Liquid-vapor Coexistence Curve Research Articles

Using the Zeno line to assess and refine molecular models.

The Zeno line is the locus of points on the temperature-density plane where the compressibility factor of the fluid is equal to one. It has been observed to be straight for a broad variety of real fluids, although the underlying reasons for this are still unclear. In this work, a detailed study of the Zeno line and its relation to the vapor-liquid coexistence curve is performed for two simple model pair-potential fluids: attractive square-well fluids with varying well-widths λ and Mie n-6 fluids with different repulsive exponents n. Interestingly, the Zeno lines of these fluids are curved, regardless of the value of λ or n. We find that for square-well fluids, λ ≈ 1.8 presents a Zeno line, which is the most linear over the largest temperature range. For Mie n-6 fluids, we find that the straightest Zeno line occurs for n between 8 and 10. Additionally, the square-well and Mie fluids with the straightest Zeno line showed the closest quantitative agreement with the vapor-liquid coexistence curve for experimental fluids that follow the principle of corresponding states (e.g., argon, xenon, krypton, methane, nitrogen, and oxygen). These results suggest that the Zeno line can provide a useful additional feature, in complement to other properties, such as the phase envelope, to evaluate molecular models.

The Influence of Wettability Effect and Adsorption Thickness on Nanoconfined Methane Phase Behavior: Vapor-Liquid Co-Existence Curves and Phase Diagrams

Research interest in the behavior of methane inside nanopores has been growing, driven by the substantial geological reserves of shale gas and coalbed methane. The phase diagram of methane in nanopores differs significantly from its bulk state, influencing its existing form and pertinent physical properties—such as density and viscosity—at specific pressures and temperatures. Currently, there is a lack of effort to understand the nanoconfinement effect on the methane phase diagram; this is a crucial issue that needs urgent attention before delving into other aspects of nanoconfined methane behavior. In this study, we establish a fully coupled model to predict the methane phase diagram across various scales. The model is based on vapor-liquid fugacity equilibrium, considering the shift in critical pressure and temperature induced by pore size shrinkage and adsorption-phase thickness. Notably, our proposed model incorporates the often-overlooked factor of capillary pressure, which is greatly amplified by nanoscale pore size and the presence of the adsorption phase. Additionally, we investigated the impact of surface wettability, correlated to capillary pressure and the shift in critical properties, on the methane phase diagram. Our results indicate that (a) as pore size decreases, the methane phase diagram becomes more vertical, suggesting a transition from a gaseous to a liquid state for some methane molecules, which is contrary to the conventional phase diagram; (b) enhancing surface wettability results in a more vertical phase diagram, with the minimum temperature corresponding to 0 MPa pressure on the phase diagram, increasing by as much as 87.3%; (c) the influence of capillary pressure on the phase diagram is more pronounced under strong wettability conditions compared to weak wettability, and the impact from the shift in critical properties can be neglected when the pore size exceeds 50 nm.

Assessment of the pseudopotential lattice-Boltzmann method for modeling multiphase fuel droplets

An improved pseudopotential lattice–Boltzmann model was proposed for simulating multiphase flow dynamics to describe fuel droplets, and its thermodynamic consistency was tested against the Peng–Robinson equation of state. The studied liquid fuels included paraffinic hydrocarbons with a different number of carbon atoms (C[Formula: see text]–C[Formula: see text]), methanol (CH[Formula: see text]OH), hydrogen (H[Formula: see text]), ammonia (NH[Formula: see text]), and water (H[Formula: see text]O). To improve accuracy and reduce the magnitude of the spurious currents, the multi-relaxation times collision operator was implemented and the forcing term was computed using the hybrid pseudopotential interaction force with an eighth-order isotropic degree. The pseudopotential lattice–Boltzmann model accurately predicted the equilibrium densities and captured satisfactorily the thermodynamic vapor-liquid coexistence curve given by the analytical solution of the Peng–Robinson equation of state for acentric factors ranging from [Formula: see text]0.22 to 0.56, keeping the maximum average error for the liquid and vapor branches below 0.8% and 3.7%, respectively. Nevertheless, Peng–Robinson was found to be insufficiently accurate to replicate the actual thermodynamic state, especially for H[Formula: see text]O and CH[Formula: see text]OH, for which the results strongly deviated from the experimental vapor-liquid equilibrium densities and reached average errors for the vapor phase of nearly 28%. Furthermore, the surface tension ([Formula: see text]) was retrieved using the multiphase pseudopotential lattice–Boltzmann results and served to verify the thermodynamic consistency of the pseudopotential lattice–Boltzmann with respect to the parachor model. Lastly, the pseudopotential lattice–Boltzmann model was also shown to predict accurately the transient behavior of oscillating droplets. Overall, the enhanced model satisfactorily predicted the properties and behavior of the substances for a wide range of conditions.

