利用高速摄影仪记录了不同液滴撞击固体表面的形态变化过程,并探讨了液滴撞击参数对撞击过程液滴形态的影响.结果表明:液滴黏度对液滴铺展过程起着决定性作用,液滴表面张力对液滴铺展后的回缩起到主导作用,两者的共同作用决定着液滴的震荡特性;撞击速度的提高会增大液滴的最大铺展因子,但达到最大铺展的时间因表面张力的不同呈现不同变化规律.

利用高速摄影仪记录了不同液滴撞击固体表面的形态变化过程,并探讨了液滴撞击参数对撞击过程液滴形态的影响.结果表明:液滴黏度对液滴铺展过程起着决定性作用,液滴表面张力对液滴铺展后的回缩起到主导作用,两者的共同作用决定着液滴的震荡特性;撞击速度的提高会增大液滴的最大铺展因子,但达到最大铺展的时间因表面张力的不同呈现不同变化规律.

液滴撞击固体壁面是一种常见的自然现象和工业过程,在这些现象和过程中液滴运动往往受到壁面可湿润性的影响.本文提出了一种可湿润性固壁边界条件的计算方法,即假设壁面粒子的亲水性以及毛细吸附作用统一表现为对支持域内流体粒子的吸附力.吸附力的大小与流体压强、材料饱和度及亲水性有关.基于光滑粒子流体动力学(SPH)方法,模拟了静态液滴在不同可湿润性壁面上由变形至稳定的过程.考虑壁面可湿润性的影响,模拟了液滴撞击疏水壁面的过程.结合试验数据,分析了壁面可湿润性对液滴运动过程的影响.研究表明:根据模拟液滴静态接触角的变化特点,本文可湿润性固壁边界条件可以较好地反映出壁面可湿润性;液滴撞击输水表面的模拟数据与试验结果趋势上吻合良好,液滴回弹时在壁面可湿润性的影响下形成液柱;壁面可湿润性对撞击后液滴的铺展过程影响很小,在该阶段壁面摩擦力起主要作用,回缩和回弹阶段壁面可湿润性对液滴运动特征的影响较明显.

液滴撞击固体壁面是一种常见的自然现象和工业过程,在这些现象和过程中液滴运动往往受到壁面可湿润性的影响.本文提出了一种可湿润性固壁边界条件的计算方法,即假设壁面粒子的亲水性以及毛细吸附作用统一表现为对支持域内流体粒子的吸附力.吸附力的大小与流体压强、材料饱和度及亲水性有关.基于光滑粒子流体动力学(SPH)方法,模拟了静态液滴在不同可湿润性壁面上由变形至稳定的过程.考虑壁面可湿润性的影响,模拟了液滴撞击疏水壁面的过程.结合试验数据,分析了壁面可湿润性对液滴运动过程的影响.研究表明:根据模拟液滴静态接触角的变化特点,本文可湿润性固壁边界条件可以较好地反映出壁面可湿润性;液滴撞击输水表面的模拟数据与试验结果趋势上吻合良好,液滴回弹时在壁面可湿润性的影响下形成液柱;壁面可湿润性对撞击后液滴的铺展过程影响很小,在该阶段壁面摩擦力起主要作用,回缩和回弹阶段壁面可湿润性对液滴运动特征的影响较明显.

液滴在固体表面上的铺展行为与润湿特性对许多工业生产过程的研究具有重要意义.根据液滴在光滑表面上的受力情况,建立了液滴平壁铺展的动力学模型.应用润滑近似方法和二维Navier-Stokes方程,建立了液滴沿理想表面铺展的动量和连续性方程.根据建立的方程,应用数值解法求解并详细分析了液滴在铺展过程中膜厚、接触线铺展半径以及铺展速度随时间的变化关系.研究结果表明：液滴的铺展过程可分为扩展和收缩两个阶段,铺展过程伴随着表面能、动能以及各种势能的相互转化,液滴最终的铺展半径大小由固体基面固有的润湿特性所决定;液滴在铺展过程中出现的＂坍塌效应＂与弯曲液面处的Laplace压力差有关;铺展半径随时间变化的标定律近似满足＂1/7＂次方标度律.

