquid Hydrogen Storage: The Lunar Perspective
by Jing Li, Fulin Fan, Jingkai Xu, Heran Li, Jian Mei, Teng Fei, Chuanyu Sun, Jinhai Jiang, Rui Xue, Wenying Yang and Kai Song
Energies 2025, 18(9), 2220; https://doi.org/10.3390/en18092220 - 27 Apr 2025
Viewed by 837
Abstract
Liquid hydrogen is regarded as a key energy source and propellant for lunar bases due to its high energy density and abundance of polar water ice resources. However, its low boiling point and high latent heat of vaporization pose severe challenges for storage [...] Read more.
Liquid hydrogen is regarded as a key energy source and propellant for lunar bases due to its high energy density and abundance of polar water ice resources. However, its low boiling point and high latent heat of vaporization pose severe challenges for storage and management under the extreme lunar environment characterized by wide temperature variations, low pressure, and low gravity. This paper reviews the strategies for siting and deployment of liquid hydrogen storage systems on the Moon and the technical challenges posed by the lunar environment, with particular attention for thermal management technologies. Passive technologies include advanced insulation materials, thermal shielding, gas-cooled shielding layers, ortho-para hydrogen conversion, and passive venting, which optimize insulation performance and structural design to effectively reduce evaporation losses and maintain storage stability. Active technologies, such as cryogenic fluid mixing, thermodynamic venting, and refrigeration systems, dynamically regulate heat transfer and pressure variations within storage tanks, further enhancing storage efficiency and system reliability. In addition, this paper explores boil-off hydrogen recovery and reutilization strategies for liquid hydrogen, including hydrogen reliquefaction, mechanical, and non-mechanical compression. By recycling vaporized hydrogen, these strategies reduce resource waste and support the sustainable development of energy systems for lunar bases. In conclusion, this paper systematically evaluates passive and active thermal management technologies as well as vapor recovery strategies along with their technical adaptability, and then proposes feasible storage designs for the lunar environment. These efforts provide critical theoretical foundations and technical references for achieving safe and efficient storage of liquid hydrogen and energy self-sufficiency in lunar bases. Full article
(This article belongs to the Section J: Thermal Management)
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23 pages, 3239 KiB  
Review
Advances in Synthesis and Ignition Performance of Ionic Liquid–Hydrogen Peroxide Green Propellants
by Yongting Zhang, Xing Zhang, Dangyue Yin and Qinghua Zhang
Molecules 2025, 30(8), 1789; https://doi.org/10.3390/molecules30081789 - 16 Apr 2025
Viewed by 651
Abstract
The ionic liquid–hydrogen peroxide propellant system has emerged as a promising green propellant candidate, synergistically combining the unique advantages of ionic liquids (such as negligible vapor pressure, low melting points, high thermal stability and structural tunability) with the merits of hydrogen peroxide (including [...] Read more.
The ionic liquid–hydrogen peroxide propellant system has emerged as a promising green propellant candidate, synergistically combining the unique advantages of ionic liquids (such as negligible vapor pressure, low melting points, high thermal stability and structural tunability) with the merits of hydrogen peroxide (including high density, low volatility, minimal viscosity, reduced corrosivity, and environmentally benign decomposition products). In this work, we provide a comprehensive review of the synthesis strategies and ignition performance of the ionic liquid–hydrogen peroxide propellant system, systematically categorizing them into two classes: “self-igniting propellants” and “promoter-dependent propellants”. This review emphasizes the critical role of anion-specific design and catalytic engineering in advancing the performance of ionic liquid–hydrogen peroxide propellant systems, while also addressing the current challenges and future directions in this rapidly evolving field. Full article
(This article belongs to the Special Issue Molecular Design and Synthesis of Novel Energetic Compounds)
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20 pages, 4816 KiB  
Article
Research Progress and Prospects of Refrigerant Replacement Under the Background of Greenhouse Gas Emission Reduction: A Visualization Analysis of the CiteSpace Map
by Shengzhong Huang, Hui Zhang and Conghui Li
Sustainability 2025, 17(5), 2199; https://doi.org/10.3390/su17052199 - 3 Mar 2025
Viewed by 811
Abstract
As global environmental consciousness continues to expand, the issue of refrigerant alternatives has increasingly become a focal point for scholarly attention. Using CiteSpace visualization technology, a comprehensive and innovative research framework for refrigerant alternatives has been developed. This framework systematically organizes and analyzes [...] Read more.
