Experimental Vapor-liquid Equilibrium Research Articles

Improving the Teaching/Learning Process in the Binary Vapor–Liquid Equilibrium Experiment Based on the Activity Coefficient Model

Improving the Teaching/Learning Process in the Binary Vapor–Liquid Equilibrium Experiment Based on the Activity Coefficient Model

Vapor-Liquid Equilibrium in the Acetic Acid-Ethanol-Ethyl Acetate-Water Quaternary System: Critical Literature Review and Thermodynamic Consistency of the Experimental Data

This study presents a critical review of the experimental vapor-liquid equilibrium (VLE) data for the quaternary acetic acid-ethanol-ethyl acetate-water system and its subsystems that are reported in the literature. The thermodynamic consistency of the VLE data were verified using two integral tests: the Redlich–Kister test and the direct integration of the Gibbs–Duhem equation. The VLE data were correlated using the NRTL equation for further integration. Additionally, the reliable value of the integral derived from the direct integration of the Gibbs–Duhem equation for multicomponent systems under isothermal-isobaric conditions was estimated. This integral can be used for testing the thermodynamic consistency of experimental VLE data.

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.

Vacuum distillation: A sustainable separation and purification approach for extracting valuable metals from In–Zn, In–Sn, and In–Sn–Zn waste alloys

The vacuum distillation (VD) method was studied for extraction of valuable metals from In–Zn, In–Sn, and In–Sn–Zn waste alloys. The VD studies were carried out between 773 K and 1073 K, at 5 Pa, and for 60 min for the In–Zn alloys. The In content in the residues was greater than 99.999 wt%, and the Zn content in the volatiles was the highest at 99.8962 wt%. For the In-Sn alloys, the VD experiments were carried out from 1323 K to 1573 K at 5 Pa for 540 min for the In–Sn alloys. The Sn content in the residues exceeded 99.9963 wt%, whereas the In content in the volatiles was 99.86 wt%. Further, the In–Sn–Zn VD was carried out between 773 K and 1073 K at 5 Pa for 90 min. The Zn content of the residues decreased from 6.0 wt% to 0.0009 wt%, while the Zn content of the volatiles was 99.79 wt%. Using the M-MIVM and vapor–liquid equilibrium (VLE) theories, the VLE data was predicted and the related phase diagrams for the binary and ternary alloys were displayed. The remarkable similarity between theoretical and experimental VLE phase diagrams demonstrates the reliability of the M-MIVM for In-based alloys.

VLE measurement of binary systems 1-butyl-3-methylimidazolium-based ionic liquids and ethanol or water

Experimental vapor–liquid equilibrium (VLE) data for binary systems of ethanol or water with four ionic liquids (ILs) comprising 1-butyl-3-methylimidazolium cation and different anions were measured at atmospheric pressure within a broad region of IL concentrations, IL mole fraction ranging between 0 and 0.7 or even 0.87. Siwoloboff procedure of vapor–liquid phase transition temperature measurement was applied to estimate VLE of the binary mixtures. Obtained t–x data were fitted assuming ideal vapor and non-ideal liquid phase behavior, using the original NRTL equation to calculate component activity coefficients. VLE description results are presented in form of equilibrium diagrams and as the variation of activity coefficients with mixture composition. Quality of the VLE data fitting was assessed based on root mean square deviations and mean deviations in temperature. Some experimental binary t–x data sets were compared to those available in literature (measured in much narrower concentration range) or predicted from ternary VLE data. The selection of ILs in this study was related to the separation of ethanol−water mixture by extractive distillation. Principal IL selection criterium was its ability to affect the ethanol–water relative volatility. Thermodynamic description of the VLE data of IL-containing systems within a wide concentration range is an essential building block of the mathematical model of separation devices, especially in case of regeneration equipment where concentrated IL is present.

Separation of near-boiling mixtures (acetic acid and water) enhanced by ionic liquid

