Search

Chemical potentials of the temperature components of the pyramid stepped basin solar distiller (PSBSD) have been evaluated to illustrate the behavior of the water vapor and condensed water droplets during the process of solar distillation. Chemical potential is one of the main criteria in terms of chemical and phase equilibrium which is obtained from the Gibbs phase rule. The application of the Gibbs phase rule established a good relationship between the design, climatic and experimental parameters of the PSBSD. The internal heat transfer coefficients of the distiller are influenced by the intensity of solar radiation and ambient temperature which in turn explains the intensive state of the PSBSD. It is found that the chemical potentials and the intensive states of the different phases of the system established a relation between the equilibrium of liquid and vapor mixture with specifications of temperature components of the PSBSD. It is also found that the efficiency of the PSBSD is 38.135% with a distillate yield of 4.280 l/m2day over 24 h cycle.

In the past decade, a literary phrase "No man's land" has been flooded in the scientific papers. The expression is used to describe a meta-stable region in the phase-diagram that cannot be accessed by experiments. It has been claimed based on the molecular dynamics (MD) simulation that there is a critical point, or the second critical point (SCP), in the "no man's land," and it has created a big dispute in the field of science. It is proved in the present paper that the hypothesis of SCP is completely against the rigorous theorem of thermodynamics, referred as the Gibbs phase rule. The reason why the simulations have found SCP erroneously is merely because the method violates the requirement which all the statistical-mechanics treatments should satisfy to reproduce the thermodynamics. That is the thermodynamic limit. It is clarified what is the identity of the "liquid-liquid phase transition" and SCP in pure liquids, discovered by the simulations and by some experiments. In order to explain the physics of liquid-liquid phase transition observed experimentally in single component liquids, a new concept is proposed. [ABSTRACT FROM AUTHOR]

In the past decade, a literary phrase “No man's land” has been flooded in the scientific papers. The expression is used to describe a meta-stable region in the phase-diagram that cannot be accessed by experiments. It has been claimed based on the molecular dynamics (MD) simulation that there is a critical point, or the second critical point (SCP), in the “no man's land,” and it has created a big dispute in the field of science. It is proved in the present paper that the hypothesis of SCP is completely against the rigorous theorem of thermodynamics, referred as the Gibbs phase rule. The reason why the simulations have found SCP erroneously is merely because the method violates the requirement which all the statistical-mechanics treatments should satisfy to reproduce the thermodynamics. That is the thermodynamic limit. It is clarified what is the identity of the ``liquid-liquid phase transition'' and SCP in pure liquids, discovered by the simulations and by some experiments. In order to explain the physics of liquid-liquid phase transition observed experimentally in single component liquids, a new concept is proposed.

Swelling behavior of polyacrylamide gels in water/acetonitrile system is examined. The linear swelling ratio of the gels decreases with increasing temperature when the water content of the mixtures is low but increases with increasing temperature for the gel in pure water. At high temperatures, the swelling ratio increases with increasing water content of the mixtures. On the other hand, swelling ratio at low temperatures shows interesting behavior: The temperature dependence curves of the linear swelling ratio became convergent for the gels in the mixed solvents, and the data points obtained in the phase-separated circumstances are well superimposed to form a single curve, which can be explained by the Gibbs phase rule. A drastic change occurs in solvent composition inside the gel as well as in the gel volume by cooling, which corresponds to a crossover from collapsed to swollen state of the polymer gels. [ABSTRACT FROM AUTHOR]

A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume–Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.

• A derivative of a density with respect to a field diverges at the critical point. • This phenomenon includes all known binary liquid mixtures with a critical point. • Phase rule predicts isomorphism of physical and chemical critical point properties. The isobaric heat capacity and the coefficient of thermal expansion of a binary liquid mixture with a critical point of solution diverge as functions of temperature in the critical region. When the same liquids are used as solvents for chemical reactions, the van't Hoff plot of the extent of reaction diverges in the critical region. According to the phase rule, the physical and chemical properties are isomorphic in the sense that in each case the critical behavior is determined by three fixed thermodynamic intensive variables. [ABSTRACT FROM AUTHOR]