High-order modeling of multiphase flows: Based on discrete Boltzmann method

The high-order kinetic model for compressible multiphase flow is presented within the framework of the discrete Boltzmann method (DBM). Based on the Carnahan–Starling state equation, this model can describe the phase transition by introducing a source term of molecular interaction on the right-hand side of the Boltzmann equation. Meanwhile, the force term is incorporated to describe the external force. Through Hermite polynomial expansion, the equilibrium distribution function is expressed. Compared to the Navier–Stokes equations, the DBM provides more detailed and accurate information on both hydrodynamic and thermodynamic non-equilibrium effects. Finally, the model is verified through several typical benchmarks, including the liquid–vapor coexistence curve, free-falling process, shock wave, sound wave, thermal phase separation, and two-bubble oblique collision.

Molecular simulations of the vapour-liquid coexistence curve of square-well dimer fluids

In this work, we evaluate the liquid-vapour coexistence diagram and the critical point for two different ranges, and of the square-well dimer fluid, using two different simulation methods: (1) In the critical point vicinity, we use a new algorithm, based on transition rates, that can obtain the chemical potential as a function of the density at a given temperature and (2) Molecular Dynamics simulations using the direct coexistence technique for temperatures far below the critical region. The transition rate method has been proposed by Sastre and was used for the evaluation of the critical temperature of square-well monomers with high accuracy. The simulations in the low-temperature region were carried out using molecular dynamics simulations with the direct coexistence method and a continuous version of the square-well potential proposed recently by Zerón et al.

Behavior of the fullerene/water system under liquid and liquid–vapor conditions: A molecular dynamics approach

Classical molecular dynamics simulations were carried out to quantify the behavior of fullerenes in water, under liquid phase and liquid–vapor conditions. Different molalities of fullerene were considered in the study. Radial distribution functions, static dielectric constant and equation of state were evaluated in liquid phase. Direct liquid–vapor coexistence simulations of water with fullerene added were conducted to explore density profiles, liquid–vapor coexistence curve, pressure tensor components and surface tension variations with respect to water. An all-atom fullerene model studied by Monticelli and the SPC/ɛ description of water were used. At ambient conditions fullerene–fullerene and fullerene-water correlations decreased as molality increased. In turn, the static dielectric constant decreased due that fullerenes hinder the dipolar orientation of water molecules. As temperature increased, the static dielectric constant lowered. Part of the study was conducted at 373 K from 10 to 24 kbar, revealing that density of the system increased as molality was higher while fullerene-fullerene correlations decreased and fullerene-water correlations increased slightly. Concerning the static dielectric constant, a decrease was observed due that fullerenes and fullerene aggregates disturbed water structure as molality increased. As the system is compressed at a fixed molality, fullerenes become more uniformly distributed and the dielectric constant increases. Therefore, increasing the pressure is a mechanism to force the dipolar orientation of water molecules. On the other hand, liquid–vapor coexistence was studied from 280 to 650 K using molalities from 0.037 to 0.695 mol/kg. Liquid–vapor simulations revealed that the location of fullerenes and the formation of aggregates affect the behavior of surface tension. Fullerenes can locate at the liquid–vapor interfaces forming aggregates that obstruct the pass of water molecules to the vapor, so surface tension increases slightly with respect to water. At 0.695 mol/kg, larger clusters were observed but they located predominantly within the liquid phase and therefore acted in the opposite direction, that is, they favored the migration of water molecules to the vapor and surface tension dropped. In addition, a peculiar behavior was observed for temperatures above 500 K: surface tension increased its value as temperature increased. This behavior could be attributed to the fact that at such high molality the calculated surface tension might not longer correspond to liquid–vapor interfaces, instead it could be related to a sort of solid–liquid interface that have formed into the system. These calculations set the basis for improving the description of fullerene/water interactions as more experimental information becomes available and also serve as reference data in the design of interaction parameters to model water-soluble fullerenes.