As global environmental consciousness continues to expand, the issue of refrigerant alternatives has increasingly become a focal point for scholarly attention. Using CiteSpace visualization technology, a comprehensive and innovative research framework for refrigerant alternatives has been developed. This framework systematically organizes and analyzes not only the volume of publications related to refrigerant alternatives but also the collaborative relationships among authors and research institutions. By employing keyword co-occurrence maps, clustering diagrams, and timeline charts, an in-depth analysis of the academic literature on refrigerant alternatives has been performed, elucidating the core research themes, evolutionary trajectories, and emerging trends in this field. Research indicates an exponential increase in the number of studies on refrigerant alternatives; however, there is insufficient collaboration and communication among researchers and institutions. Key research hotspots in this field encompass the organic Rankine cycle, vapor-liquid equilibria, pressure drop characteristics, vapor compression refrigeration systems, exergy analysis, alternative refrigerants, and performance evaluation of carbon dioxide systems. In future research, the performance of various low GWP refrigerants in refrigeration cycle systems will continue to be a focal point. To address diverse application requirements, developing blended refrigerants represents a pragmatic technical approach. From a sustainability standpoint, natural refrigerants are anticipated to emerge as the ultimate alternative, with the technical challenges associated with their application constituting a critical area for future investigation. Full article
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14 pages, 4952 KiB  
Article
Effect of Microwave Antenna Material and Diameter on the Ignition and Combustion Characteristics of ADN-Based Liquid Propellant Droplets
by Dong Li, Yangyang Hou and Yusong Yu
Energies 2024, 17(17), 4256; https://doi.org/10.3390/en17174256 - 26 Aug 2024
Viewed by 1004
Abstract
Microwave-assisted ignition is an emerging high-performance ignition method with promising future applications in aerospace. In this work, based on a rectangular waveguide resonant cavity test bed, the effects of two parameters (material and diameter) of the microwave antenna on the ignition and combustion [...] Read more.
Microwave-assisted ignition is an emerging high-performance ignition method with promising future applications in aerospace. In this work, based on a rectangular waveguide resonant cavity test bed, the effects of two parameters (material and diameter) of the microwave antenna on the ignition and combustion characteristics of ADN-based liquid propellant droplets were investigated using experimental methods. A high-speed camera was used to record the droplet combustion process in the combustion chamber, the effect of the microwave antenna on the propellant combustion response was analyzed based on the emission spectroscopy method, and finally, the loss of the microwave antenna was evaluated using a scanning electron microscope. The experimental results show that the droplet has the lowest critical ignition power (179 W) when the material of the microwave antenna is tungsten, but the ignition delay time is higher than that of copper. A finer diameter of microwave antenna is more favorable for plasma generation. At a microwave power of 260 W, the ignition delay time of the droplet with a microwave antenna diameter of 0.3 mm is 100 ms lower than that of 0.8 mm, which is about 37.5%. In addition, this study points out the mechanism of microwave discharge in the droplet combustion process. The metallic microwave antenna not only collects the electrons escaping from the gas discharge, but also generates a large amount of metallic vapor, which provides charged particles to the plasma. This study provides the possibility for the application of microwave-assisted liquid fuel ignition. Full article
(This article belongs to the Section I2: Energy and Combustion Science)
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18 pages, 31481 KiB  
Article
The Transport and Optical Characteristics of a Metal Exposed to High-Density Energy Fluxes in Compressed and Expanded States of Matter
by Nikolay B. Volkov and Alexander I. Lipchak
Condens. Matter 2023, 8(3), 70; https://doi.org/10.3390/condmat8030070 - 11 Aug 2023
Cited by 2 | Viewed by 1835
Abstract
This article presents a theoretical study of the optical and transport properties of metals. Iron, as an example, was used to discuss, through a theoretical description, the peculiarities of these properties in the compressed and expanded states under the influence of high-density energy [...] Read more.
