Liquid-vapor System Research Articles

A New Understanding of the Relationship Between Solubility and Particle Size

Most discussions of the relationships between crystal solubility and particle size have hitherto been concerned with vapor condensation and have led to the prediction that the vapor pressure increases with curvature. Here, thermodynamic arguments are presented to show that such relationships, describing crystal solubility as a function of particle size, originally put forward by Ostwald and later corrected by Freundlich, may be unjustified for determining interfacial tension at solid–liquid interfaces. The Kelvin or Gibbs–Thomson equations are valid for liquid–vapor systems, but not for solid–liquid interfaces. Recent experimental observations have demonstrated that interfacial tension data obtained by the solubility–size approach are unreasonable. This leads to the conclusion that “Ostwald ripening” may not be due to a higher solubility of smaller crystals, but rather to a net negative interfacial tension between solid and solution.

Design of Thermodynamic Charts for Hydrocarbon Mixtures and Influence of Operating Temperatures for Solar Absorption Cooling Cycle

A complete study is developed for hydrocarbon mixtures to determine their suitability as working fluids for solar absorption cooling systems. The results show that the most suitable one is composed of 50% by mole n-butane and 50% by mole h-heptane. This mixture can be used at generation temperatures t between 55°C and 65°C with a maximum working pressure of 2.722 atm. The results indicate that the highest coefficient of performance (COP) is 0.557 at tg = 60°C with cooling temperatures in the range 8–12°C. By using distillation calculations of the ideal system and the equilibrium relations concept of vapor-liquid systems, the enthalpy-concentration (H − X) and temperature-concentration (T − X) thermodynamic charts for the mixture are illustrated, sailing time and effort for those making thermodynamic calculations. The influences of the various cycle temperatures on the COP and on the circulation ratio for this mixture have been performed. It is found that there is a minimum generation temperature above which operation of the cycle is possible, which is called the cut-in/cut-off temperature. Also, it is found that there is an optimum generation temperature at which a maximum value of COP is obtained. Lowering the condensing/absorbing temperature will lower both the minimum and optimum generating temperature and circulation ratio, which tends to reduce the required solar energy for heating the generator in addition to decreasing the pumping power. The effect of increasing the evaporator temperature has the same effect as lowering the condensing/absorbing temperature.

Line Tension and the Intrinsic Contact Angle in Solid–Liquid–Fluid Systems

An approximate theory for calculating the line tension in a solid–liquid–fluid system is presented and demonstrated for a solid–liquid–vapor system. The line tension is shown to depend on the contact angle. Consequently, the classical equation for the intrinsic contact angle, in terms of the line tension, is modified. The magnitude of the line tension is shown to be less than 5 × 10−9N, and its sign is shown to be positive for acute contact angles and negative for obtuse contact angles. The deviation from the Young contact angle is shown to be negligible for drops of macroscopic size on an ideal solid surface.

Phase behavior of near-critical fluids confined in periodic gels

Experiments show that the coexistence region of a vapor-liquid system or binary liquid mixture is narrowed dramatically when the fluid is confined in a dilute porous medium such as a silica aerogel. We propose a simple model of the gel as a periodic array of cylindrical strands and study the phase behavior of an Ising system confined in this geometry. Our results suggest that the coexistence region should widen out at lower temperatures and that the narrowness observed near the critical point may be a fluctuation-induced effect.

Microscale theory of surface tension.

A phenomenological model of capillarity, which accounts for the structure of the liquid-vapor layer, is successively derived assuming that the entropy of a particle depends on the internal energy, the density, and the gradient of the density. Employing classical thermodynamic principles in combination with the balance of mass, momentum, and energy, a rheological expression for capillary stresses is obtained in terms of the free energy of a liquid-vapor system. It is demonstrated that this model admits potential solutions, provided that external forces are potential and the effects of viscous dissipation of energy and heat conductivity are neglected. Moreover, it is shown that a variational principle can be formulated for potential flows, which generalizes Luke's variational principle for free-boundary inviscid flow. This model can be applied to flows involving a topological change of the capillary interface, such as those associated with the spontaneous growth, coalescence and breakup of vaporous bubbles in a liquid.

