Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

<正>In this paper,an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface,where the surface tension is implemented.The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid,an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface,and an indicator function is introduced to update the fluid properties accurately.The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points,and then the surface tension is directly computed by using the normal vector and curvature of the interface.Two benchmark problems,including Laplace’s law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation.Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.     

Nanopore wall effect on surface tension of methane

Local pressure is known to be anisotropic across the interfaces separating fluids in equilibrium. Tangential pressure profiles show characteristic negative peaks as a result of surface tension forces parallel to the interface. Nearby attractive forces parallel to the interface are larger than the repulsive forces and, hence, constitute the surface tension. In this work, using molecular dynamics simulations of methane inside nano-scale pores, we show this surface tension behaviour could be significantly influenced by confinement effects. The layering structure, characterised by damped oscillations in local liquid density and tangential pressures, extends deep into the pore and can be a few nanometers thick. The surface tension is measured numerically using local pressures across the interface. Results show that the tension is smaller under confinement and becomes a variable in small pores, mainly controlled by the thickness of the liquid density layering (or liquid saturation) and the pore width. If the liquid saturation inside the pore is high enough, the vapour–liquid interface is not interfered by the pore wall and the surface tension remains the same as the bulk values. The results are important for understanding phase change and multi-phase transport phenomena in nanoporous materials.     

A front-tracking/ghost-fluid method for fluid interfaces in compressible flows

A front-tracking/ghost-fluid method is introduced for simulations of fluid interfaces in compressible flows. The new method captures fluid interfaces using explicit front-tracking and defines interface conditions with the ghost-fluid method. Several examples of multiphase flow simulations, including a shock–bubble interaction, the Richtmyer–Meshkov instability, the Rayleigh–Taylor instability, the collapse of an air bubble in water and the breakup of a water drop in air, using the Euler or the Navier–Stokes equations, are performed in order to demonstrate the accuracy and capability of the new method. The computational results are compared with experiments and earlier computational studies. The results show that the new method can simulate interface dynamics accurately, including the effect of surface tension. Results for compressible gas–water systems show that the new method can be used for simulations of fluid interface with large density differences.     

Simulation of phase equilibria and interfacial properties of binary mixtures on the liquid-vapour interface using lattice sums

Molecular dynamics simulations of Lennard-Jones binary mixtures were performed to obtain phase equilibria and thermodynamic properties for the liquid—vapour interface. The dispersion interactions were handled using the lattice sum method where the full interaction is obtained and there is no requirement for any long range correction to the properties. The application of the method using the Lorentz—Berthelot combining rule for unlike interactions is discussed. The coexisting densities, adsorption of molecules at the interface and surface tension are the main results of this work. Coexisting properties were compared with Gibbs ensemble Monte Carlo results and with those of the grand canonical Monte Carlo method combined with the histogram reweighting technique, and good agreement was found. The lattice sum method results were compared with those of the spherically truncated and shifted potential to analyse the truncation effect. The adsorption of molecules at the interface and surface tension increase with interaction.     

Thermodynamic and transport properties of simple fluids using lattice sums: bulk phases and liquid-vapour interface

Molecular dynamics simulations in the canonical ensemble have been performed to obtain the thermodynamic and transport properties of the Lennard-Jones fluid. The dispersion interactions were calculated using lattice sums. This method makes it possible to simulate the full potential avoiding the inclusion of the long range corrections (LRC) during or at the end of simulations. In the calculation of dynamic properties in bulk phases and thermodynamic quantities of inhomogeneous systems where the interface is physically present, in general the LRC cannot easily be included. By using the lattice sums method, the results are independent of the truncation of the potential. In the liquid-vapour interface simulations it is not necessary to make any pre-judgments about the form of the LRC formula to calculate coexisting properties such as the surface tension. The lattice sums method has been applied to evaluate how well the full interaction can be calculated in the liquid phase and in the liquid-vapour interface. In the liquid phase the pressure, configurational energy, diffusion coefficient and shear viscosity were obtained. The results of the thermodynamic properties are compared with those obtained using the spherically truncated and shifted (STS) potential with the LRC added at the end of simulations, and excellent agreement is found. The transport properties are calculated on different system sizes for a state near the triple point. The diffusion coefficient using the lattice sums method increases with the number of molecules, and the results are higher than those of the STS model truncated at 2.5σ (STS2.5). The shear viscosity does not show any system size dependence for systems with more than 256 molecules, and the lattice sums results are essentially the same as those for the STS2.5. In the liquid-vapour equilibria the coexisting densities and vapour pressures for the full potential agree well with those obtained using the Gibbs ensemble and the NPT + test particle methods. The surface tension using lattice sums and truncation of forces at 2.5σ agrees well with STS results using large system sizes and cutoff distances.     

