Liquid-vapor Phase Transition Research Articles

Numerical model for electrical explosion of copper wires in water

This paper presents a simple but quite accurate numerical model for analyzing electrical explosion of copper wires in water. The numerical model solves a circuit equation coupled with one-dimensional magneto-hydrodynamic (MHD) equations with the help of appropriate wide-range equation of state (EOS) and electrical conductivity for copper. The MHD equations are formulated in a Lagrangian form to identify the interface between the wire and surrounding water clearly. A quotidian EOS (QEOS) that is known as the simplest form of EOS is utilized to build wide-range EOS for copper. In the QEOS, we consider the liquid-vapor phase transition, which is critical in analyzing the wire explosion system. For the electrical conductivity of copper, a semi-empirical set of equations covering from solid state to partially ionized plasma state are employed. Experimental validation has been performed with copper wires of various diameters, which are exploded by a microsecond timescale pulsed capacitive discharge. The simulation results show excellent agreements with the experimental results in terms of temporal motions of a plasma channel boundary and a shock front as well as current and voltage waveforms. It is found that the wire explodes (vaporizes) along the liquid branch of a binodal curve irrespective of wire dimension and operating voltage. After the explosion, the wire becomes a plasma state right away or after the current pause (dwell), depending on the operating conditions. It is worth noting that such a peculiar characteristic of wire explosion, i.e., current pause and restrike, is well simulated with the present numerical model. In particular, it is shown that the wire cools down along the vapor branch of the binodal curve during the current dwell, due to a significant difference of thermodynamic characteristics across the binodal curve. The influence of radiation for studying nonideal plasmas with a wire explosion technique and a physical process for shock wave formation by an exploding wire is discussed as well.

One-dimensional Lagrangian implicit hydrodynamic algorithm for Inertial Confinement Fusion applications

A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The scheme uses a fully conservative Lagrangian formulation in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity formulation. The space discretized equations are advanced in time using an implicit algorithm. The method includes several numerical parameters that can be adjusted locally. In regions with low Courant–Friedrichs–Lewy (CFL) number, where stability is not an issue, they can be adjusted to optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser–matter interaction, where liquid–vapor phase transitions occur.

Improved grand canonical sampling of vapour-liquid transitions

Simulation within the grand canonical ensemble is the method of choice for accurate studies of first order vapour-liquid phase transitions in model fluids. Such simulations typically employ sampling that is biased with respect to the overall number density in order to overcome the free energy barrier associated with mixed phase states. However, at low temperature and for large system size, this approach suffers a drastic slowing down in sampling efficiency. The culprits are geometrically induced transitions (stemming from the periodic boundary conditions) which involve changes in droplet shape from sphere to cylinder and cylinder to slab. Since the overall number density does not discriminate sufficiently between these shapes, it fails as an order parameter for biasing through the transitions. Here we report two approaches to ameliorating these difficulties. The first introduces a droplet shape based order parameter that generates a transition path from vapour to slab states for which spherical and cylindrical droplets are suppressed. The second simply biases with respect to the number density in a tetragonal subvolume of the system. Compared to the standard approach, both methods offer improved sampling, allowing estimates of coexistence parameters and vapor-liquid surface tension for larger system sizes and lower temperatures.

A variational approach to the liquid-vapor phase transition for hardcore ions in the bulk and in nanopores.

We employ a field-theoretical variational approach to study the behavior of ionic solutions in the grand canonical ensemble. To describe properly the hardcore interactions between ions, we use a cutoff in Fourier space for the electrostatic contribution of the grand potential and the Carnahan-Starling equation of state with a modified chemical potential for the pressure one. We first calibrate our method by comparing its predictions at room temperature with Monte Carlo results for excess chemical potential and energy. We then validate our approach in the bulk phase by describing the classical "ionic liquid-vapor" phase transition induced by ionic correlations at low temperature, before applying it to electrolytes at room temperature confined to nanopores embedded in a low dielectric medium and coupled to an external reservoir of ions. The ionic concentration in the nanopore is then correctly described from very low bulk concentrations, where dielectric exclusion shifts the transition up to room temperature for sufficiently tight nanopores, to high concentrations where hardcore interactions dominate which, as expected, modify only slightly this ionic "capillary evaporation."