Liquid-vapor equilibrium and critical point of parabolic-well fluids of variable width derived from Gibbs Ensemble Monte Carlo simulation

The vapor-liquid coexistence curve at equilibrium of parabolic-well (PW) fluids is computed by means of Monte Carlo simulations, for a selection of well-widths. The outcome is compared with results for corresponding curves of triangle-well (TW) and square-well (SW) fluids with the same range. It is found that, for a given width, the shape of the vapor-liquid coexistence curve in the case of the parabolic-well fluid is rather similar to the one of the triangular-well fluid and a little bit different to the one of the square-well fluid. It is also found that such vapor-liquid coexistence curve shifts towards higher temperatures as the width of the parabolic-well potential increases, always falling, for the same range in all cases, between the vapor-liquid coexistence curves corresponding to the other two potentials. In addition, it was observed that the reduced critical temperature matches the theoretical prediction of the Vliegenthart and Lekkerkerker (V-L) criterion only for the smaller well-width, the accuracy of such criterion decreasing substantially as the range increases.

MoSDeF-GOMC: Python Software for the Creation of Scientific Workflows for the Monte Carlo Simulation Engine GOMC.

MoSDeF-GOMC is a python interface for the Monte Carlo software GOMC to the Molecular Simulation Design Framework (MoSDeF) ecosystem. MoSDeF-GOMC automates the process of generating initial coordinates, assigning force field parameters, and writing coordinate (PDB), connectivity (PSF), force field parameter, and simulation control files. The software lowers entry barriers for novice users while allowing advanced users to create complex workflows that encapsulate simulation setup, execution, and data analysis in a single script. All relevant simulation parameters are encoded within the workflow, ensuring reproducible simulations. MoSDeF-GOMC's capabilities are illustrated through a number of examples, including prediction of the adsorption isotherm for CO2 in IRMOF-1, free energies of hydration for neon and radon over a broad temperature range, and the vapor-liquid coexistence curve of a four-component surrogate for the jet fuel S-8. The MoSDeF-GOMC software is available on GitHub at https://github.com/GOMC-WSU/MoSDeF-GOMC.

Heterogeneous Catalytic and Non-Catalytic Supercritical Water Oxidation of Organic Pollutants in Industrial Wastewaters Effect of Operational Parameters

This work reports supercritical water oxidation (SCWO) of organic pollutants in industrial wastewater in the absence and presence of catalysts. To increase the efficiency of the oxidation process, the SCWO of organic compounds in industrial wastewater was performed in the presence of various iron- and manganese-containing heterogeneous catalysts (Fe-Ac, Fe-OH, and Mn-Al). The catalytic and non-catalytic SCWO of organic compounds in wastewater from PJSC “Nizhnekamskneftekhim”, generated from the epoxidation of propylene with ethylbenzene hydroperoxide in the process of producing propylene oxide and styrene (PO/SM), was performed. The effect of operational parameters (temperature, pressure, residence time, type of catalysts, oxygen excess ratio, etc.) on the efficiency of the process of oxidation of organic compounds in the wastewater was studied. SCWO was studied in a flow reactor with induction heating under different temperatures (between 673.15 and 873.15 K) and at a pressure of 22.5 MPa. The reaction time ranged from 1.8 to 4.83 min. Compressed air was used as an oxidizing agent (oxidant) with an oxidant ratio of two to four. A pseudo-first-order model expressed the kinetics of the SCWO processes, and the rate constants were evaluated. In the present work, in order to optimize the operation parameters of the SCWO process, we used the thermodynamic properties of near- and supercritical water by taking into account the asymmetric behavior of the liquid–vapor coexistence curve.