All thermodynamic quantities fluctuate. Understood since Gibbs in the 19th century, thermodynamic fluctuations are flickering microscopic exceptions to the first and second laws of thermodynamics: For brief moments, energy is not conserved and entropy spontaneously decreases. This paper revisits and deepens my original research, published in Infinite Energy in 2012, where I found that the second law of thermodynamics is not strictly valid at the macroscale for simple electrochemical cells using aqueous electrolytes: The coupling of the discrete physical properties of solute-cluster fluctuations to static gravitational or magnetic fields is the key dynamic bringing microscopic energy fluctuations to macroscale viability. Here I report that neither the first nor second laws of thermodynamics hold strictly true for the electrochemical systems. Those flickers of gravitational and magnetic energies spontaneously arise de novo in our universe and, as reported previously, they prefigure a viable source of primal infinite energy--a nascent and other thermodynamic domain of nature. [ABSTRACT FROM AUTHOR]

Graphical abstract Abstract Solvent-based liquid-liquid extraction and stripping is the key separation method at the basis of all hydrometallurgical processes, such as those used to retrieve strategic metals from ores or waste material. During formulation of an efficient extraction system, chemical engineers often encounter instabilities and the formation of undesired phases. In order to avoid the appearance of those in practice, we propose a simple and convenient approach of the phase diagram, based on mole ratio of cations as the variable that controls interfacial curvature. The proposed formulator's cut through the Gibbs phase prism is more adapted than fish-cuts or similar ones in the case of extraction and stripping formulation optimized against variation in the feed composition. [ABSTRACT FROM AUTHOR]

Active systems can produce a far greater variety of ordered patterns than conventional equilibrium systems. In particular, transitions between disorder and either polar- or nematically ordered phases have been predicted and observed in two-dimensional active systems. However, coexistence between phases of different types of order has not been reported. We demonstrate the emergence of dynamic coexistence of ordered states with fluctuating nematic and polar symmetry in an actomyosin motility assay. Combining experiments with agent-based simulations, we identify sufficiently weak interactions that lack a clear alignment symmetry as a prerequisite for coexistence. Thus, the symmetry of macroscopic order becomes an emergent and dynamic property of the active system. These results provide a pathway by which living systems can express different types of order by using identical building blocks. [ABSTRACT FROM AUTHOR]

The melting behavior of three linear polyethylene fractions with number average molecular weights of 11, 29, and 100.5 kg/mol was studied as a function of crystallization time with conventional and ultra-fast calorimetry. The initial melting temperatures of non-thickened lamellae formed under isothermal conditions over a range of crystallization temperatures were analyzed with the non-linear Hoffman-Weeks method to determine the equilibrium melting temperature. T m e q values of 138.4 ± 0.9 °C , 139.7.4 ± 0.9 °C , and 140.9 ± 0.8 °C were estimated for PE 11K, PE 29K, and PE 100K, respectively, in close agreement with those reported in the literature for the melting of extended-chain crystals or with the Gibbs-Thomson analysis. The Lauritzen-Hoffman theory and the non-linear Hoffman-Weeks treatment were modified to account for the effect of the tilt angle, θ , of the crystallized stems of linear polyethylene on the initial average lamellar thickness. Accuracy of the non-linear Hoffman-Weeks method was examined using initial lamellar thickness, ℓ g ∗ , data reported for PE 29K in the literature at different crystallization temperatures. The equilibrium melting temperature obtained by the Gibbs-Thomson approach and the C 2 value extracted from the ℓ g ∗ vs. 1 / Δ T plot were similar within the limits of experimental error to those obtained here through the non-linear Hoffman-Weeks method. Using the Huggins equation, the equilibrium melting temperature of an infinitely long linear polyethylene chain is found to be equal to 141.4 ± 0.8 °C , the same value proposed by Wunderlich. [ABSTRACT FROM AUTHOR]

