Liquid Coexistence Research Articles

Vapor–Liquid Equilibria of Mixtures of Molecular Fluids Using the Activity Fraction Expanded Ensemble Simulation Method

The activity fraction expanded ensemble (AFEE) simulation technique has been extended to predict the vapor–liquid coexistence behavior of binary mixtures of molecular fluids. The systems of molecular mixtures studied are thiophene–n-hexane (a mixture of an aromatic compound with a n-alkane) and methane–n-hexane (mixture of n-alkanes with significant difference in size). Comparison with results from the grand canonical transition matrix Monte Carlo method and experimental data available in the literature has also been provided. Further, we have investigated the computational efficiency of the AFEE technique at temperatures where both compounds exhibit subcritical behavior (thiophene–n-hexane at 338.15 K) and where one of the components shows supercritical behavior (methane–n-hexane at 373 K). Canonical Monte Carlo simulations are also performed to obtain the radial distribution functions which have been used to study the structure of the coexisting liquid phases to gain insights into the molecular origins ...

On Failures of van der Waals’ Equation at the Gas–Liquid Critical Point

This comment is in response to a recent “new comment” by Umirzakov on the article “Gibbs density surface of fluid argon: revised critical parameters.” It was incorrectly asserted that van der Waals equation “proves” the existence of a scaling singularity with a divergent isochoric heat capacity (Cv). Van der Waals’ equation, however, is inconsistent with the universal scaling singularity concept; it erroneously predicts, for instance, that Cv is a constant for all fluid states. Van der Waals hypothetical singular critical point is based upon a common misconception that van der Waals equation represents physical reality of fluids. A comparison with experimental properties of argon shows that state functions of van der Waals’ equation fail to describe the thermodynamic properties of low-temperature gases, liquids and of gas–liquid coexistence. The conclusion that there is no “critical point” singularity on Gibbs density surface remains scientifically sound.

Simulating phase change during the droplet deformation and impact on a wet surface in a square microchannel: An application of oil drops collision

This paper is an attempt to simulate the mathematical modelling on drop deformation in a saturated medium due to its movement and collision onto the liquid film. The reactions between fluid-fluid interaction and wall are completely simulated. Computations are performed for a two-dimensional domain under the influence of a saturation situation (that is saturation vapor and liquid co-exist) by the lattice Boltzmann method. The effects of different parameters, such as Weber number, collision angle on the drop deformation and its collision onto the liquid film, radius and initial position of the droplet are investigated. A stronger wave forms in the liquid film after collision of the drop for the case of inclined collision in comparison with the normal one. Additionally, a 5.5% increment in the maximum height of the created wave for $R_{\rm dp}=22$ Lu and normal collision when the initial position of the drop moves from H = 0.5 L to H = 0.25 L is found.

Ice-Liquid Oscillations in Nanoconfined Water.

Nanoscale confinement has a strong effect on the phase behavior of water. Studies in the last two decades have revealed a wealth of novel crystalline and quasicrystalline structures for water confined in nanoslits. Less is known, however, about the nature of ice-liquid coexistence in extremely nanoconfined systems. Here, we use molecular simulations to investigate the ice-liquid equilibrium for water confined between two nanoscopic disks. We find that the nature of ice-liquid phase coexistence in nanoconfined water is different from coexistence in both bulk water and extended nanoslits. In highly nanoconfined systems, liquid water and ice do not coexist in space because the two-phase states are unstable. The confined ice and liquid phases coexist in time, through oscillations between all-liquid and all-crystalline states. The avoidance of spatial coexistence of ice and liquid originates on the non-negligible cost of the interface between confined ice and liquid in a small system. It is the result of the small number of water molecules between the plates and has no analogue in bulk water.

