A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio

This paper reports a new numerical scheme of the lattice Boltzmann method for calculating liquid droplet behaviour on particle wetting surfaces typically for the system of liquid–gas of a large density ratio. The method combines the existing models of Inamuro et al. [T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198 (2004) 628–644] and Briant et al. [A.J. Briant, P. Papatzacos, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion in a liquid–gas system, Philos. Trans. Roy. Soc. London A 360 (2002) 485–495; A.J. Briant, A.J. Wagner, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: I. Liquid–gas systems. Phys. Rev. E 69 (2004) 031602; A.J. Briant, J.M. Yeomans, Lattice Boltzmann simulations of contact line motion: II. Binary fluids, Phys. Rev. E 69 (2004) 031603] and has developed novel treatment for partial wetting boundaries which involve droplets spreading on a hydrophobic surface combined with the surface of relative low contact angles and strips of relative high contact angles. The interaction between the fluid–fluid interface and the partial wetting wall has been typically considered. Applying the current method, the dynamics of liquid drops on uniform and heterogeneous wetting walls are simulated numerically. The results of the simulation agree well with those of theoretical prediction and show that the present LBM can be used as a reliable way to study fluidic control on heterogeneous surfaces and other wetting related subjects.     

液滴撞击圆柱内表面的数值研究

针对液滴撞击圆柱内表面的过程,利用基于相场的格子Boltzmann方法模拟液滴以不同初速度、从不同初始高度、撞击不同大小的圆柱内表面时液滴的形态变化,分析了液滴自身物性(如密度和黏性等)和圆柱内表面润湿性等因素对撞击现象的具体影响.研究发现:撞击韦伯数、密度比及动力黏性比、圆柱半径等对液滴撞击后沿圆柱内表面的铺展均有一定影响,较高的韦伯数下液滴可能会发生分裂;液滴初始高度对大密度比和动力黏性比的撞击影响较小;液滴反弹现象可能出现在接触角较大时;重力作用会抑制撞击后液滴的振荡.     

The wetting angle of very small and large drops

On the basis of Born-Green-Yvon integral equations for the density distribution functions, an approximate integral equation is established for the profile of the surface of the drop. Numerical solutions and analytical solutions for limiting cases are obtained for this profile. Equations relating the angle at the leading edge and in its vicinity to parameters characterizing the interaction forces between the molecules of the liquid and between those of the liquid and solid are derived for large and for very small drops on a horizontal solid surface. One concludes that there is a rapid spatial variation of shape near the leading edge, that for large drops the measured macroscopic wetting angle is reached at a distance of about 20 to 40 Å from the leading edge, and that for very small drops the wetting angle is weakly size dependent. A condition for drop stability is established, which if not satisfied, the liquid will spread over the surface of the solid.     

倾斜均质表面上等径水滴聚合过程的可视化实验

对倾斜均匀表面上等直径水滴的聚合过程及特性进行了可视化实验研究,获得了水滴直径和表面倾角等参数对液滴聚合过程中液滴液桥半径、接触角和接触线变化特性的影响,分析了水滴聚合对其运动的影响.实验结果表明:表面倾角越大,下滑的临界半径越小;液滴的直径越大,液滴聚合后越容易下滑;液滴聚合可以加快液滴的运动,使下滑临界半径减小.     

The Surface Wettability and Adhesion of Poly(Ester Urethane)s and Poly(Ether Urethane)s

In this study the wetting characteristics of untreated and plasma-treated polyurethane thin films were investigated. The degree of wettability was investigated by measuring the contact angle formed between a liquid drop and the solid surface. The work of adhesion, interfacial free energy, spreading coefficient, and Girifalco–Good's interaction parameter changed significantly for plasma-treated polyurethane films. Both complete and partial wetting were analyzed from the spreading coefficient of liquid drops on the solid substrate.     

