Estimation of the liquid-vapor spinodal from interfacial properties obtained from molecular dynamics and lattice Boltzmann simulations

Interfacial pressure and density profiles are calculated from molecular dynamics and lattice Boltzmann simulations of a liquid film in equilibrium with its vapor. The set of local values of tangential pressure and density along an interface exhibits a van der Waals-type loop; starting from the stable vapor bulk phase one passes through metastable and unstable states to the stable liquid bulk phase. The minimum and maximum values of the profile of tangential pressure are related to the liquid and vapor spinodal states, respectively. The spinodal pressures turn out to be linearly related to the extreme values of the tangential pressure in the interface. The comparison with equations of state shows good agreement with the simulation results of the spinodals. In addition the properties of the metastable region are obtained. Based on this investigation a method is proposed for the estimation of the liquid spinodal from experimentally obtained interfacial properties. Estimations for water and helium are presented.     

Can the speed of sound be used for detecting critical states of fluid mixtures?

The phenomenology of sound speeds in fluid mixtures is examined near and across critical lines. Using literature data for binary and ternary mixtures, it is shown that the ultrasound speed along an isotherm-isopleth passes through a minimum value in the form of an angular (or V-shaped) point at critical states. The relation between critical and pseudo-critical coordinates is discussed. For nonazeotropic fixed-composition fluid mixtures, pseudo-critical temperatures and pressures are found to be lower than the corresponding critical temperatures and pressures. The analysis shows that unstable pseudo-critical states cannot be detected using acoustic methods. The thermodynamic link between sound speeds and isochoric heat capacities is formulated and discussed in terms of p-Vm-T derivatives capable of being calculated using cubic equations of state. Based on the Griffiths-Wheeler theory of critical phenomena, a new specific link between critical sound speeds and critical isochoric heat capacities is deduced in terms of the rate of change of critical pressures and critical temperatures along the p-T projection of the critical locus of binary fluid mixtures. It is shown that the latter link can be used to obtain estimates of critical isochoric heat capacities from the experimental determination of critical speeds of sound. The applicability domain of the new link does not include binary systems at compositions along the critical line for which the rate of change in pressure with temperature changes sign. The new equation is combined with thermodynamic data to provide approximate numerical estimates for the speed of sound in two mixtures of carbon dioxide and ethane at different temperatures along their critical isochores. A clear decrease in the sound speed is found at critical points. A similar behavior is suggested by available critical heat capacity data for several binary fluid mixtures. Using an acoustic technique, the critical temperature and pressure were determined for three different mixtures of methane and propane, and compared with literature data obtained using conventional methods. It is concluded that acoustic-based techniques are reliable to determine, for the most part, critical surfaces of fluid mixtures. The remaining few cases where the present analysis cannot be applied could be tested by the thermodynamic calculation of critical sound speeds using crossover equations of state in conjunction with experimentally determined critical isochoric heat capacities.     

Thermodynamic consistency between calorimetric acoustic and volumetric measurementents

In this work, experimental measurements of isobaric heat capacity as well as speed of sound were performed in the compressed liquid phase of n-undecane from 303.15 to 373.15 K and for pressures ranging up to 60 MPa. These results were used to estimate various thermophysical properties such as density, isentropic compressibility and isochoric heat capacity in the same ranges of pressure and temperature. All these sets of data allow checking the thermodynamic consistency between calorimetric, acoustic and volumetric properties.     

Thermodynamic properties of acetone calculated from accurate experimental speed of sound measurements at low temperatures and high pressures

Thermodynamic properties of fluids are both required for designing and implementing industrial processes and in different research fields; in particular they play a fundamental role in the development of equations of state (EoS). This paper describes very accurate speed of sound measurements in liquid-phase acetone along eleven isotherms in the temperature range of (248.15 and 298.15) K and over a wide range of pressure (up to 100 MPa). Since very accurate direct measurements of the fluids properties (like density and isobaric heat capacity) are relatively easy at atmospheric pressure, but difficult at elevated pressures, a combination of speed of sound measurements and numerical integration offers a well balanced approach to determine the thermodynamic properties of liquids. In this case, density and heat capacity of the liquid at high pressures are calculated by numerical integration of u^?2(p, T), using, as initial values, the same quantities (density and heat capacity) at atmospheric pressure as a function of temperature. The experimental values of speed of sound are subjected to an overall estimated uncertainty of about 0.1%.     