Pairing effects on neutrino transport in low-density stellar matter

We investigate the impact of pairing correlations on neutrino transport in stellar matter. Our analysis is extended to nuclear matter conditions where large density fluctuations develop, associated with the onset of the liquid-vapor phase transition, and clustering phenomena occur. Within a thermodynamical treatment, we show that at moderate temperatures, where pairing effects are still active, the scattering of neutrinos in the nuclear medium is significantly affected by pairing correlations, which increase the neutrino trapping, thus modifying the cooling mechanism, by neutrino emission, of neutron stars.

Computer modeling of droplets impact on heat transfer during spray cooling under vibration environment

The heat transfer process among droplet, film and bubble is selected as the local characteristic process of spray cooling to build a multiphase flow model. Volume of fluid (VOF) method is employed to simulate the transient process, in which single or multiple droplets impact on a liquid film with a vapor bubble growing, considering the effects of surface tension, gravity and vapor-liquid phase transition. The effect of vibration environment is analyzed by setting vibration boundary condition, and a far broader range of vibration condition is calculated in light spray and dense spray to identify the effect. Heat is mainly removed by strong convection due to the droplet impact. It is significant to form stabilized and intact film during spray cooling. Heat transfer process can be mainly separated into four stages: 1. before the impact; 2. droplet impacts on the surface and forms thinner film on the surface; 3. film extends outwards; 4. film breakage. In dense spray cases, the third stage is barely observed due to continuous impacting of droplets, and mainly all the cases show that vibration has invigorating effect on heat transfer.

Manifestation of spinodal singularities in the liquid–vapor phase transition during simulation of nanosecond vaporization of a liquid film

The recent results of molecular-dynamics simulation of nanosecond vaporization of a thin liquid film are analyzed within the continual approach. The analysis shows a significant increase in the thermal conductivity at the film temperature maximum before its explosive decomposition, which indicates the closeness of the achievable limiting overheating temperature to the spinodal.

Heat transfer performance of closed loop pulsating heat pipes with methanol-based binary mixtures

In this paper, an experimental study is presented on the thermal resistance characteristics of closed loop pulsating heat pipes (CLPHPs) with methanol-based binary mixtures. The working fluids were methanol mixed with deionized water, acetone and ethanol. The volume mixing ratios used were 2:1, 4:1 and 7:1, and the heating power ranged from 10W to 100W with filling ratios of 45%, 62%, 70% and 90%. The results showed that adding other working fluids to methanol could change the thermal resistance characteristics of a PHP. At a low filling ratio (45%), adding water to methanol could prevent dry-out at a high heating power; when ethanol was added to methanol, the thermal resistance of the CLPHP was between that with pure methanol and ethanol; when acetone was added, the thermal resistance of the CLPHP was slightly lower than that with pure methanol and acetone. At a high filling ratio (62%, 70%, 90%), the thermal resistance characteristics of CLPHPs with methanol based mixtures were not much different from those with pure fluids except for methanol–water mixture where the thermal resistance was greater than that with pure methanol and pure water. It can be inferred that the heat transfer performances of CLPHPs with methanol-based binary mixtures are related to the thermal-physical properties of the working fluids, vapor–liquid phase transition properties, molecular interactions and the additional resistance to mass transfer.

Film boiling of subcooled liquids. Part I: Leidenfrost phenomenon and experimental results for subcooled water

Film boiling of subcooled liquids is important, at least, for two applications: for systems of post-accident cooling in nuclear power plants and for quenching technology. An analysis of the previous results shows that at high water subcooling film boiling presents a particular mode of boiling heat transfer, dissimilar greatly to saturated film boiling mainly by high intensity of heat transfer; this statement appears to be true, even though the researchers themselves do not recognize it. As at the temperature much higher than that of homogeneous nucleation, liquid–vapor phase transition occurs practically instantly, an actual temperature at the liquid/solid interface cannot be higher than the attainable limiting temperature of liquid. The possible mechanisms of high intensity heat transfer between the surface and subcooled liquid at the absence of liquid/solid contact and the conditions of this regime incipience require experimental and theoretical investigations. The present paper describes the method and the results of experimental study of heat transfer during cooling the spherical patterns from nickel, stainless steel, and copper with initial temperature above 700°C in water at subcoolings up to 70K. In distinction to all the previous studies temperature was measured in several points of the spheres that gives new information on the cooling process. It is revealed that at high cooling rates the temperature field can lose its spherical symmetry, high temperature gradients are observed not only in the radial direction, but also along the surface. At high subcoolings the heat transfer regime of high intensity arises at the surface temperature 600–700°C that excludes a possibility of liquid/solid direct contact; heat flux density can be as high as 5–7MW/m2.

