Densities Of Saturated Solutions Research Articles

Influence of Viscosity on Variously Scaled Batch Cooling Crystallization from Aqueous Erythritol, Glucose, Xylitol, and Xylose Solutions.

This study presents a comprehensive comparison of the batch cooling crystallization performance of aqueous solutions containing sugars and sugar alcohols, namely, erythritol, glucose, xylitol, and xylose. Erythritol and xylitol are commonly used alternative sweeteners to replace sucrose. They can be obtained by fermentation-based bioprocesses, where glucose and xylose are typical raw materials. These model compounds were selected based on their differing rheological nature: saturated erythritol solution has a viscosity lower than 3 mPa·s, whereas xylitol has the highest viscosity: greater than 90 mPa·s in the studied temperature range. Viscosities and densities of saturated solutions as well as apparent viscosities of crystal-mother liquor suspensions were measured. The purpose was to evaluate their crystallization behavior within a specific temperature range from 40 to 20 °C and batch time of 2 h, with the aim of understanding the influence of viscosity on the process more comprehensively. The comparison within the selected compound systems was carried out in terms of the physical properties of the mother liquor and the crystalline product. In addition to empirical laboratory-scale (0.1 and 1 L) studies, larger-scale simulations (1 and 100 m3) were performed with the experimental data obtained on average particle size, density, and viscosity for mother liquor and crystal-mother liquor suspensions. Mixing characteristics, such as the dissipation energy, mass transfer coefficient, energy of collisions, and micromixing time, were calculated with VisiMix software when using a single or dual impeller mixer. Furthermore, the scaling up of erythritol, xylitol, glucose, and xylose batch cooling crystallization from 40 to 20 °C based on the scaling-up rule of constant tip speed and energy of dissipation was done with VisiMix to obtain overall data on mixing conditions with crystallizers of 1 and 100 m3 in volume. Furthermore, ANSYS CFD software was used to determine the strain rates close to the impeller tip and velocity profiles on various crystallizer scales.

Phase Diagram of the Ternary System NaCl−NaBr−H2O at 348 K

The phase diagram of ternary system NaCl−NaBr−H2O at 348 K was studied by the isothermal equilibrium dissolution method. The solubilities of salts and densities of saturated solutions in the ternary system were determined experimentally. The equilibrium solid phases were also determined by chemical analysis and X-ray powder diffraction. Using the experimental data, the phase diagram of the ternary system was plotted. The diagram comprises one univariant curve and one stationary phase in crystallization filed of Na(Cl,Br).The ternary system was of solid solution type. Density values in the equilibrium solution increase with an increase in the sodium bromide concentration while decrease with an increase of the sodium chloride concentration. Based on the above experimental results, the solid solution compositions can fit well with a quadratic function of the equilibrium liquid composition.

Liquid-solid equilibria in the quaternary system NaCl–Na2SO4–Na2B4O7–H2O and the quinary system NaCl–NaBr–Na2SO4–Na2B4O7–H2O at 348 K

According to the compositions of the underground brines in the Sichuan Basin, solid-liquid equilibria in the quinary system NaCl–NaBr–Na2SO4–Na2B4O7–H2O and its quaternary subsystem NaCl–Na2SO4–Na2B4O7–H2O at 348 K were measured by isothermal solution saturation method. The solubilities of salts and the densities of saturated solutions in the systems listed above were determined. Using the experimental data, phase diagrams, water content diagrams and density-composition diagrams were constructed, respectively. The quaternary system NaCl–Na2SO4–Na2B4O7–H2O belongs to a simple type, which consists of three univariant curves, one invariant point and three crystallization regions of NaCl, Na2B4O7 · 5H2O and Na2SO4. The equilibrium phase diagram (saturated with Na2SO4) in the quinary system NaCl–NaBr–Na2SO4–Na2B4O7–H2O is a type of solid solution and has not invariant point. There are two crystallization regions (saturated with Na2SO4): Na2B4O7 · 5H2O and solid solution Na(Cl,Br), one univariant curve.

