Two-phase Boundary Research Articles

Fick diffusion coefficients of binary fluid mixtures consisting of methane, carbon dioxide, and propane via molecular dynamics simulations based on simplified pair-specific ab initio-derived force fields

For the calculation of thermophysical properties of fluids with molecular dynamics (MD) simulations, effective force fields (FFs) which are optimized against experimental vapor-liquid equilibria are often used. Examples for this FF category are TraPPE, OPLS, and AMBER. An alternative are simplified pair-specific, ab initio-based FFs (AI-FFs), which are derived from quantum-chemical calculations in the limit of zero-density in combination with the kinetic theory of gases, and, thus, feature a predictive character. In the present study, we show with the help of selected binary fluid mixtures that the predictive power of MD simulations in calculating Fick diffusion coefficients can be improved using simplified pair-specific AI-FFs based on corresponding FFs for the pure substances. To evaluate the performance of the new AI-FFs in comparison with the TraPPE FFs, binary mixtures consisting of methane, carbon dioxide, and propane were investigated from the superheated vapor to the gas state and supercritical region up to the compressed liquid state. For the determination of the Fick diffusion coefficient at pressures between (0.1 and 12) MPa, temperatures between (293 and 355) K, and mole fractions between 0.05 and 0.95, separate simulations for the analysis of the Maxwell–Stefan diffusion coefficient and the thermodynamic factor were performed considering system size effects. With the exception of the compressed liquid state and regions in vicinity of the two-phase boundary, where the TraPPE FFs are generally superior, the AI-FFs show improved predictions for the Fick diffusion coefficient with average expanded statistical uncertainties of 12%. This could be demonstrated by comparison of the simulation results with the theoretical ab initio calculations and the available experimental data, resulting in average absolute deviations of 7% and 13% for the AI-FFs and TraPPE FFs.

The Effect of Admixture of Non-Evaporating Droplets on the Flow Structure and Adiabatic Wall Temperature in a Compressible Two-Phase Boundary Layer

A mathematical model is constructed and numerical calculations of the problem of a highspeed longitudinal steady flow of a viscous heat conducting gas with an admixture of liquid droplets over a thermally insulated flat plate are performed. The droplet temperature is assumed to differ from that of the carrier gas. The range of flow parameters is considered, in which the droplet evaporation can be neglected but the temperature of droplets can vary significantly within the boundary layer. The mathematical model of two-phase boundary layer is modified taking into account the temperature nonuniformity inside the droplets. This required, along with solving the macroscopic equations of the two-fluid model, to find a solution of the heat conduction equation inside the droplets. On the basis of parametric calculations, the flow regimes with the formation of a liquid film due to droplet deposition on the wall are investigated. The similarity parameters are found and a range of governing parameters is determined in which, due to the heat exchange with the liquid phase in the boundary layer, a noticeable decrease in the adiabatic-wall temperature is manifested even at very small initial concentrations of the droplets.

Direct numerical simulation of primary breakup for power-law biodiesel sprays

Abstract Biodiesel is a very promising alternative fuel in internal combustion engines. Fragmentation of the fuel injection has a fundamental influence on engine performance. The influence factors for the spray breakup process, including near nozzle fields, are still unclear. In this study, the primary of fuel sprays occurring with turbulence perturbation is devoted to simulation. The evolutionary processes of biodiesel fuels atomization affected by turbulence are investigated in present models. A validated single-phase fully developed turbulent flow is generated first to store time-varying outlet velocity database. Then, the database is mapped as the two-phase model inlet velocities boundary. A modified VOF (Volume of Fluid) coupled with DNS (direct numerical simulation) method is applied to study the evolution of fuel spray. It is found that wavy surface, ligaments, and droplets with various scales and shapes turn up gradually in jet evolution process. Meanwhile, after being sheared, distorted and stretched, different ligaments separation patterns are captured. Larger Reynolds number and higher gas densities accelerate the jet break-up process. Higher injection velocities and lower power-law indexes (n 1) fuel jet. What’s more, similar breakup patterns are detected in shear-thinning fluid (n

Recent progresses on elliptic two-phase free boundary problems

We provide an overview of some recent results about the regularity of the solution and the free boundary for so-called two-phase free boundary problems driven by uniformly elliptic equations.