This article presents a theoretical study of the optical and transport properties of metals. Iron, as an example, was used to discuss, through a theoretical description, the peculiarities of these properties in the compressed and expanded states under the influence of high-density energy fluxes. By solving the semi-classical Boltzmann equation for conduction electrons for a broad range of densities and temperatures, the expressions of electrical conductivity, electronic thermal conductivity, and thermoelectric coefficient calculations were derived. The real and imaginary parts of the iron permittivity and the energy absorption coefficient for the first and second harmonics of Nd:YAG laser radiation were obtained. The calculation peculiarities of the metal’s optical characteristics of matter in an expanded state in a broad range of densities and temperatures were considered. The analysis of the obtained results shows their agreement with the theoretical description for cases of ideal non-degenerate and dense degenerate electron plasmas. It is shown that the behavior of the electrical conductivity and optical characteristics in the critical and supercritical regions of density and temperature are in agreement with the known experimental results. Full article
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16 pages, 1034 KiB  
Article
On Some Theoretical Aspects of The Evaporation Process of a Droplet and Its Optimal Size When Extinguishing Fires
by Sergey Oktyabrinovich Gladkov
Inventions 2023, 8(1), 35; https://doi.org/10.3390/inventions8010035 - 30 Jan 2023
Cited by 1 | Viewed by 1690
Abstract
We are proposing a model mathematical description of droplet evaporation using the kinetic approach. We have obtained the basic equation of the theory by using the law of conserving the full power of the vapor–liquid system, which has not been done before. We [...] Read more.
We are proposing a model mathematical description of droplet evaporation using the kinetic approach. We have obtained the basic equation of the theory by using the law of conserving the full power of the vapor–liquid system, which has not been done before. We have found the range of droplet sizes at which it is stable. We have given a comparison of the obtained results with the known traditional ones. We have given numerical estimates for the critical size of the fine-dispersed phase up to the value of which ordinary evaporation takes place (that is for Knudsen number Kn=lR, inequality Kn1 must be fulfilled, where l is the free path of the molecule and R is the droplet radius). We have given the optimal droplet size which is the most effective from the point of view of technical use in extinguishing flammable oil transformers. Full article
(This article belongs to the Special Issue Recent Advances in Fluid Mechanics and Transport Phenomena)
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11 pages, 942 KiB  
Article
Anomalous Concentration Dependence of Surface Tension and Concentration-Concentration Correlation Functions of Binary Non-Electrolyte Solutions
by Carlo Carbone, Eduardo Guzmán and Ramón G. Rubio
Int. J. Mol. Sci. 2023, 24(3), 2276; https://doi.org/10.3390/ijms24032276 - 23 Jan 2023
Cited by 1 | Viewed by 2329
Abstract
The concentration dependence of the surface tension of several binary mixtures of non-electrolytes has been measured at 298.15 K. The mixtures have been chosen since they presented a so-called “W-shape” concentration dependence of the excess constant pressure heat capacity and high values of [...] Read more.
The concentration dependence of the surface tension of several binary mixtures of non-electrolytes has been measured at 298.15 K. The mixtures have been chosen since they presented a so-called “W-shape” concentration dependence of the excess constant pressure heat capacity and high values of the concentration-concentration correlation function. This behavior was interpreted in terms of the existence of anomalously high concentration fluctuations that resemble those existing in the proximities of critical points. However, no liquid-liquid phase separation has been found in any of these mixtures over a wide temperature range. In this work, we have extended these studies to the liquid-air interfacial properties. The results show that the concentration dependence of the surface tension shows a plateau and the mixing surface tension presents a “W-shape” behavior. To the best of our knowledge, this is the first time that this behavior is reported. The weak anomalies of the surface tension near a liquid-liquid critical point suggest that the results obtained cannot be considered far-from-critical effects. The usual approach of substituting the activity by the concentration in the Gibbs equation for the relative surface concentration has been found to lead to large errors and the mixtures to have a fuzzy and thick liquid/vapor interface. Full article
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25 pages, 388 KiB  
Article
Global Dynamics of the Compressible Fluid Model of the Korteweg Type in Hybrid Besov Spaces
by Zihao Song and Jiang Xu
Mathematics 2023, 11(1), 174; https://doi.org/10.3390/math11010174 - 29 Dec 2022
Viewed by 1523
Abstract
We are concerned with a system of equations governing the evolution of isothermal, viscous, and compressible fluids of the Korteweg type, which is used to describe a two-phase liquid–vapor mixture. It is found that there is a “regularity-gain" dissipative structure of linearized systems [...] Read more.