Phase Equilibria in the Quaternary Systems KCl–K2B4O7–K2SO4–H2O and MgCl2–MgB4O7–MgSO4–H2O at 273 K

The method of isothermal dissolution equilibrium was used to study the solubilities of salts and the densities of saturated solutions in the two quaternary systems KCl–K2B4O7–K2SO4–H2O and MgCl2–MgB4O7–MgSO4–H2O at 273 K. The equilibrium solid phases were also determined by the method of X-ray diffraction. On the basis of experimental results, the phase diagrams and density versus composition diagrams of those quaternary systems at 273 K were plotted. The results indicate that both the phase diagrams of the two systems consist of one invariant point, three stable solubility isothermal curves, and three crystalline regions. The crystallization fields for the system KCl–K2B4O7–K2SO4–H2O correspond to K2B4O7·4H2O, KCl, and K2SO4. Those for the system MgCl2–MgB4O7–MgSO4–H2O correspond to MgB4O7·9H2O, MgCl2·6H2O and MgSO4·7H2O.

Study of Phase Equilibrium of NaBr + KBr + H2O and NaBr + MgBr2 + H2O at 313.15 K

The phase equilibrium for the ternary systems NaBr + KBr + H2O and NaBr + MgBr2 + H2O at 313.15 K was investigated by isothermal solution saturation method. The solubilities of salts and the densities of saturated solutions in these ternary systems were determined by chemical methods, while the equilibrium solid phases were analyzed by Schreinermarker wet residues method. Based on the experimental data, phase diagrams and density versus composition diagrams were plotted. The two ternary systems were type of simple common-saturation and without complex salt and solid solution. There are in all two crystalline regions, two univariant curves, and one invariant point in these phase diagrams of two ternary systems at 313.15 K. The equilibrium solid phases in the ternary system NaBr + KBr + H2O are KBr and NaBr·2H2O, and those in the ternary system NaBr + MgBr2 + H2O are NaBr·2H2O and MgBr2·6H2O.

Liquid-solid equilibria in the quinary system Na+, K+‖Br−, SO 4 2− , B4O 7 2− −H2O at 298 K

Solid-liquid equilibria in the quinary system Na+, K+‖Br−, SO42−, B4O72−−H2O at 298 K were measured by isothermal solution saturation method. The solubilities of salts and the densities of saturated solutions in the system were determined. Using the experimental data, phase diagram, Na+ content diagram, water content diagram and density-composition diagram were constructed, respectively. The double salt Na2SO4 · 3K2SO4 (Gla) was found in the quinary system Na+, K+‖Br−, SO42−, B4O72−−H2O at 298 K. In the phase diagram, there are eleven univariant curves, five invariant points and seven crystallization regions saturated with Na2B4O7 · 10H2O, where the solids are Na2SO4, K2SO4, Na2SO4 · 3K2SO4 (Gla), Na2SO4 · 10H2O, NaBr · 2H2O, KBr and K2B4O7 · 4H2O. NaBr · 2H2O has the highest concentration and strong salting-out effects on other salts.

Solid–Liquid Equilibria in the Quinary system Na+, K+//Cl–, Br–, SO42––H2O at 373 K

Solid–liquid equilibria in the quinary system Na+, K+//Cl–, Br–, SO42––H2O at 373 K were measured by the isothermal solution saturation method, and the equilibrium solid phases, solubilities and densities of saturated solutions were determined experimentally. Using the experimental results, the dry salt phase diagrams, water diagrams, and the densities versus composition diagrams were plotted (saturated with Na2SO4 and K2SO4, respectively). The experimental results show that there is solid solution formed in the quinary system Na+, K+//Cl–, Br–, SO42––H2O at 373 K. The two projected phase diagrams of this system all consist of one univariant curve, two crystallization fields, and have no invariant point. Saturated with the salt Na2SO4, the crystallization forms are the double salt Na2SO4·3K2SO4 (Gla) and the solid solution Na(Cl,Br); the two crystallization forms are Na2SO4·3K2SO4 (Gla) and the solid solution K(Cl,Br) saturated with the salt K2SO4.

Solid–Liquid Equilibria in the Systems CaBr2–MgBr2–H2O and NaBr–KBr–SrBr2 at 348 K

The solid–liquid equilibria in the ternary system CaBr2–MgBr2–H2O and quaternary system NaBr–KBr–SrBr2–H2O at 348 K were determined with the method of isothermal solution saturation. Also determined are the densities of saturated solutions. The phase diagram of the ternary system CaBr2–MgBr2–H2O has two invariant points, three univariant curves and three crystallization fields (which are saturated with MgBr2·6H2O, 2CaBr2·MgBr2·12H2O, and CaBr2·2H2O, respectively). The phase diagram of the quaternary system NaBr–KBr–SrBr2–H2O includes one invariant point, three univariant curves and three crystallization fields (which are saturated with SrBr2·6H2O, NaBr, and KBr, respectively). On the basis of the extended Harvie–Weare (HW) model and its temperature-dependent equation, the mixing ion interaction parameters θMg,Ca, ΨMg,Ca,Br and the dissolution equilibrium constant K for MgBr2·6H2O, CaBr2·2H2O, and 2CaBr2·MgBr2·12H2O in the ternary system at 348 K were fitted by using the Pitzer equations and the multiple l...

