Two-phase Equilibrium Research Articles

Mass Transfer and Droplet Behaviors in Liquid-Liquid Extraction Process Based on Multi-Scale Perspective: A Review

Liquid-liquid extraction is an important separation technology in the chemical industry, and its separation efficiency depends on thermodynamics (two-phase equilibrium), hydrodynamics (two-phase mixing and contact), and mass transfer (molecular diffusion). For hydrodynamics, the dispersion size of droplets reflects the mixing of two phases and determines the mass transfer contact area of the two phases. Therefore, a deep understanding of the droplet dispersion mechanism can help guide process intensification. The mass transfer and droplet behaviors in the liquid-liquid extraction process are reviewed based on three scales: equipment, droplets, and the interface between two liquids. Studies on the interaction between mass transfer and other performance parameters in extraction equipment as well as liquid-liquid two-phase flow models are reviewed at the equipment scale. The behaviors of droplet breakage and coalescence and the kernel function of the population balance equation are reviewed at the droplet scale. Studies on dynamic interfacial tension and interaction between interfaces are reviewed at the interface scale. Finally, the connection among each scale is summarized, the existing problems are analyzed, and some future research directions are proposed in the last section.

Phase relations in heat treated sodium borosilicate glasses

Sodium borosilicate glasses are processed to porous glasses as well as to Vycor™ type glasses via phase separation and selective leaching. Both materials consist mainly of SiO2. Thermal treatment inducing phase separation is crucial for microstructure development. Sodium borosilicate glasses with molar compositions of 8Na2O.21B2O3.71SiO2 and 8Na2O.28B2O3.64 SiO2 were melted, rapidly cooled and investigated by thermal analysis and scanning electron microscopy. The glasses were thermally treated for 120 h at 630 to 730°C, and then leached, first for 72 h in 0·1 M HCl at 60°C, and subsequently for 4 h in 0·5 M NaOH at 30°C. X-ray fluorescence was applied to characterise the chemical compositions. Microstructure development was first analysed by differential thermal analysis and dilatometry, and the pore structure was characterised by Hg porosimetry and N2 adsorption. Heat treated glasses were then analysed by low voltage scanning electron microscopy, combined in one case with chemical analysis by energy dispersive x-ray analysis. The results are discussed with respect to phase relations. After long term heat treatment, at least three phases exist in two independent metastable two-phase equilibria on different size and time scales.

Efficient high temperature PEMFC metallic stack with innovative two-phase liquid cooling

High temperature (HT) polymer electrolyte membrane fuel cells (PEMFCs) are highly beneficial for high power applications. They can be used in both stationary and portable power devices combining the advantages of the PEM type cells (flexibility in dynamic operation, compactness) and high temperature operation (elimination of fuel humidification and carbon monoxide clean up). This work focuses on the development, construction and testing of an efficient all-metallic HT-PEMFC stack with a power output of 1 kWe. The selection of the proper polymer electrolyte allowed the operation of the stack within the range of 160–190 °C. The Membrane-Electrode-Assemblies (MEA) and all components of the stack were designed and prepared in-house. The fuel cell stack characteristics and performance are affected by many parameters such as the materials, components’ design and proper assembly of the stack, as well as the operating conditions. The stack accomplished 50% electrical efficiency with power output of 1070 W and a power density of about 0.18 W/cm2 at 180 °C under pure H2 feed. The same performance was reached with reformate hydrogen feeds. The 1 kW electrical and 1 kW thermal power HT-PEMFC stack presented herein consists of thirty MEAs, metallic bipolar plates and an innovative cost-efficient internal pumpless two-phase equilibrium water-steam cooling. The effective design and construction of the latter secures temperature gradientless and isothermal operation of the stack and the production of high temperature superheated steam, which is an effective carrier of high-quality thermal energy with several commercial and industrial applications.

