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Due to discrepancies observed between many experimental results and predictions from the Bell–Cameron–Lucas–Washburn (BCLW) imbibition equation, the BCLW equation was often modified by considering the effects of pore/throat characteristics. As previous works mainly focused on liquid–gas systems, the effects of the viscosity ratios are neglected. In this study, the nonwetting-/wetting-phase-viscosity ratio ( $$ \Psi $$ ) is varied by four orders of magnitude (0.018 to 8), which covers the common fluid viscosity in waterflooded tight reservoirs. Capillaries with irregular cross sections (namely, complex capillaries), which are recognized to more representative for porous media, are used to theoretically study imbibition kinetics in both the liquid–gas and liquid–liquid system. To considering the effects of viscosity ratio, we propose a modified imbibition equation based on the Poiseuille law and a piecewise method to calculate the equivalent radius for complex capillaries. The predictivity of the new imbibition equation is mathematically validated in varying viscosity ratios and geometries characteristics (such as the radius levels and the numbers/length ratios of radius levels). The study proves that an equivalent straight capillary can globally predict imbibition behaviors in complex capillaries. Except for a few scenarios, the equivalent radius of the straight capillary is affected by capillary geometries and viscosity ratios. Only in the early stage of imbibition ( $$ l_{x} /l \le 0.12\Psi /\left( {\Psi - 1} \right) $$ ), the modified imbibition equation can be expressed as a power-law relation (i.e., $$ l_{x} /l \propto \frac{1}{\Psi }t^{\alpha } $$ ) as $$ {\Psi } $$ is higher than 1. In general, it is more suitable to express the imbibition equations in a quadratic form, especially for liquid–liquid imbibition systems.

In this paper, literature data of 719 materials on the enthalpy of evaporation hv and boiling temperature Tb, including calculated entropy of evaporation sv, have been analyzed regarding systematic correlations in phase change liquid-gas. It has been observed that several groups of materials exist that form clusters with an almost linear correlation in an hv – sv/R graph. One such cluster is formed by the metallic elements. A second cluster is formed by the halogens, the noble gases, and most of the diatomic molecules. A third cluster is formed by the linear alcanes. The knowledge about these clusters can be used to improve rules to predict certain values like in group-contribution methods, and maybe also to identify a common microscopic origin. Additionally, the analysis has shown that many materials have sv/R deviating significantly from the Trouton constant. Deviations are more frequent to higher values, and deviations are more pronounced in compounds with few atoms. A chemical reaction upon evaporation has been identified in 12 cases; the formation of larger compounds upon condensation seems to be the main reason for exceptionally high values of sv/R. The analysis thus led to a deeper understanding of the physical and chemical origins on the atomic and molecular level.

The formation of equilibrium liquid–gas interfaces in single- and two-component Lennard-Jones systems has been reproduced by molecular-dynamics simulation. The second component in the two-component system is a volatile impurity. The initial state is created by bringing in contact homogeneous liquid and gas phases having equal temperatures, pressures, and chemical potentials. The times required to establish equilibrium values of pressure, composition, shape and thickness of an interfacial layer, relative adsorption, and surface tension have been evaluated by the simulation. The calculations have been carried out at a temperature close to the triple point temperature of a solvent. It has been found that, in the course of relaxation, the maximum dynamic surface tension exceeds the equilibrium value by a factor of 1.2–1.6, while the relaxation time increases from 10 to 100 ns as the concentration of the volatile component in the solution grows to 0.25. In the two-component system with a limited volume of the gas phase, an equilibrium interfacial layer is formed in two stages. At the first stage, the volatile component is transferred into the interfacial layer from the near-surface regions of the liquid and gas phases. When an equilibrium partial density of the volatile component in the gas phase is achieved, the second stage begins, at which the surface layer is mainly supplied with liquid-phase particles. As a result, the relaxation times of relative adsorption and surface tension substantially increase. The role of the dynamic surface tension in the process of nucleation has been discussed.

The boiling liquid expanding vapor explosion (BLEVE) is a most common hazard in liquefied gas storage and transportation. The explosion is resulted from tank overpressure under external thermal attack, and its prevention depends on accurate prediction of the boiling liquid pressurization. This paper presents a mathematical model to simulate the boiling liquid pressurization in liquefied gas storage tank. The model includes a semi-empirical equation to calculate the critical subcooled degree at the onset of pressurization, an energy equation of bubble condensation to calculate the net vapor generation rate in storage tank, a thermal-response equation of the subcooled boiling liquid to calculate the transient temperature of bulk liquid, and an isochoric equation to predict the transient pressure of boiloff liquefied gas. Comparison of the model predictions with experimental data shows that the maximum deviations of the predicted transient pressure and temperature are within 15 kPa and 3 °C, respectively.