According to Gibbs phase rule, ternary two phase alloys have a single degree of freedom at equilibrium at a given temperature. Thus, multiple precipitate-matrix equilibrium compositions are possible at the interface. From Philippe-Voorhees’ (PV) theory (Philippe and Voorhees, 2013), it is known that during coarsening in multicomponent alloys, precipitate-matrix compositions at the interface during coarsening are not just dependent on the Gibbs-Thomson effect but also on the relative mobilities of the solute elements. Our computer simulations, based on a phase field model, show that this effect of different solute diffusivities on size-dependent particle composition is more pronounced in alloys richer in the slower diffusing solute. [ABSTRACT FROM AUTHOR]

Silicate slag system with additions Nb and RE formed in the utilization of REE-Nb-Fe ore deposit resources in China has industrial uses as a metallurgical slag system. The lack of a phase diagram, theoretical, and thermodynamic information for the multi-component system restrict the comprehensive utilization process. In the current work, solid phase equilibrium relations in the CaO-SiO-NbO-LaO quaternary system at 1273 K (1000 °C) were investigated experimentally by the high-temperature equilibrium experiment followed by X-ray diffraction, scanning electron microscope, and energy dispersive spectrometer. Six spatial independent tetrahedron fields in the CaO-SiO-NbO-LaO system phase diagram were determined by the Gibbs Phase Rule. The current work combines the mass fraction of equilibrium phase and corresponding geometric relation. A determinant method was deduced to calculate the mass fraction of equilibrium phase in quaternary system according to the Mass Conservation Law, the Gibbs Phase Rule, the Lever's Rule, and the Cramer Law. [ABSTRACT FROM AUTHOR]

Incorporating multicomponent, multiphase, complex chemical equilibrium calculations into process and multiphysics models can provide significant insights into industrial processes that current modelling or measurements cannot. Equilibrium calculations are however, in general, omitted or incorporated in a simplified manner due to their computational expense. Several methods have been developed to accelerate these calculations. A new accelerator algorithm was developed (Roos and Zietsman, 2021) based on phase diagram geometry, the Gibbs phase rule, and the lever rule to include equilibrium calculations into models more efficiently. This framework of established thermochemical theory provides a sound basis for discretisation and interpolation, and allows the accelerator algorithm to work in systems with any number of components. The work presented here aimed to test accelerator performance and demonstrate that it has the capability of achieving noteworthy levels of acceleration while maintaining acceptable accuracy. The accelerator was tested on ten 2-component systems, four 3-component systems, a simplified 4-component ilmenite smelting system, and a simplified 5-component iron- and steelmaking system. As the number of system components increased, so did the computational expense of direct equilibrium calculations. This translated to larger acceleration factors for higher-order systems — from 20 in 2-component systems to 1000 in the 5-component system. In a small number of cases it was observed that the acceleration factor was smaller than one during interpolation. This was attributed to slow searching times for suitable interpolation cells from the database. Phase composition interpolation errors are less than 1 × 10-2 mol mol−1. This translates to an interpolated phase composition being accurate to within 99 % of the calculated composition and results in phase fraction errors of 1 × 10-2 and less. In a very small number of cases the interpolation errors made on physical and thermochemical properties are as high 10 %. This is because system properties are calculated as a phase fraction weighted sum of phase properties and errors made on system properties can therefore become large due to interpolation errors being made twice. However, the majority of errors made on physical and thermochemical properties are in the order of 1 % and less. The level of accuracy achieved by the accelerator algorithm was acceptable for the chosen discretisation tolerances. [ABSTRACT FROM AUTHOR]

This paper describes some underlying principles of multicomponent and high entropy alloys, and gives some examples of these materials. Different types of multicomponent alloy and different methods of accessing multicomponent phase space are discussed. The alloys were manufactured by conventional and high speed solidification techniques, and their macroscopic, microscopic and nanoscale structures were studied by optical, X-ray and electron microscope methods. They exhibit a variety of amorphous, quasicrystalline, dendritic and eutectic structures.