High temperatures and high pressures Brillouin scattering studies of liquid H(2)O+CO(2) mixtures

The Brillouin scattering spectroscopy studies have been conducted in a diamond anvil cell for a liquid mixtures composed of 95 mol?% H(2)O and 5 mol?% CO(2) under high temperatures and pressures. The sound velocity, refractive index, density, and adiabatic bulk modulus of the H(2)O+CO(2) mixtures were determined under pressures up to the freezing point at 293, 453, and 575 K. It is found from the experiment that sound velocities of the liquid mixture are substantially lower than those of pure water at 575 K, but not at lower temperatures. We presented an empirical relation of the density in terms of pressure and temperature. Our results show that liquid H(2)O+CO(2) mixtures are more compressible than water obtained from an existing equation of state of at 453 and 575 K.     

Suppression of sonochemiluminescence reduction at high acoustic amplitudes by the addition of particles

The effect of particle addition to a liquid or liquid surface on the sonochemiluminescence (SCL) was investigated using a luminol aqueous solution under ultrasonic treatment at 154 kHz. The acoustic-amplitude dependence of the SCL intensity was measured, in addition to capturing images of luminescent spatial patterns. At higher acoustic amplitudes, the cavitation efficiency dramatically reduces. This behavior is suppressed in the presence of particles. Particle addition provides nucleation sites for cavitation bubbles, lowering the cavitation threshold, and weakening the liquid surface vibration as the pressure amplitude decreases. It is shown that the reduction in SCL is suppressed under the addition of alumina particles into luminol aqueous solution. As the amount of alumina particles increases, the range of acoustic amplitude for suppressing the reduction in SCL is enlarged toward high amplitude, and the intensity of the SCL increases. Simultaneous addition of alumina particles into the solution and hydrophobic polytetrafluoroethylene (Teflon) particles onto the liquid surface is also effective. Examination of SCL images revealed that alumina particles added to the liquid at high acoustic amplitude caused the entire region of the reaction volume to be homogeneously luminous. If hydrophobic particles cover the solution surface, the surface vibration at high acoustic amplitude is fixed and the sound field becomes stable. This is responsible for suppression of the reduction in SCL and leads to a high rate of sonochemical reaction, even at high acoustic amplitude.     

Molecular dynamics simulation of cavitation in a lead melt at negative pressures

The molecular dynamics method was used to simulate cavitation in a metastable lead melt and determine the stability limits. States at temperatures below critical (T < 0.5T _c) and large negative pressures were considered. Interatomic interactions were described by the realistic embedded atom potential. The kinetic boundary of liquid phase stability was shown to be different from the spinodal. The kinetics and dynamics of cavitation were studied. The pressure dependences of cavitation frequencies were obtained over the temperature range 700–2700 K. The results of molecular dynamics calculations were compared with estimates based on classical nucleation theory.     

Speed of sound,ideal-gas heat capacity at constant pressure,and second virial coefficients of HFC-227ea

The speed of sound of the gaseous 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) was measured for temperatures from 273 to 333 K and pressures from 26 to 315 kPa with a cylindrical, variable-path acoustic interferometer operating at 156.252 kHz. The uncertainty of the speed of sound was less than ±0.05%. The ideal-gas heat capacity at constant pressure and the second acoustic virial coefficients were determined over the temperature range from the speed of sound measurements. The uncertainty of the ideal-gas heat capacity at constant pressure was estimated to be less than ±0.5%. The ideal-gas heat capacity at constant pressure results and second virial coefficients calculated from the present speed of sound measurements were compared with the available data.     

The speed of sound and derived thermodynamic properties of pure water at temperatures between (253 and 473) K and at pressures up to 400 MPa

The speed of sound in high-purity water has been measured in the temperature range (253 to 473) K at pressures up to 400 MPa. The experimental technique used was based on a double-path pulse-echo method with a single 5-MHz ultrasound transducer placed between two unequally spaced reflectors. The cell was calibrated in water at T = 298.15 K and p = 1 MPa against the speed of sound given by the 1995 equation-of-state formulation of the International Association for the Properties of Water and Steam (IAPWS-95) which, for that state point, has an uncertainty of 0.005%. Corrections for the effects of temperature and pressure on the path length difference are considered in detail. The estimated expanded relative uncertainty of the speed of sound determined in this work is shown to be between 0.03% and 0.04% at a confidence level of 95%. The density and isobaric specific heat capacity of water have been obtained in the temperature range (253.15 to 473.15) K at pressure up to 400 MPa by thermodynamic integration of the sound-speed data subject to initial values computed from IAPWS-95 on the isobar at p = 0.1 MPa. The speed of sound, density, and isobaric specific heat capacity were compared with IAPWS-95 with corresponding absolute relative deviations within 0.3%, 0.03%, and 1%, respectively at T ≥ 273.15 K and p ≤ 400 MPa; larger deviations, especially for heat capacity, were found at lower temperatures. The results imply that the uncertainties of properties computed from IAPWS-95 may be significantly reduced over the major part of the region investigated in this work.     