Bubbly drag reduction investigated by time-resolved ultrasonic pulse echography for liquid films creeping inside a turbulent boundary layer

Frictional drag reduction due to bubble lubrication was investigated by measuring liquid films creeping along a wall within a two-phase turbulent boundary layer. We developed noninvasive time-resolved ultrasonic pulse echography for imaging a liquid film at a profiling rate of 3 kHz and a spatial resolution of 50 μm. Various film patterns were obtained for a 4-m-long flat-bottom model ship towed in a 100-m-long water tank, where a drag reduction rate of 30% was recorded for maximum air injection. We found that the liquid-film thickness ranged from 50 to 150 wall units of the single-phase turbulent boundary layer; this film was thicker than the buffer layer depth. With an increase in the air injection flow rate, the average thickness decreased close to the buffer layer limit while the skewness and kurtosis of the probability density function of the film thickness increased. A sudden transition of the film form was detected according to the kurtosis, allowing the monitoring of the criteria of the coalescence of dispersed bubbles into large elongated bubbles via ultrasonic pulse echography.

A two-phase free boundary problem for system of reaction-diffusion equations

A two-phase free boundary problem for system of reaction-diffusion equations

Visualizing Reversible Two-Dimensional Phase Transitions in Oxygen Chemisorbed Layers

The interactions of a metallic surface with gaseous oxygen typically result in the formation of an oxygen chemisorbed layer that represents a true two-dimensional system in the limit of one atomic layer supported on a solid substrate. Using low-energy electron microscopy that temporally and spatially resolves phase transformations in such an oxygen chemisorbed layer on Cu(110), we demonstrate that the phase transformations are nucleation-limited on each terrace, and the resulting heterophase boundaries propagate exclusively on the same terrace with coordinated migration of surface steps. Using ab initio calculations based on density functional theory and thermodynamics considerations, we show the necessity of incorporating the effect of heterophase boundaries due to the co-existence of different phases as a criterion for predicting two-phase equilibria. It is also shown that the observed surface phase transformations are limited by the mass transport of Cu and O atoms on the parent phases instead of the two-phase boundary reactions. These results demonstrate that the oxygen chemisorbed layer serves as a model system to advance the fundamental understanding of phase behavior and dynamics in systems with reduced dimensionality, which may find broader applicability because such progressive stages of oxygen chemisorption-induced surface phase transformations and restructuring are generally involved in many metal–oxygen systems.

Regularity of interfaces for a Pucci type segregation problem

We show the existence of a Lipschitz viscosity solution u in Ω to a system of fully nonlinear equations involving Pucci-type operators. We study the regularity of the interface ∂{u>0}∩Ω and we show that the viscosity inequalities of the system imply, in the weak sense, the free boundary condition uν++=uν−−, and hence u is a solution to a two-phase free boundary problem. We show that we can apply the classical method of sup-convolutions developed by the first author in [5,6], and generalized by Wang [20,21] and Feldman [11] to fully nonlinear operators, to conclude that the regular points in ∂{u>0}∩Ω form an open set of class C1,α. A novelty in our problem is that we have different operators, F+ and F−, on each side of the free boundary. In the particular case when these operators are the Pucci's extremal operators M+ and M−, our results provide an alternative approach to obtain the stationary limit of a segregation model of populations with nonlinear diffusion in [19].

Size-Dependent Memory Effect of the LiFePO4 Electrode in Li-Ion Batteries.