There are two main theoretical frameworks in statistical mechanics, one associated with Boltzmann and the other with Gibbs. Despite their well-known differences, there is a prevailing view that equilibrium values calculated in both frameworks coincide. We show that this is wrong. There are important cases in which the Boltzmannian and Gibbsian equilibrium concepts yield different outcomes. Furthermore, the conditions under which equilibriums exists are different for Gibbsian and Boltzmannian statistical mechanics. There are, however, special circumstances under which it is true that the equilibrium values coincide. We prove a new theorem providing sufficient conditions for this to be the case. [ABSTRACT FROM AUTHOR]

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the 'fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the 'fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying 'fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors. [ABSTRACT FROM AUTHOR]

In high-temperature coatings, welded parts, and a range of other applications, components in the contact zone interdiffuse at elevated temperatures and may react to change the phase composition. The diffusion zone can be complex and can consist of sequential layers of intermediate phases, solid solutions, and in the case of multicomponent systems also of multiphase layers. In this work, the interdiffusion in Ni-Cr-Al alloys is studied experimentally and modeled numerically. The diffusion multiples were prepared by hot isostatic pressing and post-annealing at 1473 K (1200 °C). The concentration profiles were measured with wide-line EDS technique which allowed obtaining high-accuracy diffusion paths. The experimental profiles and diffusion paths were compared with numerical results simulated with application of very recent model of interdiffusion in muticomponent-multiphase systems. The calculated and experimental data show good agreement. [ABSTRACT FROM AUTHOR]

The study of surfactant adsorption kinetics at a gas-liquid interface has essentially been built with the Gibbs adsorption equation. A simple one-parameter adsorption equation without using the Gibbs adsorption equation was proposed and tested on surfactants C 14 TAB and C 16 TAB [Phan et al., Colloids Surfaces A 406 (2012) 24 and Langmuir 29 (2013) 4743] to describe equilibrium surface tension. The applicability of this one-parameter adsorption equation was examined in this study. Theoretical equilibrium surface tension (ST) of nonionic and ionic surfactants generated from the Langmuir and Frumkin isotherms and several sets of experimental ST data were compared with the one-parameter adsorption equation. This study demonstrates that this one-model adsorption equation predicts the equilibrium ST of the aqueous surfactant solutions well following: (i) the nonionic Langmuir isotherm with Γ ∞ ∼ 20 × 10 −10 mol/cm 2 or (ii) the nonionic Frumkin isotherm with a specific correlation between maximum surface concentration and intermolecular interaction, K = 0.12 (Γ ∞ × 10 10 ) − 2.6. It is concluded from this study that the one-parameter adsorption equation is not a general predictive model and cannot describe general equilibrium ST data except under the above conditions. [ABSTRACT FROM AUTHOR]

High-entropy alloys (HEAs) have many attractive properties, while the thermodynamic mechanism and general behavior of the spinodal decomposition in HEAs remain unknown. In this work, we conduct an experimentally consistent calculation of the spinodal decomposition of HEAs. Against the "high mixing entropy" theory, we show that increasing the number of elements can increase the possibility of spinodal decomposition, and the effects of the temperature, entropy and enthalpy are clarified. The high entropy effect on the widely observed pseudo-binary decomposition is proposed. These results provide a necessary paradigm to understand and further harness the spinodal decomposition in HEAs. [Display omitted] [ABSTRACT FROM AUTHOR]

Natural gas hydrates (NGHs) in nature are formed from water and hydrate formers from various phases (i.e., aqueous, gas, and adsorbed phases). As a result, owing to Gibbs’ phase rule and the combined first and second laws of thermodynamics, CH 4 hydrates cannot reach thermodynamic equilibrium in real reservoir conditions. Thus, there is a competition between hydrate formers, where the most stable hydrates form first. The non-equilibrium nature of hydrates indicates a need for proper kinetic models to describe the various routes that can lead to hydrate formation. Dissociation of hydrates in sediments can also occur as a function of undersaturation of any of the thermodynamic variables. In addition to temperature and pressure being outside the stability region for hydrates, the concentration of water and hydrate formers in co-existing phases can lead to hydrate instability. CH 4 hydrate dissociation towards CH 4 gas and water has previously been implemented using the RetrasoCodeBright (RCB) hydrate simulator. In the present work, we implement an additional route for hydrate phase transitions that enables hydrate dissociation and reformation towards water and aqueous CH 4 and by considering undersaturation or supersaturation with respect to pressure, temperature, and CH 4 mole fraction. CH 4 hydrate dissociation in contact with water undersaturated with methane is considered, as well. An in-house non-equilibrium thermodynamic package has been written and is inserted into RCB to calculate Gibbs free energies. The driving forces for hydrate phase transitions are calculated from differences in the free energies of hydrates and hydrate formers. Competing phase transitions are handled by Gibbs free energy minimizations. Nucleation theory is used to calculate the impact of heat and mass transport and of non-equilibrium thermodynamics on kinetic rates of hydrate phase transitions. Our modifications are used to simulate CH 4 production, covering time spans of 290 days using the depressurization method on a simplified hypothetical model. A complete description of our methodology is presented together with a discussion of our simulation results. [ABSTRACT FROM AUTHOR]

