Fluid Phase Boundary Research Articles

Phase separation of comb polymer nanocomposite melts.

In this work, the spinodal phase demixing of branched comb polymer nanocomposite (PNC) melts is systematically investigated using the polymer reference interaction site model (PRISM) theory. To verify the reliability of the present method in characterizing the phase behavior of comb PNCs, the intermolecular correlation functions of the system for nonzero particle volume fractions are compared with our molecular dynamics simulation data. After verifying the model and discussing the structure of the comb PNCs in the dilute nanoparticle limit, the interference among the side chain number, side chain length, nanoparticle-monomer size ratio and attractive interactions between the comb polymer and nanoparticles in spinodal demixing curves is analyzed and discussed in detail. The results predict two kinds of distinct phase separation behaviors. One is called classic fluid phase boundary, which is mediated by the entropic depletion attraction and contact aggregation of nanoparticles at relatively low nanoparticle-monomer attraction strength. The second demixing transition occurs at relatively high attraction strength and involves the formation of an equilibrium physical network phase with local bridging of nanoparticles. The phase boundaries are found to be sensitive to the side chain number, side chain length, nanoparticle-monomer size ratio and attractive interactions. As the side chain length is fixed, the side chain number has a large effect on the phase behavior of comb PNCs; with increasing side chain number, the miscibility window first widens and then shrinks. When the side chain number is lower than a threshold value, the phase boundaries undergo a process from enlarging the miscibility window to narrowing as side chain length increases. Once the side chain number overtakes this threshold value, the phase boundary shifts towards less miscibility. With increasing nanoparticle-monomer size ratio, a crossover of particle size occurs, above which the phase separation is consistent with that of chain PNCs. The miscibility window for this condition gradually narrows while the other parameters of the PNCs system are held constant. These results indicate that the present PRISM theory can give molecular-level details of the underlying mechanisms of the comb PNCs. It is hoped that the results can be used to provide useful guidance for the future design control of novel, thermodynamically stable comb PNCs.

Anomalous nucleation near a fluid phase boundary created by a rapid heat pulse

We report a novel method to rapidly nucleate vapor in a liquid with an electrically pulsed wire that temporarily raises the temperature of nearby liquid. This temperature increase is sufficient to overcome the nucleation barrier to vapor formation by locally putting the system in a non-equilibrium superheated state. By observing the subsequent behavior of bubbles after nucleation and thermal relaxation, we can determine the stability of the vapor phase. We map out a phase envelope by adjustment of the ambient temperature and pressure of the fluid around the wire. We find good agreement between measurements with this method and those made using a conventional apparatus. Surprisingly, we find that rapid heating of the liquid around the wire is able to produce nucleation in certain fluid mixtures for which the temperature increase is not expected to create an unstable or even metastable liquid. Evidence suggests a temporary enrichment of the region around the wire by lighter components due to the Soret effect is responsible for nucleation in such cases.

Equation of State for Solid Phase I of Carbon Dioxide Valid for Temperatures up to 800 K and Pressures up to 12 GPa

The available thermodynamic-property data for solid phase I of carbon dioxide (“dry ice”) are reviewed and used to determine the parameters of a new fundamental equation of state constructed in the form of a Helmholtz energy function with temperature and molar volume as the independent variables. The experimental data considered include the pressure, molar volume, and isobaric heat capacity along the sublimation curve, the melting-pressure curve, and molar volume in the compressed solid at temperatures from 295 to 764 K and pressures up to 12 GPa. The equation of state is based on the quasi-harmonic approximation, incorporating a Debye oscillator distribution for the vibrons, two discrete modes for the librons and a further three distinct modes for the internal vibrations of the CO2 molecule. A small anharmonic correction term is included, which is significant mainly in the region of the triple point. The estimated relative uncertainty of molar volume at specified temperature and pressure calculated from the equation of state is 0.02% on the sublimation curve and 1.5% in the compressed solid; for isobaric heat capacity on the sublimation curve, the uncertainty varies from 5.0% to 0.5% between 2 and 195 K. Auxiliary equations for the pressure and molar volume on the sublimation and melting curves are given. The equation of state is valid at temperatures from 0 to 800 K and at pressures from the solid–fluid phase boundary to 12 GPa.

Characteristics of methane hydrate formation in carbon nanofluids

When methane hydrate is formed artificially by simply reversing its process of natural generation, the amount of methane gas consumed by hydrate formation is fairly low, which is problematic for its large scale synthesis and application. Therefore, this study examined methods for increasing the amount of gas consumed by adding MWCNTs (multi-walled carbon nanotubes) and OMWCNTs (oxidized multi-walled carbon nanotubes). The surfaces of the MWCNTs were oxidized chemically, and dispersed uniformly in distilled water after a dispersion operation. The amount of methane gas consumed during the formation of methane hydrate in the oxidized carbon nanofluid was approximately 4.5 times higher than that in distilled water. The hydrate-nanocarbon fluid phase boundary line was shifted to the right side of the hydrate-pure water phase boundary line in the pressure–temperature phase diagram. The carbon nanofluid system accelerated the rate of methane hydrate formation at low subcooling temperatures (<8 K).

