Vapor-liquid Phase Separation Research Articles

Method of Calculating a Phase Separator with Direct Capillary Channels for the Vapor-liquid Phase Separation of Superfluid Helium

Method of Calculating a Phase Separator with Direct Capillary Channels for the Vapor-liquid Phase Separation of Superfluid Helium

Phase behavior of the carbon dioxide/toluene/poly(ethylene glycol) ternary system

The phase behavior of a carbon dioxide (CO2)/toluene (Tol)/poly(ethylene glycol) (PEG) ternary system was investigated in this study to consider the effect of the polymer species on the phase diagram. Measurements were performed using a synthetic method combined with laser displacement and turbidity measurements. Bubble points (vapor–liquid phase separation) were determined from changes in the piston displacement and cloud points (liquid–liquid (LL) phase separation) were determined from changes in the turbidity. The phase boundaries of the CO2 mass fractions ranging from 0.113 to 0.496 were measured by varying the Tol/PEG mass ratio. The homogeneous phase area decreased when the mass ratio of PEG to Tol increased and/or the temperature decreased. These changes in the LL phase-separation behavior were explained by referring to the free volume fraction and solubility parameter estimated using the Sanchez–Lacombe equation of state. The free volume integral fraction could explain the phase diagram, but not the solubility parameter; the effect of polymer species on the Px phase diagram of the ternary system was explained by considering specific interactions between dissimilar components. These results could promote a comprehensive understanding of the phase diagram of CO2/organic solvent/polymer systems and aid the prediction of phase behavior.

Phase behavior of the carbon dioxide/toluene/poly(methyl methacrylate) ternary system

Carbon dioxide/organic polymer/solvent systems have several industrial applications, including supercritical polymerization. Various process parameters affect the phase behavior of these systems, thereby influencing the process design. Accordingly, the phase behavior of a carbon dioxide (CO2)/toluene (Tol)/poly(methyl methacrylate) (PMMA) ternary system was investigated in this study. Measurements were performed using a synthetic method combined with laser displacement and turbidity measurement. Bubble points (vapor–liquid phase separation) were determined from changes in the piston displacement, whereas cloud points (liquid–liquid (LL) phase separation) were determined from changes in the turbidity The phase boundaries of CO2 mass fractions ranging from 0.098 to 0.577 were measured by varying the Tol/PMMA ratio. The homogeneous phase area decreased when the ratio of PMMA to Tol increased, molecular weight of PMMA increased, and/or temperature decreased. These changes in the LL phase separation behavior were explained with reference to the free volume (vf) and solubility parameter (δ) estimated using the Sanchez–Lacombe equation of state. The estimation of vf and δ is expected to be helpful in comprehensively understanding the phase diagram and in predicting the phase behavior of CO2/organic solvent/polymer systems.

Binding potential and wetting behavior of binary liquid mixtures on surfaces.

We present a theory for the interfacial wetting phase behavior of binary liquid mixtures on rigid solid substrates, applicable to both miscible and immiscible mixtures. In particular, we calculate the binding potential as a function of the adsorptions, i.e., the excess amounts of each of the two liquids at the substrate. The binding potential fully describes the corresponding interfacial thermodynamics. Our approach is based on classical density functional theory. Binary liquid mixtures can exhibit complex bulk phase behavior, including both liquid-liquid and vapor-liquid phase separation, depending on the nature of the interactions among all the particles of the two different liquids, the temperature, and the chemical potentials. Here we show that the interplay between the bulk phase behavior of the mixture and the properties of the interactions with the substrate gives rise to a wide variety of interfacial phase behaviors, including mixing and demixing situations. We find situations where the final state is a coexistence of up to three different phases. We determine how the liquid density profiles close to the substrate change as the interaction parameters are varied and how these determine the form of the binding potential, which in certain cases can be a multivalued function of the adsorptions. We also present profiles for sessile droplets of both miscible and immiscible binary liquids.