Measurements of solid-liquid equilibria in the ternary system NaCl-NaBr-H2O at 373 K

Solid-liquid equilibria in the ternary system NaCl-NaBr-H2O at 373 K were measured by the isothermal dissolution equilibrium method. The solubilities of salts and densities of saturated solutions in the ternary system were determined experimentally. The equilibrium solid phases were also determined by chemical analysis and X-ray powder diffraction. Using the experimental data, the phase diagram of the ternary system was obtained, which comprise one univariant curve and one stationary phase in crystallization filed of Na (Cl, Br). The ternary system was solid solution type. Density values in the equilibrium solution increase with an increase of the sodium bromide concentration while decrease with an increase of the sodium chloride concentration. The relationship equation of equilibrium liquid phase and the solid phase composition data were fitted with a regression equation.

Phase equilibria in the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15 K

Solid–liquid equilibria in the ternary systems KBr–MgBr2–H2O and NaBr–MgBr2–H2O at 348.15K were determined with the method of isothermal solution saturation. Also determined are the densities of saturated solutions. According to the experimental data, the equilibrium phase diagrams of the two ternary systems were plotted. The phase diagram of first system has two invariant points, three univariant curves and three crystallization fields (which are saturated with respect to MgBr2·6H2O, KBr·MgBr2·6H2O and KBr, respectively, where KBr·MgBr2·6H2O is an incongruent double salt). The phase diagram of the second system has one invariant point, two univariant curves and two crystallization fields (which are saturated with respect to MgBr2·6H2O and NaBr, respectively). The dissolution equilibrium constant of NaBr, KBr, MgBr2·6H2O and KBr·MgBr2·6H2O at 348.15K were fitted with Pitzer equations. A chemical model based on Pitzer equations was constructed to calculate the solubilities of salts in the two systems at 348.15K. The calculated solubilities are in agreement with experimental results.

Measurements and Calculations of Solid–Liquid Equilibria in the Ternary System NaCl–NaBr–H2O at 323 K

The solubilities of salts and densities of saturated solutions in the NaCl–NaBr–H2O system at 323 K were determined with the method of isothermal solution saturation. The equilibrium solid phases in this system are solid solutions [Na(Cl,Br)]. The solid–liquid equilibrium phase diagram of the system has no invariant point. It has only one univariant curve and one crystallization region {saturated with solid solution Na(Cl,Br)}. Based on the above experimental results, the solid solution compositions fit well to a quadratic function of the equilibrium liquid composition. Based on the solubility data in the ternary systems NaCl–NaBr–H2O, the activity product (Q) of the solid solution was formulated with a polynomial of the solid solution composition. The solubilities salts in the ternary system at 323 K were calculated by Pitzer equations with the activity product of the solid solution. The results agree well with the experimental data.

Measurements of the Solid–Liquid Equilibria in the Quaternary Systems KBr–K2SO4–K2B4O7–H2O and NaBr–Na2SO4–Na2B4O7–H2O at 298 K

According to the compositions of the underground gasfield brines in the west of Sichuan Basin, in China, solid–liquid equilibria in the quaternary systems KBr–K2SO4–K2B4O7–H2O and NaBr–Na2SO4–Na2B4O7–H2O at 298 K were measured by isothermal solution saturation method. The solubilities of salts and the densities of saturated solutions in these quaternary systems were determined. Using the experimental data, phase diagrams, water content diagrams, and solution density diagrams were constructed. The two phase diagrams were simple cosaturation type without complex salt and solid solution. The phase diagram of the quaternary system KBr–K2SO4–K2B4O7–H2O has one invariant point, three univariant curves as the boundary of KBr, K2SO4 and K2B4O7·4H2O crystallization fields. The quaternary system NaBr–Na2SO4–Na2B4O7–H2O at 298 K consisted of five univariant curves, two invariant points and four crystallization regions of Na2B4O7·10H2O, Na2SO4, Na2SO4·10H2O, and NaBr·2H2O.