Acetic acid aqueous solution is a common and typical near-boiling mixture in the petroleum, chemical, polymer, pharmaceutical and food industries. Because of the large number of ideal plates for separating acetic acid and water by ordinary distillation, the energy consumption and production cost are high. Designable ionic liquids (ILs) and deep eutectic solvents (DESs) are environmentally-friendly entrainers for extractive distillation. Many azeotropic systems enhanced by adding ILs or DESs have been studied, but the near-boiling water/acetic acid system is rarely discussed.In this study, an IL 1,2,3-trimethylimidazolium dimethylphosphate ([TMIM]+[Me2PO4]−) with easy synthesis, low production cost and good thermal stability was employed as the rectification entrainer for water/acetic acid system, while the DESs were easy to react in acetic acid aqueous solution and was abandoned. First, the relative volatility of water (1) and acetic acid (2) at the more difficult separation point (x1′ = 0.9) was measured using a modified Othmer still at 101.32 kPa. When the mole fraction of entrainers was 0.071, these relative volatilities were 2.80 (n,n-dimethylformamide), 2.88 (1-methyl-2-pyrrolidinone), 4.82 ([TMIM]+[Me2PO4]−) respectively. The separation performance of [TMIM]+[Me2PO4]− was 67% higher than that of 1-methyl-2-pyrrolidinone. Then, the effect of [TMIM]+[Me2PO4]− concentration on the relative volatility was investigated. The relative volatility was dramatically increased from 1.60 to 6.85 with 0–0.103 mol fraction of [TMIM]+[Me2PO4]− and was 4.28 times that in an IL-free system. After that, isobaric vapor–liquid equilibrium (VLE) data of water + acetic acid, water + [TMIM]+[Me2PO4]− and water + acetic acid + [TMIM]+[Me2PO4]− ([TMIM]+[Me2PO4]− at ∼ 5, 15, and 25 mass%) systems were determined at 101.32 kPa. Also, Based on the chemical theory and Hayden–O’Connell method, the binary energy parameters of the NRTL (Non-Random-Two-Liquid) model for these systems were regressed and the predicted values were found to fit the experimental VLE data quite well..For the first time, we have found that [TMIM]+[Me2PO4]− as an entrainer is superior to conventional volatile solvents for water/acetic acid distillation in terms of performance, which provides more choices and imagination for industry. At the same time, it promotes understanding of the influence of IL structure on water/acetic acid separation performance, and is also an important inspiration for the distillation of other near-boiling systems.

Experimental and mechanism exploration on the separation of methanol-containing azeotropic compounds from biodiesel by phosphate esters ionic liquids

Abundant coal resources in China have led to an excess of methanol production. This work explores the separation strategy of dimethoxymethane-methanol (DMM-MeOH) and dimethyl carbonate (DMC)-MeOH binary azeotropes, which are easily produced in the production of diesel additives. Implementing energy-saving, emission reduction, and low carbon emission strategies is important. Three types of phosphate esters ionic liquids (ILs) with different chain lengths were prepared to realize the separation of DMM-MeOH and DMC-MeOH binary azeotrope. Based on the vapor-liquid equilibrium experiments, the vapor-liquid equilibrium data of the DMM-MeOH and DMC-MeOH binary azeotropes using phosphate esters ILs of three different chain lengths were measured at 101.3 kPa. The effect of phosphate esters ILs with three different chain lengths on the separation of DMM-MeOH and DMC-MeOH azeotropes was investigated. The separation mechanism of the azeotropes was studied at the molecular level. The electron density difference explores the optimal configuration between molecules. The atomic theory of molecules analysis directly displays the characteristics of bond critical points and explores the influence of hydrogen bond strength on the intermolecular bond length. The important roles of hydrogen bonds and steric hindrance in the separation process were investigated by reduced density gradient and independent gradient model. Quantum chemical calculation results showed that phosphate esters ILs have a significant effect on the molecular interactions of azeotropes, which is the main factor for phosphate esters ILs in reducing the relative volatility between azeotropes.

Correction to “Isobaric Vapor–Liquid Equilibrium Experiment of Methyl Acetate + Ethanol Containing Different Ionic Liquids at 101.3 kPa”

ADVERTISEMENT RETURN TO ARTICLES ASAPAddition/CorrectionNEXTORIGINAL ARTICLEThis notice is a correctionCorrection to “Isobaric Vapor–Liquid Equilibrium Experiment of Methyl Acetate + Ethanol Containing Different Ionic Liquids at 101.3 kPa”Feihu LiFeihu LiMore by Feihu Lihttps://orcid.org/0000-0001-5624-4467, Jiaming ZhuJiaming ZhuMore by Jiaming Zhu, Xiwei HuXiwei HuMore by Xiwei Huhttps://orcid.org/0000-0002-4383-6030, Linjun SunLinjun SunMore by Linjun Sun, Hongkang ZhaoHongkang ZhaoMore by Hongkang Zhao, Zhongqi RenZhongqi RenMore by Zhongqi Ren, and Qunsheng Li*Qunsheng LiMore by Qunsheng Lihttps://orcid.org/0000-0002-1908-9418Cite this: J. Chem. Eng. Data 2023, XXXX, XXX, XXX-XXXPublication Date (Web):June 12, 2023Publication History Received31 May 2023Published online12 June 2023https://doi.org/10.1021/acs.jced.3c00329© 2023 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views-Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (698 KB) Get e-Alertsclose Get e-Alerts