Cd isotopic constraints on the sources of Zn-Sb deposits: A case study of the Jianzhupo Zn-Sb deposit, Guangxi Province, China

Antimony (Sb) is identified as a critical metal in many countries. The source of hydrothermal Sb-bearing deposits is currently debated in two opposing models (magmatic fluids or country rocks). Some Sb-bearing hydrothermal systems host abundant cadmium (Cd). Due to the close association of Cd and Sb in hydrothermal systems and the distinct Cd isotopic signatures between magmatic and sedimentary rocks, Cd isotopes have the potential to trace the metal origin in Sb-bearing deposits. Here, we conducted Cd isotope analyses of sulfide (jamesonite and sphalerite) collected from the Jianzhupo Zn-Sb deposit, SW China. A narrow range of δ114/110Cd relative to NIST SRM 3108 Cd standard was observed in sphalerites (−0.15‰ to +0.18‰; mean = 0.03‰ ± 0.10‰, one standard deviation [1SD]), identical to that of intermediate igneous rocks (−0.20‰ to +0.15‰); in contrast, pure jamesonites show a large range of δ114/110Cd (−0.42‰ to +0.17‰; mean = −0.22‰ ± 0.20‰, 1SD), differing from those of sphalerite. Different Cd isotope signatures between jamesonite and sphalerite are unlikely to have been triggered by sulfide precipitation, vapor-liquid phase separation, diffusion, and different Cd-S bond strengths. Instead, based on a comparison of δ114/110Cd and Zn/Cd ratio of sulfide and potential source rocks, we propose that a mixing of two ore-forming endmembers, derived from igneous and sedimentary rocks, may better explain the sulfide Cd isotopic signatures. This is supported by the well-defined positive correlation between δ114/110Cd and Zn/Cd ratio in sulfides. This study shows a novel application of Cd isotopes for metallogenetic tracing and demonstrates that Sb-bearing hydrothermal systems can incorporate metals from multiple sources.

Silver isotope fractionation in ore-forming hydrothermal systems

The behavior of silver in hydrothermal ore-forming systems has been the subject of numerous studies. Equilibrium and Rayleigh-type isotope fractionation of silver during transport- and deposition-related processes in silver-bearing hydrothermal ore-forming systems are investigated experimentally and theoretically in this study. The results of open-system evaporation experiments in a simple Ag+–H2O system show that the transfer kinetics of silver from liquid to vapor follows a second-order kinetic reaction model with activation energy (Ea) values of 131.20 ± 14.63 kJ·mol−1 and 145.38 ± 2.93 kJ·mol−1 in neutral and acidic solutions, respectively. No loss of silver from the solution was observed during surface evaporation, and the rate constant, ka, increased exponentially with temperature above 343 K at ambient pressure. During vapor–liquid separation, the vapor is enriched in 107Ag, whereas the liquid is enriched in 109Ag. The silver isotope fractionation follows a Rayleigh-type fractionation model with αvapor-liquid factors of 0.99936–0.99985 at 373 K under neutral and acidic conditions, respectively, whereas the temperature-dependent equilibrium isotope fractionation follows the relationship, 1000lnαvapor-liquid = −0.0039 × 106/T2 – 0.0037 based on density functional theory (DFT) calculations. This explains the relatively narrow interval of δ109Ag values (from −0.3 to +0.4‰) analyzed in Ag-bearing veins from hydrothermal ore-deposits. Based on the bond-strength of Ag to the nearest atoms in minerals, the 109Ag enrichment decreases in the order pyrargyrite, argentite, proustite, stephanite, native silver, iodargyrite, chlorargyrite. The equilibrium silver isotope fractionation between fluid and mineral during ore formation can be considerable depending on the temperature, the nature of the silver-bearing mineral deposited, whether or not there is vapor–liquid phase separation, and whether there is a reduction of oxidized silver (Ag(+1)) to the reduced form Ag(0). Consequently, the source signatures of δ109Ag are altered significantly by transport- and deposition-related processes during ore formation (e.g., boiling, precipitation and reduction). A new silver isotope-geothermometer is proposed based on the equilibrium silver isotope fractionation between argentite and stephanite. This geothermometer, which employs the relationship 1000lnαargentite-stephanite = 0.0128 × 106/T2 + 0.0014, can be used to constrain temperature in silver-bearing hydrothermal systems provided that argentite and stephanite are in equilibrium.

