Journal articles: 'Phase rule and equilibrium'

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Seybold, Paul G., Matthew J. O'Malley, Lemont B. Kier, and Chao-Kun Cheng. "Cellular Automata Simulations of Vapor–Liquid Equilibria." Australian Journal of Chemistry 59, no. 12 (2006): 865. http://dx.doi.org/10.1071/ch06230.

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Phase transitions and phase equilibria are among the most fundamental phenomena in the physical and environmental sciences. In the present work an asynchronous stochastic cellular automata model for the equilibrium between a liquid and its vapor is presented. The model is visual, dynamic, and employs just two rules—an attraction probability and a gravitational preference. Application of the attraction rule alone yields a ‘mist’ within the vapor, whereas application of the gravitational rule by itself yields an isothermal atmospheric profile. Application of both rules together causes the vapor to evolve to a liquid phase with a vapor phase above it. Introduction of a third rule for short-range attraction/repulsion more clearly resolves the liquid/vapor interface.

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Shyu, Guor-Shiarn, Nishawn S. M. Hanif, Kenneth R. Hall, and Philip T. Eubank. "Maximum Partial Area Rule for Phase Equilibrium Calculations." Industrial & Engineering Chemistry Research 35, no. 11 (January 1996): 4348–53. http://dx.doi.org/10.1021/ie960203p.

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Chiang, C. S., and William C. Johnson. "Coherent phase equilibria in systems possessing a consolute critical point." Journal of Materials Research 4, no. 3 (June 1989): 678–87. http://dx.doi.org/10.1557/jmr.1989.0678.

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The influence of coherency strains on phase equilibria in a two-phase microstructure is examined for a binary or pseudobinary alloy system possessing a consolute critical point (chemical miscibility gap). The qualitative features of phase equilibria, including the limits of metastability (chemical spinodal), are shown to depend critically on the mechanical loading conditions and the geometric arrangement of the phases in the microstructure. If the elastic state of a phase in a two-phase coherent system is independent of the presence of the other phase, then the equilibrium characteristics usually associated with fluid systems should be observed, even though the system is nonhydrostatically stressed. If the elastic state of a phase depends upon the presence of the other phase, then the equilibrium characteristics that have come to be associated with coherent systems should be observed; tie lines and field lines do not coincide, the common tangent construction is invalid, and Gibbs phase rule is not applicable.

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Fujita, Hiroshi. "Non-equilibrium phase formation." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (August 1990): 506–7. http://dx.doi.org/10.1017/s0424820100175661.

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The most important advantage of EM’s is in situ experiments on detailed processes of the same phenomena that occur in bulk materials. In recent years, in situ experiments with HVEM’s, in particular with a 3MV ultra-HVEM , has made it possible to create non-equilibrium phases, which do not exist in nature, or to control and design materials on an atomic scale. Namely, HVEM’s have developed to “Micro-Laboratory”, in which various material-treatments can be done, for natural science from powerful tools for characterization and/or identification of materials.l.The General Rule for Solid Amorphization The author and his cowerkers have succeeded in making amorphous solids of intermetallic compounds by high energy electron irradiation. Using the electron irradiation effect, necessary conditions for the formation of both non-equilibrium phases and extremly supersaturated solid structures[3,4] can be easily and precisely controlled.

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Liu, Chengjun, Jiyu Qiu, and Zhengyue Liu. "Phase Equilibria in the System CaO-SiO2-La2O3-Nb2O5 at 1400 °C." Metals 11, no. 12 (November 24, 2021): 1892. http://dx.doi.org/10.3390/met11121892.

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CaO-SiO2-La2O3-Nb2O5 system is of great significance for the pyrometallurgical utilization of Bayan Obo tailing resources. In the present work, the phase equilibrium of this quaternary system at 1400 °C was determined by a thermodynamic equilibrium experiment. On the basis of the recently determined CaO-La2O3-Nb2O5 phase diagram, some boundary surfaces of primary phase fields of CaO-SiO2-La2O3-Nb2O5 phase diagram were modified; then, the 1400 °C isothermal surface in the primary phase fields of SiO2, CaNb2O6, Ca2Nb2O7, and LaNbO4 was constructed, respectively. On this basis, CaO-SiO2-Nb2O5 pseudo-ternary phase diagrams with w(La2O3) = 5%, 10%, 15%, and 20% were determined, respectively. Considering the importance of equilibrium crystallization reaction type, we proposed a new rule named Tangent Line Rule to judge the univariant reaction type in the quaternary phase diagram. By applying Tangent Line Rule and Tangent Plane Rule previously proposed, some univariant and bivariant crystallization reaction types in the CaO-SiO2-La2O3- Nb2O5 phase diagram were determined, respectively. The current work can provide original data for the establishment of a thermodynamic database of Nb-bearing and REE-bearing slag system; the proposed Tangent Line Rule will promote the application of a spatial quaternary phase diagram.

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Karim, Abdul M. A., and Arkan J. Hadi. "Thermodynamic Model for High Pressure Phase Behavior of Carbon Dioxide in Several Physical Solvents at Different Temperatures." Tikrit Journal of Engineering Sciences 15, no. 2 (June 30, 2008): 32–50. http://dx.doi.org/10.25130/tjes.15.2.03.

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In the present study a thermodynamic model for prediction of gas-liquid equilibrium at high pressures and different temperatures prepared for the binary systems of carbon dioxide (1) with each of the one of the liquid physical solvents (2) (sulfolane, n-methyl-2-pyrrolidone and propylene carbonate) using Peng-Robenson equation of state (PR-EOS) with different mixing rules to show the effect of the type of mixing rule used. Comparison of the experimental phase equilibrium data in the literature with the results of the model showed very good representation for some mixing rules and good for the others.

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IONIŢĂ, Mihaela, Sergiu SIMA, Martin CISMONDI, and Catinca SECUIANU. "Phase equilibria for the carbon dioxide + cyclopentane + cyclohexane system at high pressures." Revue Roumaine de Chimie 66, no. 3 (2021): 303–8. http://dx.doi.org/10.33224/rrch.2021.66.3.11.

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Isothermal vapor–liquid equilibrium measurements for the ternary mixture carbon dioxide + cyclopentane + cyclohexane at 353.15 K are reported. Phase equilibrium measurements were made in a high-pressure visual 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 analysis. The new measured data were modelled with the RK–PR equation of state (EoS) coupled with classical van der Waals (two-parameter conventional mixing rule, 2PCMR).