The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review

A sessile drop is an isolated drop which has been deposited on a solid substrate where the wetted area is limited by the three-phase contact line and characterized by contact angle, contact radius and drop height. Although, wetting has been studied using contact angles of drops on solids for more than 200 years, the question remains unanswered: Is wetting of a rough and chemically heterogeneous surface controlled by the interactions within the solid/liquid contact area beneath the droplet or only at the three-phase contact line? After the publications of Pease in 1945, Extrand in 1997, 2003 and Gao and McCarthy in 2007 and 2009, it was proposed that advancing, receding contact angles, and contact angle hysteresis of rough and chemically heterogeneous surfaces are determined by interactions of the liquid and the solid at the three-phase contact line alone and the interfacial area within the contact perimeter is irrelevant. As a consequence of this statement, the well-known Wenzel (1934) and Cassie (1945) equations which were derived using the contact area approach are proposed to be invalid and should be abandoned. A hot debate started in the field of surface science after 2007, between the three-phase contact line and interfacial contact area approach defenders. This paper presents a review of the published articles on contact angles and summarizes the views of the both sides. After presenting a brief history of the contact angles and their measurement methods, we discussed the basic contact angle theory and applications of contact angles on the characterization of flat, rough and micropatterned superhydrophobic surfaces. The weak and strong sides of both three-phase contact line and contact area approaches were discussed in detail and some practical conclusions were drawn.     

Internal circulation in a drop in an acoustic field

An investigation of the internal flow field for a drop at the antinode of a standing wave has been carried out. The main difference from the solid sphere case is the inclusion of the shear stress and velocity continuity conditions at the liquid-gas interface. To the leading order of calculation, the internal flow field was found to be quite weak. Also, this order being fully time dependent has a zero mean flow. At the next higher order, steady internal flows are predicted and, as in the case of a solid sphere, there is a recirculating layer consisting of closed streamlines near the surface. In the case of a liquid drop, however, the behavior of this recirculating Stokes layer is quite interesting. It is predicted that the layer ceases to have recirculation when [formula: see text], where [symbol: see text] is the liquid viscosity, mu is the exterior gas-phase viscosity, and M is the dimensionless frequency parameter for the gas phase, defined by M = i omega a2 rho/mu, with a being the drop radius. Thorough experimental confirmation of this interesting new development needs to be conducted. Although it seems to agree with many experiments with levitated drops where no recirculating layer has been clearly observed, a new set of experiments for specifically testing this interesting development need to be carried out.     

Line tension and nanometer drop wettability on solid surfaces

The dimensional dependence of the angle of solid surface wetting by a small drop on the latter’s size R and radius of the wetting outline r is considered. Numerical values of specific linear energy γ?(r) and line tension σ _r (r) of the wetting outline are calculated for a nanometer tin drop-substrate surface-aluminum film system. It is shown that wetting angle θ(R,r) in the drop-substrate surface system increases as the wetting outline’s radius decreases.     

Lattice Boltzmann simulation of viscous-fluid flow and conjugate heat transfer in a rectangular cavity with a heated moving wall

In the present work, conjugate heat transfer in a rectangular cavity with a heated moving lid is investigated using the lattice Boltzmann method (LBM). The simulations are performed for incompressible flow, with Reynolds numbers ranging from 100 to 500, thermal diffusivity ratios ranging from 1 to 100, and Prandtl numbers ranging from 0.7 to 7. A uniform heat flux through the top of the lid is assumed. Results show that LBM is suitable for the study of heat transfer in conjugate problems. Effects of the Reynolds number, the Prandtl number and the thermal diffusivity ratio on hydrodynamic and thermal characteristics are investigated and discussed. The streamlines and temperature distribution in flow field, dimensionless temperature and Nusselt number along the hot wall are illustrated. The results indicate that increase of thermal diffusivity yields the removal of a higher quantity of energy from lid and its temperature decreases when increasing the Reynolds and the Prandtl numbers.     