Computations of multi-fluid flows

Full numerical simulations of three-dimensional flows of two or more immiscible fluids of different densities and viscosities separated by a sharp interface with finite surface tension are discussed. The method used is based on a finite difference approximation of the full Navier-Stokes equations and explicit tracking of the interface between the fluids. Preliminary simulations of the Rayleigh-Taylor instability and the motion of bubbles are shown.     

Comprehensive study of the vapour–liquid coexistence of the truncated and shifted Lennard–Jones fluid including planar and spherical interface properties

Vapour–liquid equilibria of the Lennard–Jones potential, truncated and shifted at 2.5σ, are studied using molecular dynamics simulations, an attractive option for studying inhomogeneous systems. Comprehensive simulation data are reported for three cases: no interface, a planar interface, and a spherical interface between the coexisting phases, covering a wide range of temperatures. Spherical droplets are also studied for a range of radii between 5 and 16σ. The size dependence of the surface tension, based on the Irving–Kirkwood pressure tensor, and other properties is quantified for spherical interfaces. All simulation results are correlated with a consistent set of empirical equations. A comparison with the results of other authors as well as with experimental data for noble gases and methane is also presented.     

Heterogeneous diffuse interfaces: A new mechanism for arrested coarsening in binary mixtures Heterogeneous diffuse interfaces

We discuss the dynamics of binary fluid mixtures in which surface tension density is allowed to become locally negative within the interface, while still preserving positivity of the overall surface tension (heterogeneous diffuse interface). Numerical simulations of two-dimensional Ginzburg-Landau phase field equations implementing such mechanism and including hydrodynamic motion, show evidence of dynamically arrested domain coarsening. Under specific conditions on the functional form of the surface tension density, dynamical arrest can be interpreted in terms of the collective dynamics of metastable, non-linear excitations of the density field, named compactons, as they are localized to finite-size regions of configuration space and strictly zero elsewhere. Aside from compactons, the heterogeneous diffuse interface scenario appears to provide a robust mechanism for the interpretation of many aspects of soft-glassy behaviour in binary fluid mixtures.     

Heterogeneous diffuse interfaces: a new mechanism for arrested coarsening in binary mixtures. Heterogeneous diffuse interfaces

We discuss the dynamics of binary fluid mixtures in which surface tension density is allowed to become locally negative within the interface, while still preserving positivity of the overall surface tension (heterogeneous diffuse interface). Numerical simulations of two-dimensional Ginzburg-Landau phase field equations implementing such mechanism and including hydrodynamic motion, show evidence of dynamically arrested domain coarsening. Under specific conditions on the functional form of the surface tension density, dynamical arrest can be interpreted in terms of the collective dynamics of metastable, non-linear excitations of the density field, named compactons, as they are localized to finite-size regions of configuration space and strictly zero elsewhere. Aside from compactons, the heterogeneous diffuse interface scenario appears to provide a robust mechanism for the interpretation of many aspects of soft-glassy behaviour in binary fluid mixtures.     

Surface tension of the restrictive primitive model for ionic liquids

Hybrid molecular dynamics and Monte Carlo simulations are performed to study the liquid-vapor interface of the restricted primitive model (RPM) of ionic fluids. We report for the first time simulation results of the surface tension associated to this interface. The RPM accurately predicts experimental surface tensions of ionic salts and good agreement with theoretical predictions that include the idea of ion association is found. The simulation results indicate that the structure of an ionic liquid-vapor interface is rather rough. This is reflected in the interfacial thickness, larger than that observed in simple fluids and water.     

Delayed coalescence of droplets with miscible liquids: Lubrication and phase field theories

Mixing of droplets with a body of different liquids shows an interesting behavior for small contact angles at solid substrate. The droplets interact with each other, a liquid exchange appears between the approaching drops owing to surface tension gradients at the droplets interface. But the drops remain separated for some seconds (up to minutes), until the merging into a single drop occurs (Langmuir 24, 6395 (2008)). We investigate this phenomenon using lubrication approximation and phase field approach. For both methods, 2D quantitative computer simulations for delayed fusion of perfectly miscible thin liquid films/droplets with low contact angles are reported.     

