Vapor-liquid Phase Boundary Research Articles

Liquid Viscosity and Surface Tension of Cyclohexane Between 280 and 473 K by Surface Light Scattering

The present study provides experimental data for the liquid viscosity and surface tension of cyclohexane at or close to saturation conditions by surface light scattering between (280 and 473) K. By applying the hydrodynamic theory for surface fluctuations at the vapor–liquid phase boundary, which could be verified experimentally, the liquid viscosity and surface tension were determined simultaneously at macroscopic thermodynamic equilibrium with average relative expanded (k = 2) uncertainties of Ur(η′) = 0.020 and Ur(σ) = 0.012. For both properties, the present measurement results agree well with reference values in the literature which are restricted to a maximum temperature of 393 K for viscosity and 337 K for surface tension. The experimental results from this work contribute to an improved database for the viscosity and surface tension of cyclohexane over a wide temperature range from a temperature close to the melting point up to 473 K.

Temperature and Density on the Forsterite Liquid-Vapor Phase Boundary.

The physical processes during planet formation span a large range of pressures and temperatures. Giant impacts, such as the one that formed the Moon, achieve peak pressures of 100s of GPa. The peak shock states generate sufficient entropy such that subsequent decompression to low pressures intersects the liquid‐vapor phase boundary. The entire shock‐and‐release thermodynamic path must be calculated accurately in order to predict the post‐impact structures of planetary bodies. Forsterite (Mg2SiO4) is a commonly used mineral to represent the mantles of differentiated bodies in hydrocode models of planetary collisions. Here, we performed shock experiments on the Sandia Z Machine to obtain the density and temperature of the liquid branch of the liquid‐vapor phase boundary of forsterite. This work is combined with previous work constraining pressure, density, temperature, and entropy of the forsterite principal Hugoniot. We find that the vapor curves in previous forsterite equation of state models used in giant impacts vary substantially from our experimental results, and we compare our results to a recently updated equation of state. We have also found that due to under‐predicted entropy production on the principal Hugoniot and elevated temperatures of the liquid vapor phase boundary of these past models, past impact studies may have underestimated vapor production. Furthermore, our results provide experimental support to the idea that giant impacts can transform much of the mantles of rocky planets into supercritical fluids.

Entropy in Molecular Fluids: Interplay between Interaction Complexity and Criticality.

Using flat-histogram simulations, we calculate the entropy of molecular fluids along the vapor-liquid phase boundary. Our simulation approach is based on the evaluation of the canonical and grand-canonical partition functions, which, in turn, provide access to entropy through the statistical mechanics formalism. The results allow us to determine the critical entropy of molecular fluids and to uncover that the transition occurs symmetrically from an entropic standpoint. This can best be seen through the patterns exhibited by the thermodynamic variables temperature and pressure when plotted against the entropy of the coexisting phases. This behavior is found to hold for apolar, quadrupolar, and dipolar fluids. Finally, we identify functional forms that characterize the relation between thermodynamic variables and entropy along the coexistence curve up to the critical point.

Volumetric properties of carbon dioxide + acrylic acid binary in the context of supercritical precipitation polymerization

Acrylic acid can be polymerized by precipitation in different solvents. Carbon dioxide is an interesting solvent given its tunable density and solvent power depending on the pressure and temperature. These physicochemical characteristics make it possible to solubilize some polar compounds in CO 2 depending on temperature and pressure. In this work, we report pressure vs volume pseudo-continuous curves at constant temperature for the CO 2 + AA binary mixture. They were determined in a fully computerized variable-volume high-pressure view cell capable of monitoring the position of the piston. The experimental data is simultaneously isoplethic and isothermal and it covers a wide range of pressures (up to 20 MPa). Using this raw experimental data, other properties were determined such as liquid-vapor phase boundaries, density and excess volumes. The temperature range was 313.15–363.15 K and the mole fraction of AA in the mixture was increased from 0.044 to 0.594.

