Vapour‐Liquid Equilibrium in Binary Aqueous Mixtures using a Modified Regular Solution Model

Phase equilibrium in binary mixtures of interest in wine and must distillation processes have been modelled using the Peng‐Robinson equation of state. The mixing rules of Kwak and Mansoori and of Wong and Sandler were used. A new simple modification of the Regular Solution model for binary mixtures is also presented. The cases studied considered nine water+congener mixtures. The congeners included in the study are those regarded as legal compounds by the Chilean legislation for the production of a spirit made from grapes, called Pisco. The work allows concluding on the advantages, disadvantages and expected accuracy of the models used.     

Modeling of solid–liquid equilibria for polyethylene and polypropylene solutions with equations of state

We modeled solid–liquid equilibria (SLEs) in polyethylene and polypropylene solutions with a Soave–Redlich–Kwong (SRK) cubic equation of state (EOS) and a perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS. Two types of mixing rules were used with SRK EOS: The Wong–Sandler mixing rule and the linear combination of the Vidal and Michelsen mixing rules (LCVM), both of which incorporated the Bogdanic and Vidal activity coefficient model. The performance of these models was evaluated with atmospheric‐pressure and high‐pressure experimental SLE data obtained from literature. The basic SLE equation was solved for the equilibrium melting temperature instead of for the composition. The binary interaction parameters of SRK and PC‐SAFT EOS were estimated to best describe the experimental equilibrium behavior of 20 different polymer–solvent systems at atmospheric pressure and 31 other polymer–solvent systems at high pressure. A comparison with experimental data showed that SRK–LCVM agreed very well with the atmospheric SLE data and that PC‐SAFT EOS was more efficient in high‐pressure conditions. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

VLE calculation of carbon dioxide+n-alkanes binary mixtures with MHV2 mixing rule

Vapor-liquid equilibria for binary and asymetric systems include carbon dioxide+C₁-C₈, C₁₀ are calculated by using the Peng-Robinson-Stryjek-Vera equation of state coupled with the modified MHV2 mixing rule. The modified UNIFAC model is used for determining activity coefficient and excess Gibbs free energy. Calculated equilibrium pressures and mole fractions in vapor phase are compared with the experimental data. The average absolute deviation percent (AAD%)s indicates that the error involved in the application of the MHV2 mixing rule by optimized q₁ and q₂ is less than WS and PRSK mixing rules in most cases.     

Extending the range of COSMO‐SAC to high temperatures and high pressures

The range of the predictive Gibbs energy of solvation model, COSMO‐SAC, is extended to large ranges of density, pressure, and temperature for very nonideal mixtures by combining it with an equation of state (EOS) using the Wong‐Sandler mixing rule. The accuracy of isothermal vapor‐liquid equilibria (VLE) calculations based on using the predictive COSMO‐SAC model and separately the correlative NRTL model is compared, each combined with three different forms of the Peng‐Robinson equation of state. All the models considered require the value of the EOS mixing rule binary parameter k_ij. The NRTL model also requires three other parameters obtained from correlation low pressure VLE data. The PRSV + COSMO‐SAC model is showed, with its one adjustable parameter obtained from low temperature data leads good predictions at much higher temperatures and pressures. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1806–1813, 2018     

Numerical simulations of partially‐filled rubber mixing in a 2‐wing rotor‐equipped chamber

Partially filled internal batch mixers are used for mixing of rubber compounds in the polymer industry. The use of mixing in such mixers equipped with a rotor is critical to the process itself, and hence, understanding of mixing is important in terms of evaluating how various operating parameters such as rpm, fill factor, and ram pressure affect distribution and dispersion of materials. The objective of the current study is to gain valuable insights on the influence of fill factor, which is the volume of the material relative to the volume of the chamber. Two‐dimensional (2D) computational fluid dynamics (CFD) simulations of rubber mixing in a 2‐wing rotor‐equipped chamber are presented here, for the first time, for fully‐filled/100% and partially‐filled/75% chambers. The volume‐of‐fluid (VOF) technique is employed to capture the interface between the rubber and air in partially filled isothermal simulations. Flow patterns are visualized to analyze the material movement. Massless particles are injected and various statistics are calculated from their positions in order to compare dispersive and distributive mixing characteristics between the fully‐filled and partially‐filled cases. Specifically, quantities such as mixing index and the maximum shear stress distribution history of particles are analyzed to obtain information about dispersive mixing, while length of stretch and cluster distribution index, also calculated from particles, are presented to investigate distributive mixing capabilities. All the results consistently demonstrated the superior effectiveness of partially‐filled mixing chambers in terms of their dispersive and distributive mixing characteristics in comparison to fully‐filled chambers. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44250.     