In Situ Observation of the Zr Poisoning Effect in Al Alloys Inoculated by Al-Ti-B

In situ synchrotron X-ray radiography observations of the Zr-poisoning phenomenon of an Al-20 wt pct Zn alloy inoculated by Al-5Ti-1B were carried out. The effects of Zr addition on heterogeneous nucleation, grain growth, and final grain size were quantitatively studied and further analyzed using the interdependence model. The experimental results show that the undercooling needed for nucleation increases and the nucleation rate decreases at the early stage of solidification with Zr addition, resulting in fast grain growth, a high solidification rate and increased severity of solute segregation in the solid–liquid coexistence regions. At the same time, the poisoning is a progressive process that is enhanced with the increasing Zr content, holding temperature, and holding time. The nucleation-free zone of the Zr-containing sample, either measured from the radiographs or calculated by the interdependency theory, is larger than that of the Zr-free sample. Our analysis shows that both the increase in the nucleation-free zone and the average interparticle spacing of the most potent available nucleation particles contribute to the increase of the grain size caused by Zr poisoning.

Heterogeneous to homogeneous melting transition visualized with ultrafast electron diffraction.

The ultrafast laser excitation of matters leads to nonequilibrium states with complex solid-liquid phase-transition dynamics. We used electron diffraction at mega-electron volt energies to visualize the ultrafast melting of gold on the atomic scale length. For energy densities approaching the irreversible melting regime, we first observed heterogeneous melting on time scales of 100 to 1000 picoseconds, transitioning to homogeneous melting that occurs catastrophically within 10 to 20 picoseconds at higher energy densities. We showed evidence for the heterogeneous coexistence of solid and liquid. We determined the ion and electron temperature evolution and found superheated conditions. Our results constrain the electron-ion coupling rate, determine the Debye temperature, and reveal the melting sensitivity to nucleation seeds.

Phase behavior of hard spheres mixed with supramolecular polymers

We present a theory that predicts the phase behavior of hard spheres (HS) mixed with non-adsorbing supramolecular polymers in a common solvent. It combines Generalized Free Volume Theory with a mean-field model for equilibrium polymers in solution extended with scaling theory to incorporate excluded volume effects in a good solvent. The system displays similar phase stability as conventional HS-polymer mixtures, although there is a small preference for gas–liquid coexistence with respect to fluid–crystal equilibrium in the case of a HS-supramolecular polymer mixture. Phase transitions can be induced by external stimuli such as temperature or light due to the stimuli-responsive nature of the supramolecular polymer size.

Predicting vapor liquid equilibria using density functional theory: A case study of argon.

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell in the liquid phase.

Theoretical approach to influence of nitrogen on solidification cracking susceptibility of austenitic stainless steels: computer simulation of hot cracking by solidification/segregation models

ABSTRACTThe effect of nitrogen on the solidification cracking susceptibility of austenitic stainless steels (SUS316L and SUS310S) was quantitatively evaluated by transverse-Varestraint test. The amount of nitrogen in Ar shielding gas during GTA melt-run welding was varied in order to vary the nitrogen content in the weld metals. The solidification brittle temperature range of SUS316L was enlarged with an increase in the nitrogen content in the weld metal, while that of SUS310S was very slightly increased with an increase in the nitrogen content. Numerical analysis of solidification segregation during welding revealed that the solid–liquid coexistence temperature range of SUS316L was enlarged with an increase in the nitrogen content in the weld metal, whereas that of SUS310S was almost constant regardless of the nitrogen content. A nitrogen itself essentially had a negligible effect on the solidification cracking susceptibility of fully austenitic stainless steels because a nitrogen neither solidification-segregated in the weld metal nor reduced the solidified temperature during welding. However, the nitrogen increased the solidification cracking susceptibility of austenitic stainless steels with two-phase solidification because the solidification segregation of P and S was promoted by reducing the amount of δ-ferrite in the weld metal.