New Formulation for the Viscosity of n-Butane

A new viscosity formulation for n-butane, based on the residual quantity concept, uses the reference equation of state by Bücker and Wagner [J. Phys. Chem. Ref. Data 35, 929 (2006)] and is valid in the fluid region from the triple point to 650 K and to 100 MPa. The contributions for the zero-density viscosity and for the initial-density dependence were separately developed, whereas those for the critical enhancement and for the higher-density terms were pretreated. All contributions were given as a function of the reciprocal reduced temperature τ, while the last two contributions were correlated as a function of τ and of the reduced density δ. The different contributions were based on specific primary data sets, whose evaluation and choice were discussed in detail. The final formulation incorporates 13 coefficients derived employing a state-of-the-art linear optimization algorithm. The viscosity at low pressures p ≤ 0.2 MPa is described with an expanded uncertainty of 0.5% (coverage factor k = 2) for temperatures 293 ≤ T/K ≤ 626. The expanded uncertainty in the vapor phase at subcritical temperatures T ≥ 298 K as well as in the supercritical thermodynamic region T ≤ 448 K at pressures p ≤ 30 MPa is estimated to be 1.5%. It is raised to 4.0% in regions where only less reliable primary data sets are available and to 6.0% in ranges without any primary data, but in which the equation of state is valid. A weakness of the reference equation of state in the near-critical region prevents estimation of the expanded uncertainty in this region. Viscosity tables for the new formulation are presented in Appendix B for the single-phase region, for the vapor–liquid phase boundary, and for the near-critical region.

Vapor-liquid phase boundaries and swelling factors of C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions

Techniques have been developed to determine vapor-liquid phase boundaries and swelling factors of CO2-heavy oil systems and C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions. Experimentally, a pure substance of CO2 and a gas mixture consisting of 27.7 mol% C3H8, 23.9 mol% n-C4H10, and 48.4 mol% CO2 are respectively introduced to dilute the highly viscous heavy oil. A pressure-volume-temperature (PVT) setup is used to measure vapor-liquid phase boundaries (i.e., saturation pressures) and swelling factors at high pressures up to 11.1 MPa and elevated temperatures up to 373.35 K. Theoretically, the volume-translated Peng-Robinson equation of state (PR EOS) coupled with a recently modified alpha function is applied as the primary thermodynamic model to reproduce the experimental measurements. The heavy oil which is a complex mixture with unknown molecular structure is characterized as six pseudocomponents by using an exponential distribution splitting function and a logarithm-type lumping method. The optimal exponents in binary interaction parameter (BIP) correlations are obtained by best matching the measured saturation pressures. Subsequently, the comparisons have been performed between this work and a commercial simulator in terms of the overall prediction accuracy of saturation pressures for the quaternary C3H8-n-C4H10-CO2-heavy oil systems. It is found that the minimum absolute average relative deviation (AARD) of 6.7% is obtained by the methodology developed in this work, compared to the AARD of 35.6% obtained by running the commercial simulator.

New Formulation for the Viscosity of Propane

A new viscosity formulation for propane, using the reference equation of state for its thermodynamic properties by Lemmon et al. [J. Chem. Eng. Data 54, 3141 (2009)] and valid in the fluid region from the triple-point temperature to 650 K and pressures up to 100 MPa, is presented. At the beginning, a zero-density contribution and one for the critical enhancement, each based on the experimental data, were independently generated in parts. The higher-density contributions are correlated as a function of the reciprocal reduced temperature τ = Tc/T and of the reduced density δ = ρ/ρc (Tc—critical temperature, ρc—critical density). The final formulation includes 17 coefficients inferred by applying a state-of-the-art linear optimization algorithm. The evaluation and choice of the primary data sets are detailed due to its importance. The viscosity at low pressures p ≤ 0.2 MPa is represented with an expanded uncertainty of 0.5% (coverage factor k = 2) for temperatures 273 ≤ T/K ≤ 625. The expanded uncertainty in the vapor phase at subcritical temperatures T ≥ 273 K as well as in the supercritical thermodynamic region T ≤ 423 K at pressures p ≤ 30 MPa is assumed to be 1.5%. In the near-critical region (1.001 < 1/τ < 1.010 and 0.8 < δ < 1.2), the expanded uncertainty increases with decreasing temperature up to 3.0%. It is further increased to 4.0% in regions of less reliable primary data sets and to 6.0% in ranges in which no primary data are available but the equation of state is valid. Tables of viscosity computed for the new formulation are given in an Appendix for the single-phase region, for the vapor–liquid phase boundary, and for the near-critical region.