Investigation on the mechanical and pitting corrosion behaviour of solution-treated 22% Cr lean duplex stainless steel with different Mn/N ratio

ABSTRACT Effect of Mn/N ratio on the microstructure evolution, mechanical and pitting corrosion properties of solution-treated 22% Cr lean duplex stainless steel (DSS) was investigated. As the Mn/N ratio decreased, tensile and yied strength, as well as elongation,increased due to the strengthening solid solution effect of more nitrogen addition, and two-phase equilibrium was obtained at 17.80 Mn/N ratio. The drop in the amount of Cr2N, more dislocation cell formation in ferrite and the increase of slip bands in austenite contributed to an increase in toughness with increasing Mn/N ratio from 3.28 to 17.80, whereas more σ precipitates and ferrite fraction resulted in a decrease of it at 54.14 Mn/N ratio. Moreover, higher pitting corrosion resistance was obtained for 17.80 Mn/N ratio DSS than that for 2205 DSS due to the thicker and more compact passive film formation, but higher Mn/N ratio of 54.14 decreased it with more loose MnO formation.

Homogeneous nucleation rate of methane hydrate formation under experimental conditions from seeding simulations.

In this work, we shall estimate via computer simulations the homogeneous nucleation rate for the methane hydrate at 400 bars for a supercooling of about 35K. The TIP4P/ICE model and a Lennard-Jones center were used for water and methane, respectively. To estimate the nucleation rate, the seeding technique was employed. Clusters of the methane hydrate of different sizes were inserted into the aqueous phase of a two-phase gas-liquid equilibrium system at 260K and 400 bars. Using these systems, we determined the size at which the cluster of the hydrate is critical (i.e., it has 50% probability of either growing or melting). Since nucleation rates estimated from the seeding technique are sensitive to the choice of the order parameter used to determine the size of the cluster of the solid, we considered several possibilities. We performed brute force simulations of an aqueous solution of methane in water in which the concentration of methane was several times higher than the equilibrium concentration (i.e., the solution was supersaturated). From brute force runs, we infer the value of the nucleation rate for this system rigorously. Subsequently, seeding runs were carried out for this system, and it was found that only two of the considered order parameters were able to reproduce the value of the nucleation rate obtained from brute force simulations. By using these two order parameters, we estimated the nucleation rate under experimental conditions (400 bars and 260K) to be of the order of log10 (J/(m3 s)) = -7(5).

Elucidation of diffusion blocking effect during anomalous structural change of L12 + D022 → L12 in Ni3Al1−xVx (0.4 < x < 0.55) alloys by a first-principles calculation

The mechanical properties of Ni3Al1−xVx alloys (0.4 < x < 0.55) at elevated temperatures are deteriorated by the disappearance of D022-Ni3V regions even though two-phase equilibrium of L12-Ni3(Al, V) and D022-Ni3V is predicted from the phase diagram. This anomalous structural change of L12 + D022 → L12 stems from the stagnation of V diffusion in the L12 matrix, but the mechanism of such a “diffusion blocking effect” has not been elucidated. In this study, a first-principles calculation was employed to quantify diffusion coefficients of Al and V in stoichiometric Ni3Al and V-doped Ni3Al from the intrinsic formation energies, migration energies and activation energies required for their diffusion. The calculated diffusion coefficient of V was three orders of magnitude smaller than that of Al, and thus the shorter diffusion distance of V than the requisite diffusion length for the retention of D022 was found to be responsible for the diffusion blocking effect observed in the Ni3Al1−xVx alloys.

Thermodynamic modeling of the Mg–Nd–Sr ternary system with key experimental investigation

The phase equilibria in the Mg-rich region of the Mg–Nd–Sr ternary system at 300 and 350 °C were established using equilibrated-sample method. Powder X-ray diffraction (XRD) technique and scanning electron microscopy (SEM) equipped with energy-dispersive spectroscopy (EDS) were used for phase composition determination. Four three-phase equilibria and four two-phase equilibria have been experimentally determined at both isothermal sections of 300 and 350 °C. The phase equilibria relationships in the Mg-rich side were studied. The major invariant reaction temperatures of vertical sections with 80 at. % Mg and 10 at. % Sr were determined with differential scanning calorimetry (DSC) test. Moreover, thermodynamic modeling of Mg–Nd–Sr ternary system has been carried out by CALPHAD method based on the present key experimental results. The liquid solution was described using the modified quasi-chemical model in the pair approximation (MQMPA). The compound energy formalism (CEF) was used for the solid phases. The present obtained thermodynamic database of Mg–Nd–Sr ternary system will provide an important support for the Mg-based biodegradable implant development.