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Colin, Samuel, and Antony Valentini. "Instability of quantum equilibrium in Bohm's dynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2171 (November 8, 2014): 20140288. http://dx.doi.org/10.1098/rspa.2014.0288.

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We consider Bohm's second-order dynamics for arbitrary initial conditions in phase space. In principle, Bohm's dynamics allows for ‘extended’ non-equilibrium, with initial momenta not equal to the gradient of phase of the wave function (as well as initial positions whose distribution departs from the Born rule). We show that extended non-equilibrium does not relax in general and is in fact unstable. This is in sharp contrast with de Broglie's first-order dynamics, for which non-standard momenta are not allowed and which shows an efficient relaxation to the Born rule for positions. On this basis, we argue that, while de Broglie's dynamics is a tenable physical theory, Bohm's dynamics is not. In a world governed by Bohm's dynamics, there would be no reason to expect to see an effective quantum theory today (even approximately), in contradiction with observation.

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9

DU, P. C., and G. A. MANSOORI. "PHASE EQUILIBRIUM OF MULTICOMPONENT MIXTURES: CONTINUOUS MIXTURE GIBBS FREE ENERGY MINIMIZATION AND PHASE RULE." Chemical Engineering Communications 54, no. 1-6 (May 1987): 139–48. http://dx.doi.org/10.1080/00986448708911903.

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10

Toikka, Alexander, and Maria Toikka. "Solubility and critical phenomena in reactive liquid–liquid systems." Pure and Applied Chemistry 81, no. 9 (August 19, 2009): 1591–602. http://dx.doi.org/10.1351/pac-con-08-11-04.

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The goal of this work is to consider solubility phenomena in reactive fluid mixtures with liquid-phase splitting. One of the main tasks is to analyze peculiarities of liquid–liquid (LL) systems with equilibrium and nonequilibrium chemical reaction. The special aim is to consider the critical states in these systems. The reactive liquid–liquid equilibrium (LLE) is treated on the base of phase rule. The topology of diagrams of reactive LLE is discussed for some types of binary and ternary systems. Examples are presented of a possible transformation of phase diagrams caused by the shifting of chemical equilibrium and by changes in the shape of the binodal. The transformations resulting in the reactive critical phase formation are considered. Quaternary mixtures are also discussed with the use of experimental data on the solubility in the system with n-propyl acetate synthesis reaction. The mutual crossing of the chemical equilibrium surface and binodal in the composition tetrahedron leads to the origin of the area of simultaneous chemical and LLE with two critical points (reactive critical phases). The shape of the curve of simultaneous chemical and phase equilibrium is also presented in the square of transformed composition variables.

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PLATT, G. M., and J. L. de MEDEIROS. "Phase rule calculations and the thermodynamics of reactive systems under chemical equilibrium." Brazilian Journal of Chemical Engineering 16, no. 3 (September 1999): 247–65. http://dx.doi.org/10.1590/s0104-66321999000300004.

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12

Rajendran, Karthikeyan, and R. Ravi. "Critical Analysis of Maxwell’s Equal Area Rule: Implications for Phase Equilibrium Calculations." Industrial & Engineering Chemistry Research 49, no. 16 (August 18, 2010): 7687–92. http://dx.doi.org/10.1021/ie100571m.

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Lashgari, Hamid R., Kamy Sepehrnoori, and Mojdeh Delshad. "A Four-Phase Chemical/Gas Model in an Implicit-Pressure/Explicit-Concentration Reservoir Simulator." SPE Journal 21, no. 04 (August 15, 2016): 1086–105. http://dx.doi.org/10.2118/173250-pa.

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Summary This study describes a general four-phase model developed for gas/oil/water/microemulsion (ME) coexisting at local equilibrium. The original framework of a chemical reservoir simulator is used to implement the model. This model represents a new method to couple the black-oil model with surfactant-phase behavior [i.e., the Hand (1939) rule]. The Hand (1939) rule is used to capture the equilibrium among surfactant, oil, and water species as a function of salinity and species concentrations for oil/water/ME phases. The interphase-mass transfer between gas/oil in the presence of the ME phase is calculated at the equilibrium between phases. For this purpose, a new volume-balance equation is derived to consider the pressure equation for compressible and real mixing in such a model. Hence, the pressure equation is derived by extending the black-oil model to a pseudocompositional model for a wide range of components (water, oil, surfactant, polymer, anion, cation, alcohol, and gas). Mass-balance equations are then solved for the components to calculate the concentration. Finally, we implemented the coupled surfactant and black-oil phase-behavior models and the fluid-flow formulations in an implicit-pressure/explicit-concentration (IMPEC) chemical-flooding simulator: UTCHEM (2011) four-phase. The results were verified against existing reservoir simulators for two different three-phase test cases comprising gas/oil/water and oil/water/ME. Then, the performance of the model in the presence of four phases was tested and validated against coreflood experimental data. The results showed that the new phase behavior and the fluid-flow equations are consistent with three-phase reservoir simulators for the case studies. In addition, the findings of this work can be used to model and capture the mechanisms behind processes such as micellar slug foam and alkaline and surfactant flooding into saturated (gas cap) reservoirs as well as alternating or coinjection of surfactant and gas processes. Modeling of such processes is far from satisfactory in existing phase behavior and fluid-flow simulators.

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Oktavian, Rama, Agung Ari Wibowo, and Zuraidah Fitriah. "Study on Particle Swarm Optimization Variant and Simulated Annealing in Vapor Liquid Equilibrium Calculation." Reaktor 19, no. 2 (August 11, 2019): 77–83. http://dx.doi.org/10.14710/reaktor.19.2.77-83.