Solid–Liquid Equilibria in the Quaternary System KCl–KBr–K2B4O7–H2O at 323 K

Solid–liquid equilibria in the quaternary system KCl–KBr–K2B4O7–H2O at 323 K were measured by isothermal solution saturation method. The equilibrium solid phases, solubilities of salts, and densities of saturated solutions in the system were determined. The experimental data were used to plot the phase diagram of the quaternary system KCl–KBr–K2B4O7–H2O at 323 K. It was found that the system contains solid solution K(Cl,Br), their solubility diagram has no invariant point, but has a univariant dissolution curve, and two crystallization regions corresponding to K(Cl,Br) and potassium borate quahydrate (K2B4O7·4H2O). Density values in the equilibrium solution increase with an increase of the potassium bromide concentration but decrease with an increase of the potassium chloride concentration. On the basis of the solubility data of salts and corresponding to the solid solution composition data for the quaternary system, the solid solution compositions were fitted with quadratic equations for the equilibrium liquid composition. The calculated results for the solid solution K(Cl,Br) are discussed briefly.

Solid–Liquid Equilibria in the Ternary System KCl–KBr–H2O at 348 K

Phase equilibria in the ternary system KCl–KBr–H2O at 348 K were studied by the isothermal solution dissolution equilibrium method. The solubilities of salts and densities of saturated solutions in the ternary system were determined experimentally. The equilibrium solid phases were also determined by chemical analysis and X-ray powder diffraction. Using the experimental data, the phase diagram of the ternary system was obtained, which comprises one univariant curve and one stationary phase in the crystallization field of K(Cl,Br). The ternary system was a solid solution type. The density transformation rules were discussed simply, and the relationship equations of equilibrium liquid phase and the solid phase composition data were fitted with a cubic equation.

Phase Equilibria in the Ternary Systems KBr–K2B4O7–H2O and KCl–K2B4O7–H2O at 373 K

AbstractAccording to the compositions of the underground gasfield brines in the west of Sichuan Basin, the phase equilibria in the ternary systems KBr–K2B4O7–H2O and KCl–K2B4O7–H2O at 373 K were studied using the isothermal dissolution equilibrium method. The solubilities of salts and the densities of saturated solutions in these ternary systems were determined. Using the experimental data, phase diagrams and density‐composition diagrams were constructed. The two phase diagrams were simple co‐saturation type, each having an invariant point, two univariant curves and two crystallization regions. The equilibrium solid phases in the ternary system KBr–K2B4O7–H2O are potassium bromide (KBr) and potassium tetraborate tetrahydrate (K2B4O7·4H2O), and those in the ternary system KCl–K2B4O7–H2O are potassium chloride (KCl) and potassium tetraborate tetrahydrate (K2B4O7·4H2O). Comparisons of the phase diagrams of the two systems at different temperatures show that there is no change in the crystallization phases, but there are changes in the size of the crystallization regions. As temperature increases, the solubility of K2B4O7·4H2O increases rapidly, so the crystallization field of K2B4O7·4H2O becomes smaller.

Measurements of the Solid–Liquid Equilibria in the Quaternary System NaCl–NaBr–Na2SO4–H2O at 323 K

Phase equilibria of the quaternary NaCl–NaBr–Na2SO4–H2O system at 323 K were studied by the isothermal dissolution equilibrium method. The solubilities of salts and densities of saturated solutions were determined. Solid solutions [Na(Cl, Br)] were found in the experiments. The phase diagram of the quaternary system has no invariant point, but has one univariant curve at the boundary of Na(Cl, Br) and Na2SO4 crystallization fields. The experimental results show that an increase of the NaBr concentration is accompanied by an obvious increase of the solution density and the decrease of the solubilities of NaCl and Na2SO4.

Solid–Liquid Equilibria in the Quaternary Systems KCl–KBr–K2B4O7–H2O and KCl–KBr–K2SO4–H2O at 373 K

Solid–liquid equilibria in the quaternary systems KCl–KBr–K2B4O7–H2O and KCl–KBr–K2SO4–H2O at 373 K were measured by the isothermal solution saturation method. The equilibrium solid phases, solubilities of salts, and densities of saturated solutions in the two systems were determined. The experimental data are used to plot the solubility diagrams, water content diagrams, and solution density diagrams of the two systems. It was found that both systems contain the solid solution of KCl and KBr [K(Cl,Br)], so their solubility diagrams have no invariant point, but each has a univariant curve and two crystallization regions. In the first system, the solids are K(Cl,Br) and potassium borate aquahydrate (K2B4O7·4H2O), and in the second system, the solids are K(Cl,Br) and potassium sulfate (K2SO4).