Investigations on the Phase Transformations, Equilibria and Athermal ω in Ni-Ga-Cr Ternary System.

In the present work, the phase equilibria of the Ni-Ga-Cr ternary system at 850, 1000 and 1150 °C were experimentally investigated to provide the essential data for developing the high-entropy shape memory alloys (HESMAs) containing Ni, Ga and Cr. At 850 °C, in the Ni-rich portion, the B2 phase shows equilibrium with the L12 phase when the Cr content is less than 10.49 at. %, while displaying the equilibrium with L12 and BCC phases when the Cr content increases. The B2 + L12 + BCC changes into B2 + FCC + BCC three-phase equilibria from 850 to 1150 °C, as the L12 phase region becomes narrow with rising temperature. The two-phase equilibrium, B2 + BCC, was found at all the isothermal sections investigated. Other three-phase equilibria were also discovered: B2 + α-Cr3Ga + BCC and Ni2Ga3 + α-Cr3Ga + L at 850 °C, and B2 + α-Cr3Ga + L at 1000 °C. Significantly, an athermal ω intermetallic compound with the space group of P3¯m1 was observed distributing at the B2 phase in the quenched Ni45.98-Ga25.50-Cr28.52, Ni42.23-Ga15.70-Cr42.07 and Ni16.54-Ga13.63-Cr69.83 (at. %) alloys after being annealed at 1150 °C for 10 days. The high-resolution transmission electron microscopy (HRTEM) results reveal that the ω shows a crystallographic orientation of [11¯0]B2//[112¯0]ω; (111)B2//(0001)ω with the B2 parent phase.

A Review of Phase Behavior Mechanisms of CO2 EOR and Storage in Subsurface Formations

The emissions of CO2 have been recognized as the main cause of climate change. As an important strategy being used to reduce the CO2 concentration in the atmosphere, carbon capture, utilization and storage (CCUS) has attracted significant attention in recent years. Geological formations, including depleted oil and gas reservoirs and saline aquifers, are popular CO2 storage options. During the process of CO2 storage in subsurface formations, the interactions between CO2 and formation fluids must be considered as they could greatly affect the CO2 trapping mechanisms and CO2 storage capacity. In this paper, we give a brief review of the phase behavior mechanisms associated with CO2 storage in subsurface formations. Two different CO2-storage strategies are considered in this paper: CO2 storage in saline aquifers and CO2 storage in oil reservoirs. Multiphase equilibria, including two-phase, three-phase, and four-phase equilibria, can be observed during CO2 injection into underground formations. Both the experimental and modeling studies on the related phase behavior mechanisms are included in this Review. We also introduce some recently developed robust algorithms for the multiphase equilibria calculations, which could be essential for the design of the CO2 storage process and prediction of CO2 storage capacity.

Removal of Dye from Synthetic Wastewater by Liquid Membrane

New technologies have risen into popularity causing the Liquid membrane techniques to evolve over other separation techniques due to its high selectivity and recovery, increased fluxes, and reduced investment and operating cost. This work focuses on extracting Methylene Blue (MB), a cationic dye using a simple BLM separation technique from its aqueous phase. It combines extraction and stripping in a single unit operation. The feed phase was an aqueous solution of MB, the solvent chosen was soybean oil for the liquid/organic membrane phase, and tri-octyl amine acted as a carrier. The strip phase was a hydrochloric acid solution for this study. A two-phase equilibrium study was done to choose the correct solvent, carrier, and receiving phase (soybean oil, tri-octyl amine, and HCl) were chosen, which was then followed by a three-phase study. Effect of various parameters like equilibrium time, feed and stripping phase pH, stirring speed, carrier concentration, initial feed concentration, and strip phase concentration were all studied to find out the most optimum working condition for maximum extraction and recovery of MB. The removal efficiency of MB by using soybean oil was found as 92%, at the optimum process conditions for the transport of MB were found as follows: pH in the feed phase (11), pH in the stripping phase (5), initial concentration of MB (20 ppm), carrier concentration (7%) (v/v) TOA and stirring speed (250 rpm), respectively.