The influence of additives (alkyl polyglucoside, Glucopon 600 CS UP and alcohol ethoxylate C18E100) on the behavior of the water/toluene/Lutensol ON 50 (technical oxoalcohol, i-C10E5) microemulsion system as a function of temperature and composition has been investigated. The phase behavior of the microemulsions was determined by vertical sections through the Gibbs phase prism (fish-like phase diagrams). Alkyl polyglucoside shifts the one phase region to lower temperatures compared with water/toluene/Lutensol ON 50 mixtures. This is contrary to the expectation, considering the extreme hydrophilic nature of the sugar headgroup. The addition of hydrophilic alcohol ethoxylate (C18E100) to the water/toluene/Lutensol ON 50 system increases the solubilization capacity of the surfactant, even if the co-surfactant is used in small quantities, and shifts the one-phase region to higher temperature by a few °C. [ABSTRACT FROM AUTHOR]

Since Pourbaix presented Eh versus pH diagrams in his "Atlas of Electrochemical Equilibria in Aqueous Solution", diagrams have become extremely popular and are now used in almost every scientific area related to aqueous chemistry. Due to advances in personal computers, such diagrams can now show effects not only of Eh and pH, but also of variables, including ligand(s), temperature and pressure. Examples from various fields are illustrated in this paper. Examples include geochemical formation, corrosion and passivation, precipitation and adsorption for water treatment and leaching and metal recovery for hydrometallurgy. Two basic methods were developed to construct an Eh-pH diagram concerning the ligand component(s). The first method calculates and draws a line between two adjacent species based on their given activities. The second method performs equilibrium calculations over an array of points (500 × 800 or higher are preferred), each representing one Eh and one pH value for the whole system, then combines areas of each dominant species for the diagram. These two methods may produce different diagrams. The fundamental theories, illustrated results, comparison and required conditions behind these two methods are presented and discussed in this paper. The Gibbs phase rule equation for an Eh-pH diagram was derived and verified from actual plots. Besides indicating the stability area of water, an Eh-pH diagram normally shows only half of an overall reaction. However, merging two or more related diagrams together reveals more clearly the possibility of the reactions involved. For instance, leaching of Au with cyanide followed by cementing Au with Zn (Merrill-Crowe process) can be illustrated by combining Au-CN and Zn-CN diagrams together. A second example of the galvanic conversion of chalcopyrite can be explained by merging S, Fe-S and Cu-Fe-S diagrams. The calculation of an Eh-pH diagram can be extended easily into another dimension, such as the concentration of a given ligand, temperature or showing the solubility of stable solids. A personal computer is capable of drawing the diagram by utilizing a 3D program, such as ParaView, or VisIt, or MATLAB. Two 3D wireframe volume plots of a Uranium-carbonate system from Garrels and Christ were used to verify the Eh-pH calculation and the presentation from ParaView. Although a two-dimensional drawing is still much clearer to read, a 3D graph can allow one to visualize an entire system by executing rotation, clipping, slicing and making a movie. [ABSTRACT FROM AUTHOR]