High pressure phase equilibria in methane + waxy systems. 2. Methane + waxy ternary mixture

Liquid–vapour and fluid–solid phase transitions were experimentally determined under pressure on the system methane + a ternary waxy mixture using a full visibility cell. The wax was an approximately equimolar mixture of n-C 16, n-C 17 and n-C 18, the composition being chosen to obtain a mixture with an average molecular weight similar to heptadecane. Measurements were performed according to the synthetic method on different mixtures ranging from 0 to 99.5 mol% of methane. The liquid–solid phase transitions were investigated up to 100 MPa and fluid phase boundary was studied in the temperature domain from 293 to 373 K. Measurements performed on this pseudo-binary system were compared to the phase diagram of the binary system methane + heptadecane.

Protein Diffusion Across the Interface in Aqueous Two-Phase Systems

We present a detailed study of the diffusive transport of proteins across a fluid phase boundary within aqueous two-phase systems. The aim of the work is to investigate whether local effects at the phase boundary cause a retardation of the diffusive transport between the phases. Possible modifications of interfacial mass transfer could be due to protein adsorption at the phase boundary or local electric fields from electric double layers. Experiments with a microfluidic system have been performed in which protein diffusion (bovine serum albumin and ovalbumin) within a bilaminated configuration of two phases containing polyethylene glycol and dextran is analyzed. A one-dimensional model incorporating phase-specific diffusion constants and the difference in chemical potential between the phases has been formulated. A comparison of experimental and simulation data shows a good overall agreement and suggests that a potential local influence of the phase boundary on protein transport is insignificant for the systems under investigation.

Integral equation theory study on the phase separation in star polymer nanocomposite melts

The polymer reference interaction site model theory is used to investigate phase separation in star polymer nanocomposite melts. Two kinds of spinodal curves were obtained: classic fluid phase boundary for relatively low nanoparticle-monomer attraction strength and network phase boundary for relatively high nanoparticle-monomer attraction strength. The network phase boundaries are much more sensitive with nanoparticle-monomer attraction strength than the fluid phase boundaries. The interference among the arm number, arm length, and nanoparticle-monomer attraction strength was systematically investigated. When the arm lengths are short, the network phase boundary shows a marked shift toward less miscibility with increasing arm number. When the arm lengths are long enough, the network phase boundaries show opposite trends. There exists a crossover arm number value for star polymer nanocomposite melts, below which the network phase separation is consistent with that of chain polymer nanocomposite melts. However, the network phase separation shows qualitatively different behaviors when the arm number is larger than this value.

High pressure phase equilibria in methane + waxy systems : 1. Methane + heptadecane

Fluid–fluid and fluid–solid phase equilibrium were experimentally determined under pressure on the system methane + heptadecane using a full visibility cell. Measurements were performed using the synthetic method on mixtures ranging from pure heptadecane to 99% of methane. The liquid–solid phase transitions were investigated up to 90 MPa and fluid phase boundary was studied in the temperature domain from 293 to 373 K. The appearance of a minimum in the three phase (V–L–S) equilibrium curve is discussed and it is shown that the difference in the solid phase structure and the presence of a solid–solid phase transition do not affect significantly the phase diagram determined.

Prediction of solid–fluid phase diagrams of light gases–heavy paraffin systems up to 200 MPa using an equation of state–G E model

This paper presents a procedure for the simultaneous prediction of fluid–fluid and solid–fluid equilibria of light gases–heavy hydrocarbons systems under pressure. The fluid phases behaviour is described by the modified LCVM, an equation of state–G E model and the solid phase non-ideality is represented by the Wilson equation using the predictive local composition concept. This procedure was tested for several binary and ternary systems as well as multi-component systems leading to a good representation of both fluid–fluid and solid–fluid equilibria with a typical average absolute deviation of 1.5 K for the solid–fluid phase boundary of binary and ternary mixtures and of 0.5 K for multi-component systems. The AAD% in the fluid–fluid phase boundary of multi-component systems is of 3.2%.

Measurement and calculation of solid-liquid and liquid-vapour equilibria in a ternary mixture

Phase boundaries between homogeneous liquid phase and two-phase regions, both liquid-vapour and liquid-solid, and phase boundaries between the two-phase liquid-vapour region and the three-phase liquid-vapour-solid region were experimentally determined under pressure for the system methane+decane+docosane. The liquid solid phase transition was investigated up to 45 MPa and the fluid phase boundary was studied in the temperature range 293-423 K. The experimental data were compared with those predicted by a thermodynamic model based on the Peng-Robinson equation of state.

Phase boundary measurement on a methane + decane + multi-paraffins system

Phase boundaries between homogeneous liquid phase and two-phase regions, both liquid-vapour and liquid-solid, and the phase boundary between the two-phase liquid - vapour region and the three-phase liquid - vapour - solid region were experimentally determined under pressure on the system methane + decane + heavy fraction using a full visibility sapphire cell. Measurements were performed on different mixtures made up of 90% of the binary mixture methane + decane (with a molar fraction of methane of about 50 %) and 10 % of a heavy fraction composed of various distributions of heavy normal paraffins centered around C 22. The liquid-solid phase transition was investigated up to 45 MPa and fluid phase boundary was studied in the temperature domain from 293 K to 423 K.