Short-time dynamics of partial wetting

When a liquid drop contacts a wettable surface, the liquid spreads over the solid to minimize the total surface energy. The first moments of spreading tend to be rapid. For example, a millimeter-sized water droplet will wet an area having the same diameter as the drop within a millisecond. For perfectly wetting systems, this spreading is inertially dominated. Here we identify that even in the presence of a contact line, the initial wetting is dominated by inertia rather than viscosity. We find that the spreading radius follows a power-law scaling in time where the exponent depends on the equilibrium contact angle. We propose a model, consistent with the experimental results, in which the surface spreading is regulated by the generation of capillary waves.     

Equilibrium shape and stability of a charged drop in an air flow under an electric field

The pressure balance on the surface of a charged liquid drop moving along a uniform electrostatic field is analyzed. The liquid is assumed to be nonviscous and incompressible. In the approximation linear in deformation amplitude, the equilibrium shape of the drop as a function of the charge, field strength, and velocity of travel can be both a prolate and an oblate spheroid. Critical conditions for the surface instability of such a drop are obtained analytically in the form of a relationship between the charge, field strength, and velocity of travel. An instability criterion is found by extrapolating to large Reynolds numbers. This makes it possible to fit the earlier model of a corona-initiated lightning in the vicinity of large charged water drops or hailstones to the charges of the drops, field strengths, and velocities of travel (relative to the medium) typical of thunderclouds.     

Evaporation-coupled wetting of ZrO2 by molten Mg in Ar atmosphere

The wetting behaviors of molten Mg drops on polycrystalline ZrO₂ substrate surfaces were studied in a controlled Ar atmosphere at 948–1173 K using an improved sessile drop method. The ZrO₂ substrate is virtually not wetted by molten Mg at temperatures below 1173 K. The wetting and evaporation stages according to different variation behaviors of contact angle, contact diameter and drop height were identified. Six representative modes were proposed to describe the evaporation-coupled wetting behaviors during different stages. The competitions between surface oxidation, chemical reaction and drop evaporation were discussed to account for the mechanisms for various wetting behaviors at different temperatures. The chemical reaction leads to the formation of more wettable MgO phase at the interface; however, it yields only an inconspicuous improvement in the wetting due to enhanced Mg evaporation.     

Acoustics and hydrodynamics of a drop impact on a water surface

Hydrodynamic and acoustic processes associated with a drop impact on a water surface were studied experimentally. Acoustic signals were detected underwater (with a hydrophone) and in air (with a microphone), the flow pattern was recorded with a high-speed camera, and the surface perturbation was monitored with a laser detector. The dimensionless parameters of flows (Reynolds, Froude, and Weber numbers) induced by the impact varied with fall height within the ranges of 5000 < Re < 20000, 20 < Fr < 350, and 70 < We < 1000. The sequence of acoustic signals incorporated an impact pulse at the moment of contact between a drop and the surface and a series of acoustic packets attributable to the resonance emission of gas cavities. The top of the impact pulse, which was detected clearly in the entire fall height range, had a complex structure with short high-frequency and longer low-frequency oscillations. The total number and the parameters of emitted acoustic packets depended to a considerable extent on the fall height. The cases of lacking, one-time, and repeated emission of packets were noted in a series of experiments performed at a constant fall height. The analysis of video data showed that the signal variability was induced by considerable differences in the scenarios of water entry of a drop, which assumed an ovoid shape at the end trajectory segment, in the mentioned experiments.     