Modeling of the Vapor-Liquid Equilibria Properties of Binary Mixtures for Refrigeration Machinery

The presence of both critical and azeotropic states in the vapor-liquid equilibria (VLE) is a very important issue in the chemical and refrigeration engineering. The knowledge of the phase behavior (subcritical phase/supercritical phase) of refrigerant allows designing and optimizing the refrigeration industrials processes. However, it is rare to find data for this information, which poses a great challenge for researchers to develop predictive and correlative thermodynamic models. The present study proposes the computation of the compositions and pressures of critical and azeotropic points of the isothermal VLE as well as the correlation of experimental VLE data. Firstly, experimental data (PTxy) was used to predict the vapor-liquid phase of both critical and azeotropic behaviors and to determine their properties using the relative volatility model. Secondly, the thermodynamic model (PR-MC-WS-NRTL) was applied to correlate the data of the binary refrigerant systems and describe their isothermal (VLE) behavior. The results proved that there is good agreement between predicted values obtained by the developed model and the experimental reference data. The relative error of both critical and azeotropic properties does not exceed 4.3 % for the molar fraction and 7.5 % for the pressure using relative volatility model. On other hand the relative deviation is respectively less than 2.60 % and 2.58 % for the liquid and vapor mole fractions using (PR-MC-WS-NRTL) model. This shows the ability of these models to give a reliable solution to predict and modulate the phase behavior of the binary refrigerant systems.

Vapor–Liquid Equilibrium Experiment and Thermodynamic Model Correlation for Ethanol + Isopropyl Acetate with Ionic Liquid at 101.3 kPa

Due to the azeotrope between ethanol and isopropyl acetate, separating them and meeting the separation requirements is challenging. In this study, ethylene glycol (EG), dimethyl sulfoxide (DMSO), and 1-butyl-3-methyl-imidazole acetate ([BMIM][OAC]) were selected as entrainers, and the vapor–liquid equilibrium data of ethanol–isopropyl acetate, ethanol + isopropyl acetate + EG, ethanol + isopropyl acetate + DMSO, and ethanol-isopropyl acetate + [BMIM][OAC] were measured at atmospheric pressure. The thermodynamic NRTL model was able to fit these experimental results. It showed that the model could correctly describe the influence of these entrainers on this azeotropic system. According to the VLE data, three entrainers caused different effects on the relative volatility of ethanol–isopropyl acetate. The azeotropic point would be completely eliminated, while the mole fraction of [BMIM][OAC] added is 0.1, which performs better than EG and DMSO.

Isobaric Vapor–Liquid Equilibrium Experiment of Methyl Acetate + Ethanol Containing Different Ionic Liquids at 101.3 kPa

Vapor–liquid phase equilibrium experiments for the binary system of methyl acetate + ethanol and ternary systems of methyl acetate + ethanol + 1-ethyl-3-methylimidazole acetate ([EMIM][OAC]), methyl acetate + ethanol + 1-butyl-3-methylimidazole acetate ([BMIM][OAC]), and methyl acetate + ethanol + 1-ethyl-3-methylimidazolium methanesulfonate ([EMIM][MeSO3]) were conducted at 101.3 kPa. The results show that all three extractants can effectively break the azeotrope of methyl acetate + ethanol. The ILs produce a salting-out effect on methyl acetate and increase the relative volatility of methyl acetate to ethanol. The NRTL model has been chosen to correlate the experimental data. The ARD (average relative deviation) of the activity coefficient of NRTL for the binary system of methyl acetate + ethanol and ternary systems of methyl acetate + ethanol + [EMIM][OAC], methyl acetate + ethanol + [BMIM][OAC], and methyl acetate + ethanol + [EMIM][MeSO3] is 1.22, 1.88, 1.64, and 1.57%, respectively, indicating the good applicability of NRTL.