Isochoric pVT and Phase Equilibrium Measurements for Carbon Dioxide + Nitrogen

The authors have designed and constructed an isochoric apparatus for fast and accurate pressure-volume-temperature (pVT) and phase equilibrium measurements. The apparatus allows isochoric (p, T at constant V) measurements for noncorrosive fluids over a wide range of pressures (7--105 MPa) and temperatures (100--450 K). Densities can be derived from densities determined at one isotherm (p, V at constant T) with another apparatus, such as a pycnometer or a Burnett apparatus. Temperatures are accurate to {+-} 10 mK and precise to {+-}1 mK on ITS-90. Pressure measurements are accurate to {+-}10 kPa and precise to {+-}2 kPa. This apparatus requires about 20 min for temperature equilibration for measurements 2 K apart and about 50 min for measurements 10 K apart. The authors have measured 23 phase boundary points for three mole fractions, x{sub 1} = 0.3991, 0.4459, and 0.5037, for CO{sub 2} (1) + N{sub 2} (2) at temperatures from 207 to 268 K and pressures from 10.8 to 21.5 MPa. The estimated accuracy is {+-} 40 mK in temperature and {+-} 17 kPa in pressure. The isochoric measurements used to obtain these phase boundary points extend from 205 to 300 K and from 8 to 80 MPa. They have determined more » the saturation density for 20 of the phase boundary points. The saturation densities and the densities along the isochores were derived from density measurements at 300 and 285 K measured with a pycnometer estimated to be accurate to {+-}0.1%. The behavior of the solid + fluid phase boundary is discussed. « less

Fluid–fluid phase separations in nonadditive hard sphere mixtures

We investigated the phase stability of a system of nonadditive hard sphere (NAHS) mixtures with equal diameters, d, between like species and an unequal collision diameter, d(1+α), between unlike species. It is based on an analytic equation of state (EOS) which refines an earlier expression [J. Chem. Phys. 100, 9064 (1994)] within the mixed fluid phase range. The new EOS gives a reliable representation of Monte Carlo EOS data over a wide range of density, composition, and nonadditivity parameters (α). Comparisons with available computer simulations show that the new EOS predicts satisfactory phase boundaries and the critical density line. It is superior to results derived from integral equations (the Percus–Yevick, the Martynov–Sarkisov, and the modified Martynov–Sarkisov) and analytic theories (the MIX1 model, the van der Waals one-fluid model, and the scaled particle theory). The present study shows that, unless α exceeds 0.026, the fluid phase will remain fully miscible up to the freezing point of pure hard spheres. We have also investigated structural aspects of the phase stability by Monte Carlo computations. The radial distribution functions, the local mole fraction, and coordination numbers for like and unlike pairs of hard spheres exhibit significant number dependencies close to the fluid phase boundary. They provide precursory signals to an impending phase change. Finite systems used in the Monte Carlo sampling limit fluctuations in sizes and shapes of heterogeneous clusters. The observed number dependence simply reflects this fact.

Viscosity and self-diffusion of simple liquids. Hard-sphere treatment of molecular dynamics data

Non-equilibrium molecular dynamics computer simulations performed on the Lennard-Jones, LJ, fluid along the kT/Iµ= 1.46 isotherm give values for the Newtonian shear viscosity, η, that are, upon conversion to real units, in excellent agreement with recent experimental viscosity values for argon. These data are combined with literature LJ η and self-diffusion coefficients, D, to prove the usefulness of an MD-corrected Chapman–Enskog theory for hard-sphere fluid-transport coefficients applied to LJ fluids. The simulation LJ η and D are predicted over the fluid range up to the solid–fluid phase boundary by attaching a temperature-dependent effective hard-sphere diameter to the LJ molecule. This theory is extended to derive expressions for the constant-volume and constant-pressure activation energies, and pressure transport coefficients in terms of the isobaric thermal expansivity and isothermal compressibility of the LJ fluid. The behaviour of these “second-order transport coefficients” along isotherms is discussed, emphasising the relationship between the transport coefficients and thermodynamic properties of the LJ fluid.

The theory of capillary excess viscosities

A general phenomenological theory of capillary excess or surface viscosities is developed from considerations of momentum balance in the neighbourhood of a fluid phase boundary. It is assumed that a coordinate system may be erected in the interfacial region for which the constitutive equations are anisotropic in the normal direction but tangentially isotropic. This anisotropy together with certain assumptions regarding the continuity of the velocity vector and its derivatives leads to the identification for incompressible fluids of four surface viscosity coefficients k , n , k N and n N . The first two have been recognized since the time of Boussinesq, and experimental data regarding them are accumulating. The second two appear to be new, and experiments to measure them are only in a preliminary stage. In all cases, the surface viscosity coefficients are formally identified as integrals taken through the interfacial region from one bulk phase to the next. The theory is limited to interfacial regions whose curvatures are small with respect to the reciprocal thickness of the transition zone and of greater than ultra-low surface tension.