Thermal properties of the metastable supersaturated vapor of the Lennard-Jones fluid

p, rho, T data of the supersaturated vapor of the Lennard-Jones fluid are obtained by molecular dynamics simulations. The metastable state points are identified before a phase separation takes place. An estimation of the location of the spinodal is given. The results are compared to two theoretically based equations of state and one empirical equation of state which was parametrized also taking into account metastable state points. The pressure obtained by simulation is found to be lower than that from both theoretically based equations of state, which do not account for the inhomogeneous density distribution of the supersaturated vapor.     

Characteristic analysis of cavitation bubbles in carbon dioxide fluid

After analysing the characteristics of bubble cavitation in high-pressure carbon dioxide (CO₂) fluid, cavitation conditions and some correlative physical characteristics are investigated. The results show that the ultrasonic intensity of liquid carbon dioxide to make cavitation occur is affected by the initial radius of the bubbles, hydrostatic pressure, temperature and vapour pressure within the bubbles in liquid CO₂. At the low frequency of ultrasound, the phase-speed of the liquid CO₂ gradually approaches the sound speed of the pure liquid when void fraction increases. At high frequency, the phase-speed is nearly equal to the sound speed in the liquid under different void fractions. The attenuation of ultrasound in liquid carbon dioxide reaches a maximum near the resonance frequency and then decreases when frequency either increases or decreases. At the resonance frequency, the phase-speed and the attenuation increase when the void fraction increases.     

Density and speed of sound measurements of hexadecane

The density and speed of sound of hexadecane have been measured with two instruments. Both instruments use the vibrating-tube method for measuring density. Ambient pressure (83 kPa) density and speed of sound were measured with a commercial instrument from T = (290.65 to 343.15) K. Adiabatic compressibilities are derived from the density and speed of sound data at ambient pressure. Compressed liquid density was measured in a second instrument and ranged from T = (310 to 470) K with pressures from (1 to 50) MPa. The overall relative expanded uncertainty of the compressed liquid density measurements is 0.10–0.13% (k = 2). The overall relative expanded uncertainty (k = 2.3) of the speed of sound measurements is 0.2% and that of the ambient pressure density measurements is approximately 0.04% (k = 2.3). The ambient pressure and compressed liquid density measurements are correlated within 0.1% with a modified Tait equation.     

Calculation of isentropic compressibility and sound velocity in two-phase fluids

Derivative properties from equations of state (EoS) are well defined for homogeneous fluid systems. However, some of these properties, such as isothermal and isentropic (or adiabatic) compressibilities and sound velocity need to be calculated at conditions for which a homogeneous fluid splits into two (or more) phases, liquid or vapor. The isentropic compressibility and sound velocity of thermodynamically equilibrated fluids exhibit important discontinuities at phase boundaries, as noticed long ago by Landau and Lifschitz in the case of pure fluids. In this work, the two-phase isentropic compressibility (or inverse bulk modulus) is expressed in terms of the two-phase isothermal compressibility, two-phase thermal expansivity and an apparent heat capacity, defined as the partial derivative of total enthalpy with respect to temperature at constant pressure and composition. The proposed method is simple (simpler than previous approaches), easy to implement and versatile; it is not EoS-dependent and it requires only a flash routine and the expression of total enthalpy at given pressure, temperature and composition. Our approach is applied to a variety of fluid systems representative of reservoir applications and geophysical situations, including petroleum fluids (oil and gas condensate) and mixtures of water and gas (methane or CO₂). For low gas content in the two-phase fluid, i.e., near bubble point conditions, we obtain significantly lower bulk moduli and sound velocities than predicted within Wood's conventional approach, in which the liquid and gas phases are considered to be “frozen” at the passage of the acoustic wave.     

Dissociation behavior of C2H6 hydrate at temperatures below the ice point: melting to liquid water followed by ice nucleation

The dissociation of C(2)H(6) hydrate particles by slow depressurization at temperatures slightly below the ice melting point was studied using optical microscopy and Raman spectroscopy. Visual observations and Raman measurements revealed that ethane hydrates can be present as a metastable state at pressures lower than the dissociation pressures of the three components: ice, hydrate, and free gas. However, they decompose into liquid water and gas phases once the system pressure drops to the equilibrium boundary for supercooled water, hydrate, and free gas. Structural analyses of obtained Raman spectra indicate that structures of the metastable hydrates and liquid water from the hydrate decay are fundamentally identical to those of the stable hydrates and supercooled water without experience of the hydration. These results imply a considerably high energy barrier for the direct hydrate-to-ice transition. Water solidification, probably induced by dynamic nucleation, was also observed during melting.     