液滴在固体表面上的铺展行为与润湿特性对许多工业生产过程的研究具有重要意义.根据液滴在光滑表面上的受力情况,建立了液滴平壁铺展的动力学模型.应用润滑近似方法和二维Navier-Stokes方程,建立了液滴沿理想表面铺展的动量和连续性方程.根据建立的方程,应用数值解法求解并详细分析了液滴在铺展过程中膜厚、接触线铺展半径以及铺展速度随时间的变化关系.研究结果表明：液滴的铺展过程可分为扩展和收缩两个阶段,铺展过程伴随着表面能、动能以及各种势能的相互转化,液滴最终的铺展半径大小由固体基面固有的润湿特性所决定;液滴在铺展过程中出现的＂坍塌效应＂与弯曲液面处的Laplace压力差有关;铺展半径随时间变化的标定律近似满足＂1/7＂次方标度律.

<p>通过建立液滴撞击固体平壁的静态铺展力学平衡的数学模型，从理论上得到了静态铺展半径与液滴物性参数、以及液滴与固体壁面接触角之间关系的数学表达式，将理论结果与数值模拟的结果进行了比较，两者吻合较好.比较了不同条件下液滴的静态铺展半径的变化规律，分别得到了液滴密度、体积、表面张力和接触角等因素对液滴静态铺展半径的影响规律.</p>

<p>通过建立液滴撞击固体平壁的静态铺展力学平衡的数学模型，从理论上得到了静态铺展半径与液滴物性参数、以及液滴与固体壁面接触角之间关系的数学表达式，将理论结果与数值模拟的结果进行了比较，两者吻合较好.比较了不同条件下液滴的静态铺展半径的变化规律，分别得到了液滴密度、体积、表面张力和接触角等因素对液滴静态铺展半径的影响规律.</p>

Drop impact onto surfaces has long been a popular and important subject of experimental, numerical and theoretical studies to explain phenomena observed both in nature and in many engineering applications. Progress in understanding and describing the hydrodynamics involved in drop impacts has been rapid in recent years, due partly to the availability of high-speed cameras, but also because of accompanying advances in theoretical and numerical approaches. Thus, for simple surfaces, i.e. smooth surfaces of uniform chemistry, the outcome of a drop impact can be well predicted over a large range of impact parameters, including quantitative values of spread dynamics and splash characteristics. This article comprehensively reviews the present level of understanding for such impact situations.However many practical applications involve impacts onto surfaces of higher complexity, either morphologically or chemically, involving textured or porous surfaces or surfaces with non-uniform wettability characteristics. This expands greatly the parameter space for which descriptions of the impact must be found and the present understanding is significantly more rudimentary compared to drop impacts onto simple surfaces. In this review such impacts are discussed by considering effects introduced by morphological changes to the surface and by changes of the wettability. Comparisons to corresponding impacts onto simple surfaces are drawn to underline the additional physical mechanisms that must be considered.Graphical abstractDrop impact is a fascinating and intricate phenomenon, which is even more difficult if it happens onto complex surfaces. Year 2009: more than 600 papers have been dedicated to this topic. The present paper is trying to individuate some conclusions, addressing the most important results and forecasting future research directions.

In this work, new results of droplet impingement and breakup have been obtained using three-dimensional lattice Boltzmann method. All four phases after impingement, the kinematic, spreading, relaxation and equilibrium phases, leading to breakup have been obtained for a range of Weber number, Reynolds number and density ratio. Conditions have been chosen such that Re We for comparison with available data in the literature. The maximum spread factor compares well with experiments as well as the theoretical value of 0.5 Re 0.25. At Oh < 0.15 and Capillary number, Ca < 1.0, the relaxation phase is marked by the presence of strong oscillations in the spreading diameter. An analytical solution for breakup based on the conservation of energy is provided. Criteria for three-dimensional droplet breakup have been developed as functions of Re and We.

