Kinetic boundary condition at a vapor-liquid interface

By molecular dynamics simulations, the boundary condition for the Boltzmann equation at a vapor-liquid interface is found to be the product of three one-dimensional Maxwellian distributions for the three velocity components of vapor molecules and a factor including a well-defined condensation coefficient. The Maxwellian distribution for the velocity component normal to the interface is characterized by the liquid temperature, as in a conventional model boundary condition, while those for the tangential components are prescribed by a different temperature, which is a linear function of energy flux across the interface. The condensation coefficient is found to be constant and equal to the evaporation coefficient determined by the liquid temperature only.     

Instability of a charged plane interface between two liquids with respect to the tangential discontinuity of a time-dependent velocity field

The differential equation that describes the evolution of perturbations of a charged plane boundary between immiscible liquids when the upper liquid moves relative to the lower one with a time-dependent velocity parallel to the boundary is the Hill equation. In this system, the interface can exhibit instabilities of three types at various values of physical parameters: the Kelvin-Helmholtz, Tonks-Frenkel, and parametric instability. When physical parameters have certain values, the interface that is unstable with respect to surface charge and the tangential discontinuity of the velocity field across the interface can be parametrically stabilized.     

Hydrodynamic boundary conditions: An emergent behavior of fluid–solid interactions

By using the Onsager principle of minimum energy dissipation, the hydrodynamic boundary conditions at the fluid–solid interface are shown to be the natural emergent behavior of microscopic interactions that lead to the interfacial tension and the tangential friction at the fluid–solid interface [T. Qian, C. Qiu, P. Sheng, J. Fluid Mech. 611 (2008) 333]. This is satisfying because the equations of motion, e.g., the Stokes equation, and the hydrodynamic boundary conditions can now be derived from a unified framework. The resulting continuum hydrodynamic formulation yields predictions for immiscible two-phase flows that are in quantitative agreement with molecular dynamic simulations. In particular, the classical problem of the moving contact line is resolved. We also show results on the moving contact line over chemically patterned surfaces which exhibit striking nanoscale characteristics as well as sub-quadratic dependence of the moving contact line dissipation on its average velocity.     

On the stability of a cylindrical jet moving in a material medium along an external electrostatic field

A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a jet of an ideal incompressible dielectric liquid moving in an ideal incompressible dielectric medium along an external uniform electrostatic field. A tangential discontinuity in the velocity field on the jet surface is shown to cause Kelvin-Helmholtz periodical instability at the interface and destabilize axisymmetric, flexural, and flexural-deformational waves. Both the flexural and flexural-deformational instabilities have a threshold and are observed not at an arbitrarily small velocity of the jet but starting from a certain finite value. It is shown that the instability of waves generated by the tangential discontinuity of the velocity field is periodic only formally (from the pure mathematical point of view). Actually, the jet disintegrates within the time of instability development, which is shorter than the half-cycle of the wave.     

Evaluation of interface wave velocity, reflection coefficients and interfacial stiffnesses of contacting surfaces

The phase velocity of the antisymmetric-mode interface wave as well as the longitudinal and shear wave reflection coefficients have been measured for contacting poly(methyl methacrylate) (PMMA) surfaces subjected to different contact pressures. It has been found that while the reflection coefficients decrease as the contact pressure is increased, the phase velocity of the interface wave increases from that of the Rayleigh wave toward that of the bulk shear wave. From these measurements, the normal and tangential interfacial stiffnesses of the contacting PMMA surfaces have been evaluated as functions of the contact pressure. As a result, the two independent procedures to evaluate the tangential stiffness, namely, from the interface wave velocity and from the shear wave reflection measurements, have yielded mutually consistent results. Furthermore, it has been found that the tangential/normal stiffness ratio and the shear/longitudinal reflection ratio of the contact interface are consistent with the predictions of an existing theoretical model for kissing bond interfaces.     

Effect of tangential electric field on the evolution of the Rayleigh-Taylor instability of a dielectric liquid film

The effect of surface ponderomotive forces produced by a uniform tangential electric field on the evolution of the Rayleigh-Taylor instability of an isothermal film of a homogeneous incompressible dielectric liquid coating the lower surface of a horizontal insulating plate is studied in the long-wavelength approximation for the hydrodynamic equations and a simplified system of electrostatics equations. The lower boundary of the liquid is the interface with a stationary gas. It is shown in the framework of the linear theory that during the disruption of the continuous film, ponderomotive forces induce the formation of liquid billows extended along the applied field lines.     