Vacuum residue coking process simulation using molecular-level kinetic model coupled with vapor-liquid phase separation

In this work, a molecular-level kinetic model was built to simulate the vacuum residue (VR) coking process in a semi-batch laboratory-scale reaction kettle. A series of reaction rules for heavy oil coking were summarized and formulated based on the free radical reaction mechanism. Then, a large-scale molecular-level reaction network was automatically generated by applying the reaction rules on the vacuum residue molecules. In order to accurately describe the physical change of each molecule in the reactor, we coupled the molecular-level kinetic model with a vapor–liquid phase separation model. The vapor–liquid phase separation model adopted the Peng-Robinson equation of state to calculate vapor–liquid equilibrium. A separation efficiency coefficient was introduced to represent the mass transfer during the phase separation. We used six sets of experimental data under various reaction conditions to regress the model parameters. The tuned model showed that there was an excellent agreement between the calculated values and experimental data. Moreover, we investigated the effect of reaction temperature and reaction time on the product yields. After a comprehensive evaluation of the reaction temperature and reaction time, the optimal reaction condition for the vacuum residue coking was also obtained.

Kinetics of domain growth and aging in a two-dimensional off-lattice system.

We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single-component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth, and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-"liquid" as well as vapor-"solid" coexistence. For the vapor-liquid phase separation we observe that ℓ, the average domain length, grows with time (t) as t^{1/2}, a behavior that has connection with hydrodynamics. At low-enough temperature, a sharp crossover of this time dependence to a much slower, temperature-dependent, growth is identified within the timescale of our simulations, implying "solid"-like final state of the high-density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data collapse with respect to ℓ/ℓ_{w},ℓ, and ℓ_{w} being the average domain lengths at times t and t_{w} (≤t), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: ∼(ℓ/ℓ_{w})^{-λ} for t≫t_{w}. The decay exponent λ, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.

Wettability of ultra-small pores of carbon electrodes by size-asymmetric ionic fluids.

Recently, we studied the phase behavior of ionic fluids under confinement using the classical density functional theory within the framework of the restricted primitive model. The theoretical results indicate that narrowing the pore size may lead to a drastic reduction in the electric double layer capacitance, while increasing the surface electrical potential would improve the ionic accessibility of micropores. In this work, we extend the theoretical investigation to systems containing size-asymmetric electrolytes that may exhibit a vapor-liquid like phase transition in the bulk phase. The effects of pore size and surface electric potential on the phase diagram and microscopic structures of the confined electrolytes were studied over a broad range of parameters. We found that decreasing the pore size or increasing the surface potential could destabilize the liquid phase in micropores, and capillary evaporation could occur regardless of the size asymmetry between cations and anions. Compared to that in a symmetric ionic system, the vapor-liquid phase separation is more likely to take place as the size asymmetry becomes more pronounced. The phase transition would alter the "accessibility" of ions to micropores and lead to coexisting micropores with different surface charge densities as identified by Monte Carlo simulation.

Vapor–liquid and chemical equilibria model for formaldehyde + 1,3,5-trioxane + methanol + salt + water system

The salt effect on vapor–liquid phase equilibrium (VLE) has potential applications in industrial production of 1,3,5-trioxane. Optimizing reactive distillation process and developing new catalysts for industrial production of 1,3,5-trioxane require a reliable model for VLE of the reaction mixtures. Here an extended UNIFAC model combined a Debye–Hückel type is developed to describe the vapor–liquid and chemical equilibria of the multi-solvent salt-containing reactive mixtures associated with the 1,3,5-trioxane synthesis. New experimental data for the VLE of the quinary systems (formaldehyde + 1,3,5-trioxane + methanol + salt + water) and their ternary subsystems (1,3,5-trioxane + salt + water), (methanol + salt + water), and (formaldehyde + salt + water) are systematically measured at atmospheric pressure. The salts considered include LiCl, NaCl, KCl, NaBr, MgSO4, MgCl2, and Na2SO4. The model parameters, which are either obtained from the literature or determined from the VLE data of the above-mentioned ternary systems, are used to provide predictions for the quinary systems (formaldehyde + 1,3,5-trioxane + methanol + salt + water). The agreements between measured and predicted results are accurate. Furthermore, the model is used to uncover the effects of the salts considered on the VLE of these chemical reactive systems. The results show that MgSO4 is a potential additive that can be used to improve the vapor–liquid phase separation during the reactive distillation process of 1,3,5-trioxane production.