Laminar-turbulent reactive flows in porous media

We state some recent results concerning liquid-vapor phase transitions for a fluid flow through a porousmedium. The focus is on the friction exerted by the porous medium, which is modeled in such a way to include both laminar and turbulent flows. In this way we obtain a hyperbolic system of three balance laws with a forcing term that is discontinuous in the state variables. Existence, uniqueness and qualitative behavior of traveling waves is proved by a novel regularization technique.

Melt–vapor phase transition in the lead–selenium system at atmospheric and low pressure

The boiling temperature and the corresponding vapor phase composition in the existence domain of liquid solutions were calculated from the partial pressures of saturated vapor of the components and lead selenide over liquid melts in the lead–selenium system. The phase diagram was complemented with the liquid–vapor phase transition at atmospheric pressure and in vacuum of 100 Pa, which allowed us to judge the behavior of the components during the distillation separation.

Water Evaporation and Condensation by a Phase-Field Model

AbstractWe develop a phase-field model for the liquid–vapor phase transition. The model aims to describe in a thermodynamically consistent way the phase change phenomenon coupled with the macroscopic motion of the fluid. The phase field

A novel floating controlled release drug delivery system prepared by hot-melt extrusion

Floating dosage forms are an important formulation strategy for drugs with a narrow absorption window and low intestinal solubility, and for localized gastric treatment. Novel floating pellets were prepared using the hot-melt extrusion (HME) technology. Uniformly foamed strands were created by liquid injection pumping and screw configuration modification. The ammonio methacrylate copolymer (Eudragit® RSPO) foaming structure was formed by a liquid–vapor phase transition inside the strand upon die exiting resulting from the sudden decrease in external pressure, vaporizing the liquid ethanol and vacating the extruded material. This generated uniform vacuous regions in the extrudate. The pellets’ internal structure was investigated using scanning electron microscopy (SEM). The formulation constituents’ and processing parameters’ effects on the drug release profiles, floating force, and the pellets’ micromeritic properties were evaluated by design of experiments: all formulations showed zero lag time and excellent floating strength, indicating immediate-floating pellet formation. The pellets’ drug release profiles were controlled by multiple independent variables at different time points (⩽24h). Drug loading significantly affected drug release within the first hour, the hydroxypropyl methylcellulose (HPMC) content thereafter. Understanding the variables’ effects on the formulations allows for the tailoring of this delivery system to obtain various drug release profiles.

Influence of solid-state characteristics on critical parameters of vapor-liquid phase transition

New method for calculation of critical point parameters and binodal of vapor-liquid (dielectric-metal) phase transition is suggested. Method is based on the hypothesis that cohesion, which determines the main properties of solid state, determines also the properties in vicinity of critical point. Comparison with known experimental data for rare gases and mercury shows satisfactory agreement with our calculations.

Study of near-critical states of liquid-vapor phase transition of magnesium

Study of thermodynamic parameters of magnesium in the near-critical point region of the liquid-vapor phase transition and in the region of metal-nonmetal transition was carried out. Measurements of the electrical resistance of magnesium after shock compression and expansion into gas (helium) environment in the process of isobaric heating was carried out. Heating of the magnesium surface by heat transfer with hot helium was performed. The registered electrical resistance of expanded magnesium was about 104-105 times lower than the electrical resistance of the magnesium under normal condition at the density less than the density of the critical point. Thus, metal-nonmetal transition was found in magnesium.