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Phase equilibrium calculation plays a major rule in optimization of separation process in chemical processing. Phase equilibrium calculation is still very challenging due to highly nonlinear and non-convex of mathematical models. Recently, stochastic optimization method has been widely used to solve those problems. One of the promising stochastic methods is Particle Swarm Optimization (PSO) due to its simplicity and robustness. This study presents the capability of particle swarm optimization for correlating isothermal vapor liquid equilibrium data of water with methanol and ethanol system by optimizing Wilson, Non-Random Two Liquids (NRTL), and Universal Quasi Chemical (UNIQUAC) activity coefficient model and also presents the comparison with bare-bones PSO (BBPSO) and simulated annealing (SA). Those three optimization methods were successfully tested and validated to model vapor liquid equilibrium calculation and were successfully applied to correlate vapor liquid equilibrium data for those types of systems with deviation less than 2%. In addition, BBPSO shows a consistency result and faster convergence among those three optimization methods. Keywords: Phase equilibrium, stochastic method, particle swarm optimization, simulated annealing and activity coefficient model

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15

Podderegin, O. A. "Analysis of the Mathematical Model of Cancer Dynamics." Mathematics and Mathematical Modeling, no. 1 (September 24, 2022): 1–20. http://dx.doi.org/10.24108/mathm.0122.0000299.

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Qualitative analysis of dynamic systems is a powerful research tool used to solve a great deal of application problems. In mathematical models described by ordinary differential equations, the study of equilibrium positions has actually become the standard: their number and location depending on the parameters, as well as issues of local stability. In mathematical models in various fields of chemistry and biology, it is also important that the natural requirements for the possible values of phase variables are not violated in the process of dynamics (as a rule, this is the non-negativity condition). More sophisticated study orientation is global sustainability.The need for a qualitative analysis of a dynamic system arises because, as a rule, differential equations are not integrated and it is impossible to define the general properties of the system trajectories by integration. However, even if the system of differential equations is integrated, the formulas can be so cumbersome that their use in the analysis of the system dynamics turns out to be a challenge.In this paper, we study an 8-dimensional system of ordinary differential equations that describes the dynamics of cancer during chemotherapy and immunotherapy. The phase space of the system is a non-negative orthant.The paper studies the equilibrium positions of the system. There is always one equilibrium in a system, but there may be two more equilibria. There are conditions for the system parameters found, under which the equilibrium position, being always present is asymptotically stable. Moreover, there is a provement that the asymptotic stability is global.

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16

Malijevská, Ivona. "Evaluation of Heterodimerization Constant from Solid-Liquid and Vapor-Liquid Equilibrium Data." Collection of Czechoslovak Chemical Communications 65, no. 9 (2000): 1497–505. http://dx.doi.org/10.1135/cccc20001497.

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Activity coefficients obtained from the solid-liquid equilibrium data were used to fit the isobaric vapor-liquid equilibrium data to evaluate the vapor-phase equilibrium constant of heterodimerization of the system propanoic acid-trifluoroethanoic acid. The found hetero-dimerization constant is several times higher than that estimated on the basis of the "double-geometric-mean" rule and its temperature dependence has the form ln KAB = 7 196.7/T - 26.80.

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Taguchi, Hiroyuki, and Ganbayar Gunbileg. "Monetary Policy Rule and Taylor Principle in Mongolia: GMM and DSGE Approaches." International Journal of Financial Studies 8, no. 4 (November 16, 2020): 71. http://dx.doi.org/10.3390/ijfs8040071.

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This article aims to examine the monetary policy rule under an inflation targeting in Mongolia with a focus on its conformity to the Taylor principle, through two kinds of approaches: a monetary policy reaction function by the generalized-method-of-moments (GMM) estimation and a New Keynesian dynamic stochastic general equilibrium (DSGE) model with a small open economy version by the Bayesian estimation. The main findings are summarized as follows. First, the GMM estimation identified an inflation-responsive rule fulfilling the Taylor principle in the recent phase of the Mongolian inflation targeting. Second, the DSGE-model estimation endorsed the GMM estimation by producing a consistent outcome on the Mongolian monetary policy rule. Third, the Mongolian rule was estimated to have a weaker response to inflation than the rules of the other emerging Asian adopters of an inflation targeting.

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Lim, K. R., J. H. Na, J. M. Park, W. T. Kim, and D. H. Kim. "Enhancement of plasticity in Ti-based metallic glass matrix composites by controlling characteristic and volume fraction of primary phase." Journal of Materials Research 25, no. 11 (November 2010): 2183–91. http://dx.doi.org/10.1557/jmr.2010.0277.

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In this study, Ti-based metallic glass matrix composites with high plasticity have been developed by controlling characteristic and volume fraction of primary phase embedded in the glass matrix. By careful alloy design procedure, the compositions of β/glass phases, which are in metastable equilibrium have been properly selected, therefore the mechanical properties can be tailored by selecting the alloy compositions between the composition of β and glass phases. The relation between the compressive yield strength and volume fraction of β phase is well described using the rule of mixtures.

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Zou, Qing Hua, and Sheng Zhong Zou. "Key Program for Non-Equilibrium Phase Diagram of Ni 1 Type Steel." Advanced Materials Research 204-210 (February 2011): 1357–61. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.1357.

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The practical air-cooling new-type dynamic phase diagram and nonequilirium lever rule of Ni 1 structural steel was established, and the relevant structure and chemical composition were analyzed, which can be used in practical production. The computer programs for drawing binary non-equilibrium phase diagram of Ni type structural steel have designed.

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Arkan Jasim Hadi and Arkan Jasim Hadi. "GAS-LIQUID EQUILIBRIUM PREDICTION OF CO2-ETHANOL SYSTEM AT MODERATE PRESSURES AND DIFFERENT TEMPERATURES." Diyala Journal of Engineering Sciences 3, no. 1 (June 1, 2010): 90–105. http://dx.doi.org/10.24237/djes.2010.03107.

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In this work, a thermodynamic model for the prediction of gas-liquid equilibrium at moderate pressures (up to 19 bar) and different temperatures (288-323 K) for the binary system of carbon dioxide (1)-ethanol (2) is established using Soave-Redlich-Kwong equation of state (SRK-EOS), Peng-Robenson equation of state (PR-EOS), and HYSYS program with same equations of state. Three different mixing rules were used to show the effect of the type of mixing rule. A comparison of experimental phase equilibrium data in the literature with the predicted results showed very good representation for some mixing rules and good for the others, also the comparison with the results obtained using simulation on HYSYS program exhibits good agreement up to 11 bar with a deviation of 4*10-4 - 2*10-4 %.

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Valderrama, Jos� O., and Victor H. Alvarez. "Phase equilibrium in supercritical CO2 mixtures using a modified Kwak-Mansoori mixing rule." AIChE Journal 50, no. 2 (2004): 480–88. http://dx.doi.org/10.1002/aic.10042.