It is an experimental fact that in the neighborhood of melting curves, including those measured at above-critical pressures and temperatures, all fluids have some short- and intermediate-range order and their excitation spectra contain high-frequency transverse waves. At high pressure, both smooth and sharp first-order phase transitions involving changes in the liquid structure and properties can occur between various liquid states. However, at sufficiently high temperatures, any liquid loses its identity and turns into an unstructured dense gas in which only longitudinal waves can propagate. We discuss theoretical and experimental evidence for the existence of a boundary between a 'solid-like' melt and a dense gas at supercritical pressures.

The results of designing the mathematical model of non-stationary thermal conductivity of the bubble’s oscillating wall, with account of the changes in the aggregate state and the thermal and physical characteristics of the substance, are presented. It is shown that when applying the finite elements method, it is a system of nonlinear differential equations of the 1st order. Consideration of these features in the mathematical model allows obtaining the temperature values of liquid and solid phases at any time when changing the bubble’s size and the heat flow direction at its boundary. Based on the suggested mathematical model, a series of assessment calculations was performed. Applying mathematical modeling, the temperature fields’ distribution in the liquid under the conditions of the phase transition processes and changes in the bubble size is obtained. The performed studies show that for an immobile bubble under the boundary condition of the 2nd kind, the icing and ice melting velocities are almost equal, but the temperature on the interphase gas-water surface is approximately four times exceeding the temperature on the gas-ice surface, which corresponds to the water and ice thermal conductivity ratio. The temperature in the phase liquid-ice transition zone is practically constant. With the expansion of the bubble, liquid freezing and ice melting are going more than 1.6 times faster than in the immobile bubble. When compressing the bubble, the thickness of the ice formed or melted is approximately 1.7 times smaller than that of the immobile wall bubble. The analysis of the results obtained has shown that they are predictable and fully correspond to the physicists’ ideas of the heat transfer and phase transition processes flow in the liquid. The suggested calculation method can be used to determine the thermal characteristics of the liquid and steam in various technological processes associated with gases dissolution in the liquid, foam hardening and gas hydrates formation. The mathematical model designed can be applied as a component for calculation of more complicated physical processes. The study results can be applied to optimize various technological processes associated with materials swelling, gases adsorption, liquids boiling and gas hydrates formation

A new fundamental low-parametric equation of state in the form of reduced Helmholtz function for describing thermodynamic properties of normal substances was obtained using the methods and approaches developed earlier by the authors. It allows us to describe the thermal properties of gas, liquid, and fluid in the range from the density in ideal-gas state to the density at a triple point (except the critical region) with sufficiently high accuracy close to the accuracy of experiment. The caloric properties and sound velocity of argon, nitrogen, and carbon dioxide are calculated without involving any caloric data, except the ideal gas enthalpy. The obtained values of isochoric heat capacity, sound velocity, and other thermodynamic properties are in good agreement with experimental (reliable tabular) data.

Synthesis of a mathematical model of cooling of supercharging gas in the vapor space of cryogenic tanks containing liquefied gas is studied. Based on the model of a unidimensional dynamic thermal boundary layer, it is shown that the heat flux through the free liquid hydrogen surface in the cryogenic tank having a vapor space supercharged with gaseous hydrogen is much less than the heat flux through a wetted surface. The operational process of supercharging vapor space with gaseous hydrogen is studied by the example of a commercial liquid hydrogen tank. An example of calculation that shows the procedure of calculation of specific heat fluxes is given. The calculation results show that in the working range of fractions of the vapor space the heat flux through the liquid surface is much less than the heat flux through a wetted surface and that the heat of the supercharging gas exerts practically no influence on the change in temperature of the cryogenic liquid during its storage in the tank.

During the rapid depressurization of a liquefied gas, its superheating can lead to a boiling liquid expanding vapor explosion (BLEVE). Such an event is of enormous concern during carbon capture and storage (CCS) given the significant amounts of pressurized CO2 involved during its transportation and storage. This article presents, for the first time, the development and validation of a rigorous split-fluid blowdown model for predicting the degree of superheating following the rapid decompression of liquefied gases or two-phase mixtures with particular reference to CO2. The model was successfully validated through a comparison of the predicted vapor- and liquid-phase pressures and temperatures against the recorded data from a number of depressurization tests conducted for pure dense-phase CO2 and its mixtures representing those associated with different capture technologies. The effects of changes in the pressure-relief-valve diameter and CO2 purity on the degree of superheating and, hence, the spontaneity ...

This work analyzes the equilibrium between a liquid and a gas over this liquid separated by an interface. Various gas forms exist inside the liquid: dissolved gas molecules attached to solvent molecules, free gas molecules, and gaseous bubbles. Thermodynamic equilibrium is maintained between two phases; the first phase is the liquid containing dissolved and free molecules, and the second phase is the gas over the liquid and bubbles inside it. Kinetics of gas transition between the internal and external gas proceeds through bubbles and includes the processes of bubbles floating up and bubble growth as a result of association due to the Smoluchowski mechanism. Evolution of a gas in the liquid is considered using the example of oxygen in water, and numerical parameters of this system are given. In the regime under consideration for an oxygen–water system, transport of oxygen into the surrounding air proceeds through micron-size bubbles with lifetimes of hours. This regime is realized if the total number of oxygen molecules in water is small compared with the numbers of solvated and free molecules in the liquid.

