Tie-line Compositions Research Articles

Thermodynamic Investigation of the Aqueous Two-Phase Systems Formed by PEG 400 + Water + Either Sodium Carbonate or Potassium Carbonate at Different Temperatures: Experimental and Correlational Approaches

Systems composed of poly(ethylene)glycol (PEG 400) + water + either potassium carbonate or sodium carbonate were studied at 283.15, 298.15, and 313.15 K. The effects of temperature and the electrolyte on phase segregation were evaluated. The phase segregation process was endothermic and entropically driven. The efficacy of the cations in inducing phase formation with PEG 400 followed the order K2CO3 < Na2CO3. The binodal curves were successfully described using the empirical equation suggested by Merchuk and modified to include the effect of temperature. Tie-line compositions were correlated using the Othmer–Tobias, Bancroft, and Hand equations. The experimental tie-line data for PEG 400 + K2CO3 + water and PEG 400 + Na2CO3 + water were also correlated using the nonrandom two liquid model. The use of this thermodynamic model resulted in reliable data for the system while reducing the number of experiments needed. All of the correlations indicated satisfactory fits between the calculated and experimental data.

Phase equilibria of aqueous mixtures of PEG with formate salt: Effects of pH, type of cation, polymer molecular weight and temperature

Liquid-liquid equilibrium (LLE) data for poly (ethylene glycol) (PEG) of different molecular weights (600, 1500, 3000, 6000) + sodium formate (NaCHO2), potassium formate (KCHO2) + water at different temperatures (298.15 and 308.15 K) and for PEG (1500) + sodium formate + water at different pH values (8.05, 9.06, 10.92), were determined experimentally. The tie lines and plait point are reported at different PEG molecular weight, pH, temperature and type of cation. Furthermore, the effect of those parameters on binodal curve, tie-line length (TLL) and slope of tie line (STL) are discussed in detail by comparing the results to that of literature data. The effective excluded volume (EEV) values obtained from the LLE data were used to study the effect of the parameters on the binodal curves. The phase composition and the tie-lines’ ends were obtained by measuring the density (ρ) and refractive index (nD). Furthermore, the binodal curves and the tie-line compositions were well-fitted by using some semi empirical equations.

Liquid–Liquid Extraction of Neutral Lipids and Free Fatty Acids from Microalgae Oil

Microalgae have been established as an excellent source of biomass for biodiesel production. However, the high free fatty acids content of the oil hinders the oil refining by conventional processes. The aim of this study was to separate neutral lipids in high acidity oils, such as microalgae, by determining the equilibrium data of the extraction system including triacylglycerol, free fatty acids, hexane, and hydrous ethanol (95%). Because the microalgae oil has a complex composition, a model oil blend analogous infatty acid composition to Desmodesmus communis oil was used. Experimental equilibrium curves (binodal) and tie-line composition were determined for oil blends with 2, 20, and 40% of FFA at 308.2, 313.2, and 318.2 K. Three empirical equations were used to correlate binodal data. The parameters of the equation with the best fit were used along with the phase separation data, which were obtained by gravimetric method, for the construction of the tie lines. The consistency of experimental tie-line data was checked by using the Othmer–Tobias and Bancroft equations. Neutral lipids distribution coefficient and FFA distribution coefficient, as well as the selectivity of hydrous ethanol, were calculated for all systems.

Study of liquid-liquid equilibria in aqueous two-phase systems formed by poly (ethylene glycol) (PEG) and sodium thiosulfate pentahydrate (Na2S2O3.5H2O) at different temperatures

This study aimed at providing experimental liquid-liquid equilibrium (LLE) data for aqueous two-phase systems (ATPSs) formed by poly (ethylene glycols) (PEG) of different molecular weights (1500 or 4000 or 6000) g.mol−1 and sodium thiosulfate pentahydrate at different temperatures (293.15–313.15) K and under atmospheric pressure. Correlations of experimental data of binodal curves were carried out using the Merchuk methodology. The effects of temperature, polymer molecular weight and of the nature of the anion of salts on binodal curves were discussed. In comparison with other anions previously investigated, the salting-out ability of the thiosulfate anion was between those of citrate and tartrate anions. Finally, the Othmer-Tobias and Bancroft equations and the NRTL activity coefficient model were used for correlating tie line compositions.