We are concerned with a system of equations governing the evolution of isothermal, viscous, and compressible fluids of the Korteweg type, which is used to describe a two-phase liquid–vapor mixture. It is found that there is a “regularity-gain" dissipative structure of linearized systems in case of zero sound speed P(ρ*)=0, in comparison with the classical compressible Navier–Stokes equations. First, we establish the global-in-time existence of strong solutions in hybrid Besov spaces by using Banach’s fixed point theorem. Furthermore, we prove that the global solutions with critical regularity are Gevrey analytic in fact. Secondly, based on Gevrey’s estimates, we obtain uniform bounds on the growth of the analyticity radius of solutions in negative Besov spaces, which lead to the optimal time-decay estimates of solutions and their derivatives of arbitrary order. Full article
19 pages, 1862 KiB  
Article
Performance Study of Eductor with Finite Secondary Source for Membrane Distillation
by Ravi Koirala, Xing Zhang, Eliza Rupakheti, Kiao Inthavong and Abhijit Date
Energies 2022, 15(22), 8620; https://doi.org/10.3390/en15228620 - 17 Nov 2022
Cited by 2 | Viewed by 1764
Abstract
This is an experimental work performed to identify the influence of direct contact condensation inside an eductor. The fluid used in the experiments is water in two different phases: liquid and vapor, for primary and secondary flows, respectively. This study was conducted in [...] Read more.
This is an experimental work performed to identify the influence of direct contact condensation inside an eductor. The fluid used in the experiments is water in two different phases: liquid and vapor, for primary and secondary flows, respectively. This study was conducted in an attempt to establish the suitability of an eductor as a combined vacuum generator and condenser for membrane desalination applications. The pressure and temperature measurements at critical points in the flow paths have been summarized to identify the influence of primary flow on secondary fluid saturation and condensation. In addition, the mechanism of phase change has been explained through the photography of fluid flow in a two-dimensional eductor. A consistent oscillation of the gas-liquid interface was observed during steady-state operations of the eductor. This work also contributes to the validation of future computational research. It will provide a baseline for computational thermal fluid analysis related to the mixing of condensing and non-condensing flow. In general, the research encompasses the practical operational scenario and provides information on the heat and mass transfer of direct contact condensation with a finite secondary source. Full article
(This article belongs to the Special Issue Thermal Performance of Membrane Distillation)
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14 pages, 2995 KiB  
Article
Prediction of Critical Heat Flux for Subcooled Flow Boiling in Annulus and Transient Surface Temperature Change at CHF
by Wei Liu
Fluids 2022, 7(7), 230; https://doi.org/10.3390/fluids7070230 - 7 Jul 2022
Cited by 1 | Viewed by 2727
Abstract
The ability to predict critical heat flux (CHF) is of considerable interest for high-heat equipment, including nuclear reactors. CHF prediction from a mechanistic model for subcooled flow boiling in rod bundles still remains unsolved. In this paper, we try to predict the CHF [...] Read more.
The ability to predict critical heat flux (CHF) is of considerable interest for high-heat equipment, including nuclear reactors. CHF prediction from a mechanistic model for subcooled flow boiling in rod bundles still remains unsolved. In this paper, we try to predict the CHF in an annulus, which is the most basic flow geometry simplified from a fuel bundle, using a liquid sublayer dryout model. The prediction is validated with both water and R113 data, showing an accuracy within ±30%. After the CHF in an annulus is calculated successfully, a near-wall vapor–liquid structure is proposed on the basis of the liquid sublayer dryout model. Modeling of heat transfer modes over the heating surface at CHF is performed, and predictions of the changes in liquid sublayer thickness and heater surface temperature at the CHF occurrence point are carried out by solving the heat conduction equation in cylindrical coordinates with a convective boundary condition, which changes with the change in flow pattern over the heating surface. Transient changes in the liquid sublayer thickness and surface temperature at the CHF occurrence point are reported. Full article
(This article belongs to the Special Issue Advances in Multiphase Flow Science and Technology)
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32 pages, 3140 KiB  
Review
Ionic Liquid-Assisted DLLME and SPME for the Determination of Contaminants in Food Samples
by Lirong Nie, Chaochao Cai, Runpeng Guo, Shun Yao, Zhi Zhu, Yanchen Hong and Dong Guo
Separations 2022, 9(7), 170; https://doi.org/10.3390/separations9070170 - 6 Jul 2022
Cited by 25 | Viewed by 3986
Abstract
Developing effective and green methods for food analysis and separation has become an urgent issue regarding the ever-increasing concern of food quality and safety. Ionic liquids (ILs) are a new chemical medium and soft functional material developed under the framework of green chemistry [...] Read more.
