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Статті в журналах з теми "Equilibrium pressure"

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Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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1

Li, Zhiming, Weisheng Wu, and Yujun Zhu. "Preimage pressure, stable pressure and equilibrium states." Journal of Differential Equations 269, no. 7 (September 2020): 6311–42. http://dx.doi.org/10.1016/j.jde.2020.04.043.

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2

Ilčin, Michal, Martin Michalík, Klára Kováčiková, Lenka Káziková, and Vladimír Lukeš. "Water liquid-vapor equilibrium by molecular dynamics: Alternative equilibrium pressure estimation." Acta Chimica Slovaca 9, no. 1 (April 1, 2016): 36–43. http://dx.doi.org/10.1515/acs-2016-0007.

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Анотація:

Abstract The molecular dynamics simulations of the liquid-vapor equilibrium of water including both water phases — liquid and vapor — in one simulation are presented. Such approach is preferred if equilibrium curve data are to be collected instead of the two distinct simulations for each phase separately. Then the liquid phase is not restricted, e.g. by insufficient volume resulting in too high pressures, and can spread into its natural volume ruled by chosen force field and by the contact with vapor phase as vaporized molecules are colliding with phase interface. Averaged strongly fluctuating virial pressure values gave untrustworthy or even unreal results, so need for an alternative method arisen. The idea was inspired with the presence of vapor phase and by previous experiences in gaseous phase simulations with small fluctuations of pressure, almost matching the ideal gas value. In presented simulations, the first idea how to calculate pressure only from the vapor phase part of simulation box were applied. This resulted into very simple method based only on averaging molecules count in the vapor phase subspace of known volume. Such simple approach provided more reliable pressure estimation than statistical output of the simulation program. Contrary, also drawbacks are present in longer initial thermostatization time or more laborious estimation of the vaporization heat. What more, such heat of vaporization suffers with border effect inaccuracy slowly decreasing with the thickness of liquid phase. For more efficient and more accurate vaporization heat estimation the two distinct simulations for each phase separately should be preferred.

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3

Liu, Weiping, Lina Hu, Yongxuan Yang, and Mingfu Fu. "Limit Support Pressure of Tunnel Face in Multi-Layer Soils Below River Considering Water Pressure." Open Geosciences 10, no. 1 (December 31, 2018): 932–39. http://dx.doi.org/10.1515/geo-2018-0074.

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AbstractThis paper presents a method to determine the limit support pressure of tunnel face in multi-layer soils below river considering the water pressure. The proposed method is based on the 3D Terzaghi earth pressure theory and the wedge theory considering the water pressure. The limit support pressures are investigated using the limit equilibrium method and compared to those calculated using a numerical method, such as FLAC3D. Four cases focusing different combinations of three layers are analyzed. The results obtained by the numerical method agree well with the predictions of the proposed limit equilibrium method. The limit support pressure obtained using the limit equilibrium method is greater than that obtained by the numerical method. The limit equilibrium method is safe and conservative in obtaining the limit support pressure. The proposed limit equilibrium method is expected to be easily adaptable and to enhance the reliability of tunnel design and construction in multi-layer soils below river.

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4

Denney, Dennis. "Equilibrium Test: Determining Closure Pressure." Journal of Petroleum Technology 55, no. 03 (March 1, 2003): 52–56. http://dx.doi.org/10.2118/0303-0052-jpt.

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5

Madden, N. A., and R. J. Hastie. "Tokamak equilibrium with anisotropic pressure." Nuclear Fusion 34, no. 4 (April 1994): 519–26. http://dx.doi.org/10.1088/0029-5515/34/4/i05.

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6

Iwahashi, Makio, Akihito Iwafuji, Hideyuki Minami, Norihisa Katayama, Kenichi Iimura, and Teiji Kato. "Equilibrium Spreading Pressure of Steroids." Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals 337, no. 1 (November 1999): 117–20. http://dx.doi.org/10.1080/10587259908023391.

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7

Grove, John W. "Pressure-velocity equilibrium hydrodynamic models." Acta Mathematica Scientia 30, no. 2 (March 2010): 563–94. http://dx.doi.org/10.1016/s0252-9602(10)60063-x.

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8

Cheng, C. Z. "Magnetospheric equilibrium with anisotropic pressure." Journal of Geophysical Research 97, A2 (1992): 1497. http://dx.doi.org/10.1029/91ja02433.

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9

Kucherenko, Tamara, and Christian Wolf. "Localized Pressure and Equilibrium States." Journal of Statistical Physics 160, no. 6 (June 20, 2015): 1529–44. http://dx.doi.org/10.1007/s10955-015-1289-7.