Influence of the Temperature, Type of Salt, and Alcohol on Phase Diagrams of 2-Propanol + Inorganic Salt Aqueous Two-Phase Systems: Experimental Determination and Correlation

The liquid–liquid equilibriums (LLEs) for 2-propanol + tripotassium phosphate + water at 298.15, 308.15, and 318.15 K and 2-propanol + dipotassium hydrogen phosphate + water at 298.15 K were measured. The binodal curves of 2-propanol + potassium sulfate/potassium sulfite + water at 298.15 K were measured and compared. Accordingly, the experimental binodal data were correlated using Merchuk, Hu, and Pirdashti equations, and the tie-line compositions were correlated using Othmer–Tobias and Bancroft equations. The effect of temperature, anion type, and length of alcohol chain on the binodal curve, tie-line length (TLL), slope of tie-line (STL), and phases’ physical properties were studied. It was found that an increase in salt’s hydrophobicity and alcohol’s carbon number in low temperature led to the expanding biphasic region and approaching the binodal curve to the origin. The phase-forming ability of different anions was studied using effective excluded volume (EEV) model, and the relation between the EEV ...

Thermodynamic Studies of the Aqueous Two-Phase System Containing Polyethylene Glycol Dimethyl Ether 2000 and Sodium Nitrite at (298.15, 308.15, and 318.15) K

Liquid–liquid equilibrium data including binodals and tie-line compositions have been measured for aqueous ternary biphasic system containing polyethylene glycol dimethyl ether 2000 (PEGDME2000) and sodium nitrite at three temperatures (298.15–318.15) K and atmospheric pressure (≈ 85 kPa). The salting-out of the polymer by the salt was studied at different temperatures. Furthermore, the ΔGc, ΔHc, and ΔSc of the cloud points were computed at working temperatures from which it was found that the entropy is the driving force for phase separation. For representing the experimental binodal data two empirical equations with the temperature dependency were used. The Setschenow equation was utilized for correlating the measured tie-lines. Different versions of nonrandom two-liquid models were also selected in generating the obtained tie-lines. The plait point, and the characteristics of tie-lines (slope and the length) have been determined at working temperatures. The partitioning behavior of the iodine molecule ...

Experimental measurement and thermodynamic modelling of liquid-liquid equilibria for the separation of 1,2-dichloroethane from cyclohexane using various extractants

Experimental liquid-liquid equilibrium (LLE) data for the cyclohexane +1.2-dichloroethane+solvent ternary systems were determined at T=313.15K and p=101.3kPa, where the extracting agents are sulfolane, dimethyl sulfoxide, 1,4-butanediol and N,N-dimethylmethanamide. According to the experimental values, solute distribution coefficient and selectivity were obtained to estimate the feasibility of the utilization of the selected solvents for extraction of 1,2-dichloroethane from cyclohexane. The reliability and consistency of the experimentally measured LLE results were then corroborated by employing the Hand and Bachman equations. In addition, the experimental tie-line compositions were successfully regressed with the universal quasi-chemical (UNIQUAC) and nonrandom two-liquid (NRTL) thermodynamic models, and the values of relevant binary energy parameters were reported as well. Further, the solvent cost analysis indicated that dimethyl sulfoxide was a desirable extractant for separation of 1,2-dichloroethane from cyclohexane.

Measurement and Correlation of Ternary (Liquid + Liquid) Equilibria for Separation of Cyclohexanone from Water via Isophorone or Mesityl Oxide

Liquid–liquid equilibria provide basic data and guidance regarding the design, simulation, and development of an appropriate solvent extraction process. In the current work, the data for the liquid–liquid equilibrium (LLE) of water + cyclohexanone + isophorone and water + cyclohexanone + mesityl oxide systems have been measured at temperatures of 308.15–328.15 K and pressure of 101.3 kPa. The empirical Bachman and Hand equations were utilized to confirm the consistency of experimentally determined LLE data. Meanwhile, the solute distribution ratio and separation parameter were obtained from the experimental equilibrium data to evaluate the extraction properties of the selected solvents. Additionally, a mathematical regression of experimental tie-line compositions for all of the investigated ternary mixtures was performed by means of the nonrandom two-liquid and universal quasi-chemical activity coefficient models to acquire corresponding optimized binary interaction parameters. The correlation results were verified to be coincident with the experimental ones and revealed that the above two thermodynamic models were of high-accuracy and suitable to regress the tie-line compositions for the investigated ternary systems.