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Salgansky, E. A., D. N. Podlesniy, M. V. Tsvetkov, and A. Yu Zaichenko. "Thermodynamically Equilibrium Compositions of the Products Formed During the Filtration Combustion of the Metal-Containing Mixtures." Eurasian Chemico-Technological Journal 22, no. 4 (December 30, 2020): 263. http://dx.doi.org/10.18321/ectj998.

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Thermodynamic calculations for describing the compositions of the products formed in conditions of the filtration combustion of the metal-containing mixtures were carried out. The analysis of the equilibrium compositions of the products was carried out using the TERRA high-temperature thermochemical equilibrium calculation program. According to the results of calculations, the metals were divided into two groups. First one forms both the condensed and gaseous phases and in the second one ‒ metals that are only in the condensed phase. In case of the presence of metal compounds in the gas phase, as a rule, these are the following compounds: metals, oxides, hydroxides, hydrides, sulfides and metal sulfates. Metals of the second group cannot be subjected to mass transfer under conditions of the filtration combustion wave and will remain in solid combustion products (in ash).

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DOROTHEYEV, E. A., V. S. DOTSENKO, and B. TIROZZI. "STATISTICAL MEMORY MODEL FOR POLYMER CHAIN SHAPES." International Journal of Modern Physics B 07, no. 13 (June 15, 1993): 2509–27. http://dx.doi.org/10.1142/s0217979293002924.

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We study the equilibrium configurations of heteropolymer chains in the infinite-dimensional space. The number of sorts of monomers composing the chains is finite. The interactions between pairs of monomers are defined (using Hebbian learning rule) in such a way that in the thermodynamic limit the equilibrium configurations of the polymers are some preassigned shapes. The phase diagram of the model is obtained and the memory capacity is computed.

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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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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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Hu, Shi Ping, Juan Han, Yong Sheng Yan, and Yu Tao Hu. "Liquid-Liquid Equilibria for Acetone + Several Citrates Aqueous Two-Phase Systems at Different Temperatures." Advanced Materials Research 549 (July 2012): 30–35. http://dx.doi.org/10.4028/www.scientific.net/amr.549.30.

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Liquid-liquid equilibria for the three kinds of the ternary systems acetone + ammonium, sodium or potassium citrate + water have been determined at T= (273.15, 283.15, and 298.15) K. Binodal curves, tie-lines, and integrated phase diagrams for the ternary systems are given. The data of the experimental bimodal curve are described with a four-parameter equation. The result also shows the temperature has little influence on the liquid-liquid equilibrium within the investigated range. The tie-line data calculated according to the bimodal data fitting equation and the lever arm rule were satisfactorily described by using the Othmer-Tobias and Bancroft equations, and the result conform the reliability of the calculation method and corresponding tie-line data.

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Udovsky, A. L. "The Analytical and Computational Thermodynamics of Closed Binary Systems." Solid State Phenomena 138 (March 2008): 241–82. http://dx.doi.org/10.4028/www.scientific.net/ssp.138.241.

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The Review. The presented results got by author in the field of analytical and computing thermodynamics of the binary systems for the last 25 years. This review includes following sections. In the first section, transition from description of the equilibrium of the phases in two-phase open binary system to description of the equilibrium of the phases in two-phase closed binary system is shown. It allows to go from problem of global minimization in five-dimension space with provision for restrictions to problem of searching for of the global minimum in 3-dimension space with provision for restrictions. The derivation of the system of equations for equilibrium of two phases in closed binary system is given in the second. The third section, different interpretations (as physical, for as geometric and chemical) for the set of the equations for two phases equilibrium for closed binary system are discussed. Analytical description of invariance for the set of equations of phase equilibrium at transformation of molar Gibbs free energies relatively algebra adding of linear functions on compositions with coefficients, which are any functions of temperature and pressure, is proved in the fourth section. The generalization of the Maxwell’s rule in conjugate coordinates for closed binary systems, which is given the fifth section, has allowed to formulate the new algorithm (U-algorithm) of the calculation of the phase diagrams. The autonomous U-algorithm unlike Newton-method (and its modifications), which is describes in the sixth section, does not require the tasks of the initial approach and possesses the square-law velocity to convergence as Newton - method. Some applications of computer programs, which bases on the U-algorithm, for calculated binary phase diagrams, including solution of indirect problems, are described in the seventh section In the eight section obtained results with comparison published papers are discussed. Finally, in the ninth section, we summarize and discuss in short form of some open problems at present and on which are received only first results.

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Ahmadloo, Ebrahim, Najmeh Sobhanifar, and Fatemeh Sadat Hosseini. "Modeling of vapor-liquid equilibrium for binary polypropylene glycol/solvent solutions using cubic equation of state models: optimization and comparison of CEoS models." Journal of Polymer Engineering 34, no. 1 (February 1, 2014): 95–104. http://dx.doi.org/10.1515/polyeng-2013-0192.

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Abstract The cubic equation of state (CEoS) is a powerful method for calculation of the vapor-liquid equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EoS approach. In this research, VLE calculations of polypropylene glycol (polypropylene oxide) [PPG(PPO)]/solvent solutions were carried out. In this approach, eight models containing Peng-Robinson-Stryjek-Vera (PRSV) and Soave-Redlich-Kwong (SRK) CEoS separately combined with four mixing rules, namely van der Waals one-fluid mixing rule with one adjustable parameter (vdW1), van der Waals one-fluid mixing rule with two adjustable parameters (vdW2), Wong-Sandler (WS), and Zhong-Masuoka (ZM) were applied to calculations of bubble point pressure. For a better correlation, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. The results of absolute average deviations (%AAD) between computed results and experimental bubble point pressure data were calculated and presented. Although the capability of two CEoS had a good agreement with experimental data and illustrated the correct type of phase behavior in all cases, the performance of the PRSV+vdW2 was more reliable than the other models.

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Cvijić, Marko, and Janvit Golob. "Preparation of a solid product with high water content and water retention properties." Polish Journal of Chemical Technology 22, no. 3 (September 1, 2020): 17–23. http://dx.doi.org/10.2478/pjct-2020-0023.