Correlation in spatial intensity distribution between volumetric bubble oscillations and sonochemiluminescence in a multibubble system

The correlation in spatial intensity distribution between volumetric oscillation of multibubble and sonochemiluminescence in an ultrasonic standing-wave field is investigated through the measurements of scattered light from bubbles by changing the measuring position in the direction of sound propagation and sonochemiluminescence with luminol. When a thin light sheet, finer than half the wavelength of sound, is introduced into the cavitation bubbles at the anti-node of the sound pressure, the scattered light intensity oscillates temporally. The peak-to-peak light intensity corresponds to the number of the bubbles which contribute to the sonochemical reaction because the radius for oscillating bubbles at pressure antinode is restrictive in a certain range due to the shape instability and the action of Bjerknes force that expels from anti-node bubbles larger than the resonant size. The experimental results show that at the side near the water surface, the peak-to-peak light intensity is larger in comparison with the intensity near the sound source, and this tendency becomes apparent at higher input power. These light scattering results correspond with the spatial intensity distribution of the sonochemiluminescence with luminol. Therefore, it is interpreted that most of the cavitation bubbles contributing to the sonochemical reactions in the standing wave field exist near liquid surface. Present method of light scattering in reference with the image of the sonochemiluminescence is promising for evaluating spatial distribution of violently oscillating cavitation bubbles effective for sonochemical reactions.     

Metastable states in the system of hard spheres

Approximate equations of the theory of liquids were applied to analyze the special features of the structural behavior of the system of hard spheres in the region of densities at which crystals are stable. Correlation functions for the liquid metastable state were obtained. The correlation functions of crystal-like metastable states that can exist under the same conditions as liquid metastable states are also considered. The reliability of the results is substantiated by a thermodynamic comparison with the data obtained using analytic equations of state.     

Correlation between acoustic cavitation noise and yield enhancement of sonochemical reaction by particle addition

The mechanism of the effect of particle addition on sonochemical reaction is studied through the measurements of frequency spectrum of sound intensity for evaluating the cavitation noise and the absorbance for the liberation of iodine from an aqueous solution of KI as an index of oxidation reaction by ultrasonic irradiation in the presence or absence of alumina particles. As it is expected that both the acoustic noise and a rise in temperature in the liquid irradiated by intense ultrasound will increase with the number of collapsing bubbles, these are supposed to be the best tools for evaluating the relative number of bubbles. In the present investigation, it has been shown that the addition of particles with appropriate amount and size results in an increase in the absorbance when both the acoustic noise and the rise in the liquid temperature due to cavitation bubbles also increase. This suggests that the enhancement in the yield of sonochemical reaction by appropriate particle addition comes from an increase in the number of cavitation bubbles. The existence of particle in liquid provides a nucleation site for cavitation bubble due to its surface roughness, leading to the decrease in the cavitation threshold responsible for the increase in the number of bubbles when the liquid is irradiated by ultrasound. Thus, from the present investigation, it is clarified that the particle addition has a potential to enhance the yield in the sonochemical reaction.     

Pressure-induced reduction of shielding for improving sonochemical activity

The effect of hydrostatic pressure on chemical reactions induced by 20 kHz ultrasound has been studied using three different methods: the oxidation of potassium iodide, bubble cloud visualization studies, and sound attenuation measurements. The latter two have demonstrated that shielding of the ultrasonic wave is less pronounced at elevated pressures. Accordingly, the yield of iodine liberation increases with increasing pressure. At high static pressures, however, the less efficient cavitation dynamics dominate and the chemical reactivity decreases rapidly.     

Brillouin-scattering determination of the acoustic properties and their pressure dependence for three polymeric elastomers

The acoustic properties of three polymer elastomers, a cross-linked poly(dimethylsiloxane) (Sylgard 184), a cross-linked terpolymer poly(ethylene-vinyl acetate-vinyl alcohol), and a segmented thermoplastic poly(ester urethane) copolymer (Estane 5703), have been measured from ambient pressure to approximately 12 GPa by using Brillouin scattering in high-pressure diamond anvil cells. The Brillouin-scattering technique is a powerful tool for aiding in the determination of equations of state for a variety of materials, but to date has not been applied to polymers at pressures exceeding a few kilobars. For the three elastomers, both transverse and longitudinal acoustic modes were observed, though the transverse modes were observed only at elevated pressures (>0.7 GPa) in all cases. From the Brillouin frequency shifts, longitudinal and transverse sound speeds were calculated, as were the C(11) and C(12) elastic constants, bulk, shear, and Young's moduli, and Poisson's ratios, and their respective pressure dependencies. P-V isotherms were then constructed, and fit to several empirical/semiempirical equations of state to extract the isothermal bulk modulus and its pressure derivative for each material. Finally, the lack of shear waves observed for any polymer at ambient pressure, and the pressure dependency of their appearance is discussed with regard to instrumental and material considerations.