Influence of the molecular weight of polymer, temperature and pH on phase diagrams of poly (ethylene glycol) + di-potassium tartrate aqueous two-phase systems

Phase diagrams and liquid – liquid equilibrium (LLE) data for aqueous two-phase systems (ATPSs) containing di-potassium tartrate (DPT) and poly (ethylene glycols) (PEG) (1500 and 6000) have been determined experimentally at different pH values (6.41, 7.74 and 9.05) and temperatures (298.15 and 308.15 K). The effect of molecular weights of the PEG, temperatures, and pH on the binodal curve, tie-line length (TLL) and slope of tie line (STL) was studied. It was found that an increasing in PEG molecular weight, temperature and pH led to the binodal curve displacement towards the origin and increasing two-phase region. Accordingly, the various empirical equations were used to correlate the binodal curves of these systems such as Merchuk equation and Pirdashti equation and the tie-line compositions were correlated using Guan equation. Also, the refractive index and density of ternary (PEG 1500/6000 + di-potassium tartrate (DPT) + water) system have been measured. The density and refractive index were employed as the physical properties to obtain the phase composition and the tie-lines ends and show a linear variation with mass fraction of the polymers and the salt. Also, it was found that TLL affects the density of ATPS. The density difference between the phases (Δρ) increased with an increment in the TLL and pH values and PEG molecular weights and temperatures. Finally, the salting-out ability of the systems were explained by using “Effective Excluded Volume (EEV) model”.

Enhanced partitioning of tryptophan in aqueous biphasic systems formed by benzyltrialkylammonium based ionic liquids: Evaluation of thermophysical and phase behavior

Ionic liquids (ILs) based aqueous biphasic systems (ABS) are envisioned to be promising separation and environmentally benign extraction media. In this context, novel ternary phase diagrams were determined for two ILs namely, Benzyltrimethylammonium chloride and Benzyltributylammonium chloride in presence of various potassium salts, K3PO4, K2HPO4, K2CO3 and KOH at 298.15K. The influence of benzyl group substitution on the cation of IL and nature of various potassium salts on the phase behavior were analyzed. Experimental binodal data were fitted to Merchuk's equation and tie line compositions and tie line length were also determined. Further, these IL based ABS in presence of various potassium salts have been systematically scrutinized for their efficiency to extract Tryptophan. For the better understanding of the role of thermophysical properties on phase behavior and extraction capability, density and viscosity of coexisting phases were measured at various compositions in the temperature range from 293.15 to 328.15K. Enhanced extraction coefficients achieved for the studied combinations of ILs and inorganic salts indicate the possible use of these ABS as efficient extraction systems. Further, the study of thermophysical properties suggested that selected ternary systems present more desirable features in terms of density and viscosity as compared to traditional polymer based ABS.

Determination of liquid–liquid equilibria data for (water + propanoic acid + 3-methylbutan-1-ol) ternary mixture at 293.15 K to 313.15 K

Liquid–liquid equilibrium (LLE) data for the ternary mixture of water+propanoic acid+3-methylbutan-1-ol were determined within the temperature range (293.15 to 313.15)K and atmospheric pressure. The phase diagrams containing solubility and tie-line data show the type-1 behavior of LLE. Refractive index measurements were performed to determine the binodal curves and the tie-line compositions of the equilibrium phases. It has been found that the relative mutual solubility of propanoic acid was higher in solvent phase than aqueous phase. For evaluation of the capability of solvent for extraction of propanoic acid from aqueous solutions, distribution coefficients and separation factors were measured. The high values of separation factors confirm that 3-methylbutan-1-ol is a suitable choice for this purpose. The reliability of the experimental tie-lines was checked through the Othmer–Tobias correlation equation. The NRTL and UNIQUAC models were used to correlate the tie-line data.

Density, refractive index and liquid–liquid equilibrium data of polyethylene glycol 3000 + potassium formate + water at different pH values

Abstract New liquid–liquid equilibrium data for polyethylene glycol (PEG) 3000 + CHO 2 K + H 2 O systems were measured at 298.15 K and pH values of 7.95, 8.40 and 9.98. It was found that an increase in pH caused the binodal curve to be displaced downward and the two-phase region to expand. Accordingly, the binodal curve was adjusted to the Pirdashti equation and the tie-line compositions were correlated using the Othmer–Tobias, Bancroft and Hand equations. The study measured the refractive index and densities of several homogeneous binary and ternary solutions. The solutions were used for calibration within a range of 0% to 30% of the mass of the PEG and potassium formate. The density and refractive index data show a linear variation with the mass fraction of the polymer and the salt. The effect of pH on the binodal, tie-line lengths (TLL) and slope of the tie-line (STL) in the systems was examined. It was found that an increase in pH increased the TLL and decreased the STL. It was observed that the density of the aqueous two-phase system was influenced by the TLL. The difference in density between phases (Δ ρ ) increased as the TLL and pH increased. It was found that the TLL and Δ ρ showed a linear relationship. The effective excluded volume (EEV) of the PEG was obtained and it was found that EEV also increased as the pH increased.