Liquid-liquid equilibria for (polypropylene glycol 400 based magnetic ionic liquids + inorganic salts) aqueous two-phase systems at 298.15 K

Two polypropylene glycol 400 (PPG400) based temperature-sensitive magnetic ionic liquids were successfully used to construct the temperature-sensitive magnetic ionic liquid aqueous two-phase systems (MILATPs). This temperature-sensitive MILATPs combined temperature-controlled recovery and the advantages of a MILATPs and is showing great potential in the field of extraction and separation. In this work, aqueous two-phase equilibrium data of the temperature-sensitive MILATPs ([HOPPG400BMIM][Tempo-OSO3] + K3PO4/K2CO3/ Na2CO3 + H2O systems and [BMIMPPG400BMIM][Tempo-OSO3]2 + K3PO4/K2CO3/ Na2CO3 + H2O systems) were determined at 298.15 K under 0.1 MPa. Three common empirical equations including Merchuk equation were adopted to fit the experimental binodal data with satisfactory correlation performances. Inorganic salts screening demonstrated that K3PO4 and K2CO3 have better phase-forming ability than Na2CO3. Morever, [HOPPG400BMIM][Tempo-OSO3] has a better phase-forming ability than [BMIMPPG400BMIM][Tempo-OSO3]2. Subsequently, tie line data for systems containing K3PO4 or K2CO3 were determined and correlated by two empirical equations with satisfactory correlation performances. Furthermore, the temperature- controlled recovery of temperature-sensitive magnetic ionic liquid was ideally realized simply by heating. All these experimentally measured liquid–liquid equilibrium data and the theoretical correlations can provide valuable reference for future application in the field of extraction and separation.

Calculation of thermodynamic properties of mixtures in two-phase equilibrium

Thermodynamic properties of mixtures in vapor-liquid equilibrium (VLE) were studied. Thermodynamic properties of the methane-ethane mixtures in VLE were calculated with highly accurate Helmholtz free energy equation of state GERG-2008, simplified GERG-2008 and common cubic PR equation of state (EOS). Results show that GERG-2008 has high accuracy in VLE calculations. However, simplified GERG-2008 and PR-EOS both work unsatisfactorily in VLE calculations.

Steady-State Thermal-Hydraulic Analysis of Steam Generator with Axial Economizer Based on Node Method

Based on the one-dimensional flow hypothesis, heat transfer hypothesis, and two-phase thermal equilibrium hypothesis, a lumped parameter method and a distributed parameter method are used to establish a one-dimensional steady-state thermal-hydraulic analysis model of the steam generator with axial economizer. Using C++ language programming, the calculation results are compared with the design values of the thermal-hydraulic parameters of a typical steam generator with axial economizer. The results show that the relative error of most of the overall parameter calculation results is within 3%, which verifies the rationality of the model. The analysis of the temperature, cavitation share, pressure and other parameters of the steam generator along the direction of the measured fluid flow trend consist well with the results of thermal hydraulics and qualitative mechanism analysis, indicating that the model and solution method established in this paper can accurately predict the steady-state thermal hydraulic parameter distribution of the steam generator with axial economizer.

Determination and correlation of phase equilibria of chiral magnetic ionic liquid aqueous two-phase systems with different inorganic salts at 298.15 K

Three novel chiral magnetic ionic liquids (MILs) with L-Pro anion were synthesized and applied to construct chiral magnetic ionic liquid aqueous two-phase systems (chiral MILATPs). This is the first reported chiral MILATPs and is showing great potential in the extractive resolution of racemic amino acids. In this work, aqueous two phase equilibrium binodal data of these chiral MILATPs ([CnMIM-Tempo][L-Pro](n = 2–4) + K2CO3/K3PO4/Na2CO3/Na2SO4 + H2O) were measured at temperature of 298.15 K. Three classical empirical equations including Merchuk equation were applied for the correlation of the experimental binodal data to obtain the binodal curve. Satisfactory correlation performances were achieved. The screening of inorganic salt revealed that K2CO3 and K3PO4 are better salting-out reagents than Na2CO3 and Na2SO4. Investigation of chiral MIL species demonstrated that chiral MIL with longer alkyl chain length of cation has better phase forming ability when the values of n are in the ranges of 2–4. Moreover, tie-line data for systems containing K2CO3 or K3PO4 were measured and correlated by Othmer-Tobias equation with satisfactory fitting performances (all R2 higher than 0.99). These results has ensured the reliability of these experimental data. The phase behaviors of these chiral MILATPs in this work has proved to meet the need of practical application and all these tested aqueous two-phase equilibrium data as well as the corresponding thermodynamic fitting can provide us useful reference for the future application in the field of extractive resolution of racemic amino acids.