Erosion–corrosion experiments of copper elbow were performed by acidified dichromate. Mass transfer coefficient inside 90° copper elbow has been investigated. The results showed that the mass transfer coefficient increases as solution velocity increases in both cases of one- and two-phase flow. The mass transfer coefficient can be related to the solution velocity in case one-phase flow by the following equations: $$k \, \alpha \, v^{ 0. 4 4}\quad{\text{for\,Sc\,from\,678 to 845}}$$ $$k \, \alpha \, v^{ 0. 3}\quad{\text{for\,Sc\,from\,1040\,to\,1445}}$$ In case of liquid–solid flow $$k \, \alpha \, v^{ 0. 3 3}$$ In case of liquid–gas flow $$k \, \alpha \, vg^{ 0. 2 4}$$ The importance of these equations is to understand and predict erosion corrosion inside 90o copper elbow.

The heat transfer between the deep sea waters and the oil and gas mixtures flowing through production lines is a common situation in the petroleum industry. The optimum prediction of the liquid–gas flow parameters along those lines, when the intermittent flow pattern known as slug flow is dominant, has extreme importance in facilities' design. The mixture temperature drop caused by the colder sea waters, which can be regarded as an infinite medium with constant temperature, directly affects physical properties of the fluids such as the viscosity and specific mass. Gas expansion may also occur due to pressure and temperature gradients, thus changing the flow hydrodynamics. Finally, the temperature gradient affects the thermodynamic equilibrium between the phases, favoring wax deposition and thus increasing pressure drops or even blocking the production line. With those issues in mind, the present work proposes a stationary model to predict the mixture temperature distribution and the two-phase flow heat transfer coefficient based on the mass, momentum and energy conservation equations applied to different unit cell regions. The main contribution of the present work is the modeling of the thermal scooping phenomenon, i.e., the heat transfer between two adjacent unit cells due to the mass flux known as scooping. The model was implemented as a structured Fortran95 code with an upwind difference scheme. The results were compared to experimental data and presented good agreement. The analysis showed that the inclusion of the scooping phenomenon into the model resulted in an averaged 8% improvement in the temperature gradient calculation and heat transfer coefficient prediction for the flowing mixture.

High-temperature and pressure boundaries of the liquid and gas states have not been defined thermodynamically. Standard liquid-state physics texts use either critical isotherms or isobars as ad hoc boundaries in phase diagrams. Here we report that percolation transition loci can define liquid and gas states, extending from super-critical temperatures or pressures to “ideal gas” states. Using computational methodology described previously we present results for the thermodynamic states at which clusters of excluded volume (VE) and pockets of available volume (VA), for a spherical molecule diameter σ, percolate the whole volume (V = VE + VA) of the ideal gas. The molecular-reduced temperature (T)/pressure(p) ratios ( ) for the percolation transitions are = 1.495 ± 0.015 and = 1.100 ± 0.015. Further MD computations of percolation loci, for the Widom-Rowlinson (W-R) model of a partially miscible binary liquid (A-B), show the connection between the ideal gas percolation transitions and the 1st-order phase-separation transition. A phase diagram for the penetrable cohesive sphere (PCS) model of a one-component liquid-gas is then obtained by analytic transcription of the W-R model thermodynamic properties. The PCS percolation loci extend from a critical coexistence of gas plus liquid to the low-density limit ideal gas. Extended percolation loci for argon, determined from literature equation-of-state measurements exhibit similar phenomena. When percolation loci define phase bounds, the liquid phase spans the whole density range, whereas the gas phase is confined by its percolation boundary within an area of low T and p on the density surface. This is contrary to a general perception and opens a debate on the definitions of gaseous and liquid states. info:eu-repo/semantics/publishedVersion

Using methods and approaches, previously developed by the authors, a new fundamental low-parametric equation of state for methane (in the form of the reduced Helmholtz function) has obtained to describe the thermodynamic properties. It allows describing the thermal properties of gas, liquid, and fluid at pressures of up to 20 MPa with sufficiently high accuracy close to the experimental one (with the exception of the critical region). The sound speed and caloric properties of methane have been calculated without involving any caloric data, with the exception of ideal gas enthalpy. The values of speed of sound, isochoric heat capacity, and other thermodynamic properties obtained by calculations are in good agreement with the experimental data.