The knowledge of vapour-liquid equilibrium (VLE) and thermodynamic properties plays a pivotal role in the process development of absorption systems for acid gas capture in precombustion and postcombustion streams. A large number of thermodynamic modelling approaches for acid gas absorption in aqueous alkanolamine solutions are published in the literature. However, the reviews of these modelling techniques are limited and scattered. Moreover, poor guidelines exist for the selection of an appropriate modelling approach for the VLE prediction of the aforementioned system. Therefore, the current study presents a concise classification and review of classical thermodynamic models for acid gas absorption in aqueous alkanolamine solutions since their inception. The article systematically details the chronological development and highlights the major capabilities and limitations of classical thermodynamic approaches, namely, semiempirical models, activity coefficient models, and equation of state (and equation of state/excess Gibbs energy) models. A graphical comparison of VLE prediction by each classical approach is presented to form a general guideline in the selection of a suitable approach for process development studies. The review precisely discusses the issues, challenges, and future prospects of each classical thermodynamic approach in the context of application, complexity, and development. [ABSTRACT FROM AUTHOR]

An example of a Gibbs ensemble for a system of N Brownian particles is given, and the relation with Kolmogorov complexity is considered. The irreversibility of the process is analyzed and shown to be a consequence of the loss of numbering of the particles. The dependence of the measure in the semiclassicalGibbs distribution on temperature is studied in examples. [ABSTRACT FROM AUTHOR]

Copyright of Scientific Journal of National University of Life & Environmental Sciences of Ukraine. Series: Technique & Energy of APK is the property of National University of Life & Environmental Sciences of Ukraine and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The melting temperature of a nanoscaled particle is known to decrease as the curvature of the solid-melt interface increases. This relationship is most often modelled by a Gibbs-Thomson law, with the decrease in melting temperature proposed to be a product of the curvature of the solid-melt interface and the surface tension. Such a law must break down for sufficiently small particles, since the curvature becomes singular in the limit that the particle radius vanishes. Furthermore, the use of this law as a boundary condition for a Stefan-type continuum model is problematic because it leads to a physically unrealistic form of mathematical blow-up at a finite particle radius. By numerical simulation, we show that the inclusion of nonequilibrium interface kinetics in the Gibbs-Thomson law regularises the continuum model, so that the mathematical blow up is suppressed. As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time. The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles. This small-particle regime appears to be closely related to the problem of melting a superheated particle. [ABSTRACT FROM AUTHOR]

Most hydrate that forms or dissociates are in situations of constant non-equilibrium. This is due to the boundary conditions and Gibbs Phase rule. At a minimum this leaves a hydrate with two adsorbed phases in addition to hydrate and fluids. One adsorbed phase is governed by the mineral surfaces and the other by the hydrate surface. With pressure and temperature defined by local conditions, hydrate formation will never be able to reach any state of equilibrium. The kinetics of hydrate formation and dissociation are a complex function of competing phase transitions. This requires kinetic theories that include minimization of free energy under constraints of mass and energy transport. Since phase transitions also change density, further constraints are given by fluid dynamics. In this work, we describe a new approach for non-equilibrium theory of hydrates together with a Phase Field Theory for simulation of phase transition kinetics. We choose a three component system of water, methane and carbon dioxide for illustration. Conversion of methane hydrate into carbon dioxide hydrate is a win–win situation of energy production combined with safe long term storage of carbon dioxide. Carbon dioxide is able to induce and proceed with a solid-state exchange, but is slow due to mass transport limitations. A faster process is the formation of new hydrate from injected carbon dioxide and residual pore water. This formation releases substantial heat. This assists in dissociating in situ methane hydrate, making the conversion progress substantially faster, because heat transport is very rapid in these systems. But conversion of liquid water into carbon dioxide hydrate, in the vicinity of the hydrate core will increase temperatures to some portions of the surface. The dissociating regions of the methane hydrate core will show a local decrease in temperature, due to extraction of heat for methane hydrate dissociation from surroundings. Another reason for heat transport implementation is that regions of the system that contains non-polar gas phase will have low heat conductivity and low heat convection. At this stage we apply a simplified heat transport model in which “lumped” efficient heat conductivity is used. We illustrate the theory on the conversion of methane hydrate to mix methane–carbon dioxide hydrate using three initial hydrate sizes: 150 Å × 150 Å, 500 Å × 500 Å and 5000 Å × 5000 Å. The hydrate cores used are spherical because it makes it easier to illustrate the impact of curvature. Symmetrical aspects simplifies the dependency to a two dimensional problem – although there are no such limitations in theory. The mineral surfaces are considered to be water wetting in these examples. It was observed that the smaller sizes convert to a more unstable mix hydrate for some periods of the simulation time, during which there were significant losses of the initial methane hydrate core. These instabilities are caused by local under saturated fluid phases around the hydrate core. Eventually a steady state progress was observed. The largest size system appeared to reach a steady state situation comparable faster than the two smaller systems. [ABSTRACT FROM AUTHOR]