Numerical analysis on solidification cracking susceptibility of type 316 stainless steel considering solidification mode and morphology computer simulation of hot cracking by solidification/segregation models

ABSTRACTThe two-phase solidification model was constructed considering the solidification mode and morphology. The effects of the solidification mode and morphology as well as δ-ferrite on the solidification cracking susceptibility of austenitic stainless steels (SUS316L) were clarified by a numerical analysis. The solid–liquid coexistence temperature range (SLCTR), correlating the solidification brittle temperature range (solidification cracking susceptibility), was calculated based on the computer simulation of supercooling and solidification segregation behaviours. In the peritectic–eutectic solidification model, the solidification mode greatly influenced the solidification segregation as well as the SLCTR, although the solidification segregation and the SLCTR would be discontinuously changed at the solidification mode transition. The SLCTR calculated by peritectic–eutectic solidification model was larger than that by divorced eutectic solidification model at the ferritic–austenitic mode solidification, while an opposite tendency was observed at the austenitic–ferritic mode solidification. The amounts of δ-ferrite calculated by each solidification model were comparable in any solidification modes. The SLCTR was approximately decreased with an increase in the amount of δ-ferrite in any solidification models. It followed that solidification cracking susceptibility would be dominantly influenced by δ-ferrite and additionally by the solidification mode and morphology.

On the Primary Solidification of Compacted Graphite Iron: Microstructure Evolution during Isothermal Coarsening

It is widely accepted that in most commercial hypoeutectic alloys, both static mechanical properties and feeding characteristics during solidification, are extremely linked to the coarseness of the primary phase. It is therefore of critical importance to provide tools to control and predict the coarsening process of the dendritic phase present in hypoeutectic melts. The characterization of the primary phase, a product of the primary solidification, has traditionally been neglected when compared to the eutectic solidification characterization in cast iron investigations. This work presents the morphological evolution of the primary austenite present in a hypoeutectic compacted graphite cast iron (CGI) under isothermal conditions. To that purpose, a base spheroidal graphite cast iron (SGI) material with high Mg content is re-melted in a controlled atmosphere and reversed into a CGI melt by controlling the Mg fading. An experimental isothermal profile is applied to the solidification process of the experimental alloy to promote an isothermal coarsening process of the primary austenite dendrite network during solid and liquid coexistence. Through interrupted solidification experiments, the primary austenite is preserved and observed at room temperature. By application of stereological relations, the primary phase and its isothermal coarsening process are characterized as a function of the coarsening time applied. The microstructural evolution observed in the primary austenite in CGI and the measured morphological parameters show a similar trend to that observed for lamellar graphite cast iron (LGI) in previous investigations. The modulus of the primary austenite, Mγ, and the nearest distance between the centre of gravity of neighbouring austenite particles, Dγ, followed a linear relation with the cube root of coarsening time.

Liquid–liquid equilibrium, heat capacity and turbidity of binary solution nitrobenzene + n -pentadecane

Abstract The liquid–liquid coexistence curve, the isobaric heat capacity per unit volume and the turbidity for the binary solution of nitrobenzene + n-pentadecane have been measured at various temperatures. The upper consolute mole fraction xc of nitrobenzene and the upper consolute temperature Tc of the binary solution were determined to be xc = 0.696 and Tc = 307.298 K, respectively. The values of the critical exponents related to the width of the coexistence curve, the heat capacity, the osmotic compressibility and the correlation length were deduced and found to be in good agreements with that of the 3-D Ising universality. With the heat capacity data the asymmetric behavior of the diameter of the coexistence curve was studied in terms of the complete scaling theory. The critical amplitudes related to the above four quantities were used to calculate the universal scaling ratios and to confirm their theoretical predictions.

Plotting of phase (vapor-liquid) transition surface near the critical point out of data from isochoric experiment. Experimental procedure

This paper suggests a mathematical model of processing experimental data that allows to plot the surface of the phase transition in near critical region, using the results of isochoric experiment. The model is based on proven approximation methods. The model was tested on 20 binary mixtures (10 mixtures of С2-С7 linear alkanes, five mixtures of propane and branched С5-С6 alkanes, two mixtures of haloalkanes, one mixture each of pentane with toluene, cyclohexane with benzene and toluene) with the difference in critical temperatures from 45 to 235 K. As the result, in the 0.5≤ρDew/ρc < 1.5 range of reduced density the average error in predicting temperatures of phase transition is 2.2 K, 1.2 K for critical temperatures, 3 K for maximum temperature of liquid and vapor phase coexistence.