LBM study of ice nucleation induced by the collapse of cavitation bubbles

In this study, we extended the conventional lattice Boltzmann method (LBM) to numerically examine ice nucleation induced by the collapse of a cavitation bubble. Specifically, a pseudo-potential multi-relaxation-time lattice Boltzmann method (MRT-LBM) coupled with a thermal LBM and a criterion for pressure-dependent ice nucleation onset was developed to investigate the cavitation bubble dynamics including growth and collapse, and the subsequently induced ice nucleation. Using the present model, the water vapour-liquid coexistence curve was extended to temperatures lower than 42% of its critical point, excellently matching the Maxwell construction curve. Two practical application scenarios of ice nucleation were investigated: I, near a solid boundary and II, within a pressurised space. Effects of key system parameters including the stand-off distance (λ), differential pressure (Δp) and initial bubble size (R0) on the maximum collapse pressure (pmax) were examined. The results show that under the same conditions, a much higher pmax is generated in scenario II than that in scenario I, thus more readily initialises ice nucleation. After initialisation, part of the initially formed ice melts when the local temperature exceeds the ice melting temperature due to the rapid dissipation of pressure wave. To ensure the complete freezing of water, a large initial supercooling is required for scenario II.

MD simulation estimation of saturation pressure and vapor-liquid equilibrium for binary blends of HFO-1234yf and HFO-1123

Saturation pressure and vapor-liquid equilibrium data of low GWP hydrofluoroolefin compound HFO-1234yf (2,3,3,3-tetrafluoropropene) and its binary blends with HFO-1123 (1,1,2-trifluoroethene) were estimated using molecular dynamics (MD) simulation with the aid of COMPASS force field from 214.15 K to 330.15 K. The maximum absolute deviations of present saturated vapor pressure data from published experimental results were 0.03% for HFO-1123 system and 0.017% for HFO-1234yf system. These models were used to estimate the saturated vapor pressure for six different mixtures of HFO-1234yf and HFO-1123. The saturated liquid and vapor densities, the vapor-liquid coexistence curve (VLCC), and the critical points of the blended refrigerants with various molecular mass fractions were predicted using MD simulations and Gibbs ensemble Monte Carlo (GEMC) simulations. The critical points of HFO-1234yf and HFO-1123 matched well with published data.

Lattice-Boltzmann model for van der Waals fluids with liquid-vapor phase transition

A lattice Boltzmann model (LBM) for two-phase flows with liquid-vapor phase transition based on a dynamic van der Waals theory [Phys. Rev. Lett. 94, 054501 (2005)] is proposed. The proposed model consists of two lattice Boltzmann equations (LBE): one for the Navier-Stokes-Korteweg (NSK) equations and the other for the temperature equation. In the thermal LBE, the equilibrium distribution function is redesigned by introducing a reference temperature, which is used to reduce the numerical errors of velocity divergence in the thermal LBE. A free-energy-based LBE is developed for the hydrodynamic equations and a novel force term is used to correctly recover the NSK equations. Several numerical simulations, including the liquid-vapor coexistence curve, phase separation, stationary droplet, droplet on partially wetting surface, droplet evaporation and bubble nucleate and departure, are conducted to validate the capability and performance of the present model. The numerical results of the proposed model are found to be in excellent agreement with the results of theoretical and/or the hybrid method. It is also shown that numerical stability and accuracy of the present models can be greatly improved by adjusting the reference temperature. The present models provide an effective predictive tool for two-phase flows involving phase change.