声悬浮液滴的表面毛细波及八阶扇谐振荡

采用声悬浮方法研究了自由液滴表面的毛细波形成机理,并利用主动调制声场技术激发了液滴的八阶扇谐振荡.实验结果表明,当声场调制频率接近液滴本征频率的两倍时,液滴将由轴对称受迫振荡向非轴对称扇谐振荡模态转变.实验与理论分析证实,参数共振是毛细波与扇谐振荡的形成原因.扇谐振荡的本征频率随液滴赤道半径的增大而减小,可通过修正的Rayleigh方程来描述. 关键词： 声悬浮 液滴 毛细波 扇谐振荡     

A mesoscopic model for (de)wetting

We present a mesoscopic model for simulating the dynamics of a non-volatile liquid on a solid substrate. The wetting properties of the solid can be tuned from complete wetting to total non-wetting. This model opens the way to study the dynamics of drops and liquid thin films at mesoscopic length scales of the order of the nanometer. As particular applications, we analyze the kinetics of spreading of a liquid drop wetting a solid substrate and the dewetting of a liquid film on a hydrophobic substrate. In all these cases, very good agreement is found between simulations and theoretical predictions.     

Supersonic Turbulent Boundary Layer： DNS and RANS

We assess the performance of a few turbulence models for Reynolds averaged Navier-Stokes （RANS） simulation of supersonic boundary layers, compared to the direct numerical simulations （DNS） of supersonic flat-plate turbulent boundary layers, carried out by Gao et al. [Chin. Phys. Lett. 22（2005）1709] and Huang et al. [Sci. Chin. 48 （2005） 614], as well as some available experimental data. The assessment is made for two test cases, with incoming Mach numbers and Reynolds numbers M = 2.25, Re = 365, 000//in, and M = 4.5, Re = 1.7 × 10^7/m, respectively. It is found that in the first case the prediction of RANS models agrees well with the DNS and the experimental data, while for the second case the agreement of the DNS models with experiment is less satisfactory. The compressibility effect on the RANS models is discussed.     

倾斜均质表面上非等径液滴的聚合特性

对倾斜均匀表面上非等径液滴的聚合过程及特性进行了可视化实验研究,获得了液滴半径和表面倾角等参数对液滴聚合过程中液滴液桥半径、接触角和接触线变化特性的影响规律,进一步说明了倾斜表面上液滴聚合可以加快液滴的运动.     

Threshold criterion for wetting at the triple point

Grand canonical simulations are used to calculate adsorption isotherms of various classical gases on alkali metal and Mg surfaces. Ab initio adsorption potentials and Lennard-Jones gas-gas interactions are used. Depending on the system, the resulting behavior can be nonwetting for all temperatures studied, complete wetting, or (in the intermediate case) exhibit a wetting transition. An unusual variety of wetting transitions at the triple point is found in the case of a specific adsorption potential of intermediate strength. The general threshold for wetting near the triple point is found to be close to that predicted with a heuristic model of Cheng et al. This same conclusion was drawn in a recent experimental and simulation study of Ar on CO2 by Mistura et al. These results imply that a dimensionless wetting parameter w is useful for predicting whether wetting behavior is present at and above the triple temperature. The nonwetting/wetting crossover value found here is w approximately 3.3.     

Phase field modeling of liquid jets in low gravity

An axisymmetric phase field model is developed and used to model surface tension forces on liquid jets in microgravity. The previous work in this area is reviewed and a baseline drop tower experiment selected for model comparison. The model is solved numerically with a compact fourth order stencil on an equally spaced axisymmetric grid. After grid convergence studies, a grid is selected and all drop tower tests modeled. Agreement was assessed by comparing predicted and measured free surface rise. Trend wise agreement is good but agreement in magnitude is only fair. Suspected sources of disagreement are the simple turbulence model and the existence of slosh baffles in the experiment that were not included in the model. Parametric investigation was conducted to study the influence of key parameters on the geysers formed by jets in microgravity. Investigation of the contact angle showed the expected trend of increasing contact angle increasing geyser height. Investigation of the tank radius showed some interesting effects and demonstrated the zone of free surface deformation is quite large. Variation of the surface tension with a laminar jet showed clearly the evolution of free surface shape with Weber number. A breakthrough Weber number of 1 was predicted by the variation of the surface tension model which is close to the experimentally measured Weber number of 1.5 found in prior experimental work.