Gas bubbles are introduced in water to absorb or strip volatile substances in a variety of unit operations, for example during (waste)water treatment. To calculate the transfer rate of substances between the liquid phase and the gas phase, different assumptions have been made in literature regarding the gas phase composition and hydraulic pressure, which both vary along the reactor height. In this study, analytical expressions were derived for the total (macroscopic) liquid-gas transfer rate, using either the complete gradients of the mole fraction and pressure (comprehensive approach) or a uniform value, for one or both of them. Simulations with the comprehensive model were performed to understand the effect of the type of volatile substance and of the reactor design and operating conditions on the total liquid-gas transfer rate. These effects were found to be highly interactive and often non-linear. Next, the simulation results of the comprehensive model were compared with those from models that assume either a uniform mole fraction or a uniform pressure in the complete reactor volume. This illustrated that for soluble substances, the mole fraction gradient strongly affects the total liquid-gas transfer rate, while the pressure gradient became only important under operating conditions that promote stripping (i.e., for a high concentration in the liquid phase and low concentration in the inlet gas). For very poorly soluble substances, the pressure became more important under conditions that promote absorption. These results on the importance of the mole fraction and pressure gradients remained equally valid when explicitly considering a typical variation of the volumetric overall transfer coefficient (KLa) along the reactor height. Finally, a simple and fast procedure was made available through a spreadsheet to select appropriate simplifying assumptions in reactor or plant-wide models. By applying the procedure to oxygen (O2), carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O) and nitrogen gas (N2) in an aerobic biological wastewater treatment reactor, it was demonstrated that some common simplifications can lead to significant errors, for which corrections were proposed.

A non-equilibrium molecular dynamics (NEMD) simulation method has been developed to simulate mixing of a liquid with a vapor and identify the characteristics of the liquid-vapor interface in the mixing process. Our results show that for the case of subcritical mixing, local phase equilibrium is established, and saturated liquid and saturated vapor are formed on either side of the interface at the prevailing saturation temperature that is fixed by the pressure of the system independent of the temperature difference across the interface. For transcritical mixing, significant clustering of molecules is found at the “transitional diffuse” interface. We found that the local density and local temperature of the transcritical interface can be directly mapped to the near critical region of the Ar/Ar and Kr/Ar vapor-liquid phase diagram. Finally, for the case of supercritical mixing, our simulations show a gradual change of density consistent with diffusion-controlled fluid mixing.

International audience; The Noble-Abel-Stiffened-Gas (NASG) equation of state (Le Métayer and Saurel, 2016) is extended to variable attractive and repulsive effects to improve the liquid phase accuracy when large temperature and pressure variation ranges are under consideration. The transition from pure phase to supercritical state is of interest as well. The gas phase is considered through the ideal gas assumption with variable specific heat rendering the formulation valid for high temperatures. The liquid equation-of-state constants are determined through the saturation curves making the formulation suitable for two-phase mixtures at thermodynamic equilibrium. The overall formulation is compared to experimental characteristic curves of the phase diagram showing good agreement for various fluids (water, oxygen). Compared to existing cubic equations of state the present one is convex, a key feature for computations with hyperbolic flow models.

Mass transfer of a range of volatile substances was studied under highly turbulent conditions. The applied setup mimicked drop structures, where the release of volatile organic carbons likely occurs at a high rate. The experiments covered several substances in a range of resistances from residing entirely in the liquid film to being fully in the gas film. The twofilm theory yielded a good prediction of the whole measured range. This allowed the experimental validation of a method where two reference substances are applied, to determine the transfer of any other substance - independently of where its resistance to mass transfer resides. One finding was that the range of dimensionless Henry's constants, where both films contributed by more than 5%, was 0.0027 to 1.05, which is over five times higher than the accepted rule of thumb (0.0005-0.18). Another finding was that the ratio between the liquid and the gas film mass transfer coefficients of the reference substances was similar for the two drop configurations studied. If this holds true over a wider range of configurations, such a ratio constitutes a valuable shortcut to the current practice of ignoring gas film resistance in the estimation of mass transfer rates.

The isochoric heat capacity of the n-hexane–water system was studied on an adiabatic calorimeter at 300–600 K and molar fractions of water of 0.256–0.935 in a wide range of densities. The experimental critical curves of the liquid–vapor phase equilibrium were described by the equation corresponding to the theory of critical phenomena.

Two-layer gas-liquid flows and evaporation intensity at the interface were studied. The influence of gas flow rate, longitudinal gradient of temperature, the Soret effect on the nature of flow and transfer processes was demonstrated. Experimental and theoretical results were compared; they show dependence of evaporation at the interface on gas flow rates.

A method to find the liquid-gas critical parameters of metallic elements is offered. It takes into account a nonanalytic behavior in the critical point vicinity and the Clapeyron-Clausius asymptotic behavior at low temperatures. The present approach provides good agreement with experimental data for a wide wealth of non-metallic substances and mercury and alkali metals, where the critical parameters and binodals are known from the measurements. We have also found the critical parameters and binodals for Al, Cu, Fe, and Zr, for which corresponding measurements are yet to be obtained.