In Li-ion batteries, the phase transition usually determines the electrochemical kinetics of some two-phase electrode materials, and it can be adopted to excellently interpret the memory effect of Li-ion batteries, therefore the size dependence of phase transition was expected to affect the memory effect significantly. In this work, we investigated the memory effect and phase transition of olivine LiFePO4 in Li-ion batteries. Through electrochemical measurements, we found that the memory effect of LiFePO4 was dependent on the particle size, especially after a long-time relaxation. By using the in situ X-ray diffraction, we found that the phase transition of nano-LiFePO4 was ahead of the charging and discharging processes, while it took place concurrently or later for micro-LiFePO4, which might be attributed to the high-specific two-phase boundary of nano-LiFePO4. Furthermore, the phase-transition diagram was adopted to interpret the size-dependent memory effect schematically. Notably, it is the first time to report the phase transition ahead of (dis)charging for nano-LiFePO4, which is significant to understand the phase transition of two-phase electrode materials, as well as the relevant phenomena, such as the memory effect.

Bubbly drag reduction accompanied by void wave generation inside turbulent boundary layers

Frictional drag reduction, a technique by which bubbles are injected into the turbulent boundary layer surrounding the hull of a marine vessel, is now at the stage of practical applications. In achieving drag reduction, void waves often stand out naturally, the reason for which still remains unclear. The present study aims at an experimental characterization of void waves along a flat-bottom ship. A 100-m-long water reservoir is used in which a 4-m-long fully transparent experimental model ship, equipped with wall shear stress sensors and cameras, is towed by a train at speeds of up to 3 m/s. From measurements of the transition of the bubble distribution from random to wavy accumulated swarms downstream, the accompanying intrinsic passing frequency of void waves is examined. A 30% drag reduction rate was recorded with the appearance of void waves in the boundary layer at an average void fraction of 4%. This is much greater than the trivial inertia effect from drag reduction. To clarify the characteristics of the measured void waves, we compare the void wave frequency range to those of several flow instabilities that may occur in bubbly two-phase boundary layer flows.

Regularity of higher order in two-phase free boundary problems

We develop further our strategy from our 2014 paper showing that flat or Lipschitz-free boundaries of two-phase problems with forcing terms are locally C 2 , γ . C^{2,\gamma }.

Air Entrainment and Surface Fluctuations in a Turbulent Ship Hull Boundary Layer

The air entrainment due to the turbulence in a free surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations. In the experiments, a laboratory-scale device was built that utilizes a surface-piercing stainless steel belt that travels in a loop around two vertical rollers, with one length of the belt between the rollers acting as a horizontally-moving flat wall. To complement the experiments, Direct Numerical Simulations (DNS) of the two-phase boundary layer problem were carried out with the domain including a streamwise belt section simulated with periodic boundary conditions. Cinematic Laser-Induced Fluorescence (LIF) measurements of water surface profiles in two vertical planes oriented parallel to the belt surface (wall-parallel profiles) are presented and compared to previous measurements of profiles in a vertical plane oriented normal to the belt surface (wall-normal profiles). Additionally, photographic observations of air entrainment and measurements of air bubble size distributions and motions are reported herein. The bubble entrainment mechanisms are studied in detail through the results obtained by the DNS simulations. Free surface features resembling breaking waves and traveling parallel to the belt are observed in the wall-parallel LIF movies. These breaking events are thought to be one of the mechanisms by which the air is entrained into the underlying flow. The bubble size distribution is found to have a characteristic break in slope, similar to the Hinze scale previously observed in breaking waves. Finally, several entrainment mechanisms are found in the simulations and their prevalence in the free surface boundary layer is assessed.