Isothermal (Vapour + Liquid) Equilibrium Measurements and Correlation of the Binary Mixture {3,3,3-Trifluoropropene (HFO-1243zf) + 2,3,3,3-tetrafluoropropene (HFO-1234yf)} at Temperatures from 283.15 K to 323.15 K

The many constrains introduced by the F-gas Regulation and the Kigali Amendment to the Montreal Protocol have resulted in an intense search for alternatives to fluorinated greenhouses gases for air conditioning and refrigeration purposes (Mota-Babiloni A, Makhnatch P, in Int J Refrig 127:101–110, 2021). With respect to the urge of new low-GWP and low-ODP refrigerants, blends composed of hydrofluoroolefins (HFO) are considered promising possible substitutes to hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs) for HVAC&R applications (Sovacool et al., in Renew Sustain Energy Rev 141:110759), but thermophysical properties data for these blends are still scarce (Bell et al., in: J Chem Eng Data, 2021). In the present study, the vapor–liquid equilibrium (VLE) for the binary system (HFO-1243zf + HFO-1234yf), for which just one set of data on the VLE is available to date in literature, has been experimentally studied by means of a vapor recirculation apparatus. The measurements have been performed at isothermal conditions in the range of temperatures between 283.15 K and 323.15 K, while the composition of both the phases in equilibrium has been measured by gas-chromatographic analysis. The experimental VLE data have been correlated by two different equations of state (EoS): the Peng-Robinson (PR) EoS combined with Mathias–Copeman (MC) alpha function and van der Waals (vdW) mixing rules, and the Helmoltz EoS with dedicated binary interaction parameters. Correlated results showed a good agreement with the experimental data for the binary system.

Isobaric Vapor–Liquid Equilibrium Experiment of N-Propanol and N-Propyl Acetate at 101.3 kPa

N-Propanol (NPA) and n-propyl acetate (NPAC) can form an azeotrope under normal pressure, so their separation cannot be carried out by conventional distillation. Therefore, 1-butyl-3-methylimidazole acetate ([BMIM][OAC]) and ethylene glycol (EG) were selected as entrainers for extractive distillation of the two substances. Isobaric vapor–liquid equilibrium data were obtained by experiments of NPA + NPAC, NPA + NPAC + [BMIM][OAC], and NPA + NPAC + EG at normal pressure; the experimental results showed that the separation effect of [BMIM][OAC] is significantly better than that of EG. Finally, the data were fitted and correlated with the NRTL model. The ARD (average relative deviation) of NPA + NPAC, NPA + NPAC + [BMIM][OAC], and NPA + NPAC + EG is less than 5%, indicating that the NRTL model has good applicability to the vapor–liquid system.

Isobaric Vapor–Liquid Equilibria of Binary Systems Containing Oxygenated Biofuel Compounds (Ethanol + Cyclopentanone, Propyl Butanoate + 4-Methylphenol, Cyclopentanone + Propane-1,2-diol) at Atmospheric Pressure

The isobaric phase equilibrium data for the binary systems of ethanol + cyclopentanone, propyl butanoate + 4-methylphenol, and cyclopentanone + propane-1,2-diol at atmospheric pressure were measured using a modified distillation apparatus. The Herington and Van Ness tests were employed to confirm the thermodynamic consistency of the experimental data. In addition, the Wilson, NRTL, and UNIQUAC models were used to correlate experimental vapor–liquid equilibrium data. The corresponding binary interaction parameters (BIPs) for the three models, which are useful for the modeling and designing separation processes involving biofuel, were obtained using a maximum likelihood objective function. It has been confirmed that when appropriate BIPs are used in each model, the outputs are consistent with each other and with experimental data.

Experimental VLE Data of Binary Systems of Ester + Alcohol at 0.6 MPa. Verification using new Association Parameters for the Point– to–Point Test

Experimental data of vapor–liquid equilibria (VLE) are reported for the following binary systems: butyl acetate+ethanol, butyl acetate+1–propanol and butyl acetate+1–butanol at 0.6 MPa. No azeotrope was found in the butyl acetate+1–butanol system at 0.6 MPa. The thermodynamic consistency of the obtained data was analyzed using some equations of state (EOS) in the point–to–point test. The phase behavior was satisfactorily modelled using the Peng–Robinson EOS. The new association parameter of the Hayden–O’Connell method was determined from 144 pure substances and the influence of the second virial coefficient calculations in the point–to–point test was evaluated.

Structure-activity relationship and experimental study of organic solvents and deep eutectic solvents in separation of cyclohexane-ethyl acetate

Selecting the appropriate extractant is of great significance for solving the problems of high energy consumption and difficult separation in the extractive distillation process. In this study, four deep eutectic solvents (DESs) were designed by combining menthol hydrogen bond acceptors with lauric acid and capric acid hydrogen bond donors and tetrabutylammonium bromide hydrogen bond acceptors with levulinic acid and ethylene glycol hydrogen bond donors. The interaction mechanism and structure–activity relationship between azeotropic system, hydrogen bond donor, hydrogen bond acceptor and deep eutectic solvent were studied. σ-profile, interaction energy, reduced density gradient, electrostatic potential, and natural bond orbital were used to study the microscopic mechanism and structure–activity relationship of azeotropes separated by DESs. On this basis, the vapor–liquid equilibrium experiments of separating ethyl acetate-cyclohexane azeotrope by DESs were carried out. The results showed that separating ethyl acetate-cyclohexane by using DESs is feasible and that the DES synthesized by using levulinic acid and tetrabutylammonium bromide is preferable for separation. Studying the relationship between DES structures and the azeotrope provides a theoretical basis for the screening and design of DES extractants for the separation of alkane-ester azeotropes using extractive distillation.