Theoretical and Numerical Study of Growth in Multi-Component Alloys

In multi-component systems, during diffusion-controlled growth of a precipitate from a supersaturated matrix, differential diffusivities lead to a selection of tie-line compositions different from the thermodynamic tie-line containing the alloy composition. In this paper, we address the multi-component version of the growth problem by extending Zener’s theory, and derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar, cylindrical, and spherical precipitates for independent as well as coupled diffusion of solutes in the scaling regime. We confirm our calculations by sharp interface and phase-field simulations in a ternary setting, in which we also extend the tie-line and growth constant predictions for two well-known limiting cases, namely partition and negligible partition under local equilibrium (PLE and NPLE).

An analytical model with interaction between species for growth and dissolution of precipitates

An analytical model for growth in a semi-infinite matrix with cross-diffusion between species is presented. Application is given for precipitation of the γ′-phase in the γ-matrix during isothermal holding at 600 °C in the Ni - 7.56 at.% Al - 8.56 at.% Cr alloy. The exact time-dependent solutions for the solute profiles and the growth kinetics are validated with a numerical front-tracking simulation. The simulation of cross diffusion terms in a multicomponent alloy is thus demonstrated. Extension of the analytical solution is given for growth in a matrix of finite size. The driving force is then based on a mathematical estimation of the far-field composition. The Gibbs-Thomson effect is also accounted for to consider the effect of curvature on the equilibrium tie-lines. Comparison of analytical solution with the numerical front-tracking simulation shows excellent agreement. Results also point out the detrimental approximation of using the average composition of the matrix for computing the driving force as well as the limitation of the solution proposed by Chen et al. [Acta Mater. 56 (2008) 1890]. A detailed discussion is finally given on the origin of oscillations observed for the time evolution of the precipitate radius which alternates between growth and dissolution regimes, pointing out the combined role of solute fluxes and tie-lines compositions at the precipitate/matrix interface.

Liquid–Liquid Equilibrium and Physical Properties of Aqueous Mixtures of Poly(ethylene glycol) with Zinc Sulfate at Different pH Values: Experiment, Correlation, and Thermodynamic Modeling

The current study measured liquid–liquid equilibrium data for poly(ethylene glycol) (PEG) 1500 + zinc sulfate + water at 298.15 K and in various pH values (2.54, 3.57, and 4.70). Accordingly, the binodal curve was fitted to the Merchuk equation, and the tie-line compositions were fitted to the equations of Othmer–Tobias and Bancroft. Moreover, the study measured the refractive indices and densities of several homogeneous binary and ternary solutions. These solutions are used for calibration within a range of 0–35 mass % of PEG and 0–30 mass % of ZnSO4. Then, the viscosities, densities, electrical conductivities, and refractive indices of binary (PEG 1500 + water; zinc sulfate + water) and ternary (PEG 1500 + zinc sulfate + water) systems were measured and correlated. According to the results obtained from the density data, there was a linear variation of the polymer and the salt mass fractions. The viscosity data of PEG 1500 solutions were correlated as a function of the mass fractions by using a nonlinea...

Liquid-liquid equilibrium and physical properties of aqueous mixtures of poly(vinyl pyrrolidone) with potassium phosphate at different pH: Experiments and modeling

Liquid-liquid equilibrium data for poly vinyl pyrrolidone (PVP) K30+K2HPO4+H2O system were measured at 298.15 K and different pH values (7.54, 8.05, and 9.47). A binodal curve was fitted to the Merchuk equation and the tie line compositions were fitted to both the Othmer-Tobias and Bancroft equations. The refractive indices and densities of several homogeneous binary and ternary solutions used for calibration were also measured within a range of 0–30 mass% of PVP and 0–50 mass% of K2HPO4. Then, the viscosities, densities, electrical conductivities, and refractive indices of binary (PVP K30+water; potassium phosphate+water) and ternary (PVP K30+potassium phosphate+water) systems were measured and correlated at different pH values. The density data showed a linear variation of the polymer and salt mass fractions. The viscosity data of PVP K30 solutions were correlated as a function of the mass fractions by using a nonlinear equation. The effects of the tie line lengths on the densities and viscosities of the aqueous two-phase systems were represented. Also, the modified UNIFAC-NRF is used to calculate the phase equilibria of the mention system. The fitted binary interaction parameters of the model were reported.