Density equilibration near the liquid-vapor critical point of a pure fluid. II. Coexisting phases for T

Measurements were carried out on the density change \ensuremath{\delta}\ensuremath{\rho}(t) in a pure fluid ${(}^{3}$He) after a small step change in the temperature of its container. The sample fluid was kept at constant average densities \ensuremath{\Delta}\ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{} and in the coexisting liquid and vapor phases below the critical temperature ${\mathit{T}}_{\mathit{c}}$. The measurements were performed via two superposed capacitive sensors. At temperatures far below ${\mathit{T}}_{\mathit{c}}$, the equilibration in the liquid and vapor phases, measured, respectively, by the top and bottom sensors, are found to proceed very differently. As ${\mathit{T}}_{\mathit{c}}$ is approached, this difference diminishes; both the measured effective relaxation times level off and join smoothly the data obtained above ${\mathit{T}}_{\mathit{c}}$. This coexisting liquid-vapor system of $^{3}\mathrm{He}$ is simulated in one dimension. The results are presented for the spatial and temporal evolution of temperature and density in the fluid following a temperature step of the enclosure. The profiles \ensuremath{\delta}\ensuremath{\rho}(t) and their effective relaxation times are compared with the experimental observations in both phases. There is a qualitative agreement between the simulation and experiment for (${\mathit{T}}_{\mathit{c}}$-T)/${\mathit{T}}_{\mathit{c}}$\ensuremath{\lesssim}${10}^{\mathrm{\ensuremath{-}}3}$, and the quantitative differences further away from ${\mathit{T}}_{\mathit{c}}$ are discussed. The results of experimental measurements and of computer simulations along isotherms are discussed and lead to complementary information on the equilibration dynamics as a function of average density. The asymptotic relaxation times obtained from simulation and from a formula based on the average thermal diffusivity of the entire fluid sample are compared and discussed, both for normal gravity, and also under microgravity conditions where both diverge as ${\mathit{T}}_{\mathit{c}}$ is approached. \textcopyright{} 1996 The American Physical Society.

Heat capacity anomaly near the lower critical consolute point of triethylamine–water

The heat capacity of the binary liquid mixture triethylamine–water has been measured near its lower critical consolute point using a scanning, adiabatic calorimeter. Two data runs are analyzed to provide heat capacity and enthalpy data that are fitted by equations with background terms and a critical term that includes correction to scaling. The critical exponent α was determined to be 0.107±0.006, consistent with theoretical predictions. When α was fixed at 0.11 to determine various amplitudes consistently, our values of A + and A− agreed with a previous heat capacity measurement, but the value of A+ was inconsistent with values determined by density or refractive index measurements. While our value for the amplitude ratio A+/A −=0.56±0.02 was consistent with other recent experimental determinations in binary liquid mixtures, it was slightly larger than either theoretical predictions or recent experimental values in liquid-vapor systems. The correction to scaling amplitude ratio D+/D −=0.5±0.1 was half of that predicted. As a result of several more precise theoretical calculations and experimental determinations, the two-scale-factor universality ratio X, which we found to be 0.019±0.003, now is consistent among experiments and theories. A new ‘‘universal’’ amplitude ratio RBcr± involving the amplitudes for the specific heat was tested. Our determination of RBcr+=−0.5±0.1 and R Bcr−=−1.1±0.1 is smaller in magnitude than predicted and is the first such determination in a binary fluid mixture.

Development of hydrodynamic instability in film condensation on a cylindrical tube in weightlessness

In the process of film condensation on an heat exchanger tube in weightlessness the evolution of small perturbations of the free surface is determined not only by capillary forces but also by the nature of the heat and mass exchange in the liquid-vapor system. In the present paper it is shown that simultaneously taking all these factors into account, even within the framework of a very simple model, leads to results which differ qualitatively from the known formulas for the case of thermal equilibrium. Under the assumption that the velocity profile is quasi-steady, both analytic formulas and corrections to these formulas associated with the unsteady term in the equation of motion are obtained.

Isothermal Vapor-Liquid Equilibrium with Computer-Aided Measurement.

Isothermal vapor-liquid equilibrium measurement system with the computer was developed in the region of less than atmospheric pressure. Vapor-liquid equilibria were measured using a still with the aid of computer for control of temperature and measurement of total pressure. A modified Rogalski-Malanowski still with a provision for both vapor and liquid re-circulation was used for the determination of vapor-liquid equilibrium values. The performance of the apparatus was shown by the results of thermodynamic consistency tests for the experimental isothermal vapor-liquid equilibria.

A Model for the Two-Phase Behavior of Fluids in Dilute Porous Media

ABSTRACTExperiments show that the coexistence region of a vapor-liquid system or binary liquid mixture is dramatically narrowed when the fluid is confined in a dilute porous medium such as a silica aerogel. We propose a simple model of the gel as a periodic array of cylindrical strands, and study the phase behavior of an Ising system confined in this geometry. Our results suggest that the coexistence region should widen out at lower temperatures, and that the narrowness observed near the critical point may be a fluctuation-induced effect.