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AbstractThis work presents the development of a solid product with a high water content (99.08%) and water retention properties. Water was chosen as a potential carrier of a volatile active substance and water retaining properties of material were studied at a temperatures and relative air humidity values with the support of the theory of drying. The study first confirmed the role of Gibbs’ phase rule in the research of solid-gas phase equilibrium, and second presented drying kinetics developed from Fick’s second law and expressed with the first term of the Fourier equation. Solutions of equations for phase equilibrium and mass transfer enabled the calculation of Luikov’s parameters, which are important for equilibrium relations and for the diffusivity of water in a solid for mass transfer prediction. The obtained thermodynamic and kinetic parameters enabled product characterisation that may be important for the prediction of retention times.

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Beltran, Juan G., Hallvard Bruusgaard, and Phillip Servio. "Gas hydrate phase equilibria measurement techniques and phase rule considerations." Journal of Chemical Thermodynamics 44, no. 1 (January 2012): 1–4. http://dx.doi.org/10.1016/j.jct.2011.08.026.

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Oh, Seokjin, Jiyong An, Seungmyeong Cho, Rina Yoon, and Kyeong-Sik Min. "Memristor Crossbar Circuits Implementing Equilibrium Propagation for On-Device Learning." Micromachines 14, no. 7 (July 3, 2023): 1367. http://dx.doi.org/10.3390/mi14071367.

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Equilibrium propagation (EP) has been proposed recently as a new neural network training algorithm based on a local learning concept, where only local information is used to calculate the weight update of the neural network. Despite the advantages of local learning, numerical iteration for solving the EP dynamic equations makes the EP algorithm less practical for realizing edge intelligence hardware. Some analog circuits have been suggested to solve the EP dynamic equations physically, not numerically, using the original EP algorithm. However, there are still a few problems in terms of circuit implementation: for example, the need for storing the free-phase solution and the lack of essential peripheral circuits for calculating and updating synaptic weights. Therefore, in this paper, a new analog circuit technique is proposed to realize the EP algorithm in practical and implementable hardware. This work has two major contributions in achieving this objective. First, the free-phase and nudge-phase solutions are calculated by the proposed analog circuits simultaneously, not at different times. With this process, analog voltage memories or digital memories with converting circuits between digital and analog domains for storing the free-phase solution temporarily can be eliminated in the proposed EP circuit. Second, a simple EP learning rule relying on a fixed amount of conductance change per programming pulse is newly proposed and implemented in peripheral circuits. The modified EP learning rule can make the weight update circuit practical and implementable without requiring the use of a complicated program verification scheme. The proposed memristor conductance update circuit is simulated and verified for training synaptic weights on memristor crossbars. The simulation results showed that the proposed EP circuit could be used for realizing on-device learning in edge intelligence hardware.

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Surový, Július, Jana Ovečková, and Elena Graczová. "The Effect of Vapour Space Volume on Vapour-Liquid Equilibrium Measured by Stripping with an Inert Gas Stream." Collection of Czechoslovak Chemical Communications 58, no. 9 (1993): 2069–78. http://dx.doi.org/10.1135/cccc19932069.

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The effect of vapour space size when measuring the vapour-liquide equilibrium by a modified saturation method based on the change in the liquid phase concentration with time is studied in this work. The relation was derived for calculating the correction for the vapour space volume. On using some model solutions of different degree of non-ideality and of different concentrations, the magnitude of this correlation and its influence on the calculated vapour-liquid equilibrium data is studied. In case of systems of completely miscible liquids, it is not necessary, as a rule, to expect a more significant effect of the vapour space size on vapor-liquid equilibrium.

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32

Sima, Sergiu, Catinca Secuianu, Viorel Feroiu, and Dan Geană. "New high-pressures vapor-liquid equilibrium data for the carbon dioxide + 2-methyl-2-propanol binary system." Open Chemistry 12, no. 9 (September 1, 2014): 893–900. http://dx.doi.org/10.2478/s11532-013-0392-3.

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AbstractNew vapor-liquid equilibria (VLE) data at 323.15, 333.15, 343.15, and 353.15 K and pressures up to 112.9 bar are reported for the carbon dioxide + 2-methyl-2-propanol system. The experimental method used in this work was a static analytical method with liquid and vapor phases sampling using a rapid online sampler injector (ROLSI™) coupled to a gas chromatograph (GC) for analysis. Measured VLE data and literature data for carbon dioxide + 2-methyl-2-propanol system were modeled with the Soave-Redlich-Kwong (SRK) cubic equation of state with classical van der Waals (two-parameter conventional mixing rule, 2PCMR) mixing rules. A single set of interaction parameters that lead to a correct phase behavior was used in this work to model the new VLE data and critical points of the mixtures in a wide range of temperature and pressure. The SRK prediction results were compared to the new data measured in this study and to available literature data.

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Rai, Nirmal K., and Tariq D. Aslam. "Evaluation of thermodynamic closure models for partially reacted two-phase mixture of condensed phase explosives." Journal of Applied Physics 131, no. 18 (May 14, 2022): 185902. http://dx.doi.org/10.1063/5.0085208.

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One of the key fundamental issues that is crucial in the continuum modeling of reactive flow phenomena is the thermodynamically consistent description of reaction mixture properties. To define the mixture properties, thermodynamic closure rules that relate the properties of the individual reaction components to the mixture properties are required. In the context of reactive two-phase modeling approaches, various strategies to define the thermodynamic closures have been adopted such as pressure temperature (PT) equilibrium between the individual reaction components, pressure (specific) volume (PV) equilibrium, etc. The choice of closure rules determines the relative distribution of specific volume and energy across the reaction components that comprise the mixture. Therefore, depending on the choice of the closure, the mixture thermodynamic behavior can vary. The present work examines the effect of different closure approaches on the thermodynamic properties of the reaction mixture. The analysis is performed for a condensed phase HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) based plastic bonded explosive (PBX) 9501 explosive using four different thermodynamic closures, viz., PT equilibrium, PV equilibrium, volume temperature (VT) equilibrium, and pressure (P) equilibrium with reactants on an isentrope. The relative variations in the thermodynamic properties of the mixture are analyzed and compared under both compression and expansion loading regimes. It is shown that out of the four closure models, only PT equilibrium and P equilibrium closures lead to a thermodynamically accurate description of the mixture under both compression and expansion.

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Sima, Sergiu, Catinca Secuianu, Viorel Feroiu, and Dan Geană. "New high-pressures vapor-liquid equilibrium data for the carbon dioxide + 2-methyl-1-propanol (isobutanol) binary system." Open Chemistry 12, no. 9 (September 1, 2014): 953–61. http://dx.doi.org/10.2478/s11532-013-0394-1.