The BLEVE (boiling liquid expanding vapor explosion) effect that involves the formation of a fireball occurs at the engulfment by fire of a tank with a highly flammable liquid or a liquid gas. Heating of the tank causes elevation of the liquid phase temperature and pressure inside the tank. A partial rupture of the dry tank walls is possible, with the formation of a rarefaction wave propagating into the liquid phase. An evaporation wave moves after the rarefaction wave and cause a rapid increase of pressure, exceeding the initial pressure before depressurization. Rapid violent destruction of the tank occurs. The mechanism of a BLEVE initiation is considered using Van der Waals isotherms. The following criterion for the possibility of a BLEVE was formulated. If the final state is located on an unstable part of the Van der Waals isotherm, a BLEVE takes place. Limiting values of the temperatures for overheating of certain highly flammable liquids and liquid gases (propane, n-butane, n-pentane, isopentane) were calculated using the proposed method, and were found to be in good agreement with experimental data available in the literature.

We investigate a longwave Marangoni convection in a two-layer system which consists of a liquid layer and a poorly conductive gas layer. The system is heated from below and confined between two rigid walls: the upper wall is ideally conductive, the lower one is thermally insulated. We aim at finding the analogue of the novel oscillatory mode that was detected analytically within the one-layer approach in [S. Shklyaev, M. Khenner, and A. A. Alabuzhev, “Oscillatory and monotonic modes of long-wave Marangoni convection in a thin film,” Phys. Rev. E 82, 025302 (2010)]. To properly account for the influence of processes in gas on deformation of the interface we apply the two-layer approach. Considering only the heat transfer in gas phase we derive nonlinear amplitude equations that describe the coupled evolution of the layer thickness and temperature perturbation. Linear stability analysis of these equations yields the results similar to those obtained for a single layer whereas nonlinear equations reveal certain differences. The new oscillatory mode is found to be critical in a certain range of parameters, which allows us to provide the recommendations for a possible experiment.

We study liquid-gas transitions of heat conduction systems in contact with two heat baths under constant pressure in the linear response regime. On the basis of local equilibrium thermodynamics, we propose an equality with a global temperature, which determines the volume near the equilibrium liquid-gas transition. We find that the formation of the liquid-gas interface is accompanied by a discontinuous change in the volume when increasing the mean temperature of the baths. A super-cooled gas near the interface is observed as a stable steady state., 6 pages, 4 figures and 9 pages, 1 figure for supplemental material

The pVT-properties of water + n-pentane and water + n-hexane mixtures in temperature intervals from 305 to 542 K and pressures up to 15 MPa were measured in a constant-volume piezometer. The line of phase equilibrium hydrocarbon–vapor with water and their critical parameters were determined. Critical temperatures and pressures are constant and close to 0.9 mol fraction of water, remaining the same as for the upper critical end-point, while the densities increase. All critical parameters decrease above 0.93 mol fraction of water. The common three-phase lines for measured systems are presented.

Storage of pressurized liquified gases is a growing safety concern in many industries. Knowledge of the thermodynamics and kinetics involved in the rapid depressurization and evaporation of such substances is key to the design and implementation of effective safety measures in storage and transportation situations. In the present study, experiments on the rapid depressurization of liquid $$\hbox {CO}_{2}$$ are conducted in a vertical transparent shock tube which enables the observation of evaporation waves and other structures. The depressurization was initiated by puncturing a membrane in one end of the tube. The thermodynamic mechanisms that govern the evaporation process are not unique to $$\hbox {CO}_{2}$$ , and the same principles can be applied to any liquified gas. The experiments were photographed by a high-speed camera. Evaporation waves propagating into the liquid were observed, traveling at a near constant velocity on the order of 20–30 m/s. A contact surface between the vapor and the liquid–vapor mixture was also observed, accelerating out of the tube. Pressure readings in the tube suggest that the evaporation wave could be similar to a spinodal decomposition wave, but further experiments are needed to confirm this. When the membrane was in direct contact with the liquified $$\hbox {CO}_2$$ , some indications of homogeneous nucleation were observed.

A linear fractional transformation is proposed, which establishes the relationship between the liquid–gas coexistence curve of real substances and binodal of lattice models. Herewith the substance critical point with some density ρc and some temperature Tc is mapped in the critical point of a lattice model with density x = 0.5 and temperature t = 1. We found the ‘lattice analogues’ for binodals of mercury, cesium argon, ammonia and binodals of two model systems (van der Waals and Lennard-Jones). They are compared with analytical and numerical binodals known in the theory of lattice systems.

A low-parametric equation for calculating the CH4 viscosity coefficient in liquid, gaseous, and fluid states was derived using previously obtained unambiguous dependence of the “excess” viscosity of liquids and dense gases on the density of internal energy. The equation describes the viscosity of methane at the temperatures from 91 K to 620 K and pressures of up to 50 MPa in the limits of experimental error.