A lattice Boltzmann model for multi-component two-phase gas-liquid flow with realistic fluid properties

Multi-component multi-phase flows are of significant interests in nature and engineering problems of different fields. Modeling the phenomena involved in multi-phase flows is challenging, attributed to the complexity in simulating phase interface dynamics and diffusion processes. Owing to its kinetic nature, lattice Boltzmann (LB) method emerges as an attractive computational approach, in dealing with complicated fluid flow problems and microstructure geometries with effectiveness of parallelized processing. However, some critical drawbacks of basic multi-phase LB models, such as the low density and kinematic viscosity ratios, thermodynamic inconsistency, and dependence of surface tension and density distribution on relaxation times, limit its application in realistic multi-component multi-phase systems. Based on the original pseudopotential model and progresses in single-component multi-phase model, a multi-component LB model was proposed to study the two-phase gas-liquid flow with realistic fluid properties. The importance of improved model is in simultaneously realizing the realistic fluid flow characteristics for multi-component two-phase system, including high density and viscosity ratios, good thermodynamic consistency, independently tunable surface tension and appropriate two-phase boundaries. The proposed LB model is validated with Laplace law and visualization experiment results, and the effects of surface tension, gas flow velocity and wall wettability on dynamic behaviors of fluid flow are investigated.

Multiscale reconstruction in physics for compositional simulation

A compositional formulation is a reliable option for understanding the complex subsurface processes and the associated physical changes. However, this type of model has a great computational cost, since the number of equations that needs to be solved in each grid block increases proportionally with the number of components employed. To address this issue, we herewith propose a multiscale reconstruction in physics for compositional simulation. The ideology consists of two stages, wherein two different sets of restriction and prolongation operators are defined based on the dynamics of compositional transport. In the first stage, an operator restricting the arbitrary number of components to only two equations for flow and transport is implemented with the objective of accurately reconstructing the multiphase boundaries in space. The prediction of multiphase front propagation is the most critical aspect of the approach, as they involve a lot of uncertainties. Once the position of two-phase boundaries is identified, the full conservative solution in the single-phase region can be accurately reconstructed based on the prolongation interpolation operator. Subsequently, in the second stage, the solution for the multicomponent problem (full system) in the two-phase region is reconstructed by solving just two transport equations with the aid of restriction operator defined based on an invariant thermodynamic path. The proposed reconstruction strategy results in coarsening of the compositional problem in terms of the physical representation (number of equations), thereby appreciably reducing the simulation time by several folds without significant loss in the accuracy. We demonstrate the applicability of the proposed multiscale strategy for several challenging gas injection problems.

On the phase behaviors of hydrocarbon and noble gas clathrate hydrates: Dissociation pressures, phase diagram, occupancies, and equilibrium with aqueous solution.

We apply a statistical mechanical theory on clathrate hydrates to an exploration of the phase behaviors of hydrocarbon and noble gas clathrate hydrates. Two- and three-phase coexisting conditions in the whole space of thermodynamic variables (temperature, pressure, and composition) are evaluated only from intermolecular interactions for water and guest species. The occupancy of guest molecules in various types of cages is also calculated. We find that a small difference in the guest size gives rise to a rich variety of phase behaviors, notably for the shape of the two-phase boundary and the occupancy. Ethane clathrate hydrate is found to exhibit the most drastic and intriguing features in various properties arising from its non-stoichiometry. We investigate the phase behaviors of clathrate hydrate in terms of the partial molar quantities derived from the chemical potentials of guest and water. Our method also allows exploring the aqueous solution of an apolar guest molecule in the low temperature and high pressure regime coexisting with the corresponding clathrate hydrate for which the free guest fluid phase is substituted at high temperatures. It is shown that the temperature dependence of methane solubility in liquid water in the presence of clathrate hydrate is opposite to that being in equilibrium with the methane fluid without clathrate hydrate. This phenomenon is elucidated by a substantial decrease in the chemical potential of methane from the hydrate/guest boundary to the hydrate/water.