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10

Rauter, Michael T., Olav Galteland, Máté Erdős, Othonas A. Moultos, Thijs J. H. Vlugt, Sondre K. Schnell, Dick Bedeaux, and Signe Kjelstrup. "Two-Phase Equilibrium Conditions in Nanopores." Nanomaterials 10, no. 4 (March 26, 2020): 608. http://dx.doi.org/10.3390/nano10040608.

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Анотація:

It is known that thermodynamic properties of a system change upon confinement. To know how, is important for modelling of porous media. We propose to use Hill’s systematic thermodynamic analysis of confined systems to describe two-phase equilibrium in a nanopore. The integral pressure, as defined by the compression energy of a small volume, is then central. We show that the integral pressure is constant along a slit pore with a liquid and vapor in equilibrium, when Young and Young–Laplace’s laws apply. The integral pressure of a bulk fluid in a slit pore at mechanical equilibrium can be understood as the average tangential pressure inside the pore. The pressure at mechanical equilibrium, now named differential pressure, is the average of the trace of the mechanical pressure tensor divided by three as before. Using molecular dynamics simulations, we computed the integral and differential pressures, p ^ and p, respectively, analysing the data with a growing-core methodology. The value of the bulk pressure was confirmed by Gibbs ensemble Monte Carlo simulations. The pressure difference times the volume, V, is the subdivision potential of Hill, ( p − p ^ ) V = ϵ . The combined simulation results confirm that the integral pressure is constant along the pore, and that ϵ / V scales with the inverse pore width. This scaling law will be useful for prediction of thermodynamic properties of confined systems in more complicated geometries.

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11

Sultan, Nabil, and Sara Lafuerza. "In situ equilibrium pore-water pressures derived from partial piezoprobe dissipation tests in marine sediments." Canadian Geotechnical Journal 50, no. 12 (December 2013): 1294–305. http://dx.doi.org/10.1139/cgj-2013-0062.

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Excess pore-water pressure has a significant effect on submarine slope stability and sediment deformation, and therefore its in situ equilibrium measurement is crucial in carrying out accurate slope stability assessments and accurately deriving geotechnical design parameters. In situ equilibrium pore-water pressure is usually obtained from pore pressure decay during piezocone tests. However, submarine shelves and slopes are often characterized by the existence of low-permeability (fine-grained) sediments involving long dissipation tests that are an important issue for offshore operational costs. Consequently, short-term and (or) partial dissipation tests are usually performed and in situ equilibrium pore-water pressures are predicted from partial measurements. Using a modified cavity expansion approach, this paper aims to predict for four different sites the in situ equilibrium pore-water pressures. Comparisons between predicted and observed in situ equilibrium pore-water pressures allowed the development of a guide to evaluate the minimum time required to perform short-term dissipation tests for a given marine sediment. The main finding of this Note is that the second derivative of the pore pressure, u, versus the logarithm of time, t, ∂2u/∂ln(t)2 must be positive to calculate accurately the in situ equilibrium pore-water pressures from partial measurements.

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12

Clarke, Colin W., and David N. Glew. "Aqueous nonelectrolyte solutions. Part XV. The deuterium sulfide - deuterium oxide system and the deuterium sulfide D-hydrate." Canadian Journal of Chemistry 76, no. 8 (August 1, 1998): 1119–29. http://dx.doi.org/10.1139/v98-133.