Fowkes' surface tension component approach revisited

By comparing the number of degrees of freedom obtained from the phase rule for capillary systems, the Fowkes surface tension component approach for interfacial tensions is shown to require more degrees of freedom than are available for a two-component solid—liquid—vapour system. Only in a special case has the Fowkes approach two degrees of freedom: a dispersive liquid on a dispersive solid, suggesting that there are no surface tension components. Experimental results suggest that the Fowkes component approach does not describe physical reality; only the liquid and solid surface tensions, γ1v and γsv, are operative in the two-component solid—liquid—vapour system. Generalization of the Fowkes component approach, of course, will increase the number of independent variables and hence definitely require more degrees of freedom than are available. The number of degrees of freedom of the equation of state for interfacial tensions is shown to agree with that predicted from the phase rule for capillary systems as well as with experimental results. By using the empirical form of the equation of state, essentially constant solid tensions, γsv, are obtained from a variety of dispersive and non-dispersive liquids for three solid surfaces: fluorocarbon (FC721), Teflon (FEP) and poly(ethylene terephthalate) (PET).

An Apparatus and Procedure for Measuring Mutual Solubilities of Hydrocarbons + Water: Benzene + Water from 303 to 373 K

A continuous-flow-type liquid-liquid equilibrium apparatus has been designed, constructed, and used to measure the mutual solubilities of hydrocarbon + water systems. New results for benzene + water have been determined in the temperature range of 303-373 K at pressures within 1 bar of the three-phase curve. The results compare favorably with the literature values in the 303-333 K temperature range. The solubility of benzene in water matches the lower range of the high-temperature data (373-473 K). The relative errors in both liquid-phase compositions are less than 6% for all values. For benzene + water, the mutual solubility is correlated and used to estimate enthalpies of solution of benzene in water and water in benzene; results are in good agreement with literature values based on calorimetric measurements. Increasingly stringent emission standards are forcing many refineries and petrochemical plants to modify or totally replace waste water treatment systems (I). While solvent extraction has been recognized as one of the best developed available technologies for refinery waste water treatment, reliable liquid-liquid equilibrium data needed for the design of extraction processes are not plentiful. The very low liquidliquid mutual solubilities of water and hydrocarbons pose significant difficulties in performing accurate and reliable measurements (2). Large variations, and even conflicts, are common in the values reported in the temperature range of 303-373 K. To resolve conflicts in the liquid-liquid mutual solubility data for hydrocarbon + water mixtures in this temperature range and to obtain reliable new measurements, we constructed and operated a liquid-liquid equilibrium apparatus. The flow-through unit facilitates sampling equilibrium phases and subsequent sample treatment and analysis. We began our measurements with the benzene + water binary system because it has been extensively studied (3) and could serve as a basis for testing the performance of both the equilibrium unit and overall experimental procedures. In addition, this system is of immediate practical concern with the promulgation of the National Emission Standards for Hazardous Air Pollutants; Benzene (4). Experimental Section Two key points had to be addressed to successfully design and operate a continuous-flow-type equilibrium unit to obtain equilibrium mutual solubilities for water + hydrocarbon systems. First, mass transfer between the two liquid phases must be accomplished well before the two phases are separated at equilibrium. Second, the two phases must be completely separated after equilibrium is reached. The physical properties of the aqueous systems considered are different from most of the previous vapor-liquid or liquid-liquid equilibrium systems which have been experimentally studied using flowtype equilibrium cells (5-7). The liquid water and liquid hydrocarbon mixtures have very high interfacial tensions in the temperature range studied. This results in a high mass transfer resistance between the two phases. Meanwhile, the tendency to form emulsions prohibits the vigorous mixing of the two phases. The design of the experimental apparatus must provide mixing at a level to promote mass transfer while avoiding the formation of emulsions which hinders subsequent phase separation.

Critical Fluids in Porous Media

The behavior of fluids confined in porous materials has been of interest to engineers and scientists for many decades. Among the applications driving this research are the use of porous membranes to achieve liquid-liquid separations and to deionize water, the use of porous materials as beds for catalysis, and the need to extract liquids (especially oil and water) from such media. Many of these applications depend on transport, which is governed by flow or diffusion in the imbibed fluids. Both the flow and diffusion of multiphase fluids in porous media, however, strongly depend on the morphology of phase-separated domains, and on the kinetics of domain growth. Thus, it is worthwhile to study the behavior of multiphase fluids in porous media in the absence of flow. Recently, much attention has focused on even simpler systems that still capture these essential features, namely, near-critical binary liquid mixtures and vapor-liquid systems in model porous media, such as Vycor and dilute silica gels. Although near-critical fluids may seem rather artificial as models for multiphase liquids, there are several advantages associated with them. In general, domain morphology and growth kinetics are governed primarily by competition between interfacial tension and the preferential attraction of one phase to the surface of the medium. In near-critical fluids, the relative strength of these two energy scales is sensitive to temperature, and can therefore be altered in a controlled fashion. In addition, the kinetics of domain growth are sensitive to the temperature quench depth, and can be controlled.