Non-intrusive, high-resolution, real-time, two-dimensional imaging of multiphase materials using acoustic array sensors.

Two parallel multi-element ultrasonic acoustic arrays combined with sets of focal laws for acoustic signal generation and a classical tomographic inversion algorithm are used to generate real-time two-dimensional micro seismic acoustic images of multiphase materials. Proof of concept and calibration measurements were performed for single phase and two phase liquids, uniform polyvinyl chloride (PVC) plates, and aluminum cylinders imbedded in PVC plates. Measurement artefacts, arising from the limited range of viewing angles, and the compromise between data acquisition rate and image quality are discussed. The angle range of scanning and the image resolution were varied, and the effects on the quality of the reproduction of the speed of sound profiles of model solids and liquids with known geometries and compositions were analysed in detail. The best image quality results were obtained for a scanning angle range of [-35°, 35°] at a step size of 2.5° post processed to generate images on a 40 μm square grid. The data acquisition time for high quality images with a 30 mm × 40 mm view field is 10 min. Representation of two-phase solids with large differences in speed of sound between phases and where one phase is dispersed in the form of macroscopic objects (greater than 1 mm in diameter) proved to be the most difficult to image accurately. Liquid-liquid and liquid-vapor phase boundaries, in micro porous solids by contrast, were more readily defined. Displacement of air by water and water by heptane in natural porous limestone provides illustrative kinetic examples. Measurement results with these realistic cases demonstrate the feasibility of the technique to monitor in real time and on the micrometer length scale local composition and flow of organic liquids in inorganic porous media, one of many envisioned engineering applications. Improvement of data acquisition rate is an area for future collaborative study.

An experimental method to simultaneously measure the dynamics and heat transfer associated with a single bubble during nucleate boiling on a horizontal surface

The heat transfer mechanisms of nucleate boiling are associated with how the liquid–vapor phase and the surface temperature are distributed and interact beneath a single bubble on a heated surface. A comparative analysis of the hydrodynamic and thermal behavior of a single bubble may contribute greatly to the understanding of nucleate boiling heat transfer. In this paper, a technique to simultaneously measure the liquid–vapor phase boundary, temperature distribution, and heat transfer distribution at a boiling surface is described. The technique is fully synchronized in time and spatially resolved, and is applied to explore single-bubble nucleate boiling phenomena in a pool of water subcooled by 3°C under atmospheric pressure. The temperature and heat flux distributions at the boiling surface are quantitatively interpreted in relation to the distribution and dynamics of the dry and wet areas, the triple contact line, and the microlayer underneath the single bubble. The results show that intensive wall heat transfer during single-bubble nucleate boiling exactly corresponds to the extended microlayer region. However, the overall contribution of the microlayer evaporation to the growth of a bubble is relatively small, and amounts to less than 17% of the total heat transport.