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The univariant (l1l2g) saturation vapor pressure of liquid deuterium oxide (phase l1) with liquid deuterium sulfide (phase l2) in equilibrium with a gas phase (g) has been measured in a stirred titanium reaction vessel at 19 temperatures from 33.003 to 18.905°C and at total pressures from 2.4500 to 1.7428 MPa. The univariant (hl1g) saturation vapor pressure of deuterium sulfide D-hydrate (phase h) in equilibrium with liquid deuterium oxide and a gas phase has been measured at 58 temperatures from 30.666 to 2.798°C and at pressures from 2.2959 to 0.11629 MPa. The maximum temperature for deuterium sulfide D-hydrate with a gas phase, the invariant quadruple point Q(hl1l2g), has been determined from the cut of the (hl1g) and the (l1l2g) curves at temperature 30.770°C with standard error 0.0043°C and at pressure 2.3263 MPa with standard error 0.00018 MPa. The univariant (s1l1g) equilibrium of D-ice (phase s1) with liquid deuterium oxide and a gas phase containing deuterium sulfide has been measured at 11 temperatures from 3.8061 to 3.4540°C and at pressures between 0.00242 and 0.10542 MPa. The lowest temperature for stability of deuterium sulfide D-hydrate with liquid deuterium oxide, the invariant quadruple point Q(hs1l1g), has been determined directly at 3.3917°C with standard error 0.0009°C and at pressure 0.12364 MPa with standard error 0.000011 MPa. This quadruple point Q(hs1l1g) has also been defined by the cut of the (hl1g) and the (s1l1g) curves at temperature 3.3912°C with standard error 0.0006°C and at pressure 0.12363 MPa with standard error 0.000002 MPa. The deuterium sulfide - deuterium oxide gas mixture, represented by a Redlich-Kwong equation of state, has been used to evaluate the fugacities and compositions of the gaseous and liquid deuterium oxide phases for all equilibria. Raoult's law using fugacities has been used to evaluate the saturation mole fraction of deuterium oxide in liquid deuterium sulfide and the Henry's law constant for deuterium oxide solubility in liquid deuterium sulfide between 33.003 and 18.905°C. Data for the (l1l2g) and (s1l1g) equilibria have been accurately represented by simple two-parameter equations. Data for the (hl1g) equilibrium have required a model with seven significant parameters for proper representation betweem 30.666 and 2.798°C.Key words: deuterium sulfide - deuterium oxide system, clathrate D-hydrate of deuterium sulfide, deuterium sulfide D-hydrate stability, freezing of deuterium oxide - deuterium sulfide, phase equilibria of deuterium sulfide - deuterium oxide.

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13

Deckman, H. W., E. W. Corcoran, J. A. McHenry, J. H. Meldon, and V. A. Papavassiliou. "Pressure drop membrane reactor equilibrium analysis." Catalysis Today 25, no. 3-4 (August 1995): 357–63. http://dx.doi.org/10.1016/0920-5861(95)00108-r.

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14

Sovová, Helena, Roumiana P. Stateva, and Anatolii A. Galushko. "High-pressure equilibrium of menthol+CO2." Journal of Supercritical Fluids 41, no. 1 (May 2007): 1–9. http://dx.doi.org/10.1016/j.supflu.2006.08.007.

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15

Hobbs, Bruce E., and Alison Ord. "Pressure and equilibrium in deforming rocks." Journal of Metamorphic Geology 35, no. 9 (September 20, 2017): 967–82. http://dx.doi.org/10.1111/jmg.12263.

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16

Davanger, Martin, and Öivin Holter. "INTRAOCULAR PRESSURE IN NON-EQUILIBRIUM STATES." Acta Ophthalmologica 45, no. 4 (May 27, 2009): 510–24. http://dx.doi.org/10.1111/j.1755-3768.1967.tb06515.x.

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17

Hiura, Ken, and Shin-ichi Sasa. "How Does Pressure Fluctuate in Equilibrium?" Journal of Statistical Physics 173, no. 2 (August 11, 2018): 285–94. http://dx.doi.org/10.1007/s10955-018-2134-6.

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18

Corcuera, José Manuel, Giulia Di Nunno, and José Fajardo. "Kyle equilibrium under random price pressure." Decisions in Economics and Finance 42, no. 1 (February 1, 2019): 77–101. http://dx.doi.org/10.1007/s10203-019-00231-4.

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19

Han, Guofeng, Yang Chen, and Xiaoli Liu. "Investigation of Analysis Methods for Pulse Decay Tests Considering Gas Adsorption." Energies 12, no. 13 (July 3, 2019): 2562. http://dx.doi.org/10.3390/en12132562.

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Анотація:

The pulse decay test is the main method employed to determine permeability for tight rocks, and is widely used. The testing gas can be strongly adsorbed on the pore surface of unconventional reservoir cores, such as shale and coal rock. However, gas adsorption has not been well considered in analysis pulse decay tests. In this study, the conventional flow model of adsorbed gas in porous media was modified by considering the volume of the adsorbed phase. Then, pulse decay tests of equilibrium sorption, unsteady state and pseudo-steady-state non-equilibrium sorption models, were analyzed by simulations. For equilibrium sorption, it is found that the Cui-correction method is excessive when the adsorbed phase volume is considered. This method is good at very low pressure, and is worse than the non-correction method at high pressure. When the testing pressure and Langmuir volume are large and the vessel volumes are small, a non-negligible error exists when using the Cui-correction method. If the vessel volumes are very large, gas adsorption can be ignored. For non-equilibrium sorption, the pulse decay characteristics of unsteady state and pseudo-steady-state non-equilibrium sorption models are similar to those of unsteady state and pseudo-steady-state dual-porosity models, respectively. When the upstream and downstream pressures become equal, they continue to decay until all of the pressures reach equilibrium. The Langmuir volume and pressure, the testing pressure and the porosity, affect the pseudo-storativity ratio and the pseudo-interporosity flow coefficient. Their impacts on non-equilibrium sorption models are similar to those of the storativity ratio and the interporosity flow coefficient in dual-porosity models. Like dual-porosity models, the pseudo-pressure derivative can be used to identify equilibrium and non-equilibrium sorption models at the early stage, and also the unsteady state and pseudo-steady-state non-equilibrium sorption models at the late stage. To identify models using the pseudo-pressure derivative at the early stage, the suitable vessel volumes should be chosen according to the core adsorption property, porosity and the testing pressure. Finally, experimental data are analyzed using the method proposed in this study, and the results are sufficient.

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20

Morrison Jr., Ernest E., and Robert M. Ebeling. "Limit equilibrium computation of dynamic passive earth pressure." Canadian Geotechnical Journal 32, no. 3 (June 1, 1995): 481–87. http://dx.doi.org/10.1139/t95-050.

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Анотація:

Few solution techniques exist for the determination of pseudostatic dynamic passive earth pressures for cohesionless soils. The widely accepted Mononobe–Okabe equation can result in the computing of unconservative values if the wall interface friction angle is greater than half the soil internal friction angle. As an alternate solution, equilibrium equations were formulated assuming a log spiral failure surface, and a research computer program was written to calculate the dynamic passive earth pressure coefficient. The primary purpose of this paper is to present a comparison of results obtained using the Mononobe–Okabe equation with those obtained using the log spiral formulation. Key words : pseudostatic, dynamic, passive earth pressure.

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21

Hudson, S. R., J. Loizu, C. Zhu, Z. S. Qu, C. Nührenberg, S. Lazerson, C. B. Smiet, and M. J. Hole. "Free-boundary MRxMHD equilibrium calculations using the stepped-pressure equilibrium code." Plasma Physics and Controlled Fusion 62, no. 8 (July 16, 2020): 084002. http://dx.doi.org/10.1088/1361-6587/ab9a61.

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22

Levinsky, Yu V., M. M. Alymov, and L. L. Rokhlin. "The p–T–x-State Diagram of the Mg–Ni System." Advanced Materials & Technologies, no. 3(19) (2020): 003–7. http://dx.doi.org/10.17277/amt.2020.03.pp.003-007.

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The analysis of equilibrium in the Mg–Ni system was carried out. Alloys on its basis are promising for use as sorbents and hydrogen storage (START). The conditions for the production and operation of such alloys imply strict control of the pressure of hydrogen. In this regard, phase equilibria in the Mg–Ni system must be considered not only depending on the composition and temperature, but also on the pressure of hydrogen. The most complete graphical representation of the equilibrium in the Mg–Ni system is given by a three-dimensional state diagram: pressure-temperature-composition (p–T–x), the projection of the three-phase equilibrium lines of this diagram on the pressure-temperature plane (p–T-state diagram), isobaric and isothermal sections of the diagram, diagram in pMg–T coordinates. Based on the analysis of experimental data on equilibrium in this system, the article presents the most important options of the listed types of diagrams. The presented diagram variants can be useful in optimizing the technology and operation of sorbents and START alloys of the Mg–Ni system.

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23

Nakajima, Tasuku, Ken-ichi Hoshino, Honglei Guo, Takayuki Kurokawa, and Jian Ping Gong. "Experimental Verification of the Balance between Elastic Pressure and Ionic Osmotic Pressure of Highly Swollen Charged Gels." Gels 7, no. 2 (April 1, 2021): 39. http://dx.doi.org/10.3390/gels7020039.

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The equilibrium swelling degree of a highly swollen charged gel has been thought to be determined by the balance between its elastic pressure and ionic osmotic pressure. However, the full experimental verification of this balance has not previously been conducted. In this study, we verified the balance between the elastic pressure and ionic osmotic pressure of charged gels using purely experimental methods. We used tetra-PEG gels created using the molecular stent method (St-tetra-PEG gels) as the highly swollen charged gels to precisely and separately control their network structure and charge density. The elastic pressure of the gels was measured through the indentation test, whereas the ionic osmotic pressure was determined by electric potential measurement without any strong assumptions or fittings. We confirmed that the two experimentally determined pressures of the St-tetra-PEG gels were well balanced at their swelling equilibrium, suggesting the validity of the aforementioned relationship. Furthermore, from single-strand level analysis, we investigated the structural requirements of the highly swollen charged gels in which the elasticity and ionic osmosis are balanced at their swelling equilibrium.