<p>壁面液体层的存在对液滴撞击壁面的运动具有重要的影响。采用气液两相流动相界面追踪的水平集和流体体积复合方法和壁面润湿模型，实现了液滴撞击湿润壁面运动的数值求解；在此基础上，开展了液滴撞击湿润壁面运动的研究。研究结果表明：液滴以不同速度撞击湿润壁面时，会呈现出黏附铺展、波动运动、皇冠几何体运动以及飞溅运动等几种不同的运动形态，液滴撞击湿润壁面后的压力分布是不同运动形态形成的主要原因；飞溅运动是一定条件下皇冠几何体运动的一种特殊形态，液滴从皇冠几何体侧壁顶端的飞溅分离满足毛细破碎理论；撞击速度对分离液滴的运动方向影响较小，而对壁面液体层厚度的影响则较大；撞击速度和壁面液体层厚度对分离液滴形态、飞溅分离位置、飞溅速度以及飞溅发生时刻等都具有一定的影响。</p>

<p>壁面液体层的存在对液滴撞击壁面的运动具有重要的影响。采用气液两相流动相界面追踪的水平集和流体体积复合方法和壁面润湿模型，实现了液滴撞击湿润壁面运动的数值求解；在此基础上，开展了液滴撞击湿润壁面运动的研究。研究结果表明：液滴以不同速度撞击湿润壁面时，会呈现出黏附铺展、波动运动、皇冠几何体运动以及飞溅运动等几种不同的运动形态，液滴撞击湿润壁面后的压力分布是不同运动形态形成的主要原因；飞溅运动是一定条件下皇冠几何体运动的一种特殊形态，液滴从皇冠几何体侧壁顶端的飞溅分离满足毛细破碎理论；撞击速度对分离液滴的运动方向影响较小，而对壁面液体层厚度的影响则较大；撞击速度和壁面液体层厚度对分离液滴形态、飞溅分离位置、飞溅速度以及飞溅发生时刻等都具有一定的影响。</p>

A drop hitting a solid surface, can deposit, bounce or splash. Splashing arises from the breakup of a fine liquid sheet which is ejected radially along the substrate. Bouncing and deposition depend crucially on the wetting properties of the substrate. In this review we focus on recent experimental and theoretical studies, which aim at unraveling the underlying physics, characterized by the delicate interplay of not only liquid inertia, viscosity and surface tension, but also the surrounding gas. The gas cushions the initial contact, it is entrapped into a central microbubble on the substrate and it promotes the so-called corona-splash, by lifting the lamella away from the solid. Particular attention is paid to the influence of surface roughness, natural or engineered to enhance repellency, relevant in many applications. 1 Figure 1 (a) Worthington's drop-release setup and (b) his sketches of an impacting mercury drop. (c) Using modern video technology for mercury on glass under similar impact conditions. (d) Prompt splash for mercury drop impacting superhydrophobized glass and (e) corona splash for ethanol drop on glass (courtesy of Erqiang Li). See also supplemental video clips.

Technologies including (3D-) (bio-)printing, diesel engines, laser-induced forward transfer, and spray cleaning require optimization and therefore understanding of micrometer-sized droplets impacting at velocities beyond 10 m s 1. However, as yet, this regime has hardly been addressed. Here we present the first time-resolved experimental investigation of microdroplet impact at velocities up toV0= 50 m s 1, on hydrophilic and -phobic surfaces at frame rates exceeding 107frames per second. A novel method to determine the 3D-droplet profile at sub-micron resolution at the same frame rates is presented, using the fringe pattern observed from a bottom view. A numerical model, which is validated by the side- and bottom-view measurements, is employed to study the viscous boundary layer inside the droplet and the development of the rim. The spreading dynamics, the maximal spreading diameter, the boundary layer thickness, the rim formation, and the air bubble entrainment are compared to theory and previous experiments. In general, the impact dynamics are equal to millimeter-sized droplet impact for equal Reynolds-, Weber- and Stokes numbers (Re, We, and St, respectively). Using our numerical model, effective scaling laws for the progression of the boundary layer thickness and the rim diameter are provided. The dimensionless boundary layer thickness develops in time (t) according to, and the diameter of the rim develops as, with drop diameterD0and inertial time scale =D0/V0. These scalings differ from previously assumed, but never validated, values. Finally, no splash is observed, at variance with many predictions but in agreement with models including the influence of the surrounding gas. This confirms that the ambient gas properties are key ingredients for splash threshold predictions.