Miscibility, phase separation and volumetric properties in solutions of poly(ɛ-caprolactone) in acetone + CO2 binary fluid mixtures at high pressures

Miscibility and phase separation behavior, and the volumetric properties of poly(ɛ-caprolactone) (PCL) solutions in acetone+CO2 binary fluid mixtures were investigated for PCL concentrations of 2.0, 5.0, 9.0, 12.0, 15.0, 25.0 and 34.9wt% at temperatures up to 410K and pressures up to 28MPa. Experiments were carried out by using a unique high pressure variable-volume view-cell equipped with a dual set of pistons and dual set of sapphire windows which permit measurements of both the transmitted light intensities for determination of phase boundaries, and the scattered light intensities for assessment of the mechanism and the kinetics of phase separation. The system allows the continuous recording of the piston positions and thus the solution densities as a function of pressure at a given temperature from which liquid–vapor or liquid–liquid–vapor phase boundaries are easily assessed and the isothermal compressibilities and isobaric expansivities are readily evaluated. It is shown that these solutions display lower critical solution temperature (LCST) type behavior with respect to their liquid–liquid (LL) phase boundaries and the LL phase separation proceeds via nucleation and growth for 2.0, 5.0, 25.0 and 34.9wt% solutions and via spinodal decomposition for 9.0, 12.0, and 15.0wt% solutions. It is shown that the LL phase separation pressure which is a function of temperature scales with the solution density and shifts to higher densities with increasing polymer concentration, with the rate of change of LL phase separation pressure with density becoming higher at concentrations above the critical polymer concentration. The compressibilities in the homogeneous mixtures are found to decrease with increasing PCL concentration. At pressures below the LL phase separation pressures, the rate of decrease in compressibility with pressure is higher which is interpreted as being a consequence of the difference in the phase compositions of the polymer-lean and polymer-rich phases that develop at pressures below LL phase separation. Isobaric expansivities increase with temperature at a given pressure. They become more sensitive to temperature at lower pressures. The excess volumes for all PCL solutions display large negative values, indicative of close-packing of the polymer plus solvent molecules.

Vapor–liquid phase equilibrium of carbon dioxide with mixed solvents of DMSO + ethanol and chloroform + methanol including near critical regions

A visual and volume-variable high-pressure phase equilibrium analyzer was used for measuring the vapor–liquid phase boundaries of the ternary systems containing carbon dioxide and mixed solvents of dimethyl sulfoxide (DMSO)+ethanol or chloroform+methanol at temperatures from 298.15K to 348.15K over wide composition ranges including near critical points. Four pseudo-binary systems of carbon dioxide plus mixed solvents with constant molar ratios of DMSO/ethanol=3/7, 5/5, 7/3, and chloroform/methanol=1/2, were studied in this work. The critical conditions at each investigated temperature were estimated from the experimental isothermal phase boundaries by interpolation. The Peng–Robinson equation of state with the two-parameter van der Waals mixing rules was applied to calculate the phase boundaries. The experimental values were compared with the predicted results from the Peng–Robinson equation using the binary interaction parameters determined from the vapor–liquid equilibrium data of the constituent binaries. The agreement is reasonably well for carbon dioxide+chloroform+methanol, but obvious overestimations are found near the critical regions of carbon dioxide+DMSO+ethanol, especially at higher temperatures.

Suppression of oscillations of the vapor–liquid phase boundary in boiling of superfluid helium inside a porous body