A study has been made of the conditions of equilibrium and stability of microheterogeneous system of “a vapor bubble in liquid” and “a liquid droplet in vapor” type forming in the process of isothermal decay of a metastable or a labile state of a Lennard-Jones fluid located in a small-volume spherical cell with ‘tracking’ boundary conditions. Homogeneous phases are described by the equation of state of a Lennard-Jones fluid (Baidakov, 2016). It is shown that four types of equilibrium configurations of different stability may form at fixed values of the temperature, initial density and cell volume. Thus, as a result of the decay of a superheated liquid, in a small-volume cell there form configurations of “a vapor bubble in liquid” type and an “inverted” configuration of “a liquid droplet in vapor” type. Each of these configurations may be in a state of stable and unstable equilibrium. The dependence of thermodynamic parameters of a microheterogeneous system on the temperature, initial density and cell volume has been investigated. All calculations have been made in the approximation of independence of the surface tension of a disperse phase on its size.

Our early experimental investigation has demonstrated the anomalous surface tension temperature dependence σ(T) at the interface between coexisting liquid-gas phases in magnetic fluids that undergo field-induced first-order phase transition. The σ(T) dependence is anomalous because the drops of a liquid phase condensed under the action of the applied magnetic field H at high temperature T2 exhibit larger surface tension σ(T2) > σ(T1) than the drops condensed at low temperature T1 σ(T1) than the drops condensed at low temperature T1 < T2. This study verifies and confirms the results of the previous experimental investigation of σ(T) in magnetic fluids by performing the experiment, which is based on the analysis of the Plateau-Rayleigh instability of a gas-liquid interface in a zero magnetic field. A novel explanation of this phenomenon is given in the framework of the Stockmayer model. The anomalous increase in σ(T) is explained by the increase in particle concentration difference in gas and liquid phases, which can be attributed to the high field intensity ...

The thermal stratification of liquefied gas influences the equipment safety. To find the factors and principles governing the thermal stratification, a device was set up to simulate the thermal response of a liquefied gas tank. A small steel vessel was used to simulate the tank, and two working fluids were used: water and R22. The heating region and liquid level were precisely adjusted in the tests to simulate different accident conditions. The experimental results showed saturation pressure of the working fluid affected the thermal stratification when the liquid wall was heated solely. For the case the liquid and vapor wall were heated together, evident thermal stratifications formed both in R22 and water tests. The degree and duration of thermal stratification are affected by the intensity of heat loading on the surface liquid. It is concluded that nucleate boiling in the lower liquid has great power to eliminate the thermal stratification. When the nucleate boiling is suppressed by hydrostatic pressure or saturation pressure of the warm surface liquid, the thermal stratification can form and maintain by natural convection. The stratifying process can be explained by a natural convection model.

This work presents a consistent thermodynamic model to describe the gas release and gas absorption phenomena in homogeneous liquid–gas flows undergoing isothermal transformations. The liquid–gas mixture is regarded as a pseudo-fluid whose constitutive behavior is obtained from two thermodynamic potentials: the Helmholtz free energy and a pseudo-potential of dissipation. Thanks to the inclusion of the concentration of dissolved gas in the liquid in the list of state variables, along with the gas volume fraction and the mass densities of the liquid and gas constituents, a suitable and simple expression for the rate of mass transfer of gas is derived. Besides of unconditionally satisfying the Second Law of the Thermodynamics, the proposed expression is capable to properly describe experimental data available in the literature with great accuracy for a relatively wide range of saturation pressures. Numerical simulations carried out for an water–air mixture, subjected to a single expansion and cyclic expansion–contraction loadings, illustrate the influence of the gas release on the mechanical response of the fluid, which exhibits dispersion and attenuation and also hysteresis.

The thermodynamic behavior of the system H2O/BSA was studied at 25 °C within the entire composition range: vapor pressure measurements via head space sampling gas chromatography demonstrate that the attainment of equilibria takes more than one week. A miscibility gap was detected via turbidity and the coexisting phases were analyzed. At 6 °C the two phase region extends from ca. 34 to 40 wt % BSA; it shrinks upon heating. The polymer rich phase is locally ordered, as can be seen under the optical microscope using crossed polarizers. The Flory-Huggins theory turns out to be inappropriate for the modeling of experimental results. A phenomenological expression is employed which uses three adjustable parameters and describes the vapor pressures quantitatively; it also forecasts the existence of a miscibility gap.

A new method of describing the liquid-gas phase transition is presented. It is assumed that the phase transition is characterized by a significant change of the particle density distribution as a result of energy supply at the boiling point that leads to structural changes but not to heating. Structural changes are described by an additional state characteristics of the system—the distribution density of the particles which is presented by an independent balance equation. The mathematical treatment is based on a special form of the internal energy and a source term in the particle balance equation. The presented method allows to model continua which have different specific heat capacities in liquid and in gas state.