Solubility of Clonazepam and Diazepam in Polyethylene Glycol 200, Propylene Glycol, N-Methyl Pyrrolidone, Ethanol, and Water at (298.2 to 318.2) K and in Binary and Ternary Mixtures of Polyethylene Glycol 200, Propylene Glycol, and Water at 298.2 K

Experimental molar solubility of clonazepam and diazepam in binary and ternary mixtures of polyethylene glycol 200 (PEG 200), propylene glycol (PG), and water (116 data points) along with the density of saturated solutions at 298.2 K were reported. Also, the experimental solubilities of clonazepam and diazepam in the monosolvents of PEG 200, PG, N-methyl pyrrolidone (NMP), ethanol (EtOH), and water at five different temperatures, (298.2, 303.2, 308.2, 313.2, and 318.2) K (50 data points), have been reported. The Jouyban–Acree model was used to fit to the measurements for providing a computational method. Employing the solubilities in the neat solvents, the measured solubilities were back-calculated, and the overall mean percentage deviations (OMPDs) of the model were 21.4 % and 19.5 % for clonazepam and diazepam, respectively. An addition of the Hansen solubility parameters to the model helps us to train all of the data sets (clonazepam and diazepam) at once, and the back-calculated OMPD was 20.7 %.

Solubility of sulfapyridine in propylene glycol + water mixtures and correlation with the Jouyban–Acree model

The solubility of sulfapyridine (SP) in propylene glycol+water mixtures was determined at temperatures from 293.15K to 313.15K. The solubility was maximal in pure propylene glycol and minimum in pure water at all the temperatures. The thermodynamic functions; Gibbs energy, enthalpy, and entropy of solution were obtained from these solubility data by using the van’t Hoff and Gibbs equations. Thermodynamic quantities of mixing were also calculated by using calorimetric values related to drug fusion process. A nonlinear enthalpy–entropy relationship was observed from a plot of enthalpy vs. Gibbs energy of solution. The plot of ΔsolnH° vs. ΔsolnG° shows two different trends, one with negative slope from pure water up to 0.30 mass fraction of propylene glycol and the other one positive beyond this composition up to pure propylene glycol. Accordingly, the driving mechanism for SP solubility in water-rich mixtures is the entropy, probably due to water-structure loss around the drug non-polar moieties by effect of propylene glycol, whereas, above 0.30 mass fraction of propylene glycol the driving mechanism is the enthalpy, probably due to SP solvation increase by the co-solvent molecules. This behavior is similar to the one exhibited by sulfanilamide, sulfamethizole and other drugs in the same co-solvent mixtures. The Generated solubility data were calculated (correlated and/or predicted) with the Jouyban–Acree model in which the mean percentage deviation (MPD) of the correlated and predicted data were 9.3±8.6%, and 12.1±9.9%, respectively. The corresponding MPDs for the correlated and predicted solubilities using the log-linear model were 25.1±19.8%, and 55.1±32.4%. The density of saturated solutions was predicted using a previously trained model. The ΔsolnH° and ΔsolnG° values were also correlated using a proposed model.

Solubility of Acetaminophen and Ibuprofen in the Mixtures of Polyethylene Glycol 200 or 400 with Ethanol and Water and the Density of Solute-Free Mixed Solvents at 298.2 K

Experimental solubilities of acetaminophen and ibuprofen in binary and ternary mixtures of polyethylene glycols (PEGs) 200 and 400 with ethanol and water, along with the densities of the saturated and solute-free solvent mixtures at T = 298.2 K, are reported. The solubility data of each drug in the ternary and sub-binary solvent mixtures were correlated with the Jouyban−Acree model. The mean relative deviations of the derived correlations were 6.4 % and 14.2 % for acetaminophen and ibuprofen, respectively, and the overall value was 9.4 %. Densities of solute-free solvent mixtures are used to train the Jouyban−Acree model, and then the densities of saturated solutions are predicted using the trained versions in which the overall mean relative deviation was 1.7 %.