Extension to mixtures of two robust hard‐sphere equations of state satisfying the ordered close‐packed limit

Two new hard‐sphere EOS are proposed and tested using the same attractive potential terms used by the SAFT EOS. Generalized expressions for the pair RDF at contact value, the compressibility factor, and the excess chemical potentials have been derived. Extension to mixtures is tested using three mixing rules for multicomponent hard‐sphere fluids. The proposed EOS combined with the Santos et al. and the Barrio‐Solana mixing rules reproduced the compressibility factors and the excess chemical potentials more accurately than the Boublik‐Mansoori‐Camahan‐Starling‐Leland (BMCSL) EOS. However the pair RDF at contact value had larger deviations than those obtained with the BMCSL EOS. The combination of the proposed equations and the Barrio‐Solana mixing rule gave an accurate reproduction of the compressibility factor for binary hard‐sphere fluids with high diameter ratio even in the low concentration regions of the larger spheres.     

A modified Kurihara mixing rule and a comparison of density-independent mixing rules

A modified density-independent Kurihara mixing rule is developed by introducing the low density limit condition into the excess Helmholtz free-energy function at infinite pressure. A parallel comparison of the new mixing rule and existing density-independent mixing rules was performed using the same equation of state and excess function and the same experimental data sets. Five existing density-independent mixing rules were examined: Huron and Vidal (1979), Kurihara et al. (1987), Wong and Sandler (1992) and van der Waals mixing rules with one or two binary interaction coefficients. Non-polar, non-polar-polar and polar-polar binary and ternary systems have been tested.     

Application of cubic equation of state models in prediction of vapor–liquid equilibria for binary polyvinyl acetate/solvent solutions

The cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non‐ideality of polymer solutions based on a single EoS approach. In this research, vapor–liquid equilibria calculations of polyvinyl acetate (PVAc)/solvent solutions were performed. In this approach, eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely vdW1, vdW2, Wong–Sandler (WS), and Zhong–Masuoka (ZM) were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. Absolute average deviations (%AAD) between predicted results and experimental bubble point pressure data were calculated and presented. The capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, but the performance of the PRSV + vdW2 was more reliable than the other models with 2.65% in AAD for total of solution systems. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40651.     

Thermo‐physical properties of n‐pentane/bitumen and n‐hexane/bitumen mixture systems

The gravity drainage as a result of viscosity reduction is the main governing mechanism of the solvent‐aided thermal bitumen recovery processes. Therefore, the density and viscosity of the diluted or heated bitumen are essential to predict the oil production rate. In this paper, we report thermo‐physical properties of n‐pentane/bitumen and n‐hexane/bitumen mixtures. The density and viscosity of Athabasca bitumen diluted with n‐pentane and n‐hexane were measured at different temperatures (30 to 190 °C), pressures (2 to 8 MPa), and solvent mass fractions (0.05 to 0.5). Various correlations and mixing rules proposed in the literature were examined to calculate the density and viscosity of the diluted bitumen. This study proposes appropriate mixing rules and generalized parameters for predicting the density and viscosity of solvent‐bitumen systems. Our findings will find applications in the design and simulation of heavy oil and bitumen solvent‐aided thermal recovery processes.     

Influence of Mixing on the Precipitation of Organic Nanoparticles: A Lagrangian Perspective on Scale‐up Based on Self‐Similar Distributions

Precipitation of nanoparticles is applied in various fields with a rising interest in the formulation of poorly soluble drugs. The impact of fluid mixing on the precipitation of organic nanoparticles is analyzed. Direct numerical simulations are applied to determine the spatiotemporal evolution of the liquid phase composition and to estimate the particle evolution along Langragian trajectories. The simulation results are compared with laboratory experiments of mixing and particle size evolution, which use a recently developed approach to rapidly stabilize the precipitated nanoparticles. The impact of mixing on precipitation is revealed, thereby enabling a parameter‐free estimation of the mean particle sizes and the particle size distributions. The distributions of residence time, supersaturation time, and particle size are self‐similar for Reynolds numbers in the turbulent regime and allow the derivation of scale‐up rules.     