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24

Jiang, Dawei, Min Cao, Xiaotong Zhang, Yang Gao, and Yonghao Han. "Pressure evolution in a diamond anvil cell without a pressure medium." Journal of Applied Physics 131, no. 12 (March 28, 2022): 125904. http://dx.doi.org/10.1063/5.0086792.

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The inhomogeneity in pressure inside the sample chamber of a diamond anvil cell (DAC) poses a major challenge to the accurate measurement of the properties of materials under high pressures, especially when the pressure medium solidifies under compression or is prohibited in the experiment. In this paper, the authors systematically investigate the pressure gradient in a DAC sample chamber and its evolution over time with changes in temperature. The results show that pressure gradients were formed along both the radial and the axial directions upon compression, and gradually decayed with time and increasing temperature. After a period of relaxation at room temperature, the pressure gradient along the axial direction gradually decayed and a new equilibrium was established. A similar process was observed along the radial direction but required a longer period before reaching equilibrium. Appropriate heating of the sample can cut the relaxation time to the order of tens of minutes and smoothen the pressure gradient in both directions. The electrical properties of olivine were significantly different when the measurements were conducted before and after relaxation was complete, indicating that the relaxation in pressure is essential for acquiring reliable data in a DAC under high pressures.

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25

ZHANG, SHIMIN. "THE STABILITY OF LIQUID EVAPORATION EQUILIBRIUM." Surface Review and Letters 12, no. 01 (February 2005): 115–21. http://dx.doi.org/10.1142/s0218625x05006846.

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For the evaporation of the pure liquid under the condition of constant temperature and constant external pressure, the phase equilibrium of the liquid vapor in the bubble and the liquid outside the bubble is always a kind of stable equilibrium whether there is air or not in the bubble. If there is no air in the bubble, the bubble and liquid cannot coexist in the mechanical equilibrium when the vapor pressure of the liquid in the bubble is less than or equal to the external pressure; the bubble and liquid can coexist in an unstable equilibrium of mechanics when the vapor pressure of the liquid is greater than the external pressure. If there is air in the bubble, the bubble and liquid can coexist in a stable equilibrium of mechanics when the vapor pressure of the liquid is less than or equal to the external pressure; the bubble and liquid can coexist in a stable and an unstable equilibrium of mechanics when the vapor pressure of the liquid is greater than the external pressure and less than a certain pressure pm; the bubble and liquid cannot coexist in the mechanical equilibrium when the vapor pressure of the liquid is equal to or greater than pm.

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26

Bräysy, V. "Pressure dependence of Tc from chemical equilibrium." Physica B: Condensed Matter 284-288 (July 2000): 1063–64. http://dx.doi.org/10.1016/s0921-4526(99)02412-6.

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27

DIGGINS, DAVID, and JOHN RALSTON. "Particle Wettability by Equilibrium Capillary Pressure Measurements." Coal Preparation 13, no. 1-2 (January 1993): 1–19. http://dx.doi.org/10.1080/07349349308905118.

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28

Bruggeman, Peter J., Felipe Iza, and Ronny Brandenburg. "Foundations of atmospheric pressure non-equilibrium plasmas." Plasma Sources Science and Technology 26, no. 12 (November 23, 2017): 123002. http://dx.doi.org/10.1088/1361-6595/aa97af.

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29

Kodejška, Č., S. Ganci, J. Říha, and H. Sedláčková. "Hydrostatic paradox: experimental verification of pressure equilibrium." Physics Education 52, no. 6 (September 21, 2017): 065010. http://dx.doi.org/10.1088/1361-6552/aa85ee.

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30

Cheng, C. Z. "Three-dimensional magnetospheric equilibrium with isotropic pressure." Geophysical Research Letters 22, no. 17 (September 1, 1995): 2401–4. http://dx.doi.org/10.1029/95gl02308.

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31

Marcus, P. M., and S. L. Qiu. "Equilibrium lines and crystal phases under pressure." Journal of Physics: Condensed Matter 21, no. 12 (March 3, 2009): 125404. http://dx.doi.org/10.1088/0953-8984/21/12/125404.

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32

Kitahara, Masaaki, Mikio Suzuki, and Akira Kodama. "Equilibrium of Inner and Middle Ear Pressure." Acta Oto-Laryngologica 114, sup510 (January 1994): 113–15. http://dx.doi.org/10.3109/00016489409127317.