Phase equilibrium behavior of the carbon dioxide + benzophenone binary system

Phase equilibrium behavior of various binary CO[sub 2] + hydrocarbon mixtures has been studied by many researchers, providing data which are useful in the design of economically attractive separation processes using carbon dioxide as a solvent. Pressure, liquid-phase composition, and liquid-phase molar volumes are presented for the binary vapor-liquid system CO[sub 2] + benzophenone at 25, 35, and 50 C. Also, pressure, liquid-phase compositions, and liquid-phase molar volumes on the S[sub 1]-L[sub 1]-V curve and L[sub 1]-L[sub 2]-V curve are presented. The termination points of these loci are located and characterized.

Analysis of Steady-state, Vapor-Liquid Concurrent Flow

ABSTRACT Steady-state methods are commonly used for the determination of the relative permeabilities of single component vapor-liquid systems, such as steam-water. Even though such experiments are performed under adiabatic conditions, the interpretation of results has proved to be difficult. Reasons involve phase change, heat transfer, capillarity and rate considerations. This paper presents a systematic study of the saturation and temperature distributions in steady-state, vapor-liquid flows and examines their sensitivity to parameters such as injection rate, permeability and core length. Two sets are analyzed, one pertaining to the simultaneous injection of a two-phase mixture (Sanchez and Schechter, 1987) and another involving phase change (liquid to vapor) within the core (Miller, 1951). End effects and, in general, effects associated with capillary heterogeneity are also analyzed. Solution trajectories in the temperature-saturation plane are constructed. They allow a unified approach to the two problems (two-phase or single-phase injection), which are shown to lie on different parts of the same trajectory. Minimum conditions for the development of in-situ evaporation are developed. Then, the process sensitivity to parameter values is examined for steady-state two-phase injection and relative permeability estimation. It is found that a plateau region develops, within which the inlet saturation is approximately constant, although corresponding saturation profiles are not necessarily flat. Numerical estimates show that the estimation error involved increases with decreasing enthalpy and decreasing permeability.

Vapor-liquid coexistent system applied to a high compliance cabinet for loudspeaker system.

In the enclosed-box type direct-radiation loudspeaker system that has been invented to improve radiation efficiency in the low frequency range, Takahashi has offered an effective system which uses a vapor-liquid coexistence system. If operated under ideal-con ditions, it prevents the enclosed cabinet system from having the disadvantage of rais-ed fundamental resonance frequency, and improves radiation efficiency. We made an experiment using Freon 11 as working liquid and wick in the cabinet. The stiffness of the enclosed cabinet was observed to decrease to approximately 1/8 when the volume velocity is under 7×10-5m3/s. This means that we can reduce the volume of the cabinet to about 1/8 of the conventional size without compromising the performance.

Development of Vapor-Liquid Equilibrium Prediction Expert System by AI Language ART.

Development of Vapor-Liquid Equilibrium Prediction Expert System by AI Language ART.

Self-excitation of oscillatory processes when a liquid is injected into a plasma jet

The process of cooling of a wall by a liquid injected into a plasma jet through a circular opening is studied experimentally. Different flow regimes in a vaporliquid system, including self-excited oscillatory regimes associated with the transfer of the region of boiling from the exterior side of the wall into the interior cavity of the casing, were obtained. Self-excited oscillations of the wall temperature are described with the help of approximation formulas.

Phase behavior of reservoir fluids III: Molecular lumping and characterization

Uniform lumping is often adequate for predicting vapor-liquid equilibria in petroleum-derived distillates that are Gaussian-distributed. However, for non-Gaussian, asymmetrically distributed systems, such as Gamma-distributed fractions, resids, and resid-containing oils and bitumens, nonuniform lumping is found to be more efficient. For example, a log-type lumping, that is fine near the light end but coarse near the heavy end, is found to be very efficient for predicting the solubility of heavy oils in supercritical components. One of the benchmarks used in this work to compare efficiency of various lumping approaches is a continuous thermodynamic model of phase equilibria. A typical minimum number of distillable lumps is found to vary from six to eight for real vapor-liquid equilibrium systems studied in this work. A practical yet conservative method is to use eight GCD lumps, and to test for at least two lumps in the overhead light end.

Critical-point analysis of the liquid-vapor interfacial surface tension.

The interfacial surface tension of the liquid-vapor system is analyzed near the critical point in a manner similar to bulk thermodynamic critical-point analyses. This is accomplished by a critical-point analysis of the single-phase hard-wall surface tension. Both a Landau expansion and a scaling theory equation of state are investigated. Some general exponent relations are derived and, in addition, some thermodynamically defined correlation lengths are discussed.