Effects of the repulsive and attractive forces on phase equilibrium and critical properties of two-dimensional non-conformal simple fluids

Molecular simulations in the canonical and isothermal-isobaric ensembles were performed for a two-dimensional simple fluid using a set of non conformal molecular interactions. The specific characteristics of this interaction model give it some advantages over other well known interaction potentials employed traditionally in the study of thermodynamic properties of soft matter systems. The functional form employed for modelling the effective potentials is the one proposed by the so-called ANC theory (Approximate Non-Conformal Theory), which allows to modify separately the contributions of the repulsive and attractive terms by means of a molecular parameter called softness. The effect of both, repulsive and attractive softness, on the liquid-vapour coexistence, liquid-solid transition and vaporization curve as well as on the value of the critical properties were explored. In fact, the linear dependence on the softness parameters exhibited by the critical properties, allows to extrapolate the linear correlations presented in this work, to reproduce the critical point of a two-dimensional Lennard-Jones fluid. With the aim of showing how versatile is the interaction model presented in this work, adequate values of the softness parameters were selected to reproduce qualitatively the liquid-vapour coexistence and critical points for both, a two-dimensional model fluid with a double exponential interaction potential, widely employed in molecular simulations of simple fluids; and a thin monolayer of methane molecules adsorbed on a planar graphite substrate, a system that can be considered in good approximation as two-dimensional and that has been studied in a lot of work for four decades. Finally, the effects of the dimensionality of the system was evaluated by quantifying the relative percentage differences exhibited by the thermodynamic properties explored in this paper with respect to its three-dimensional counterpart. The results presented in this work show not only the predictive capacity of the linear correlations mentioned, but the robustness of the ANC interactions to reproduce thermophysical properties and phase equilibria for model and real two-dimensional fluids. Discriminating the influence of repulsive and attractive contributions in molecular interaction models is undoubtedly of great relevance to have a better understanding of thermodynamic properties of simple and complex fluids.

Атомистическое моделирование параметров критической области золота с использованием кривой сосуществования жидкость-пар

The liquid-vapor coexistence curve for gold was obtained by molecular dynamics (MD) modeling and the critical parameters were determined: temperature, density and pressure. The interaction potential of particles of the “embedded atom” family EAM is used. The critical temperature Tcr was determined from the results of MD simulation using the method of the average cluster size in the critical region. To clarify the value of the critical density, the empirical rule of the rectilinear diameter was used. The comparison of the simulation results of this work with the results of the assessment of the critical parameters of gold by other authors using different approaches.

Metal–non-metal transition of expanded liquid Caesium

ABSTRACT The electrical resistivity and the thermoelectric power of liquid metal Cs have been theoretically investigated using the muffin-tin potential approach with the help of an accurate experimentally measured structure factor, S(q), and radial distribution function, g(r) measured along the liquid–vapour coexistence curve. Our procedure provides a clear evidence of the existence of metal–non-metal transition in the temperature region 1500–1800 K. Furthermore, this transition was apprehended by monitoring the shift of the position of the Fermi energy relative to the muffin-tin-zero potential, as well as the effective number of conduction electrons, N c, in the conduction band.

Calculation of the thermodynamic properties of R448A and R449A in a saturation temperature range of 233.15 K to 343.15 K using molecular dynamics simulations

R448A, which is a quinary mixture and has a global warming potential (GWP) of 1390, and R449A, which is a quaternary mixture and has a GWP of 1282, have been recommended for commercial refrigeration systems to replace R404A, which has a GWP of 3943 as per EU Regulation No. 517/2014. The thermodynamic properties of R448A and R449A, such as vapor pressure, saturated density, and vapor-liquid coexistence curve with critical points were computed for temperatures ranging from 233.15 K to 343.15 K via molecular dynamics (MD) simulations. The computed vapor pressures of R448A and R449A closely match that of R404A. The MD simulations predict the saturated densities of R448A and R449A very well in the subcritical region. The computed critical points of the three blend refrigerants were compared with published data. The radial distribution functions (RDFs) show that intra-molecular and inter-molecular interactions occur in the vapor and liquid phases for R448A and R449A. The thermodynamic properties of R448A and R449A estimated in this work will be useful for analyzing the performance of commercial refrigeration systems operating with these new blend refrigerants.