Liquid–Liquid Equilibrium Data for the Pseudoternary Model System of Refined Sunflower Seed Oil + (n-Hexanal, or 2-Nonenal, or 2,4-Decadienal) + Anhydrous Ethanol at 298.15 K

In this work, experimental liquid–liquid equilibrium data for three pseudoternary systems containing {refined sunflower seed oil + aldehyde + anhydrous ethanol} were determined at a temperature T of 298.15 K with u(T) = 0.05 K and atmospheric pressure. Binodal curves and tie line compositions are reported for n-hexanal, 2-nonenal, or 2,4-decadienal as solutes. The nonrandom two-liquid1 and universal quasichemical2 models satisfactorily correlated experimental tie line data. Othmer–Tobias3 and Hand4 methods attested the quality of experimental data. Further, the predictive capabilities of four versions5−9 of the UNIFAC10 method were analyzed.

Aqueous biphasic system formation using 1-alkyl-3-ethylimidazolium bromide ionic liquids as new extractants

In this work three 1-alkyl-3-ethylimidazolium bromide ionic liquids (alkyl=ethyl, hexyl and octyl) were synthesized applying both, conventional and microwave assisted synthetic paths. The phase diagrams for aqueous solutions of 1-alkyl-3-ethylimidazolium bromide ionic liquids as novel extractants combined with phosphate-based salts are reported and discussed in terms of aqueous biphasic system (ABS) formation. Merchuk equation was applied in order to correlate the experimental binodal data. The liquid⿿liquid equilibrium data (tie-line compositions and tie-line length) were also experimentally determined by a gravimetric method. The influence of the alkyl chain length on ABS formation ability was investigated. It was found that ability to form ABS increases with the increase of the alkyl chain length on the imidazolium cation. Also, it was found that ionic liquids with ethyl group in the N-3 position better form ABS compared to those with methyl substituent. This was discussed in terms of increasing ionic liquid hydrophobicity and poor affinity for water. In order to better understand the impact of the alkyl side chain of the imidazolium ion and the efficiency of ABS formation, computer simulations were performed using investigated ionic liquids with the ethyl group in the position N-3 of the cation and different alkyl substituents in the position N-1. Also, extraction of selected organic dyes was performed to demonstrate application of studied ionic liquids as novel extractants.

Comparative study of the LLE of the quaternary and ternary systems involving benzene, n-octane, n-decane and the ionic liquid [BMpyr][NTf2

In this work, the suitability of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide, [BMpyr][NTf2], as an extraction agent to replace the traditional organic solvents in the separation of aromatic/aliphatic hydrocarbons was evaluated. Following this aim, the (liquid+liquid) equilibrium (LLE) of the quaternary system {n-octane (1)+n-decane (2)+benzene (3)+[BMpyr][NTf2] (4)} and its corresponding ternary systems {n-octane or n-decane (1)+benzene (2)+[BMpyr][NTf2] (3)} was determined at T=298.15K and at 101.3kPa. Solute distribution ratio and selectivity were calculated from the experimental LLE values in order to evaluate the capability of this ionic liquid to accomplish the separation of benzene from its mixtures with n-octane and n-decane. A comparison of the results obtained from the LLE results of the ternary and quaternary systems was carried out. Finally, the experimental tie-lines compositions were correlated using the NRTL thermodynamic model.

Study of the suitability of two ammonium-based ionic liquids for the extraction of benzene from its mixtures with aliphatic hydrocarbons

The ammonium-based ionic liquids butyltrimethylammonium bis(trifluoromethylsulfonyl)imide, [N4111][NTf2] and tributylmethylammonium bis(trifluoromethylsulfonyl)imide, [N4441][NTf2] have been studied as separation agents on the extraction of benzene from its mixtures with the long chain aliphatic hydrocarbons octane, decane and dodecane. The liquid–liquid equilibria of the ternary systems {octane (1) + benzene (2) + [N4111][NTf2] (3)}, {decane (1) + benzene (2) + [N4111][NTf2] (3)}, {dodecane (1) + benzene (2) + [N4111][NTf2] (3)} and {dodecane (1) + benzene (2) + [N4441][NTf2] (3)} at T = 298.15 K and {octane (1) + benzene (2) + [N4441][NTf2] (3)} at T = (298.15, 308.15 and 318.15) K and atmospheric pressure were determined. From the experimental results, an analysis of the influence of the cation of the ammonium-based ionic liquids and the alkyl chain length of the aliphatic hydrocarbons was performed; together with a study of the effect of the temperature on the liquid-liquid extraction of benzene. The extraction effectiveness was evaluated by the calculation of solute distribution ratio and selectivity derived from the tie-lines compositions. Besides, a comparison of the obtained results with those found in literature for systems with sulfolane, which is the most industrially used solvent, was performed. Finally, the experimental tie-lines were correlated using the NRTL thermodynamic model.