Developing effective and green methods for food analysis and separation has become an urgent issue regarding the ever-increasing concern of food quality and safety. Ionic liquids (ILs) are a new chemical medium and soft functional material developed under the framework of green chemistry and possess many unique properties, such as low melting points, low-to-negligible vapor pressures, excellent solubility, structural designability and high thermal stability. Combining ILs with extraction techniques not only takes advantage of ILs but also overcomes the disadvantages of traditional extraction methods. This subject has attracted intensive research efforts recently. Here, we present a brief review of the current research status and latest developments regarding the application of IL-assisted microextraction, including dispersive liquid–liquid microextraction (DLLME) and solid-phase microextraction (SPME), in food analysis and separation. The practical applications of ILs in determining toxic and harmful substances in food specimens with quite different natures are summarized and discussed. The critical function of ILs and the advantages of IL-based microextraction techniques over conventional extraction techniques are discussed in detail. Additionally, the recovery of ILs using different approaches is also presented to comply with green analytical chemistry requirements. Full article
(This article belongs to the Section Purification Technology)
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16 pages, 3697 KiB  
Article
Thermophysical Properties of Liquids in Not Fully Stable States—From the First Steps to the Current Trends
by Pavel Skripov
Energies 2022, 15(12), 4440; https://doi.org/10.3390/en15124440 - 18 Jun 2022
Cited by 10 | Viewed by 2063
Abstract
The present article marks the 95th anniversary of the birth of Vladimir P. Skripov, author of the classic study of superheated and supercooled liquids. It presents a discussion based on the early work carried out by Skripov and his research team in Ekaterinburg [...] Read more.
The present article marks the 95th anniversary of the birth of Vladimir P. Skripov, author of the classic study of superheated and supercooled liquids. It presents a discussion based on the early work carried out by Skripov and his research team in Ekaterinburg during the 1950s and 1960s. Due to their pioneering nature, these works laid the foundation for the study of metastable liquid states. For various reasons, although they remain relevant to this day, these groundbreaking works remain unknown to most non-Russian-speaking readers. As well as elucidating the behavior of the heat capacity of a solution in the liquid–liquid critical region, the presented research also concerns the characteristic features of light scattering and free-convective heat transfer in the liquid–vapor critical region of a one-component system, discussing two options for the position of the superheated liquid spinodal on the phase diagram of water, including the area of supercooled states and negative pressures. The issues involved in the discussion are united by the fluctuating nature of such phenomena. Indeed, the very possibility of their experimental study is due to a significant increase in the scale of fluctuations of the corresponding quantities when approaching the critical point or spinodal. The ongoing development of the approaches proposed in these papers for solving contemporary problems in the thermophysics of superheated liquids is discussed. Full article
(This article belongs to the Special Issue Heat and Mass Transfer)
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18 pages, 8019 KiB  
Article
Unveiling the Molecular Origin of Vapor-Liquid Phase Transition of Bulk and Confined Fluids
by Sorrasit Jitmitsumphan, Tirayoot Sripetdee, Tharathep Chaimueangchuen, Htet Myet Tun, Sorayot Chinkanjanarot, Nikom Klomkliang, Sira Srinives, Woranart Jonglertjunya, Tau Chuan Ling and Poomiwat Phadungbut
Molecules 2022, 27(9), 2656; https://doi.org/10.3390/molecules27092656 - 20 Apr 2022
Cited by 1 | Viewed by 2756
Abstract
At temperatures below the critical temperature, discontinuities in the isotherms are one critical issue in the design and construction of separation units, affecting the level of confidence for a prediction of vapor–liquid equilibriums and phase transitions. In this work, we study the molecular [...] Read more.