Phase behavior of mixture of supercritical CO2 + ionic liquid: Thermodynamic consistency test of experimental data

Various models have been applied composed of the Peng‐Robinson equation of state (PR‐EoS) and the Soave‐Redlich‐Kwong equation of state (SRK‐EoS) associated with three mixing rules including the following: Wong‐Sandler (WS), van der Waals one (vdW1), and van der Waals two (vdW2) for phase behavior modeling of mixtures of supercritical CO₂ + different ionic liquids in vapor–liquid equilibrium (VLE) region. It has been found that the PR EoS implying the WS mixing rule can be used as a reliable thermodynamic model to perform a thermodynamic consistency test on the experimental data of phase behaviors of the supercritical CO₂ + ionic liquid systems (19 commonly‐used ionic liquids have been studied). The results show that 40% of the experimental data seem to be thermodynamically consistent, 55.5% seem to be thermodynamically inconsistent, and 4.5% seem to be not fully consistent. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3892–3913, 2013     

Prediction of High‐Pressure Phase Equilibria using Cubic EOS: What Can Be Learned?

Modern semi‐empirical cubic EOSs are usually attached by complex functionalities, such as Huron‐Vidal (HV)‐type mixing rules. Although this practice improves the flexibility of the models, it also complicates consideration of an overall picture of phase behavior. As a result, G^E‐based equations are usually adjusted to the experimental data by way of a local fit. The latter approach tends to ignore that different regions of the thermodynamic phase space are closely inter‐related. The present study demonstrates that the contribution of (HV)‐type mixing rules to predicting high‐pressure phase equilibria can be quite modest and that in addition they may generate non‐realistic phase diagrams.     

3‐D numerical analysis on the mixing performance for assemblies with filled zone of right‐handed and left‐handed double‐flighted screws and kneading blocks in twin‐screw extruders

We have calculated and visualized numerically the mixing performances of four kinds of assemblies in twin‐screw extruders that were composed of right‐handed or left‐handed double‐flighted full flight screws and neutral or left‐handed stagger angle kneading blocks, taking into consideration industrial usage. We have found that the mixing performance of a kneading block interposed between full flighted screws is strongly influenced by the flow of full flighted screws, in particular that of a neutral kneading block. Furthermore, we have proposed the simple mixing indices, which could describe both uniform mixing and heterogeneous mixing, and also applied them to our marker tracking results of four kinds of assemblies. We found that more uniform mixing is obtained for the assembly that has a neutral kneading block before the right‐handed full flight screw, and a more enhanced heterogeneous mixing is obtained for the assembly that has a left‐handed kneading block before the left‐handed full flight screw. The reason for the latter mixing ability will relate to the quasi‐channels of the left‐handed kneading block, through which marker clusters flow while elongating.     

Löslichkeit von überkritischen Fluiden in Ionischen Flüssigkeiten

A review of existing experimental phase equilibrium data for systems of near‐ and/or supercritical fluids (SCF) and ionic liquids (IL) shows that usually the SCF solubility increases with increasing pressure and decreasing temperature. Additionally, polar SCF are better soluble in IL than nonpolar SCF. The experimental data could be correlated by means of the Peng‐Robinson equation of state as well as the Van der Waals mixing rules. As a result, the experimental solubility can be calculated reasonably well using two binary interaction parameters.     

A Comparison of the Mixing Characteristics in Single‐ and Two‐Phase Grid‐Generated Turbulent Flow Systems

The mixing process is studied in grid‐generated turbulent flow for single‐ and bubbly two‐phase flow systems. Concentration and mixing characteristics in the liquid phase are measured with the aid of a PLIF/PLIF arrangement. A nearly isotropic turbulent flow field is generated at the center of the vertical pipe by using a honeycomb, three grids and a contraction. In two‐phase flow experiments, air bubbles were injected into the flow from a rectangular grid, with mesh size M = 6 mm, which is placed midway between two circular grids each with a mesh size of M = 2 mm. For single‐phase flow, the normalized mean concentration cross‐stream profiles have rather similar Gaussian shapes, and the cross‐stream profiles of the normalized root‐mean‐square (RMS) values of concentration were found to be quite similar. Cross‐stream profiles of the mean concentration, for bubbly two‐phase flow, were also found to be quite similar, but they did not have the Gaussian shape of the profiles for single‐phase flow. Almost self‐similar behavior was also found for the RMS values of the concentration in two‐phase systems. The turbulent diffusion coefficient in the liquid phase was also calculated. At the center of the plume, the flow was found to have a periodic coherent structure, probably of vortex shedding character. Observations showed that the period of oscillation is higher in the case of two‐phase flow than in single‐phase flow.     