Modeling Thermodynamic Properties of Isomeric Alkanes with a New Branched Equation of State

In this paper we present an extension of the statistical associating fluid theory (SAFT) for branched molecules with a Lennard-Jones dimer reference fluid (SAFTD-LJ-Branch). The theory successfully predicts how branched architecture affects the attraction and repulsion between molecules. SAFTD-LJ-Branch takes a form similar to SAFTD-LJ with an additional parameter NB introduced to account for the branching effect. We propose an approach relating NB to the number of different types of articulation segments. The theory is used to study the effect of chain architecture on the thermodynamic properties of isomeric alkanes. SAFTD-LJ-Branch accurately predicts the phase diagram of pure butane, pentane or hexane isomers. Further, vapor pressures of n-triacontane and squalane are predicted without further fitting and shown to be in semiquantitative agreement with experimental data. Finally, SAFTD-LJ-Branch is demonstrated to be well applicable to mixtures as we model the vapor–liquid coexistence of binary alkane mixtures containing different hexane isomers and recover the experimental trends.

Predicted melt curve and liquid-state transport properties of TATB from molecular dynamics simulations

The melt curve and the liquid-state transport properties shear viscosity, self-diffusion coefficient and thermal conductivity of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) were predicted using all-atom molecular dynamics simulations. The TATB melt curve was obtained using solid–liquid coexistence simulations and is in good accord with the Simon–Glatzel equation. The temperature dependencies of the shear viscosity and self-diffusion coefficient are predicted to obey Arrhenius behaviour for pressures up to P = 20 kbar. The thermal conductivity has a linear temperature dependence for P < 15 kbar and a linear density (ρ) dependence for ρ > 1200 kg m−3. At similar densities the shear viscosity of liquid TATB is close to the predictions for liquid nitromethane [58] but lower than the predictions for liquid HMX [24] and RDX [59]. The self-diffusion coefficient for TATB is predicted to be higher than predictions for nitromethane, HMX and RDX at similar densities. The conductivity of TATB is ≈20% greater than the conductivity of liquid HMX at a given density.

In situ laser-induced breakdown spectroscopy measurements of chemical compositions in stainless steels during tungsten inert gas welding

A laser-induced breakdown spectroscopy (LIBS) system was combined with a bead-on-plate Tungsten Inert Gas (TIG) welding process for the in situ measurement of chemical compositions in austenitic stainless steels during welding. Monitoring the weld pool's chemical composition allows governing the weld pool solidification behavior, and thus enables the reduction of susceptibility to weld defects. Conventional inspection methods for weld seams (e.g. ultrasonic inspection) cannot be performed during the welding process. The analysis system also allows in situ study of the correlation between the occurrence of weld defects and changes in the chemical composition in the weld pool or in the two-phase region where solid and liquid phase coexist. First experiments showed that both the shielding Ar gas and the welding arc plasma have a significant effect on the selected Cr II, Ni II and Mn II characteristic emissions, namely an artificial increase of intensity values via unspecific emission in the spectra. In situ investigations showed that this artificial intensity increase reached a maximum in presence of weld plume. Moreover, an explicit decay has been observed with the termination of the welding plume due to infrared radiation during sample cooling. Furthermore, LIBS can be used after welding to map element distribution. For austenitic stainless steels, Mn accumulations on both sides of the weld could be detected between the heat affected zone (HAZ) and the base material.