At temperatures below the critical temperature, discontinuities in the isotherms are one critical issue in the design and construction of separation units, affecting the level of confidence for a prediction of vapor–liquid equilibriums and phase transitions. In this work, we study the molecular mechanisms of fluids that involve the vapor–liquid phase transition in bulk and confinement, utilizing grand canonical (GCE) and meso-canonical (MCE) ensembles of the Monte Carlo simulation. Different geometries of the mesopores, including slit, cylindrical, and spherical, were studied. During phase transitions, condensation/evaporation hysteretic isotherms can be detected by GCE simulation, whereas employing MCE simulation allows us to investigate van der Waals (vdW) loop with a vapor spinodal point, intermediate states, and a liquid spinodal point in the isotherms. Depending on the system, the size of the simulation box, and the MCE method, we are able to identify three distinct groups of vdW-type isotherms for the first time: (1) a smooth S-shaped loop, (2) a stepwise S-shaped loop, and (3) a stepwise S-shaped loop with just a vertical segment. The first isotherm type is noticed in the bulk and pores having small box sizes, in which vapor and liquid phases are close and not clearly identified. The second and the third types occurred in the bulk, cylindrical, and slit mesopores with sufficiently large spaces, where vapor and liquid phases are distinctly separated. Results from our studies provide an insight analysis into vapor–liquid phase transitions, elucidating the effect of the confinement of fluid behaviors in a visual manner. Full article
(This article belongs to the Collection Molecular Liquids)
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19 pages, 2650 KiB  
Article
Phase Behavior of Carbon Dioxide + Isobutanol and Carbon Dioxide + tert-Butanol Binary Systems
by Sergiu Sima, Adrian Victor Crişciu and Catinca Secuianu
Energies 2022, 15(7), 2625; https://doi.org/10.3390/en15072625 - 3 Apr 2022
Cited by 5 | Viewed by 2822
Abstract
In recent years, the dramatic increase of greenhouse gases concentration in atmosphere, especially of carbon dioxide, determined many researchers to investigate new mitigation options. Thermodynamic studies play an important role in the development of new technologies for reducing the carbon levels. In this [...] Read more.
In recent years, the dramatic increase of greenhouse gases concentration in atmosphere, especially of carbon dioxide, determined many researchers to investigate new mitigation options. Thermodynamic studies play an important role in the development of new technologies for reducing the carbon levels. In this context, our group investigated the phase behavior (vapor–liquid equilibrium (VLE), vapor–liquid–liquid equilibrium (VLLE), liquid–liquid equilibrium (LLE), upper critical endpoints (UCEPs), critical curves) of binary and ternary systems containing organic substances with different functional groups to determine their ability to dissolve carbon dioxide. This study presents our results for the phase behavior of carbon dioxide + n-butanol structural isomers binary systems at high-pressures. Liquid–vapor critical curves are measured for carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems at pressures up to 147.3 bar, as only few scattered critical points are available in the literature. New isothermal vapor–liquid equilibrium data are also reported at 363.15 and 373.15 K. New VLE data at higher temperature are necessary, as only another group reported some data for the carbon dioxide + isobutanol system, but with high errors. Phase behavior experiments were performed in a high-pressure two opposite sapphire windows cell with variable volume, using a static-analytical method with phases sampling by rapid online sample injectors (ROLSI) coupled to a gas chromatograph (GC) for phases analysis. The measurement results of this study are compared with the literature data when available. The new and all available literature data for the carbon dioxide + isobutanol and carbon dioxide + tert-butanol binary systems are successfully modeled with three cubic equations of state, namely, General Equation of State (GEOS), Soave–Redlich–Kwong (SRK), and Peng–Robinson (PR), coupled with classical van der Waals mixing rules (two-parameter conventional mixing rules, 2PCMR), using a predictive method. Full article
(This article belongs to the Special Issue Thermodynamics for Net-Zero Energy Systems)
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21 pages, 592 KiB  
Article
Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point
by Juan Carlos Obeso-Jureidini, Daniela Olascoaga and Victor Romero-Rochín
Entropy 2021, 23(6), 720; https://doi.org/10.3390/e23060720 - 5 Jun 2021
Viewed by 2662
Abstract
With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the [...] Read more.
With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so. Full article
(This article belongs to the Collection Foundations and Ubiquity of Classical Thermodynamics)
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