Induced electric current-based formulation in computations of low magnetic Reynolds number magnetohydrodynamic flows

We use the induced electric current as the main electromagnetic variable to compute low magnetic Reynolds number magnetohydrodynamic (MHD) flows. The equation for the induced electric current is derived by taking the curl of the induction equation and using Ampère’s law. Boundary conditions on the induced electric current are derived at the interface between the liquid and the thin conducting wall by considering the current loop closing in the wall and the adjacent liquid. These boundary conditions at the liquid–solid interface include the Robin boundary condition for the wall-normal component of the current and an additional equation for the wall potential to compute the tangential current component. The suggested formulation (denominated j-formulation) is applied to three common types of MHD wall-bounded flows by implementing the finite-difference technique: (i) high Hartmann number fully developed flows in a rectangular duct with conducting walls; (ii) quasi-two-dimensional duct flow in the entry into a magnet; and (iii) flow past a magnetic obstacle. Comparisons have been performed against the traditional formulation based on the induced magnetic field (B-formulation), demonstrating very good agreement.     

On derivation of the analytical expression for damping ratios in a low-viscosity approximation

The damping ratios of waves and oscillations in nonlinear dispersion equations are found for planar, cylindrical, and spherical geometries as applied to finite-volume liquids. For a cylindrical jet and a plane interface between viscous liquids, the damping ratios are determined for the first time. When the radius of curvature of the liquid jet surface decreases, so does the damping ratio of capillary waves. In a system of immiscible liquids, the damping ratio may be both larger and smaller than that for the pure liquid depending on the viscosity of the liquids and the ratio of their densities. This is because the damping ratio depends on the kinematic viscosities of pure liquids. The damping ratio is also estimated for waves arising at the liquidgas interface due to a tangential discontinuity of the velocity field.     

Liquid flow over a substrate structured by seeded nanoparticles

Recent experiments have demonstrated that nanoparticles which sparsely distributed over a solid substrate can substantially change the flow conditions at the solid surface in the presence of slip. Inspired by these observations, the flow past tiny particles seeded on a solid substrate is investigated theoretically in the framework of an interface formation model. It has been shown, that even a single seeded nanoparticle can reduce significantly the measurable tangential component of hydrodynamic velocity at the substrate and affect the amount of the observed apparent slippage of the liquid. The effect from the particle manifests in a form of a long relaxation tail defined by the characteristic time of the interface formation process. A comparison with experiments has demonstrated a good agreement between theoretically predicted and experimentally observed values of the relaxation tail length scale.     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

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.     

SPH方法气-液界面边界条件研究

针对界面附近粒子光滑函数截断和非物理穿透问题,提出一种气-液界面边界条件的处理方法.当界面附近支持域出现不同材料粒子,每步计算可在支持域设置虚粒子,按照密度分配方法给虚粒子物理量赋值,并对界面附近粒子引入气-液两相阻力.采用SPH方法和Level-Set方法,计算运动激波对气-液界面作用问题,两者计算结果一致,初步验证了气-液界面边界条件处理的适用性.用SPH方法分别计算超声速气流中的圆截面液柱绕流和下落问题,界面两侧粒子压力和法向速度连续,给出弓形激波、回流区和下游回流区等定性合理结果.表明本文方法可适度避免界面附近流体粒子光滑截断和粒子非物理穿透现象、界面附近流场数值振荡.     

Triple-decker: Interfacing atomistic–mesoscopic–continuum flow regimes

Multiscale flow phenomena in microfluidic and biomedical applications require the use of heterogeneous modeling approaches. In this paper we present a hybrid method based on coupling the Molecular Dynamics (MD) method, the Dissipative Particle Dynamics (DPD) method, and the incompressible Navier–Stokes (NS) equations. MD, DPD, and NS are formulated in separate subdomains and are coupled via an overlapping region by communicating state information at the subdomain boundaries. Imposition of boundary conditions in the MD and DPD systems involves particle insertion and deletion, specular wall reflection and body force terms. The latter includes a boundary pressure force in order to minimize near-boundary density fluctuations, and an adaptive shear force which enforces the tangential velocity component of boundary conditions. The triple-decker algorithm is verified for prototype flows, including simple and multi-layer fluids (Couette, Poiseuille, and lid-driven cavity), using highly accurate reference solutions. A zero-thickness interface is also possible if it is aligned with the flow streamlines.     

液态锂在铜的微通道中的流动行为

本文采用分子动力学方法模拟了液态锂在铜的微通道内的流动行为. 通过构建铜(111), (100)和(110)晶面的微通道内壁, 研究了液态锂在流固界面上的微观结构以及在铜微通道中的流动速度分布情况, 并探讨了微通道尺寸对液态锂流动行为的影响. 研究结果表明铜微通道内的液态锂在靠近铜固体壁附近区域呈有序的层状结构分布, 并受铜内壁晶面微观结构的影响. 铜(111)和(100)面内壁附近的液态锂有序层分布结构更明显. 外驱力作用下的液态锂在微通道内的流动速度呈抛物线分布, 流固界面和流动方向对液态锂的流动速度都会产生影响. 液态锂在铜(111)面内壁上流动的速度最大, 且出现了速度滑移; 在铜(110)面内壁上流动速度最小. 通过对不同尺寸的微通道内液态锂流动行为的研究, 发现流动速度的大小随着微通道尺寸的增加而增大, 且最大速度与微通道尺寸呈二次函数关系, 与有关理论计算结果符合得很好.     