Fundamentals‐based low‐dimensional combustion modeling of spark‐ignited internal combustion engines

A four‐mode low‐dimensional model for the in‐cylinder combustion process in an internal combustion engine is developed. The lumped parameter ordinary differential equation model is based on two mixing times that capture the reactant mixing limitations inside the cylinder and mixing limitations caused by the input and exit stream distribution. For a given inlet and operating conditions, the model predicts the exhaust composition of regulated gases (total unburned HCs, CO, and NO_x) as well as the in‐cylinder pressure and temperature. The model is able to capture the qualitative trends observed with change in fuel composition (gasoline and ethanol blending), air/fuel ratio, spark timing, engine load, and speed. The results show good qualitative and fair quantitative agreement with the experimental results published in the literature and demonstrate the possibility of such low‐dimensional model for real‐time control. Improvements and extensions to the model are discussed. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Regulation of trans‐1,4‐polyisoprene crystallinity and mechanical properties of styrene‐butadiene rubber/trans‐1,4‐polyisoprene vulcanizate

The effects of processing temperature and bis‐[γ‐(triethoxysilyl)‐propyl]‐tetrasulfide (Si69) on crystallization, morphology, and mechanical properties of styrene‐butadiene rubber (SBR)/trans‐1,4‐polyisoprene (TPI) vulcanizate are investigated. The crystallinity and crystalline melting temperature (T_m) of TPI in the vulcanizates with TPI/silica/(Si69) pre‐mixed at 150 °C are much lower than that pre‐mixed at 80 °C. At the same pre‐mixing temperature, the presence of 1 phr Si69 leads to a decreased crystallinity and T_m. The TPI domains with phase size of about 1 μm and silica are well dispersed in the vulcanizate, and TPI crystals get smaller in size and less in amount by pre‐mixing TPI, silica and Si69 at 150 °C. The vulcanizates with TPI/silica/(Si69) pre‐mixed at 150 °C have decreased tensile strength and modulus at a given extension than that pre‐mixed at 80 °C. At the same pre‐mixing temperature, the tensile strength and modulus of the vulcanizate increase with the addition of 1 phr Si69. The crystallinity of TPI component in SBR/TPI vulcanizate is effectively controlled by changing processing temperature and adding Si69, which is important for theoretical research and practical application of TPI. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44395.     

High‐Throughput T‐Jets Mixers: An Innovative Scale‐Up Concept

The influence of geometrical and design parameters of T‐jets mixers on flow dynamics and mixing patterns is studied by means of two‐dimensional computational fluid dynamics simulations, planar laser‐induced fluorescence, and test chemical reactions. The ratios between injector width and mixing chamber width and between width and depth of the mixing chamber were evaluated as parameters. These ratios determine the flow regime in T‐jets mixers: high values of injector/chamber width ratio favor mixing and high depth values also increase the flow dynamics and thus mixing. A strategy for scale‐up of T‐jets mixers is devised, based on increasing a noncritical dimension (depth) while keeping other dimensions small.     

Thermodynamic modeling of vapor–liquid equilibrium for binary polyethylene glycol/solvent solutions using cubic equations of state: optimization and comparison of CEoS models

The cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EoS approach. In this research, vapor–liquid equilibrium calculations of Polyethylene glycol(Polyethylene oxide)/solvent solutions were carried out. In this approach eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely one-parameter van der Waals one-fluid, two-parameter van der Waals one-fluid (vdW2), Wong–Sandler, and Zhong–Masuoka were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. The results of absolute average deviations between predicted results and experimental bubble point pressure data were calculated and presented. Although the capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, the performance of the PRSV+vdW2 was more reliable than the other models.     

Basic properties of palm oil biodiesel–diesel blends

The basic properties of several palm oil biodiesel–diesel fuel blends were measured according to the corresponding ASTM standards. In order to predict these properties, mixing rules are evaluated as a function of the volume fraction of biodiesel in the blend. Kay’s mixing rule is used for predicting density, heating value, three different points of the distillation curve (T10, T50 and T90), cloud point and calculated cetane index, while an Arrhenius mixing rule is used for viscosity. The absolute average deviations (AAD) obtained were low, demonstrating the suitability of the used mixing rules. It was found that the calculated cetane index of palm oil biodiesel obtained using ASTM D4737 is in better agreement with the reported cetane number than the one corresponding to the ASTM D976. This result is most likely due to the fact that the former standard takes into account the particular characteristics of the distillation curve.