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33

Taylor, K. H., S. R. M. Ellis, and C. H. G. Hands. "A low pressure vapour-liquid equilibrium still." Journal of Applied Chemistry 16, no. 8 (May 4, 2007): 245–47. http://dx.doi.org/10.1002/jctb.5010160806.

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34

Granados, S. J., M. J. Salazar, R. A. Toral, R. F. Tavera, A. J. M. Velázquez, L. R. T. Hernández, R. A. Cid, G. G. López, and R. A. González. "Pressure wave equation far from thermodynamics equilibrium." Journal of Physics: Conference Series 1221 (June 2019): 012055. http://dx.doi.org/10.1088/1742-6596/1221/1/012055.

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35

Salberta, E. R., R. C. Grimm, J. L. Johnson, J. Manickam, and W. M. Tang. "Anisotropic pressure tokamak equilibrium and stability considerations." Physics of Fluids 30, no. 9 (September 1987): 2796–805. http://dx.doi.org/10.1063/1.866505.

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36

KALLIO, A., J. HISSA, T. HÄYRYNEN, and V. BRÄYSY. "PRESSURE DEPENDENCE OF Tc FROM CHEMICAL EQUILIBRIUM." International Journal of Modern Physics B 13, no. 29n31 (December 20, 1999): 3532–37. http://dx.doi.org/10.1142/s0217979299003374.

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Анотація:

Chemical equilibrium theory analogous with dissociation of molecules or ionization of gas of atoms is applied to high-Tc superconductors. The starting point are preformed pairs, which exist in the normal state and can be treated as Coulomb bosons with charge 2e. Above Tc the pairs (B++) decay into fermions (h+) according to the equilibrium reaction B++⇌2h+. Using an approximate chemical equilibrium constant, proportional to pressure we derive a universal two-parameter expression for the pressurized optimum transition temperature [Formula: see text]. The formula shows that [Formula: see text] developes a maximum and beyond the maximum it starts to come down. We also show that in interesting pressure range P>10 GPa, the expansion in powers of pressure diverges.

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37

Spence, A., S. Avery, and C. Smith. "Laryngeal cuff pressure - a recoil equilibrium technique." Anaesthesia 70, no. 3 (February 11, 2015): 371. http://dx.doi.org/10.1111/anae.13024.

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38

Cochrane, J., and A. Cullen. "Laryngeal cuff pressure - an equilibrium recoil technique." Anaesthesia 70, no. 4 (March 12, 2015): 507. http://dx.doi.org/10.1111/anae.13051.

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39

Kitahara, Masaaki, Mikio Suzuki, and Akira Kodama. "Equilibrium in Inner and Middle Ear Pressure." Practica oto-rhino-laryngologica. Suppl. 1993, Supplement66 (1993): 110–13. http://dx.doi.org/10.5631/jibirinsuppl1986.1993.supplement66_110.

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40

Polyakov, V. B., and N. N. Kharlashina. "Effect of pressure on equilibrium isotopic fractionation." Geochimica et Cosmochimica Acta 58, no. 21 (November 1994): 4739–50. http://dx.doi.org/10.1016/0016-7037(94)90204-6.

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41

Bruin, Henk, Dalia Terhesiu, and Mike Todd. "The pressure function for infinite equilibrium measures." Israel Journal of Mathematics 232, no. 2 (June 20, 2019): 775–826. http://dx.doi.org/10.1007/s11856-019-1887-1.

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42

Hikosaka, M., K. Tsukijima, S. Rastogi, and A. Keller. "Equilibrium triple point pressure and pressure-temperature phase diagram of polyethylene." Polymer 33, no. 12 (January 1992): 2502–7. http://dx.doi.org/10.1016/0032-3861(92)91130-t.

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43

Fakhari-Kisomi, Behnam, Lutfi Erden, Armin D. Ebner, and James A. Ritter. "Equilibrium Theory Analysis of Pressure Equalization Steps in Pressure Swing Adsorption." Industrial & Engineering Chemistry Research 60, no. 27 (June 28, 2021): 9928–39. http://dx.doi.org/10.1021/acs.iecr.1c01144.

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44

Saiz, E., J. Gutierrez, and Y. Cerrato. "An inhomogeneous plasma equilibrium: asymptotic self-similar solutions." Journal of Plasma Physics 47, no. 3 (June 1992): 491–503. http://dx.doi.org/10.1017/s0022377800024375.