A new accelerator algorithm was developed based on phase diagram geometry to include large number of equilibrium calculations into process and multiphysics models more efficiently. These models require thermochemical properties from equilibrium calculations such as phase compositions and phase fractions, heat capacity and enthalpy. When an equilibrium calculation is performed, the calculated thermochemical properties are stored in a geometrical database on the boundaries of the phase region at the calculated phase compositions. The developed accelerator can function with any commercial or open source equilibrium calculation software. In this work, ChemAppPy was used. The lever rule can be used to interpolate thermochemical properties at any system composition within a phase region based on thermochemical properties stored on the phase region's boundaries. It is therefore only necessary to discretise boundaries and not entire phase regions, except for single-phase regions. A generic form of the lever rule is presented that can be used in any phase region and in systems with any number of system components. The Gibbs phase rule is used to calculate the dimensionality of phase region boundaries and to determine the minimum number of equilibrium calculations needed to discretise these boundaries. This framework of established thermochemical theory provides a sound basis for the discretisation and interpolation routines of the algorithm and allows the accelerator to be used with systems with any number of components. The functionality of the accelerator algorithm was tested in a number of two- and three-component systems as these systems could still be easily visualised to verify the functioning of the newly developed algorithm. [ABSTRACT FROM AUTHOR]

Highlights: [•] This shows how to find a limit size below which micro methods are needed; above, macro methods apply. [•] The lower size limit for applicability of the Gibbs Phase Rule illustrates application of the method. [•] The method can be generalized to other phenomena, as suggested. [Copyright &y& Elsevier]

An integration by parts formula is derived for the first-order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on ℝd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime. [ABSTRACT FROM AUTHOR]

A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume–Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points. [ABSTRACT FROM AUTHOR]

Phase equilibria in ternary systems ionic surfactant—long chain alcohol—water are discussed in relation to Per Ekwall's pioneering contributions to the field. It is described how modeling of the thermodynamic behavior leads to a better understanding of what molecular interactions cause the rich phase behavior of these systems. [ABSTRACT FROM AUTHOR]

The thermodynamic behavior of multicomponent, elastic, crystalline solids is developed, including Euler''s equation, the Gibbs equation, the Gibbs–Duhem equation, the conditions to be expected at equilibrium including a new description of stress-deformation behavior, and an extension of the Gibbs phase rule. The predictions of the phase rule are compared with two types of experimental observations including the ten triple points of water. [Copyright &y& Elsevier]

We consider extended Pirogov–Sinai models including lattice and continuum particle systems with Kac potentials. Call λ an intensive variable conjugate to an extensive quantity α appearing in the Hamiltonian via the additive term -λα. We suppose that a Pirogov–Sinai phase transition with order parameter α occurs at λ=0, and that there are two distinct classes of DLR measures, the plus and the minus DLR measures, with the expectation of α respectively positive and negative in the two classes. We then prove that λ=0 is the only point in an interval I of values of λ centered at 0 where this occurs, namely the expected value of α is positive, respectively negative, in all translational invariant DLR measures at {λ>0}⊓I and {λ<0}⊓I. [ABSTRACT FROM AUTHOR]

A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume-Capel models, as well as q -state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.

The article focuses on formulation related to the convergence to invariant Gibbs measure. It outlines the phase space with N degrees of freedom, the subset of phase space L, and the classes of Hamiltonian systems. It states that the generalized Gaussian process with the white noise with covariance was distinguished, and the stationary Gaussian process with zero mean and covariance was also considered.