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AbstractNew vapor-liquid equilibria (VLE) data at 333.15, 343.15, and 353.15 K and pressures up to 130.0 bar are reported for the carbon dioxide + 2-methyl-1-propanol (isobutanol) system. The experimental method used in this work was a static analytical method with liquid and vapor phases sampling using a rapid online sampler injector (ROLSITM) coupled to a gas chromatograph (GC) for analysis. Measured VLE data and literature data for carbon dioxide + 2-methyl-1-propanol system were modeled with the Soave-Redlich-Kwong (SRK) cubic equation of state with classical van der Waals (two-parameter conventional mixing rule, 2PCMR) mixing rules. A single set of interaction parameters that lead to a correct phase behavior was used in this work to model the new VLE data and critical points of the mixtures in a wide range of temperature and pressure. The SRK prediction results were compared to the new data measured in this study and to available literature data.

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35

Towler, M. D., N. J. Russell, and Antony Valentini. "Time scales for dynamical relaxation to the Born rule." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2140 (November 30, 2011): 990–1013. http://dx.doi.org/10.1098/rspa.2011.0598.

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We illustrate through explicit numerical calculations how the Born rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie–Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie–Bohm ontology, the box contains an objectively existing ‘pilot wave’ which guides the electron trajectory, and this is represented mathematically by a Schrödinger wave function composed of a finite out-of-phase superposition of M energy eigenstates (with M ranging from 4 to 64). The electron density distributions are found to evolve naturally into the Born rule ones and stay there; in analogy with the classical case this represents a decay to ‘quantum equilibrium’. The proximity to equilibrium is characterized by the coarse-grained subquantum H -function which is found to decrease roughly exponentially towards zero over the course of time. The time scale τ for this relaxation is calculated for various values of M and the coarse-graining length ε . Its dependence on M is found to disagree with an earlier theoretical prediction. A power law, τ ∝ M −1 , is found to be fairly robust for all coarse-graining lengths and, although a weak dependence of τ on ε is observed, it does not appear to follow any straightforward scaling. A theoretical analysis is presented to explain these results. This improvement in our understanding of time scales for relaxation to quantum equilibrium is likely to be of use in the development of models of relaxation in the early Universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.

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Frolova, S., and O. Sobol. "Dynamics of cluster structure change in melts that forms a continuous series of solid solutions during equilibrium and nonequilibrium crystallization." BULLETIN of the L.N. Gumilyov Eurasian National University. Chemistry. Geography. Ecology Series 143, no. 2 (2023): 45–51. http://dx.doi.org/10.32523/2616-6771-2023-143-2-45-51.

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The article describes the dynamics of changes in the melt structure during cooling of solid substitution solutions in the process of quasi-equilibrium (CRC) and non-equilibrium explosive crystallization (NRCC), taking into account clustering processes. The boundaries of the transition to the solid state are determined as the structure of clusters changes during crystallizations of the KRK and NRK types. The boundaries are determined taking into account the critical overheating and pre-crystallization supercooling relative to the liquidus line . It is determined that during quasi–equilibrium crystallization, the melt changes its structure in the following sequence , and during non-equilibrium explosive crystallization - in the sequence . The phase rule is used to calculate the first crystals that appeared during various types of crystallization. Alloy cooling curves describing various types of alloy crystallization.

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Debien, Isabel C. N., Aline A. Rigo, Marcos L. Corazza, Marcio A. Mazutti, and J. Vladimir Oliveira. "Thermodynamic Modeling of High-pressure Equilibrium Data for the Systems L-lactic Acid + (Propane + Ethanol) and L-lactic Acid + (Carbon Dioxide + Ethanol)." Open Chemical Engineering Journal 9, no. 1 (February 26, 2015): 1–6. http://dx.doi.org/10.2174/1874123101509010001.

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This short communication reports the thermodynamic modeling of high-pressure equilibrium data (cloud points) for the systems L-lactic acid + (propane + ethanol) and L-lactic acid + (carbon dioxide + ethanol) from 323.15 K to 353.15 K and at pressures up to 25 MPa.The experimental data were modeled using the Peng-Robinson equation of state with the classical van der Waals quadratic mixing rule (PR-vdW2) and with the Wong-Sandler mixing rule (PR-WS). It is shown that the PR-vdW2 and PR-WS models were both able to satisfactorily represent the phase behavior of the system L-lactic acid + (carbon dioxide + ethanol). However, for the system L-lactic acid + (propane + ethanol), the PR-vdW2 model was not able to appropriately describe its phase behavior.

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Sun, Li, Jierong Liang, and Tingting Zhu. "A Numerical Study of Vapor–Liquid Equilibrium in Binary Refrigerant Mixtures Based on 2,3,3,3-Tetrafluoroprop-1-ene." Sustainability 15, no. 19 (October 4, 2023): 14482. http://dx.doi.org/10.3390/su151914482.

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The binary refrigerant mixtures containing 2,3,3,3-Tetrafluoroprop-1-ene are considered as excellent substitutes for traditional refrigerants. Weak hydrogen bonds exist in hydrofluorocarbons and hydrofluoroolefins. However, for several recently published binary refrigerant mixtures, there is no Vapor–Liquid Equilibrium calculation study considering hydrogen-bonding associations. This work presents a calculation work of the saturated properties of nine pure refrigerants using the Cubic-Plus-Association Equation of State, considering the hydrogen-bonding association in refrigerant fluids. The average relative deviations of the saturated vapor pressure, liquid, and vapor density are less than 1.0%, 1.5%, and 3.5%, respectively. The Vapor–Liquid Equilibrium of ten binary refrigerant mixtures containing 2,3,3,3-Tetrafluoroprop-1-ene is also calculated using the Cubic-Plus-Association Equation of State with the van der Waals mixing rule. The average relative deviations of the liquid-phase and vapor-phase mole fractions are less than 1.0% and 2.0%, respectively. Moreover, the Vapor–Liquid Equilibrium data and the model’s adaptability are analyzed and discussed.

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39

Adachi, Yoshinori, and Hidezumi Sugie. "Effects of mixing rules on phase equilibrium calculations." Fluid Phase Equilibria 24, no. 3 (1985): 353–62. http://dx.doi.org/10.1016/0378-3812(85)85013-5.