A preliminary assessment on a two-phase steam condensation model in nuclear containment applications

Steam condensation in the presence of air is a vital heat transfer process in postulated loss of coolant accidents. To numerically evaluate local and global thermal hydraulic properties, several single-phase models have been developed in previous studies. However, potential mutual interactions between the liquid and gas phase (e.g. evaporation, radioactive material retention, etc.) impose requirements on two-phase models. Accordingly, the present work performed CFD evaluations on a two-phase boundary layer model (TPBL) which concerned the gas phase, liquid phase and their mutual interactions. Assessments were performed by comparing calculated results with the COPAIN and TOSQAN experimental data. The COPAIN cases show that predicted local and average heat fluxes are generally within 25% and 15% deviation, respectively. Detailed properties were obtained on the formation, distribution, and thermal resistance of liquid film as well as the model computational costs. In the TOSQAN cases, two steady states, including steam-air mixtures and steam-air-helium mixtures were considered. Via these cases, the applicability of the TPBL model in predicting local field profiles like velocity, temperature and concentration distribution was discussed. Results demonstrate that the calculated results overall agree well with the experimental ones. In general, the TPBL model is feasible in postulated accident analysis.

Phase Equilibrium and Critical Phenomena in the n-Pentan–Water and n-Hexane–Water Systems at High Temperatures and Pressures

PVTx-properties of the H2O – n-C5H12 and H2O – n-C6H14 mixtures are measured in the temperature range 303-680 K at pressures up to 60 MPa. The measurements were carried out along 265 liquid and vapor isochors in a density range of 63-713 kg/m3. The measurements were performed for 15 concentrations between 0.110 and 0.987 mole fractions of H2O for the C5H12 mixtures and for 11 concentrations between 0.166 and 0.977 mole fractions of H2O for the C6H14 mixtures. The temperatures and pressures on the three-phase and two-phase boundary curves were obtained for the mixtures from isochors using the kink or inflection method. The data for the critical parameters of the upper and lower branches of the critical curves were obtained from the boundary curves by the method of rectilinear diameter. The measured three-phase data were used to estimate the value of the upper final critical point.

Quantitative Analysis of Microstructures and Reaction Interfaces on Composite Cathodes in All-Solid-State Batteries Using a Three-Dimensional Reconstruction Technique.

The composite cathode of an all-solid-state battery composed of various solid-state components requires a dense microstructure and a highly percolated solid-state interface different from that of a conventional liquid-electrolyte-based Li-ion battery. Indeed, the preparation of such a system is particularly challenging. In this study, quantitative analyses of composite cathodes by three-dimensional reconstruction analysis were performed beyond the existing qualitative analysis, and their microstructures and reaction interfaces were successfully analyzed. Interestingly, various quantitative values of structure properties (such as the volume ratio, connectivity, tortuosity, and pore formation) associated with material optimization and process development were predicted, and they were found to result in limited electrochemical charge/discharge performances. We also verified that the effective two-phase boundaries were significantly suppressed to ∼23% of the total volume because of component dispersion and packing issues.

A new discrete monotonicity formula with application to a two-phase free boundary problem in dimension two

We continue the analysis of the two-phase free boundary problems initiated by ourselves, studying where we studied the linear growth of minimizers in a Bernoulli-type free boundary problem at the non-flat points and the related regularity of free boundary. There, among other things, we also defined the functionalwhere x0 is a free boundary point, i.e. and u is a minimizer of the functional for some bounded smooth domain and positive constants with . Here we show in discrete monotone at non-flat points x0, when N = 2 and p is sufficiently close to 2, and then establish the linear growth of u. A new feature of our approach is the anisotropic scaling argument discussed in Section 4.

Solutions to a two-dimensional, Neumann free boundary problem

ABSTRACTWe explore regularity properties of solutions to a two-phase elliptic free boundary problem near a Neumann fixed boundary in two dimensions. Consider a function u, which is harmonic where it is not zero and satisfies a gradient jump condition weakly along the free boundary. Our main result is that u is Lipschitz continuous up to the Neumann fixed boundary. We also present a numerical exploration of the way in which the free and fixed boundaries interact.