Liquid–Liquid Demonstrations: Phase Equilibria and the Lever Rule

The lever rule applies to any two-component system existing in a state of two-phase equilibrium. Here, several classroom demonstrations are described to help students understand liquid–liquid coexistence and the lever rule using a set of isobutyric acid + water + dye samples ranging in composition from water + dye to isobutyric acid + dye. The critical temperature of the partially miscible isobutyric acid + water system is just above room temperature, so students can perceive the general shape of the coexistence curve by watching a progression of phase separations take place over time as the set of prewarmed single-phase samples are allowed to cool. Qualitative visualization of the lever rule is demonstrated by showing students the set of samples after equilibration at a temperature well below the critical temperature. An interactive Excel spreadsheet is provided to help students connect their observations of the samples with the phase diagram. Quantitative and intuitive interpretation of the lever rule can be achieved through height measurements of the biphasic sample layers, leading to immediate graphical determination of the compositions of the isothermal equilibrated phases in the classroom. The set of samples may also be used in an extended classroom or laboratory project to map out the coexistence curve, and advanced students can use the coexistence data to estimate the critical composition of the system, as well as the universal critical exponent β. Finally, preparation of a stable hexaphasic immiscible liquid mixture is described.

An approach based on consecutive high-speed counter-current chromatography for preparation of an active compound rutin from Apocynum venetum L

Apocynum venetum is a kind of plant with high medicinal value. Its main component is rutin, which is widely used. In the present study, an efficient method based on high-speed counter-current chromatography (HSCCC) was established to separate rutin from A. venetum. The optimized solvent system composed of ethyl acetate-n-butanol-water (4:1:5, v/v) was selected for HSCCC separation. It was found that the maximum loading amount was 1 g, but the loading amount did not affect the two-phase equilibrium of solvent system. Therefore, consecutive high-speed counter-current chromatography was introduced to further improve the yield in the present study. As a result, 292 mg of rutin with 95% purity was obtained from 2.4 g crude sample. The retention of the stationary phase was 27%, which was almost unchanged. The current strategy can not only be used for the scale-up preparation of rutin, but also provide an example for the preparation of other natural active compounds.

Development of ultrasound-assisted centrifugal extraction combined with two countercurrent chromatography systems for the simultaneous extraction and isolation of phytochemicals.

We proposed a method for the extraction of medicinal herbs, called ultrasound-assisted centrifugal extraction, and an online solvent concentration method. These techniques were coupled with two countercurrent chromatography systems and applied to the continuous extraction and online isolation of chemical constituents from Inonotus obliquus. Raw plants were extracted using a two-phase petroleum-ethanol-water (2.0:1.0:2.0, v/v/v) process, and then the aqueous and organic phases were concentrated using the proposed online solvent concentrator. The countercurrent chromatography preparation prior to separation includes pumping of the two-phase solution, rotating column, and equilibrium column. Following online concentration, the extracted solution was pumped into a second countercurrent chromatography process for separation. During separation, the extraction solution and concentrated extract were prepared automatically. Upon completion of the first cycle of ultrasound-assisted centrifugal extraction/two countercurrent chromatography, the second cycle experiment starts. This process can be indefinitely repeated. In this study, six target compounds with purities above 97.71% were successfully extracted and isolated online using a two-phase solvent system consisting of n-hexane-ethyl acetate-acetonitrile (4.5:1.5:5.5, v/v/v) and n-hexane-ethyl acetate-methanol-water (0.4:3.0:1.5:2.5, v/v/v/v). Compared to conventional extraction methods, the instrumental setup of the proposed method provides enhanced automation, efficiency, purity, and systematic extraction and isolation of natural products.