UDC 536.24,614.83 The results of numerical investigation of the influence of wind velocity and degree of atmospheric stability on the process of toxic cloud formation on outpouring ejection of liquefied chlorine are presented. The computa- tional procedure is realized with the use of the hydrodynamic analysis package FLUENT. The proposed model describes the distribution of two clouds: primary and secondary. The primary aerosol cloud is formed as a result of instantaneous boiling up of a part of the liquid phase, and the secondary one, on evaporation (boiling) of a spill. Introduction. An analysis of the danger of emergencies often requires estimation of the propagation of toxic or explosive substances in the atmosphere. The source of information for predicting the evolution of the cloud is the intensity of entrance of the dangerous substance into the environment as a result of vaporization. The processes of va- porization and scattering of vapor in air are noted for the complex interrelation, which can hardly be taken into ac- count within the framework of simplified analytical and empirical relations. This requires using methods of numerical simulation based on packages of hydrodynamic analysis CFD for the solution of the above-mentioned problems. Within the framework of numerical simulation, the mutual effect of heat- and mass transfer processes that accompany the development of the emergency is taken into account directly by jointly solving differential equations of transfer of mass, momentum, energy, components, and turbulent characteristics. The problems of numerical simulation of the propagation of gaseous substances in the atmosphere were con- sidered in a large number of works, e.g., (1-9), however, in the existing models the description of the vaporization process is schematic only, which can be an obstacle to the reliable estimation of the zones of toxic injury or the di- mensions of a dangerous explosive cloud. With regard to the aforesaid, the problem of developing the mathematical apparatus for simulating the forma- tion of a vapor-air cloud in the case of emergency ejection of a liquefied gas as applied to the description of the source of ejection would seem urgent. In the present work, for determining the zones of toxic damage on outpouring ejection of liquefied chlorine, we suggest a model based on the program complex FLUENT. The model includes description of basic physical phe- nomena that determine the dynamics of formation of a toxic cloud: evaporation of aerosol in a cloud, vaporization in boiling (evaporation) of a spill, scattering of gas with droplet inclusions in the atmosphere, and condensation of steam in the cloud. Mathematical Model of Vaporization. On breakake of a vessel with a superheated liquid, instantaneous boil- ing up of a certain portion of the liquid phase takes place as a result of the sharp decrease in pressure and violation of the thermodynamic balance through the liberation of internal energy. This is followed by establishment of a new equilibrium state, with the temperature of the remaining portion of the liquid phase decreasing to the boiling point at atmospheric pressure. The instantaneous evaporation of liquid leads to the formation of the primary vapor cloud. To es- timate the fraction of substance x v that "instantaneously" converts into vapor, the following relation can be used (10)

We study experimentally the atomization of a thick liquid film by a parallel gas flow, in order to understand the conditions of destabilization of the liquid film and the conditions of drop creation. We study in particular the regimes at low M (ratio of gas/liquid dynamic pressures), to test the scaling law proposed and validated in previous studies at large M ( M = 16 ). The spatial inviscid stability analysis of the system is carried out with a new velocity profile taking into account the wake of the splitter plate (zero speed at the level of the splitter plate): the influence of liquid velocity on the shear instability frequency turns out to be significantly stronger for this type of velocity profile than for continuous profile. An asymptotic study of the dispersion relation leads to a new scaling law giving the wavenumber of the shear instability as a function of gas velocity U g , with a corrective term in M . Frequency measurements carried out by a spectral method show a good agreement with this corrected law. We investigate by way of optical probe measurements the size distribution of produced drops downstream. The difficulty of these measurements live in the decrease of the number density flux of drops at low M . Results obtained for the mean chord are consistent with previous studies. Diameter distributions are obtained from chord distributions with a numerical conversion procedure.

International audience; This paper proposes an efficient splitting algorithm to solve coupled liquid gas Darcy and free gas flows at the interface between a porous medium and a free-flow domain. This model is compared to the reduced model introduced in \cite{BMTZ-fvca7} using a 1D approximation of the gas free flow. For that purpose, the gas molar fraction diffusive flux at the interface in the free-flow domain is approximated by a two point flux approximation based on a low frequency diagonal approximation of a Steklov-Poincar\'e type operator. The splitting algorithm and the reduced model are applied in particular to the modelling of the mass exchanges at the interface between the storage and the ventilation galleries in radioactive waste deposits.

We have studied 4 He confined in a 95% porosity silica aerogel in the vicinity of the bulk liquid gas critical point. Both thermodynamic measurements and light scattering experiments were performed to probe the effect of a quenched disorder on the liquid gas transition, in relation with the Random Field Ising Model (RFIM). We find that the hysteresis between condensation and evaporation present at lower temperatures disappears at a temperature T ch between 25 and 30 mK below the critical point. Slow relaxations are observed for temperatures slightly below T ch , indicating that some energy barriers, but not all, can be overcome. Above T ch , no density step is observed along the (reversible) isotherms, showing that the critical behavior of the equilibrium phase transition in presence of disorder, if it exists, is shifted to smaller temperatures, where it cannot be observed due to the impossibility to reach equilibrium. Above T ch , light scattering exhibits a weak maximum close to the pressure where the isotherm slope is maximal. This behavior can be accounted for by a simple model incorporating the compression of 4 He close to the silica strands., Comment: 6 pages

In this paper, we get a unique local strong solution to a 3D viscous liquid–gas two-phase flow model in a smooth bounded domain. Besides, a blow-up criterion of the strong solution for 25 3 μ > λ is obtained. The method can be applied to study a blow-up criterion of the strong solution to Navier–Stokes equations for 25 3 μ > λ , which improves the corresponding result about Navier–Stokes equations in Sun et al. (2011) [15] where 7 μ > λ . Moreover, all the results permit the appearance of vacuum.