An empirical constitutive model for complex glass-forming liquids using bitumen as a model material

While extensive research efforts have been devoted to understand the dynamics of chemically and structurally simple glass-forming liquids (SGFLs), the viscoelasticity of chemically and structurally complex glass-forming liquids (CGFLs) has received only little attention. This study explores the rheological properties of CGFLs in the vicinity of the glass transition. Bitumen is selected as the model material for CGFLs due to its extremely complex chemical composition and microstructure, fast physical aging and thermorheological simplicity, and abundant availability. A comprehensive rheological analysis reveals a significant broadening of the glass transition dynamics in bitumen as compared to SGFLs. In particular, the relaxation time spectrum of bitumen is characterized by a broad distribution of long relaxation modes. This observation leads to the development of a new constitutive equation, named the broadened power-law spectrum model. In this model, the wide distribution of long relaxation times is described by a power-law with positive exponent and a stretched exponential cut-off, with parameter β serving as a measure of the broadness of the distribution. This characteristic shape of the bitumen spectrum is attributed to the heterogeneous freezing of different molecular components of bitumen, i.e., to the coexistence of liquid and glassy micro-phases. Furthermore, as this type of heterogeneous glass transition behavior can be considered as a general feature of complex glass-forming systems, the broadened power-law spectrum model is expected to be valid for all types of CGFLs. Examples of the applicability of this model in various complex glass-forming systems are given.

Performance of density functionals for modeling vapor liquid equilibria of CO2 and SO2.

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE-D3, BLYP-D3, PBE0-D3, M062X-D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal van der Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP-D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Overall, the BLYP-D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO2 and SO2 . © 2017 Wiley Periodicals, Inc.

A unified momentum equation approach for computing thermal residual stresses during melting and solidification

In this article, we present a novel numerical method for computing thermal residual stresses from a viewpoint of fluid–structure interaction (FSI). In a thermal processing of a material, residual stresses are developed as the material undergoes melting and solidification, and liquid, solid, and a mixture of liquid and solid (or mushy state) coexist and interact with each other during the process. In order to accurately account for the stress development during phase changes, we derived a unified momentum equation from the momentum equations of incompressible fluids and elastoplastic solids. In this approach, the whole fluid–structure system is treated as a single continuum, and the interaction between fluid and solid phases across the mushy zone is naturally taken into account in a monolithic way. For thermal analysis, an enthalpy-based method was employed. As a numerical example, a two-dimensional laser heating problem was considered, where a carbon steel sheet was heated by a Gaussian laser beam. Momentum and energy equations were discretized on a uniform Cartesian grid in a finite volume framework, and temperature-dependent material properties were used. The austenite–martensite phase transformation of carbon steel was also considered. In this study, the effects of solid strains, fluid flow, mushy zone size, and laser heating time on residual stress formation were investigated.

Microscopic theory of simple fluids

Analyzing the basic details of a simple fluid, we developed its microscopic theory and discovered that (i) every fluid is a homogeneous mixture of two fluids, SUB1 and SUB2, respectively, composed of non-interacting quasi-particles (QP1) and interacting QP2, and (ii) its behavior is controlled by Pin(q)+Pin(K)=Pex+Pcoh as its equation of state (EOS) where Pin(q) and Pin(K) are two components of its internal pressure, while Pex and Pcoh, respectively, represent external and cohesive pressures. It further reveals the temperature (T) and pressure (P) dependence of compressibility factor (Z) of the fluid and its universal component Z(T)Vc=1+B2(T)/Vc (with B2(T) being its second virial coefficient), the reasons for the coexistence of liquid and vapor and the relation between their particle number densities ρl and ρg. It explains criticality and critical condensation/evaporation and, for the first time, unravels the microscopic origin of important empirical rules such as Trouton rule and Guldberg rule (discovered about 130years back) and several principles of corresponding states (PCS) discovered by Guggenheim. Our results have very good agreement with experiments. We hope our theory may emerge as an important means to (i) explain different properties of simple fluids, (ii) provide necessary foundation to develop similar theories of polar, strongly polar, ionic and complex fluids, and (iii) render useful direction for better understanding of widely different physico-chemical, bio-chemical and bio-physical processes and related aspects.