Nonphysical Behavior in Several Statistical Mechanically Based Equations of State

In this work, we utilize bifurcation diagrams to study the role of mathematical artifacts in deteriorating the physical behavior in statistical mechanically based equations of state of pure fluids. We study the impact of common empirical approximations usually employed to overcome some of the mathematical and physical challenges such as the parametrization of mean field models or pair correlations functions at contact. The proposed diagrams elucidate how the reduced molar volume bifurcates with the variation of temperature at constant pressure. We generate bifurcation diagrams for the modified van der Waals equation of state (EOS) of Poole et al, SAFT-VR Mie, Soft-SAFT, CK-SAFT, and the original SAFT EOSs for spherical and nonspherical molecules. We find that the bifurcation diagram can serve as a useful schematic tool to reveal the unphysical PVT behavior, demonstrate the existence of physical and spurious two-phase separation regions, and illustrate how the number of molar volume roots vary with temperatures. Our method shows that the presence of unphysical branches can cause spurious two-phase separation regions and create erroneous behavior in the stability limit of vapor–liquid equilibrium. We demonstrate that the existence of customary and spurious phase envelopes is accompanied by S-shaped behavior in the volume-temperature bifurcation diagrams. The study reveals that none of the SAFT models is free from producing unphysical behavior. While the SAFT-VR Mie EOS exhibits solid–liquid-like behavior for nonspherical molecules, the CK-SAFT EOS shows liquid–liquid demixing behavior for spherical and nonspherical compounds. For the soft-SAFT EOS, three different two-phase separation regions are observed in addition to the common vapor–liquid phase separation region.

Does capillary evaporation limit the accessibility of nonaqueous electrolytes to the ultrasmall pores of carbon electrodes?

Porous carbons have been widely utilized as electrode materials for capacitive energy storage. Whereas the importance of pore size and geometry on the device performance has been well recognized, little guidance is available for identification of carbon materials with ideal porous structures. In this work, we study the phase behavior of ionic fluids in slit pores using the classical density functional theory. Within the framework of the restricted primitive model for nonaqueous electrolytes, we demonstrate that the accessibility of micropores depends not only on the ionic diameters (or desolvation) but also on their wetting behavior intrinsically related to the vapor-liquid or liquid-liquid phase separation of the bulk ionic systems. Narrowing the pore size from several tens of nanometers to subnanometers may lead to a drastic reduction in the capacitance due to capillary evaporation. The wettability of micropores deteriorates as the pore size is reduced but can be noticeably improved by raising the surface electrical potential. The theoretical results provide fresh insights into the properties of confined ionic systems beyond electric double layer models commonly employed for rational design/selection of electrolytes and electrode materials.

Perspective: The Asakura Oosawa model: a colloid prototype for bulk and interfacial phase behavior.

In many colloidal suspensions, the micrometer-sized particles behave like hard spheres, but when non-adsorbing polymers are added to the solution a depletion attraction (of entropic origin) is created. Since 60 years the Asakura-Oosawa model, which simply describes the polymers as ideal soft spheres, is an archetypical description for the statistical thermodynamics of such systems, accounting for many features of real colloid-polymer mixtures very well. While the fugacity of the polymers (which controls their concentration in the solution) plays a role like inverse temperature, the size ratio of polymer versus colloid radii acts as a control parameter to modify the phase diagram: when this ratio is large enough, a vapor-liquid like phase separation occurs at low enough colloid packing fractions, up to a triple point where a liquid-solid two-phase coexistence region takes over. For smaller size ratios, the critical point of the phase separation and the triple point merge, resulting in a single two-phase coexistence region between fluid and crystalline phases (of "inverted swan neck"-topology, with possibly a hidden metastable phase separation). Furthermore, liquid-crystalline ordering may be found if colloidal particles of non-spherical shape (e.g., rod like) are considered. Also interactions of the particles with solid surfaces should be tunable (e.g., walls coated by polymer brushes), and interfacial phenomena are particularly interesting experimentally, since fluctuations can be studied in the microscope on all length scales, down to the particle level. Due to its simplicity this model has become a workhorse for both analytical theory and computer simulation. Recently, generalizations addressing dynamic phenomena (phase separation, crystal nucleation, etc.) have become the focus of studies.

Gelation in semiflexible polymers

Molecular dynamics simulations have been employed to study the formation of a physical gel by semiflexible polymer chains. The formation of a geometrically connected network of these chains is investigated as a function of temperature and rate of cooling. The stiffness of the molecules is controlled via a potential between beads separated by two bonds. As the temperature is lowered, a percolated homogeneous solution phase separates to form a high-density, non-percolated nematic fluid and a low-density gas phase. On further decreasing the temperature, the chains are dynamically arrested preventing the completion of the vapor-liquid (VL) phase separation. As a result, the chains are stuck in a three-dimensional network of nematic bundles forming a percolated gel. Apart from temperature, the rate of cooling also plays an important role in the formation of the gel. Cooling the system at a faster rate yields gel while slower rates result in complete VL phase separation.