On the Stability of the Surface of a Short Charged Jet Moving with Respect to an External Material Medium

The problem of the stability of capillary waves on the surface of a charged jet of an ideal incompressible electroconducting liquid, which moves with respect to a material dielectric medium, is considered. There is a tangential discontinuity of the velocity field on the interface between the media. Solutions to the problem in two idealized models have been compared, i.e., when the jet has a finite and infinite length. It has been shown that the instability increments and the wave numbers of the most unstable waves, computed in both models, are linearly related, and velocity of motion of the jet acts as a coefficient of proportionality.     

Numerical simulation of non-viscous liquid pinch-off using a coupled level set-boundary integral method

Simulations of the pinch-off of an inviscid fluid column are carried out based upon a potential flow model with capillary forces. The interface location and the time evolution of the free surface boundary condition are both approximated by means of level set techniques on a fixed domain. The interface velocity is obtained via a Galerkin boundary integral solution of the 3D axisymmetric Laplace equation. A short-time analytical solution of the Raleigh–Taylor instability in a liquid column is available, and this result is compared with our numerical experiments to validate the algorithm. The method is capable of handling pinch-off and after pinch-off events, and simulations showing the time evolution of the fluid tube are presented.     

Nonlinear dynamics of the interface between fluids at the suppression of Kelvin–Helmholtz instability by a tangential electric field

The nonlinear dynamics of the interface between ideal dielectric fluids in the presence of tangential discontinuity of the velocity at the interface and the stabilizing action of the horizontal electric field is examined. It is shown that the regime of motion of the interface where liquids move along the field lines occurs in the state of neutral equilibrium where electrostatic forces suppress Kelvin–Helmholtz instability. The equations of motion of the interface describing this regime can be reduced to an arbitrary number of ordinary differential equations describing the propagation and interaction of structurally stable solitary waves, viz. rational solitons. It is shown that weakly interacting solitary waves recover their shape and velocity after collision, whereas strongly interacting solitary waves can form a wave packet (breather).     

Diffusion-stress coupling in liquid phase during rapid solidification of binary mixtures

An analytical model has been developed to describe the diffusion-viscous stress coupling in the liquid phase during rapid solidification of binary mixtures. The model starts with a set of evolution equations for diffusion flux and viscous pressure tensor, based on extended irreversible thermodynamics. It has been demonstrated that the diffusion-stress coupling leads to non-Fickian diffusion effects in the liquid phase. With only diffusive dynamics, the model results in the nonlocal diffusion equations of parabolic type, which imply the transition to complete solute trapping only asymptotically at an infinite interface velocity. With the wavelike dynamics, the model leads to the nonlocal diffusion equations of hyperbolic type and describes the transition to complete solute trapping and diffusionless solidification at a finite interface velocity in accordance with experimental data and molecular dynamic simulation.     

Photoinduced Ordering Transition in Microdroplets of Liquid Crystals with Azo‐Dendrimer

Ordering transitions are observed in azo‐dendrimer‐dissolved nematic liquid crystal (NLC) droplets dispersed in a glycerol matrix. The dendrimer molecules are spontaneously attached at the interface between NLC and glycerol, so that the nematic directors orient perpendicular to the interface, in the radial configuration. Photoisomerization makes the directors be tangential to the interface, in a photoinduced ordering transition from radial to bipolar structure. Similar experiments are conducted both in cholesteric (Ch) and smectic‐A (SmA) LC droplets. Complicated photoinduced ordering transitions are also observed in Ch and SmA droplets, and the associated molecular orientation changes are discussed. Photoisomerizable azo‐dendrimer molecules provide a possible way to control orientation, even in microdroplet systems in which the interface cannot be treated by conventional surface agents.     

Boundary conditions in the vicinity of a dynamic contact line: experimental investigation of viscous drops sliding down an inclined plane

To probe the microscopic balance of forces close to a moving contact line, the boundary conditions around viscous drops sliding down an inclined plane are investigated. At first, the variation of the contact angle as a function of the scale of analysis is discussed. The dynamic contact angle is measured at a scale of 6 mum all around sliding drops for different volumes and speeds. We show that it depends only on the capillary number based on the local liquid velocity, measured by particle tracking. This velocity turns out to be normal to the contact line everywhere. It indirectly proves that, in comparison with the divergence involved in the normal direction, the viscous stress is not balanced by intermolecular forces in the direction tangential to the contact line, so that any motion in this last direction gets damped.