Nonlocal density functional theory of water taking into account many-body dipole correlations: binodal and surface tension of ‘liquid–vapour’ interface

In this paper we formulate a nonlocal density functional theory of inhomogeneous water. We model a water molecule as a couple of oppositely charged sites. The negatively charged sites interact with each other through the Lennard–Jones potential (steric and dispersion interactions), square-well potential (short-range specific interactions due to electron charge transfer), and Coulomb potential, whereas the positively charged sites interact with all types of sites by applying the Coulomb potential only. Taking into account the nonlocal packing effects via the fundamental measure theory, dispersion and specific interactions in the mean-field approximation, and electrostatic interactions at the many-body level through the random phase approximation, we describe the liquid–vapour interface. We demonstrate that our model without explicit account of the association of water molecules due to hydrogen bonding and with explicit account of the electrostatic interactions at the many-body level is able to describe the liquid–vapour coexistence curve and the surface tension at the ambient pressures and temperatures. We obtain very good agreement with available in the literature MD simulation results for density profile of liquid–vapour interface at ambient state parameters. The formulated theory can be used as a theoretical background for describing of the capillary phenomena, occurring in micro- and mesoporous materials.

Effect of shape on liquid-vapor coexistence and surface properties of parallelepiped molecules.

Liquid-vapor coexistence is calculated via molecular dynamics for a variety of parallelepiped shaped molecules. Models are constructed as an array of tangential hard spheres interacting with an attractive square-well potential. Each shape is formed by varying the number of spheres in their three sides. The initial density of the system is chosen close to the critical density of a SW fluid to obtain an equilibrated liquid-vapor coexistence curve by the process of spinodal decomposition. A pattern that relates the geometry of the molecular models and the existence or non-existence of a liquid-vapor orthobaric curve is shown.

The effect of surface roughness on the phase behavior of colloidal particles.

Shape anisotropy of colloidal particles can give rise to complex intermolecular interactions that determine particle packing and phase behavior. The vapor-liquid coexistence curves of attractive rough particles display a shift when compared to attractive smooth spherical particles. We use Integral Equation Theory (IET) to determine the vapor-liquid spinodal phase diagram of smooth and rough colloidal particles interacting through square-well attraction. Additionally, we use Gibbs Ensemble Monte Carlo (GEMC) simulations to locate their vapor-liquid coexistence curves. We model a rough colloidal particle as a spherical core with small beads embedded on its surface. The critical point of smooth spherical particle systems predicted by theory and simulations is in quantitative agreement. An increase in surface roughness due to an increase in either the number of beads or the diameter of the beads has a modest effect on the local structure of the system in the supercritical region. In contrast, increasing surface roughness consistently shifts the vapor-liquid coexistence curves to higher temperatures. The critical temperature is found to be a quadratic function of the number of beads. At a fixed bead size and number of beads, the critical temperature does not vary with the arrangement of beads on the core. Both IET and GEMC simulations predict that unlike critical temperatures, critical packing fractions vary non-monotonically with surface roughness. We find that the feasibility and accuracy of the integral equation theory depend sensitively on the chosen closure combination.

On the liquid–vapour coexistence curve in a Lennard–Jones fluid

A hard-core double Yukawa potential is taken as an approximation of the Lennard–Jones (LJ) potential. Using first-order thermodynamic perturbation theory with a hard-sphere fluid as the reference system, the equation of state of the hard-core double Yukawa fluid is derived analytically. Adjusting the hard-core diameter with the Barker and Henderson prescription to account for the repulsive part of the LJ potential, the liquid–vapour coexistence curve of the LJ fluid is computed with such equation of state. The results are compared with simulation data for the LJ fluid and very good agreement is observed.