Reply to “Comment on ‘Equilibrium polymerization and gas-liquid critical behavior in the Stockmayer fluid'”

In their Comment, Ivanov, Kantorovich, and Camp [Phys. Rev. E. 77, 013501 (2008)] analyze molecular dynamics simulation data on the gas-liquid critical point of the Stockmayer fluid obtained recently by the authors. Based on this analysis they conclude that vapor-liquid phase separation may occur in purely dipolar systems. In this reply we argue that the existing data for the Stockmayer fluid as well as a related system are consistent with the nonexistence of vapor-liquid phase separation in purely dipolar systems.

Method for Locating the Vapor−Liquid Critical Point of Multicomponent Fluid Mixtures Using a Shear Mode Piezoelectric Sensor

A new approach to locating the critical point of fluid mixtures is reported, utilizing a shear mode piezoelectric sensor. This technique employs a single piece of quartz crystal that is installed at the bottom of a strongly stirred high-pressure vessel. The sensor response indicates whether liquid or gas is in contact with its surfaces. Thus, the sensor is able to identify vapor-liquid phase separation by registering a discontinuity in the impedance minimum of the sensor as a function of pressure. Two systems (methanol + CO2 and H2 + CO2) have been investigated using this method. The critical point data of the methanol + CO2 system were chosen to validate the approach against a wealth of literature data, and good agreement was obtained. The sensor behavior in the two-phase region, as well as the effect of stirring, is discussed. The method is general and can be used with other sensors.

Density inhomogeneity and diffusion behavior of fluids in micropores by molecular-dynamics simulation.

The density profiles and the diffusion behavior of fluid argon confined in micropores were studied by molecular-dynamics simulations. The effects of pore size (width), temperature and number density on the density profiles and the self-diffusion coefficients in micropores were simulated with pore widths from 0.6 to 4.0 nm. The density profiles are greatly affected by the pore size. Strong inhomogeneities in the channel direction and vapor-liquid phase separation in the micropores were observed when initial conditions were chosen in the coexistence region of the fluid. The self-diffusion coefficient in the channel direction in the pores was found to be much lower than in the bulk, and decreasing with decreasing pore size, decreasing temperature, and increasing density.

Hydrodynamic bubble coarsening in off-critical vapor-liquid phase separation.

Late-stage coarsening in off-critical vapor-liquid phase separation is reexamined. In the limit of bubbles of vapor distributed throughout a continuous liquid phase, it is argued that coarsening proceeds via inertial hydrodynamic bubble collapse. This replaces the Lifshitz-Slyozov-Wagner mechanism seen in binary liquid mixtures. The arguments are strongly supported by simulations in two dimensions using a novel single-component soft-sphere fluid.

Vapor–Liquid Phase separation of He II

A theory is proposed which uses both the permeability and bubble point diameter of the porous plug to characterize the full range operation of the Vapor Liquid Phase Separation (VLPS) of liquid helium. A computer model has been written based on the theory presented in this paper, which gives good correlation with VLPS data in the literature. The predicted performance of the SIRTF flight plug is also presented.

Computer Simulation of Vapor-Liquid Phase Separation

Abstract A late-time growth law of domains undergoing vapor-liquid phase separation is studied for two- and three-dimensional Lennard-Jones fluids by molecular dynamics simulations. The characteristic domain size shows a power law growth in a late stage with the growth exponent of ½ for both two- and three-dimensional fluids. This study concerns also the relationship between statistical properties of domain patterns and temperatures. The asymptotic form factor of each system is obtained using scaling and the asymptotic tail of the form factor is analyzed. This tail is related to the domain-wall structure. At low system temperatures, the form factor satisfies Porod's law; the asymptotic tail decreases as S(k) ∼ k −(D+ 1) where D is the system dimensionality. However, it is found that the decay of the asymptotic tail becomes slower than that of the Porod tail at higher temperatures in both two- and three-dimensional systems. This indicates that the dimension of the domain wall is fractal and increases with ...