Simulation of liquid–vapour phase transitions and multiphase flows by an improved lattice Boltzmann model

An improved lattice Boltzmann (LB) model with a new scheme for the interparticle interaction force term is proposed in this paper. Based on the improved LB model, the equation-free method is implemented for simulating liquid–vapour phase change and multiphase flows. The details of phase separation are presented by numerical simulation results in terms of coexistence curves and spurious currents. Compared with existing models, the proposed model can give more accurate results in a wider temperature range with the spurious currents reduced and less time consumed. Characteristics of phase separation can be quickly and accurately reflected by the proposed method. Then, the contact angle of the solid surface is numerically investigated based on the proposed model. The proposed model is valid for steady flow with near zero velocity; unsteady cases will be investigated in further studies. This work will be helpful for our long-term aim of multi-scale modelling of convective boiling.

Liquid nanodroplet formation through phase explosion mechanism in laser-irradiated metal targets.

Some quantitative aspects of laser-irradiated pure metals, while approaching phase explosion, are still not completely understood. Here, we develop a model that describes the main quantities regulating the liquid-vapor explosive phase transition and the expulsion of liquid nanodroplets that, by solidifying, give rise to nanoparticle formation. The model combines both a thermodynamics description of the explosive phase change and a Monte Carlo simulation of the randomly generated critical vapor bubbles. The calculation is performed on a set of seven metals (Al, Fe, Co, Ni, Cu, Ag, and Au) which are frequently used in pulsed laser ablation experiments. Our final predictions about the size distribution of the liquid nanodroplets and the number ratio of liquid/vapor ejected atoms are compared, whenever possible, with available molecular dynamics simulations and experimental data.

Critical points of metal vapors

A new method is proposed for calculating the parameters of critical points and binodals for the vapor–liquid (insulator–metal) phase transition in vapors of metals with multielectron valence shells. The method is based on a model developed earlier for the vapors of alkali metals, atomic hydrogen, and exciton gas, proceeding from the assumption that the cohesion determining the basic characteristics of metals under normal conditions is also responsible for their properties in the vicinity of the critical point. It is proposed to calculate the cohesion of multielectron atoms using well-known scaling relations for the binding energy, which are constructed for most metals in the periodic table by processing the results of many numerical calculations. The adopted model allows the parameters of critical points and binodals for the vapor–liquid phase transition in metal vapors to be calculated using published data on the properties of metals under normal conditions. The parameters of critical points have been calculated for a large number of metals and show satisfactory agreement with experimental data for alkali metals and with available estimates for all other metals. Binodals of metals have been calculated for the first time.

Phase equilibrium data for ternary (carbon dioxide + dichloromethane + eugenol) and quaternary systems (carbon dioxide + dichloromethane + eugenol + poly-ε-caprolactone)

Experimental phase equilibrium values for the ternary (carbon dioxide+dichloromethane+eugenol) and quaternary systems (carbon dioxide+dichloromethane+eugenol+poly-ε-caprolactone) have been determined in order to provide fundamental information to conduct microencapsulation of eugenol in supercritical carbon dioxide medium. The experiments were performed using a variable-volume view cell over the temperature range from (308.15 to 323.15)K. For the ternary system, three different values of mole ratios eugenol to dichloromethane (1:1, 1:5 and 1:10) were evaluated. Phase transitions of vapour–liquid type bubble point and vapour–liquid type dew point were observed at pressures between (0.73 and 12.43)MPa. Experimental results were modelled using the Peng–Robinson (PR) equation of state with the Wong–Sandler (PR–WS) mixing rule, providing a satisfactory representation of the experimental phase equilibrium data, with an average absolute deviation of 2.61MPa. For the quaternary system two mole ratios of eugenol to poly-ε-caprolactone (PCL) to dicholoromethane (1:0.002:5 and 1:0.004:10) were adopted. For this system, only vapour–liquid phase transitions of the bubble point type were observed. It was observed that an increase in the temperature as well as in PCL concentration increased the transition pressures for these systems evaluated.

Comment on Gibbs Density Surface of Fluid Argon, L.V. Woodcock, Int. J. Thermophys. (2014) 35:1770–1784

It has been established experimentally that the thermodynamic properties of fluids satisfy scaling laws with universal critical exponents asymptotically close to a single critical point of the vapor–liquid phase transition. In contrast to the conjecture of Woodcock, there is no reliable experimental evidence to doubt the existence of such a single critical point in the thermodynamic limit and of the validity of the scaling theory for critical thermodynamic behavior.