Experiment and Molecular Mechanism of Two Chlorinated Volatile Organic Compounds in Ionic Liquids

The structure–property relationship between ionic liquids (ILs) and two chlorinated volatile organic compounds (CVOCs), dichloromethane (DCM) and 1,2-dichloroethane (DCE), was systematically investigated. The suitable IL was screened using the COSMO-RS model, and 1-ethyl-3-methylimidazolium acetate [EMIM][Ac] was considered the optimal absorbent to capture the two CVOCs. The vapor–liquid equilibrium experiment demonstrates that the addition of the IL significantly reduces the vapor pressures of the IL + DCM (or DCE) systems. The structure of ILs on the absorption performance was investigated by absorption capacity experiments. Then, the absorption mechanism was investigated through QC calculations and wavefunction analysis. The consistency between the experiments and the molecular mechanism reveals that the formation of the hydrogen bond between the IL and CVOC enhances the absorption process.

Prediction of the volumetric and vapor-liquid equilibrium properties of CO2-N2-O2-Ar fluid mixtures with a general Helmholtz equation of state

A general equation of state (EOS) explicit in the form of Helmholtz free energy has been developed to predict the pressure-volume-temperature-composition (PVTx) and vapor-liquid equilibrium (VLE) properties of the CO2N2O2-Ar fluid mixtures. The EOS, which uses four mixing parameters, is based on highly accurate EOS for pure CO2, N2, O2 and Ar fluids and contains a simple generalized departure function presented by Lemmon and Jacobsen (1999). Four mixing parameters are fitted from the experimental PVTx and VLE data of binary systems available. Comparison with experimental data available indicates that the EOS can reproduce the PVTx and VLE properties of CO2N2O2-Ar fluid mixtures up to 453 K and 1000 bar within or close to experimental uncertainties. The general EOS can be used to evaluate the change of density and VLE composition from impurities N2, O2 and Ar during the CO2 capture and sequestration process.

Vapour-liquid equilibrium for xylenes + tetrapropylene glycol binary systems: Experimental data and regression

In this study are reported vapour-liquid equilibrium (VLE) data for three binary systems such as xylenes + tetrapropylene glycol (TePG). These data have been measured in the temperature range (310.15 to 538.15) K for the systems involving o-xylene, m-xylene, p-xylene and TePG. The VLE experimental data were determined by using static equilibrium apparatus. The p-T-x data were regressed using the NRTL model with three, five and eight parameters. The results obtained using NRTL with eight parameters presents the smallest relative deviations of the calculated values for vapour pressure and composition compared to experimental values. A comparison was made using the T-x-y diagrams between the data obtained with the NRTL resulted parameters based on experimental VLE data and the data calculated using the UNIFAC predictive model.

Vapor-liquid equilibrium of acid gases with imidazolium-based ionic liquids using the UMR-PRU model

The UMR-PRU group contribution equation of state (EoS), which couples the Peng-Robinson EoS with UNIFAC via the Universal Mixing Rules, is extended to pure imidazolium-based ionic liquids (ILs), as well as to their mixtures with CO2 and H2S. The studied ILs consist of alkyl-methylimidazolium cations and tetrafluoroborate, hexafluorophosphate and bis(trifluoromethylsulfonyl)imide anions. The EoS parameters of pure ionic liquids, are determined by fitting experimental vapor pressure and liquid density data. For the extension of UMR-PRU to binary CO2/IL and H2S/IL mixtures, the model parameters are determined by fitting experimental binary vapor-liquid equilibrium data of acid gases with ionic liquids. For comparison, the Peng-Robinson coupled with the conventional van der Waals one-fluid mixing rules (vdW1f) is also applied to the same systems, using adjustable attractive and co-volume cross interaction parameter. It is shown that Peng-Robinson accurately describes pure ionic liquid vapor pressures and liquid densities, while UMR-PRU yields very satisfactory vapor-liquid equilibrium results for binary and ternary mixtures containing ILs and acid gases. Overall, UMR-PRU yields much better results than Peng-Robinson coupled with the vdW1f mixing rules, which indicates the superiority of the UMR mixing rules over the vdW1f ones.