Introduction. The recent decade has seen an active development of the technology of space applications of superfluid helium. Among the achievements one should note the launching of the two space observatories-telescopes Herschel and Planck, which took place in 2009. For the Herschel observatory, 2300 liters of liquid helium at a temperature of 1.65 K, placed in the cryostat before the launch, determine the lifetime of the entire structure (expected life is about 4 years) and ensure the efficiency and stability of both the guidance systems and the scientific instrumental base [1]. At the same time, creation of the Laboratory of Low-Temperature Investigations within the framework of the Russian Segment of the International Space Station assumes the extension of the base of basic research. Therefore, for a number of years, we have seen the development of the project of experiment investigations of boiling of superfluid helium under zero gravity. To ensure the preservation of helium in the cryostat volume, it is proposed that a porous shell coaxial with a cylindrical heater be used [2]. For corresponding experiments under laboratory conditions, it is planned to use a bench of the Department of Low Temperatures of the National Research University "Moscow Power Institute;" which bench has been created to investigate processes in superfluid helium in heat supply, including the case of constrained conditions. The corresponding mathematical model of an experimental cell is presented below. Furthermore, it is of separate interest to investigate the dynamics of a vapor film and flow of a quantum liquid in small-diameter channels under a thermal load of 10 4 W/m 2 . Formulation of the Problem and Mathematical Description. The heater in the form of a thin wire of prescribed radius R w is arranged inside a coaxial shell with internal radius R 0 and thickness L; the wire is manufactured from a material with known structural characteristics (porosity m and characteristic dimension d). The experimental cell is closed, on the ends, by optically transparent plugs and is fully submerged in the liquid volume to a depth h. Helium-II fills the internal space and the porous-shell channels. Above the free surface of the liquid, a constant pressure P b is maintained, to which there corresponds the liquid temperature T b as far as the saturation line is concerned. Once the thermal load q w has been applied, a vapor film of radius R 1 is formed on the heater surface, which expels the liquid through the channels in the porous body (Fig. 1). The objective of the work is to calculate the process of heat and mass transfer in the experimental cell with the aim of determining a combination of parameters at which a steady state can be reached. The system of equations is formulated under the assumption that the heat- and mass-transfer processes in helium-II are quasisteady. The liquid is assumed incompressible; the dependence of the processes on the local temperature is not considered.

Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. I. Thermodynamic properties in the bulk and at the liquid-vapor phase boundary

The Wang-Landau sampling is a powerful method that allows for a direct determination of the density of states. However, applications to the calculation of the thermodynamic properties of realistic fluids have been limited so far. By combining the Wang-Landau method with expanded grand-canonical simulations, we obtain a high-accuracy estimate for the grand-canonical partition function for atomic and molecular fluids. Then, using the formalism of statistical thermodynamics, we are able to calculate the thermodynamic properties of these systems, for a wide range of conditions spanning the single-phase regions as well as the vapor-liquid phase boundary. Excellent agreement with prior simulation work and with the available experimental data is obtained for argon and CO(2), thereby establishing the accuracy of the method for the calculation of thermodynamic properties such as free energies and entropies.

Shock‐induced silicate vaporization: The role of electrons

We conducted a spectroscopic study of shock‐heated silicate (diopside) and obtained the time evolution of the spectral contents, the line widths of emission lines, and the time‐ and irradiance‐averaged peak shock temperatures. The peak shock pressures ranged from 330 to 760 GPa. Time‐resolved emission spectra indicated that the initial spectrum was blackbody radiation; the spectrum evolved to yield several ionic emission lines, which in turn evolved to yield atomic lines at the later stages. The shock‐heated diopside was highly dissociated and ionized, even though it is likely to have been subjected to high‐pressure conditions near the liquid–vapor phase boundary. The time evolution of the spectra, from ions to atoms, strongly suggests that electron recombination occurred in the expanding shock‐induced diopside vapor. The time‐ and irradiance‐averaged peak shock temperatures at >330 GPa were lower than the theoretical Hugoniot curve, with a constant isochoric specific heat, indicating endothermic shock‐induced ionization. Thus, we conclude that electrons behave as an important energy reservoir in energy partitioning via endothermic shock‐induced ionization and subsequent exothermic electron recombination. This electron behavior leads to a higher degree of vaporization after isentropic release and a lower cooling rate due to the exothermic electron recombination in expanding impact‐induced silicate vapors than previously expected. These results will affect the predictions associated with hypervelocity impact events in planetary science, such as the origin of the Moon and chemical reactions and production of silicate dust particles in impact‐generated silicate vapor clouds.