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Thakre, Niraj, and Amiya K. Jana. "Modeling phase equilibrium with a modified Wong-Sandler mixing rule for natural gas hydrates: Experimental validation." Applied Energy 205 (November 2017): 749–60. http://dx.doi.org/10.1016/j.apenergy.2017.08.083.

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41

Zeng, Dan, Yang Li, and Tao Fang. "Production of Biodiesel in Supercritical Methanol and Related Correlation on Phase Equilibrium." Advanced Materials Research 560-561 (August 2012): 555–62. http://dx.doi.org/10.4028/www.scientific.net/amr.560-561.555.

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Biodiesel was prepared by methyl esterification and effects of different reaction conditions on the yield of fatty acid methyl esters (FAMEs) were investigated. The result of the orthogonal experiment analysis shows that the order of influential factors is ranked as reaction temperature > methanol-to-soybean-oil (M/O) ratio > reaction time. The maximum yield of 94.8 % has been achieved by reacting supercritical methanol and soybean oil in M/O ratio 4:2 (v/v) at 573 K for 45 min. Moreover, the higher M/O ratio, the higher yield of FAMEs will be obtained. At the temperature ranging from 533 k to 573 k, the yield rises significantly; however, since soybean oil decomposes over 573 K, the yield decreases oppositely. Time longer than 45 min has less effect on the final yield. In addition, the phase equilibrium data of supercritical methanol + C12 methyl esters and supercritical methanol + C18 methyl esters were separately correlated using the Peng-Robinson (PR) equation of state (EOS) with the Adachi-Sugie (AS) mixing rule.

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Williamson, J. Charles. "Liquid–Liquid Demonstrations: Phase Equilibria and the Lever Rule." Journal of Chemical Education 98, no. 7 (May 26, 2021): 2356–63. http://dx.doi.org/10.1021/acs.jchemed.0c01517.

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43

Kastanidis, Panagiotis, George E. Romanos, Athanasios K. Stubos, Georgia Pappa, Epaminondas Voutsas, and Ioannis N. Tsimpanogiannis. "Evaluation of a Simplified Model for Three-Phase Equilibrium Calculations of Mixed Gas Hydrates." Energies 17, no. 2 (January 16, 2024): 440. http://dx.doi.org/10.3390/en17020440.

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In this study, we perform an extensive evaluation of a simple model for hydrate equilibrium calculations of binary, ternary, and limited quaternary gas hydrate systems that are of practical interest for separation of gas mixtures. We adopt the model developed by Lipenkov and Istomin and analyze its performance at temperature conditions higher than the lower quadruple point. The model of interest calculates the dissociation pressure of mixed gas hydrate systems using a simple combination rule that involves the hydrate dissociation pressures of the pure gases and the gas mixture composition, which is at equilibrium with the aqueous and hydrate phases. Such an approach has been used extensively and successfully in polar science, as well as research related to space science where the temperatures are very low. However, the particular method has not been examined for cases of higher temperatures (i.e., above the melting point of the pure water). Such temperatures are of interest to practical industrial applications. Gases of interest for this study include eleven chemical components that are related to industrial gas-mixture separations. Calculations using the examined methodology, along with the commercial simulator CSMGem, are compared against experimental measurements, and the range of applicability of the method is delineated. Reasonable agreement (particularly at lower hydrate equilibrium pressures) between experiments and calculations is obtained considering the simplicity of the methodology. Depending on the hydrate-forming mixture considered, the percentage of absolute average deviation in predicting the hydrate equilibrium pressure is found to be in the range 3–91%, with the majority of systems having deviations that are less than 30%.

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Kornyushin, Yuri. "Studying thermodynamics of metastable states." Facta universitatis - series: Physics, Chemistry and Technology 3, no. 2 (2005): 115–28. http://dx.doi.org/10.2298/fupct0502115k.

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Simple classical thermodynamic approach to the general description of metastable states is presented. It makes it possible to calculate the explicit dependence of the Gibbs free energy on temperature, to calculate the heat capacity, the thermodynamic barrier, dividing metastable and more stable states, and the thermal expansion coefficient. Thermodynamic stability under mechanical loading is considered. The influence of the heating (cooling) rate on the measured dynamic heat capacity is investigated. A phase shift of the temperature oscillations of an ac heated sample is shown to be determined by the relaxation time of the relaxation of the metastable nonequilibrium state back to the metastable equilibrium one. This dependence allows one to calculate the relaxation time. A general description of the metastable phase equilibrium is proposed. Metastable states in AB3 alloys are considered. Reasons for the change from the diffusional mechanism of the supercritical nucleus growth to the martensitic one as the heating rate increases are discussed. The Ostwald stage rule is derived.

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Hansson, Per. "Volume Transition and Phase Coexistence in Polyelectrolyte Gels Interacting with Amphiphiles and Proteins." Gels 6, no. 3 (August 13, 2020): 24. http://dx.doi.org/10.3390/gels6030024.

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Polyelectrolyte gels have the capacity to absorb large amounts of multivalent species of opposite charge from aqueous solutions of low ionic strength, and release them at elevated ionic strengths. The reversibility offers the possibility to switch between “storage” and “release” modes, useful in applications such as drug delivery. The review focuses on systems where so-called volume phase transitions (VPT) of the gel network take place upon the absorption and release of proteins and self-assembling amphiphiles. We discuss the background in terms of thermodynamic driving forces behind complex formation in oppositely charged mixtures, the role played by cross-links in covalent gels, and general aspects of phase coexistence in networks in relation to Gibbs’ phase rule. We also briefly discuss a gel model frequently used in papers covered by the review. After that, we review papers dealing with collapse and swelling transitions of gels in contact with solution reservoirs of macroions and surfactants. Here we describe recent progress in our understanding of the conditions required for VPT, competing mechanisms, and hysteresis effects. We then review papers addressing equilibrium aspects of core–shell phase coexistence in gels in equilibrium. Here we first discuss early observations of phase separated gels and results showing how the phases affect each other. Then follows a review of recent theoretical and experimental studies providing evidence of thermodynamically stable core–shell phase separated states, and detailed analyses of the conditions under which they exist. Finally, we describe the results from investigations of mechanisms and kinetics of the collapse/swelling transitions induced by the loading/release of proteins, surfactants, and amphiphilic drug molecules.

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46

Ghent, Edward. "Metamorphic facies: A review and some suggestions for changes." Canadian Mineralogist 58, no. 4 (July 1, 2020): 437–44. http://dx.doi.org/10.3749/canmin.1900078.