An Accurate Model to Calculate CO2 Solubility in Pure Water and in Seawater at Hydrate–Liquid Water Two-Phase Equilibrium

Understanding of CO2 hydrate–liquid water two-phase equilibrium is very important for CO2 storage in deep sea and in submarine sediments. This study proposed an accurate thermodynamic model to calculate CO2 solubility in pure water and in seawater at hydrate–liquid water equilibrium (HLWE). The van der Waals–Platteeuw model coupling with angle-dependent ab initio intermolecular potentials was used to calculate the chemical potential of hydrate phase. Two methods were used to describe the aqueous phase. One is using the Pitzer model to calculate the activity of water and using the Poynting correction to calculate the fugacity of CO2 dissolved in water. Another is using the Lennard–Jones-referenced Statistical Associating Fluid Theory (SAFT-LJ) equation of state (EOS) to calculate the activity of water and the fugacity of dissolved CO2. There are no parameters evaluated from experimental data of HLWE in this model. Comparison with experimental data indicates that this model can calculate CO2 solubility in pure water and in seawater at HLWE with high accuracy. This model predicts that CO2 solubility at HLWE increases with the increasing temperature, which agrees well with available experimental data. In regards to the pressure and salinity dependences of CO2 solubility at HLWE, there are some discrepancies among experimental data. This model predicts that CO2 solubility at HLWE decreases with the increasing pressure and salinity, which is consistent with most of experimental data sets. Compared to previous models, this model covers a wider range of pressure (up to 1000 bar) and is generally more accurate in CO2 solubility in aqueous solutions and in composition of hydrate phase. A computer program for the calculation of CO2 solubility in pure water and in seawater at hydrate–liquid water equilibrium can be obtained from the corresponding author via email.

Experimental measurement on the phase equilibria of the Mg–Ag–Cu ternary system at 350 and 400 °C

The phase equilibria of the Mg–Ag–Cu ternary system at 350 and 400 °C were experimentally investigated using twenty-eight key samples. The phase equilibria and compositions in key samples were investigated using scanning electron microscopy (SEM) equipped with energy-dispersive spectroscopy (EDS). Powder X-ray diffraction (XRD) technique was used to analyze the crystal structure and solid solubility of compounds. Five three-phase equilibria and several two-phase equilibria have been determined at 350 and 400 °C. The solid solubility range of Cu in the compounds Mg 3 Ag, MgAg and fcc(Ag) were examined at 350 and 400 °C. The maximum solid solubility of Ag in the compound MgCu 2 was found to be 11.46 at.% and 11.25 at.% with a constant value of about 66 at.% Cu at 350 and 400 °C, respectively. Besides, the solid solubility limits of Ag in the compounds Mg 2 Cu and fcc(Cu) were found to be less than 5 at.% at 350 and 400 °C. No ternary compound was observed in the present work.

Thermodynamics of phase transitions in the subsolidus domain of the FeO–MgO–TiO2 system

This paper gives consideration to the three-component FeO–MgO–TiO2 system that is a part of the four-component MgO–Al2O3–FeO–TiO2 system which serves to produce materials with valuable properties. The structure of binary FeO–TiO2 and MgO–TiO2 systems is described and the available data on the FeO–MgO–TiO2 system are analyzed. We present the thermodynamic data on all system compounds and calculate change of the free Gibbs energy in the temperature range of 800 to 1900 K for three exchange reactions. It was established that the triangulation of the FeO–MgO–TiO2 system changes in three following temperature ranges: at the temperatures of up to 1115 К, at 1115 to 1413 К (the restructuring of conodes here occurs) and above 1413 K (stable pseudobrookite is formed). It was shown that the following two-phase equilibria are stable: MgTi2O5–FeTiO3, FeTiO3–MgTiO3, MgTiO3–Fe2TiO4, Fe2TiO4–Mg2TiO4 and Mg2TiO4–FeO at the temperatures of up to 1115 K; MgTi2O5–FeTiO3, FeTiO3–MgTiO3, FeTiO3–Mg2TiO4, Fe2TiO4–Mg2TiO4 and Mg2TiO4–FeO in the temperature range of 1115 to 1413 K; and MgTi2O5–FeTi2O5, MgTi2O5–FeTiO3, FeTiO3–MgTiO3, FeTiO3–Mg2TiO4, Fe2TiO4–Mg2TiO4 and Mg2TiO4–FeO at the temperatures of above 1413 K.