Supersonic Beams at High Particle Densities: Model Description beyond the Ideal Gas Approximation

Supersonic molecular beams constitute a very powerful technique in modern chemical physics. They offer several unique features such as a directed, collision-free flow of particles, very high luminosity, and an unsurpassed strong adiabatic cooling during the jet expansion. While it is generally recognized that their maximum flow velocity depends on the molecular weight and the temperature of the working fluid in the stagnation reservoir, not a lot is known on the effects of elevated particle densities. Frequently, the characteristics of supersonic beams are treated in diverse approximations of an ideal gas expansion. In these simplified model descriptions, the real gas character of fluid systems is ignored, although particle associations are responsible for fundamental processes such as the formation of clusters, both in the reservoir at increased densities and during the jet expansion. In this contribution, the various assumptions of ideal gas treatments of supersonic beams and their shortcomings are reviewed. It is shown in detail that a straightforward thermodynamic approach considering the initial and final enthalpy is capable of characterizing the terminal mean beam velocity, even at the liquid-vapor phase boundary and the critical point. Fluid properties are obtained using the most accurate equations of state available at present. This procedure provides the opportunity to naturally include the dramatic effects of nonideal gas behavior for a large variety of fluid systems. Besides the prediction of the terminal flow velocity, thermodynamic models of isentropic jet expansions permit an estimate of the upper limit of the beam temperature and the amount of condensation in the beam. These descriptions can even be extended to include spinodal decomposition processes, thus providing a generally applicable tool for investigating the two-phase region of high supersaturations not easily accessible otherwise.

A Reference Equation of State for the Thermodynamic Properties of Sulfur Hexafluoride (SF6) for Temperatures from the Melting Line to 625K and Pressures up to 150MPa

A new equation of state for the thermodynamic properties of the fluid phase of sulfur hexafluoride (SF6) in the form of a fundamental equation explicit in the Helmholtz energy is presented. The functional form consists of a part describing the ideal-gas state and the residual part as the difference between the real-fluid and the ideal-gas behavior. The residual part was developed using state-of-the-art linear and nonlinear optimization algorithms. It contains 36 coefficients, which were fitted to selected data for the thermal and caloric properties of sulfur hexafluoride in the single-phase region and on the vapor-liquid phase boundary. Especially for the thermal properties in the critical region, a very extensive and high-precision data set was available. In this work, information on the experimental data for the thermodynamic properties and all details of the new equation are presented. The new equation of state describes the pρT surface of sulfur hexafluoride with an uncertainty in density of less than 0.02%–0.03% from the melting line up to temperatures of 500K and pressures of 30MPa. In the critical region, including the immediate vicinity of the critical point, the uncertainty in pressure is less than 0.01%. Reliable data sets of other thermodynamic properties are reproduced within their experimental uncertainties. The primary data, to which the equation was fitted, cover the fluid region from the melting line to temperatures of 625K and pressures up to 150MPa. Beyond this range, the equation can be extrapolated with a physically reasonable behavior up to very high temperatures and pressures. In addition to the equation of state, independent equations for the vapor pressure, the saturated-liquid and saturated-vapor densities, the melting pressure, and the sublimation pressure are given. Tables of thermodynamic properties calculated from the new equation of state are listed in the Appendix.

Vapor–liquid phase equilibrium behavior of mixtures containing supercritical carbon dioxide near critical region

A new visual and volume-variable high-pressure phase equilibrium analyzer (PEA) was installed for determining the vapor–liquid phase boundaries over a wide pressure range, including near critical region, by a synthetic method. This apparatus was tested with the measurement of CO 2 + 1-octanol. The PEA was also utilized to measure the isothermal vapor–liquid phase boundaries of CO 2 + dimethyl sulfoxide, CO 2 + propylene glycol monomethyl ether acetate, and CO 2 + quinoline at temperatures from 308.15 to 358.15 K and pressures up to 28 MPa or near critical pressures. These phase boundary data were correlated with the Soave, the Peng–Robinson and the Patel–Teja equations of state, respectively.