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Анотація:

A perfectly conducting hot plasma in thermodynamic equilibrium is studied without taking account of the effects of collisions and viscosity. The medium is inhomogeneous, unbounded, axisymmetric and subject to a magnetic field B0 parallel to the axis of symmetry of the cylinder. Plasma equilibrium is investigated using a magnetohydrodynamic model, and the system of equations is closed with an equation of state corresponding to the adiabatic law for an ideal gas. Transformation groups are applied to generate asymptotic selfsimilar solutions for the density, pressure and magnetic field magnitudes on the equilibrium, and thus to obtain the spatial dependence of the invariant solutions since the temporal variable is eliminated. From consideration of the nature of these solutions, necessary conditions for equilibria in finite inhomogeneous media are obtained. Results are given for inhomogeneous media with finite conductivity. The degrees of inhomogeneity for pressure and density and their relations with dimensionless constants, arising from the group parameters, provide information on certain drastic changes in equilibrium temperature profiles.

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45

Tang, Dafeng, C. W. Lim, Ling Hong, Jun Jiang, and S. K. Lai. "Dynamic Response and Stability Analysis with Newton Harmonic Balance Method for Nonlinear Oscillating Dielectric Elastomer Balloons." International Journal of Structural Stability and Dynamics 18, no. 12 (November 9, 2018): 1850152. http://dx.doi.org/10.1142/s0219455418501523.

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Subject to various pressure and voltage values, the deformation of a hyperelastic dielectric elastomer membrane may attain different stable and unstable equilibria. In this paper, the neo-Hookean material model is adopted to describe the hyperelastic behavior of a dielectric elastomer membrane. The effects of initial stretch ratio, pressure and voltage on the nonlinear free vibration of a spherical dielectric elastomer balloon are investigated qualitatively and quantitatively. Through a linear stability analysis of the equilibrium states, the safe regime of initial stretch ratio for the deformation of dielectric elastomer balloon is confined. Under specific static driving pressure and voltage, the system oscillates about the stable equilibrium and there is no oscillation in the neighborhood of the unstable equilibrium. Besides, the critical pressure and voltage values are determined. Beyond the critical values, there is no periodic oscillation. Along with the stability analysis, complex dynamical behavior such as drastic change of output regime, sporadic instability and sudden bifurcations can be predicted. By applying the Newton Harmonic Balance (NHB) method for quantitative analysis, the frequency response can be readily predicted. It is found that the nonlinear free vibration frequency decreases with increasing initial stretch ratio and control parameters (pressure and voltage).

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46

Yue, Zongyu, and Rolf D. Reitz. "An equilibrium phase spray model for high-pressure fuel injection and engine combustion simulations." International Journal of Engine Research 20, no. 2 (December 6, 2017): 203–15. http://dx.doi.org/10.1177/1468087417744144.

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High-pressure fuel injection impacts mixture preparation, ignition and combustion in engines and other applications. Experimental studies have revealed the mixing-controlled and local phase equilibrium characteristics of liquid vaporization in high injection pressure diesel engine sprays. However, most computational fluid dynamics models for engine simulations spend much effort in solving for non-equilibrium spray processes. In this study, an equilibrium phase spray model is explored. The model is developed based on jet theory and a phase equilibrium assumption, without modeling drop breakup, collision and finite-rate interfacial vaporization processes. The proposed equilibrium phase spray model is validated extensively against experimental data in simulations of the engine combustion network Spray A and in an optical diesel engine. Predictions of liquid/vapor penetration, fuel mass fraction distribution, heat release rate and emission formation are all in good agreement with experimental data. In addition, good computational efficiency and grid-independency are also seen with the present equilibrium phase model. The examined operating conditions cover wide ranges that are relevant to internal combustion engines, which include ambient temperatures from 700 to 1400 K, ambient densities from 7.6 to 22.8 kg/m3 and injection pressures from 1200 to 1500 bar for diesel sprays.

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47

Nichita, Dan Vladimir, Daniel Broseta, and François Montel. "Application of near critical behavior of equilibrium ratios to phase equilibrium calculations." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 74 (2019): 77. http://dx.doi.org/10.2516/ogst/2019049.