Novel surface tension isotherm for surfactants based on local density functional theory

In this Letter we report a new general method for calculating of surface tension isotherms in the presence of surfactants, based on a local density functional. We illustrate this method by deriving the interfacial tension isotherm for nonionic surfactants at an air-water or oil-water interface by using the self-consistent field theory of polymer brushes. We consider a particular case of local density functional to calculate explicitly how the interfacial tension and the surfactant adsorption depend on the surfactant bulk concentration. Experimental data for the surface tension and the surfactant adsorption isotherm for nonionic surfactants were interpreted with the help of the new isotherm. Very good agreement between the adsorption of n-dodecyl pentaoxyethylene glycol ether (C12E5) at an air-water interface, calculated from the surface tension isotherm and small-angle neutron-scattering is obtained.     

A molecular dynamics study of effective parameters on nano-droplet surface tension

The main purpose of this paper is to numerically study the effect of droplet radius, temperature, and surface wettability on droplet surface tension. Moreover, the validity of Young-Laplace equation (Y-L) for nano-droplet is examined. Simulations of droplet surrounded by its vapor and droplet on solid surface are carried out and the results are compared to each other in order to comprehend the role of surface wettability on droplet surface tension. The pair potential for the liquid-liquid and liquid-solid interaction is considered using Lennard-Jones model. Different numbers of atoms and surface wettabilities are employed to generate droplet of different radiuses. In addition, contact angle of droplet on solid surface is computed. Pressure tensor and density profile is locally calculated. Furthermore, liquid pressure is evaluated far from the interface using the virial theorem and gas pressure is obtained using an equation of state. In order to calculate the surface tension, two different approaches are employed; Young-Laplace equation and direct molecular dynamics (MD) simulation. The surface tension increases with increase in droplet radius and it is seen that the surface wettability does not directly influence the surface tension.     

Gas—liquid interfaces of room temperature ionic liquids

The structure of the gas-liquid surface of dimethylimidazolium chloride has been studied using atomistic simulation. We find that there is a region of enhanced density immediately below the interface in which the cations are oriented with their planes perpendicular to the surface and their dipoles in the surface plane. There is negligible segregation of cations and anions. The temperature dependence of the surface tension is predicted to be anomalously low or be reversed in sign. The vapour-liquid interfaces between mixtures of water and dimethylimidazolium chloride show similar regions of enhanced density and preferential orientation of the cations. Water molecules also show preferential orientation in the interface region and are preferentially adsorbed on the vapour side of the interface. The surface tension decreases with increase in the mole fraction of water.     

A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young–Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.     

A Volume of Fluid Based Method for Fluid Flows with Phase Change

This paper presents a numerical method directed towards the simulation of flows with mass transfer due to changes of phase. We use a volume of fluid (VOF) based interface tracking method in conjunction with a mass transfer model and a model for surface tension. The bulk fluids are viscous, conducting, and incompressible. A one-dimensional test problem is developed with the feature that a thin thermal layer propagates with the moving phase interface. This test problem isolates the ability of a method to accurately calculate the thermal layers responsible for driving the mass transfer in boiling flows. The numerical method is tested on this problem and then is used in simulations of horizontal film boiling.     

Simulations of MHD flows with moving interfaces

We report on the numerical simulation of a two-fluid magnetohydrodynamics problem arising in the industrial production of aluminium. The motion of the two non-miscible fluids is modeled through the incompressible Navier–Stokes equations coupled with the Maxwell equations. Stabilized finite elements techniques and an arbitrary Lagrangian–Eulerian formulation (for the motion of the interface separating the two fluids) are used in the numerical simulation. With a view to justifying our strategy, details on the numerical analysis of the problem, with a special emphasis on conservation and stability properties and on the surface tension discretization, as well as results on tests cases are provided. Examples of numerical simulations of the industrial case are eventually presented.     

Liquid-Vapor Interfaces and Surface Tension in a Mesoscopic Model of Fluid with Nonlocal Interactions

We analyze the problem of phase coexistence, surface tension and the interface patterns between liquid and vapour for the nonlocal free energy functional derived by Lebowitz, Mazel, and Presutti from a system of particles interacting through Kac potentials in the continuum. We study the sharp interface limit in d dimensions and characterize the shape of the interface profiles in the temperature region where a monotonicity property is valid. We further extend our analysis beyond this domain by performing numerical simulations.     

带自由面流体的多体耗散粒子动力学模拟

利用多体耗散粒子动力学(MDPD)方法对介观尺度下液滴动力学进行了模拟分析,探讨了MDPD系统中液气共存界面的形成,并对表面张力进行了模拟研究,研究结果表明,MDPD方法形成的液气共存界面满足Laplace定律,通过改变不同的粒子间保守力作用参数,获得了液滴在固体壁面上不同的接触角,并研究了保守力作用参数与接触角之间的变化规律,进一步模拟了液滴在复杂微通道内的流动,研究结果有助于解释带自由面流体在粗糙表面上的运动行为。