Exploiting the pressure effect on lipase‐catalyzed wax ester synthesis in dense carbon dioxide

The present work focuses on the thermodynamic interpretation of the lauryl oleate biosynthesis in high-pressure carbon dioxide. Lipase-catalyzed lauryl oleate production by oleic acid esterification with 1-dodecanol over immobilized lipase from Rhizomucor miehei (Lipozyme RM IM) was successfully performed in a sapphire window batch stirred tank reactor (BSTR) using dense CO(2) as reaction medium. The experiments were planned to elucidate the pressure effect on the reaction performance. With increasing the pressure up to 10 MPa, the catalytic efficiency of the studied enzyme improved rising up to a maximum and decreased at higher pressure values. Kinetic observations, exhibiting that dense CO(2) expanded reaction mixture in subcritical conditions led to higher performance than when diluted in a single supercritical phase, were elucidated by phase-equilibrium arguments. The experimental results were justified with emphasis on thermodynamic interpretation of the studied system. Particularly, the different reaction performances obtained were related to the position of the operating point with respect to the location of liquid-vapor phase boundaries of the reactant fatty acid/alcohol/CO(2) ternary system. The outlook for exploitation of CO(2) expanded phase at lower pressure compared to supercritical phase, with heterogeneous system in which the solid catalyst particles are exposed to dense CO(2) expanded reaction mixture, in developing new biotransformation schemes is promising.

Ultra-fine particles formation of C.I. Pigment Green 36 in different phase regions via a supercritical anti-solvent process

Ultra-fine particles of C.I. Pigment Green 36 were prepared using a continuous supercritical anti-solvent (SAS) apparatus employing quinoline as solvent and supercritical carbon dioxide as anti-solvent. A series of precipitation experiments were conducted at different temperatures, pressures, and flow rates of pigment solution. The vapor–liquid phase boundaries of carbon dioxide + quinoline mixtures were also measured with a volume-variable phase equilibrium analyzer at temperatures from 308.2 K to 328.2 K. Mapping the estimated composition of mixtures in a model CSTR (continuously stirred tank reactor) precipitator at the end of injection of pigment solution onto the phase diagram found that the morphology of prepared particles was mainly governed by the phase behavior of anti-solvent + solvent mixtures. Nano-particles were obtained as the precipitation loci were manipulated within either supercritical or superheated vapor region through the SAS process, whereas micro-metric aggregated ball-like particles were produced as the precipitation loci passed by the vapor–liquid coexistence region.

Reference Equations of State for the Thermodynamic Properties of Fluid Phase n-Butane and Isobutane

New formulations for the thermodynamic properties of fluid phase n-butane and isobutane in the form of fundamental equations explicit in the Helmholtz energy are presented. The functional form of the correlation equations for the residual parts was developed simultaneously for both substances considering data for the thermodynamic properties of ethane, propane, n-butane, and isobutane. Each contains 25 coefficients which were fitted to selected data for the thermal and caloric properties of the respective fluid both in the single-phase region and on the vapor–liquid phase boundary. This work provides information on the available experimental data for the thermodynamic properties of n- and isobutane, and presents all details of the new formulations. The new equations of state describe the pρT surfaces with uncertainties in density of 0.02% (coverage factor k=2 corresponding to a confidence level of about 95%) from the melting line up to temperatures of 340 K and pressures of 12 MPa. The available reliable data sets in other regions are represented within their experimental uncertainties. The primary data, to which the equation for n-butane was fitted, cover the fluid region from the melting line to temperatures of 575 K and pressures of 69 MPa. The equation for isobutane was fitted to primary data that cover the fluid region from the melting line to temperatures of 575 K and pressures of 35 MPa. Beyond the range described by experimental data, the equations yield reasonable extrapolation behavior up to very high temperatures and pressures. In addition to the equations of state, independent equations for the vapor pressures, the saturated-liquid and saturated-vapor densities, and the melting pressures are given. Tables of thermodynamic properties calculated from the new formulations are listed in Appendix 2. Additionally, a preliminary equation of state for propane is presented that was developed in the course of the simultaneous optimization. This equation has the same functional form as the equations of state for n- and isobutane.