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ABSTRACT The concept of metamorphic facies has been used as a tool in the interpretation of metamorphic rocks for almost 100 years. The preferred definition is a set of mineral assemblages which are repeatedly associated in space and time. Equilibrium or physical conditions (pressure-temperature) should not be part of the definition. The emphasis has always been on identification of the minerals with the petrographic microscope. Chemical analyses of the minerals using the electron microprobe is not necessary. The original definition of metamorphic facies used the metamorphic mineralogy of metabasic rocks. This bulk composition is not useful for the definition of all metamorphic facies. Several critical minerals in metabasic rocks cannot be readily identified with a petrographic microscope (albite versus oligoclase and actinolite versus hornblende). A revised set of metamorphic facies is proposed and mineral assemblages in both metabasic and pelitic rocks are outlined to provide definitions of the individual facies. Metamorphic facies should not be used to give quantitative estimates of P-T conditions. Only relative P-T can be estimated. The interpretation of “equilibrium” in metamorphic facies can be modeled using the Gibbs phase rule and simple assumptions about phases and components. This leads to an interpretation that metamorphic facies could represent divariant or higher variance equilibrium.

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Qin, Mingde, Heidy Vega, Dawei Zhang, Sarath Adapa, Andrew J. Wright, Renkun Chen, and Jian Luo. "21-Component compositionally complex ceramics: Discovery of ultrahigh-entropy weberite and fergusonite phases and a pyrochlore-weberite transition." Journal of Advanced Ceramics 11, no. 4 (March 8, 2022): 641–55. http://dx.doi.org/10.1007/s40145-022-0575-5.

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AbstractTwo new high-entropy ceramics (HECs) in the weberite and fergusonite structures, along with the unexpected formation of ordered pyrochlore phases with ultrahigh-entropy compositions and an abrupt pyrochlore-weberite transition, are discovered in a 21-component oxide system. While the Gibbs phase rule allows 21 equilibrium phases, 9 out of the 13 compositions examined possess single HEC phases (with ultrahigh ideal configurational entropies: ∼2.7kB per cation or higher on one sublattice in most cases). Notably, (15RE1/15)(Nb1/2Ta1/2)O4 possess a single monoclinic fergusonite (C2/c) phase, and (15RE1/15)3(Nb1/2Ta1/2)1O7 form a single orthorhombic (C2221) weberite phase, where 15RE1/15 represents Sc1/15Y1/15La1/15Pr1/15Nd1/15Sm1/15Eu1/15Gd1/15Tb1/15Dy1/15Ho1/15Er1/15Tm1/15 Yb1/15Lu1/15. Moreover, a series of eight (15RE1/15)2+x(Ti1/4Zr1/4Ce1/4H1/4)2−2x(Nb1/2Ta1/2)xO7 specimens all exhibit single phases, where a pyrochlore-weberite transition occurs within 0.75 < x < 0.8125. This cubic-to-orthorhombic transition does not change the temperature-dependent thermal conductivity appreciably, as the amorphous limit may have already been achieved in the ultrahigh-entropy 21-component oxides. These discoveries expand the diversity and complexity of HECs, towards many-component compositionally complex ceramics (CCCs) and ultrahigh-entropy ceramics.

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Maity, J., B. S. Poona, M. Kumar, A. Pal, B. Hazra, S. Sahin, and A. Biswas. "Quantitative hardness‐carbon content‐microstructure correlation in normalized plain carbon steel." Materialwissenschaft und Werkstofftechnik 54, no. 11 (November 2023): 1444–53. http://dx.doi.org/10.1002/mawe.202300146.

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AbstractComposition (carbon content) dependent critical structural evolution in correlation to hardness attained is judiciously investigated for plain carbon steel, the most widely used cost‐effective structural material, under normalizing treatment of industrial relevance involving non‐equilibrium still air cooling. The solid state phase transformation under non‐equilibrium still air cooling is conceived in terms of a logarithmic variation of eutectoid carbon content with the gross carbon content of steel in view of maintaining fixed maximum solubility of carbon in α‐iron with an assumption of the prevailing para‐equilibrium condition. Such a unique formulation for non‐equilibrium condition together with consideration of Hall–Petch type relationship and rule of mixture for two prime microconstituents (proeutectoid α‐ferrite and pearlite) finally results in a new mathematical relationship for chemical composition‐structure‐property correlation for the non‐equilibrium normalizing treatment readily practiced in industry. Indeed, a composition dependent structural refinement effect is established that is exemplified with the rise in hardness level in plain carbon steel under conventional normalizing treatment. Most importantly, the experimentally measured overall hardness values closely follow those obtained by the developed mathematical relationship, thereby meeting an ever‐needed requirement of direct determination of steel hardness of practical relevance from microstructural parameters.

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Poirier, Jacques. "Analysis and Interpretation of Microstructures after Liquid Oxide Corrosion." Advances in Science and Technology 70 (October 2010): 114–29. http://dx.doi.org/10.4028/www.scientific.net/ast.70.114.

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Corrosion by liquid oxides is one of the most severe modes of degradations which limit the lifetime of the refractory linings. The study of the microstructures of corroded refractories provides essential information. However, the interpretation of the microscopic observations is difficult : - The refractories are multi-component and heterogeneous ceramics, - The microscopic observations are carried out at room temperature. They are not representative of the mineral and vitreous phases existing at high temperature, - During cooling, new solid phases appear by crystallization of liquid oxides. The composition of the vitreous phases also evolves with the temperature. Consequently, the information obtained is often limited. In this paper , we will present a method to analyse and interpret the microstructures of refractories after use. The concept of local thermodynamic equilibrium and the use of the phase rule make it possible to interpret the microstructures of corroded refractories, to explain the observed mineral zonation and to quantify the composition of the liquid phase at high temperature from chemical profiles established by S.E.M. Experimental data from corrosion of MgO-C, Al2O3-MgO and high alumina refractories will illustrate and validate this theoretical approach.

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Sima, Sergiu, Adrian Victor Crişciu, and Catinca Secuianu. "Phase Behavior of Carbon Dioxide + Isobutanol and Carbon Dioxide + tert-Butanol Binary Systems." Energies 15, no. 7 (April 3, 2022): 2625. http://dx.doi.org/10.3390/en15072625.

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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.

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Journal articles on the topic 'Phase rule and equilibrium'

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