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We examine the asymptotic behavior of the equilibrium ratios (Ki) near the convergence locus in the pressure-temperature plane. When the Equation of State (EoS) is analytical, which is the case of most EoS of engineering purpose, Ki tends towards unity or, equivalently, its logarithm lnKi tends to zero, according to a power ½ of the distance to this locus. As a consequence, if lnKi is expressed as a linear combination of pure component parameters with coefficients only depending on mixture phase properties (i.e., reduction parameters), these coefficients obey a similar power law. Deviations from the ½ power law are thus fairly limited for lnKi and for the reduction parameters (at least in the negative flash window between the convergence locus and the phase boundaries), which can be exploited to speed up flash calculations and for quickly determining approximate saturation points and convergence pressures and temperatures. The chosen examples are representative synthetic and natural hydrocarbon mixtures, as well as various injection gas-hydrocarbon systems.

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48

Zakrzewska, Małgorzata E., Ana B. Paninho, M. Fátima C. Guedes da Silva, and Ana V. M. Nunes. "High-Pressure Phase Equilibrium Studies of Multicomponent (Alcohol-Water-Ionic Liquid-CO2) Systems." C — Journal of Carbon Research 6, no. 1 (February 25, 2020): 9. http://dx.doi.org/10.3390/c6010009.

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Selective water (by-product) separation from reaction mixtures stands as an important process intensification strategy for equilibrium-limited reactions. In this work, the possibility of using a high-pressure biphasic reaction media composed of a hydrophobic ionic liquid, 1-hexy-3-methylimidazolium tetracyanoborate, and carbon dioxide was explored for levulinic acid production from 1,4-butanediol. Vapour-liquid equilibrium measurements were performed for the binary (diol+CO2), ternary (diol+CO2+IL), and quaternary systems (diol+CO2+IL+water), at 313.2 K and pressures up to 18 MPa. The static analytical method was used in a high-pressure phase equilibrium apparatus equipped with a visual sapphire cell. The capability of the quaternary system to perform physical water separation is discussed in this paper.

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49

Turkevych, V. Z., Yu Yu Rumiantseva, I. О. Hnatenko, I. O. Hladkyi, and Yu I. Sadova. "Thermodynamic Calculation of Fe–N and Fe–Ga Melting Diagrams at Pressures from 0.1 MPa to 7 GPa." Uspehi Fiziki Metallov 22, no. 4 (December 2021): 531–38. http://dx.doi.org/10.15407/ufm.22.04.531.

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This paper presents results of melting-diagrams’ calculations for the Fe–N and Fe–Ga systems at atmospheric pressure (0.1 MPa) and at high pressures (3, 5, and 7 GPa). Thermodynamic calculations are performed within the models of phenomenological thermodynamics. As shown, the increase of pressure results in destabilization of high-temperature b.c.c.-Fe modification in Fe–N system and stabilization of Fe4N equilibrium with the liquid phase. In Fe–Ga system, the intermetallic compounds Fe3Ga, Fe6Ga5, Fe3Ga4, and FeGa3 retain their stability up to pressure of 7 GPa. The stabilization of Fe4N equilibrium with the liquid phase at high pressures indicates that the Fe4N can be a competing phase in the gallium-nitride crystallization from the Fe–Ga–N system melt.

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50

GIRIMAJI, SHARATH S. "Pressure–strain correlation modelling of complex turbulent flows." Journal of Fluid Mechanics 422 (November 3, 2000): 91–123. http://dx.doi.org/10.1017/s0022112000001336.

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Анотація:

A methodology for deriving a pressure–strain correlation model with variable coefficients is developed. The methodology is based on two important premises: (i) the extreme states of turbulence – the rapid distortion and equilibrium limits – are more amenable to mathematically rigorous modelling because of significant simplifications not possible at other states; and (ii) the models of the extreme states collectively contain all of the relevant physics so that models for any intermediate state can be obtained by suitable interpolation. A pressure–strain model of the standard form is considered and the coefficients are determined from linear analysis in the rapid distortion limit and from a fixed point analysis in the equilibrium limit. The model coefficients, which depend on the mean deformation and turbulence state, vary from flow to flow in a manner consistent with Navier–Stokes physics.The exact causal relationship between the model coefficients and the model's equilibrium behaviour is established by fixed point analysis performed using representation theory. Then, the equilibrium values of the model coefficients are chosen to yield the observed equilibrium behaviour. The values of the model coefficients in the rapid distortion limit are determined by enforcing consistency with the Crow constraint. The new variable-coefficient model reduces to the traditional constant-coefficient model in strain-dominated turbulent flows near equilibrium. The model performance in bench-mark turbulent flows, in which the traditional models have been calibrated extensively, is preserved intact. The new model is significantly different from the traditional one in mean vorticity-dominated and non-equilibrium turbulence. These two important classes of flows, in which traditional models fail, are successfully captured by the new model.

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