Measurements and correlations are reported for the interfacial area and mass transfer coefficients as a function of energy dissipation in a liquid-gas ejector. The correlations for interfacial area and mass transfer coefficients have been developed using Kolmogorov’s theory and Levich’s hydrodynamic derivations. The present developed correlations are validated using experimental results.

The present work described experimental and numerical investigations of ejectors using water as the motive fluid and water and gas as the entrained fluid. These ejectors are used in low temperature thermal desalination systems to entrain the brine and non-condensable gases to keep the desalination systems operating on condition of the vacuum. The numerical simulations were based on the Euler–Euler multiphase model, with a simplified slip velocity ratio, determined by comparing the experimental and the simulation results. The simulations showed that the slip velocity between phases is 11% and 12%. The simulations examined the influence of several variables, including the primary fluid pressure, the suction fluid pressure and the discharge pressure, on the volumetric entrainment ratio and efficiency. The results show that, if the structural variables are fixed, the volumetric entrainment ratio is determined by the pressure ratio ΔPp/ΔPc with the maximum efficiency obtained for a pressure ratio equal to the throat aspect ratio (DT/DN)2.

In this paper, we prove a blow-up criterion in terms of the upper bound of the liquid mass for the strong solution to the two-dimensional (2D) viscous liquid-gas two-phase flow model in a smooth bounded domain. The result also applies to three-dimensional (3D) case.

No-vent fill is a promising technology for ground filling applications of dangerous cryogens such as liquefied natural gas and precious liquefied gas such as liquid helium and liquid hydrogen. A finite difference lumped analysis using a Python computer program that predicts no-vent fill performance in a 1 g environment for the top filling configurations is described. The tank system is divided into four lumps: the tank wall in contact with the ullage space, tank wall in contact with the bulk liquid, tank wall in contact with the spray incoming liquid, and the cryogen. A new method of dealing with heat transfer between the tank wall and the cryogen is introduced to improve the reliability of the simulation. Corrections of assumptions on the initial distribution of the wall temperature and the inflow rate of the incoming liquid are proposed. Experiments of both the top-spray and the top-nozzle filling configurations are conducted to validate the new model. The results are shown to match the test results within the measurement uncertainty of the test data.

Ejectors are widely used as effective distributors in many chemical and bioprocess industries. Gas entrainment rate as a function of liquid flow rate in ejectors is investigated using nozzles of different geometries. The data are analyzed through macro-energy balance for each phase considering air and water inlet line discharge coefficients. Nozzles with smaller discharge coefficients are effective in producing higher vacuum and hence higher entrainment rates. It has been observed that the factor limiting the air entrainment rate is the low discharge coefficient in the air inlet line. Higher air inlet line discharge coefficients can increase the entrainment rate.

We modify the projective transformation suggested earlier. (7) Within this modified transformation, the critical point and the Zeno-line of the lattice model are moved to the critical point and Zeno-line of simple liquids. Using analytical lattice calculations and numerical simulations, we show that the lattice binodals and critical isotherms transforms with sufficient accuracy into binodals and critical isotherms of real substances such as Cs, Hg, and NH(3), and other model systems with real system properties such as the van der Waals equation, Lennard-Jones systems.

Condensation and evaporation are ubiquitous phenomena in nature. When we have a liquid partially filling a closed container, evaporation starts to happen, causing vapour formation in the remaining space. As the gaseous molecules bounce around, some of them hit the liquid surface and condense back into their original phase. This process evolves until there are as many molecules condensing as there are evaporating, that is, when the system reaches equilibrium. In this paper we introduce a very simple model addressed to undergraduate students and teachers that provides the temporal behaviour of this process. Using the results we propose an experimental technique to measure condensation coefficients.

During gas-phase release from the tank containing liquefied gas, the phenomenon of boiling, heat transfer from moist air to the tank, heat exchange between shell, liquid, and vapor, and mass loss can be observed. The aim of this paper is modelling the thermal response of the tank containing liquefied gas during jet emission of the vapor phase. The model takes into account heat exchange between air, tank’s shell, liquid phase, vapor phase and mass balance. The proposed model predicts: pressure inside the tank, tank’s shell temperature in part with liquid and vapor, the temperature of the liquid phase and vapor phase, and mass loss from the tank. The results of the theoretical model were compared with experimental results. An experiment based on the typical home container for LPG, containing 10 kg of propane (27 dm3 volume) was conducted. In general, the proposed model predicts well the changes in measured parameters temperatures and pressure - during vapor phase emission from a tank containing liquefied gas.