We study the impact and subsequent retraction dynamics of liquid droplets upon high-speed impact on hydrophobic surfaces. Performing extensive experiments, we show that the drop retraction rate is a material constant and does not depend on the impact velocity. We show that when increasing the Ohnesorge number, $\Oh=\eta/\sqrt{\rho R_{\rm I} \gamma}$, the retraction, i.e. dewetting, dynamics crosses over from a capillaro-inertial regime to a capillaro-viscous regime. We rationalize the experimental observations by a simple but robust semi-quantitative model for the solid-liquid contact line dynamics inspired by the standard theories for thin film dewetting.

A mathematical representation has been developed and computed results are presented describing the spreading of droplets impacting onto a solid substrate. Problems of this type are of major practical interest in plasma spraying (PS) and in spray forming (SF) operations. While the present study was confined to the fluid flow aspects of the process, information has been generated on both the final splat dimensions and on the time required to complete the spreading process. Through this treatment, it is possible to relate these quantities (the splat size and the spreading time) to the operating conditions, i.e. , droplet size and droplet velocity, and material properties. The theoretical predictions were found to be in good agreement with both Madejski asymptotic solution [17] and with available experimental results. For typical SF conditions (droplet sizes in the 100-碌m range and droplet velocities in the 100 m/s range), the spreading times were of the order of microseconds, i.e. , significantly shorter than the estimated solidification time.

We study the impact of a fluid drop onto a planar solid surface at high speed so that at impact, kinetic energy dominates over surface energy and inertia dominates over viscous effects. As the drop spreads, it deforms into a thin film, whose thickness is limited by the growth of a viscous boundary layer near the solid wall. Owing to surface tension, the edge of the film retracts relative to the flow in the film and fluid collects into a toroidal rim bounding the film. Using mass and momentum conservation, we construct a model for the radius of the deposit as a function of time. At each stage, we perform detailed comparisons between theory and numerical simulations of the Navier tokes equation.

We first study the impact of a liquid drop of low viscosity on a super-hydrophobic surface. Denoting the drop size and speed as D_{0} and U_{0}, we find that the maximal spreading D_{scriptsizemax} scales as D_{0}We(1/4) where We is the Weber number associated with the shock (We {equiv} rho U_{0}(2) D_{0}/sigma, where rho and sigma are the liquid density and surface tension). This law is also observed to hold on partially wettable surfaces, provided that liquids of low viscosity (such as water) are used. The law is interpreted as resulting from the effective acceleration experienced by the drop during its impact. Viscous drops are also analysed, allowing us to propose a criterion for predicting if the spreading is limited by capillarity, or by viscosity.

The dynamics of water drop impact at high impinging velocity onto superhydrophobic substrates is experimentally investigated. The solid substrate—comprised of regular and hydrophobic micropillars—is transparent, thereby facilitating close-up, top-or-bottom-view, high-speed imaging. With a sufficient impact velocity, instead of a completely-bouncing “Fakir” droplet, wetting splashing can occur, with an entrapped air bubble at the centre surrounded by a wetted area as well as an emission of satellite droplets during the advancing phase of spreading lamella. A large portion of the lamella travels upon air and subsequently recoils due to surface tension, forming a partial rebound on the central wet spot. We present and discuss quantitative results of the entrapped air bubble, the central wetted area, and the maximal spreading lamella as the impact velocity is increased. We further vary the lattice periodicity of the micro-patterns and find its profound influence on the macroscopic flow. More specifically, directional splashing can emerge, emitting secondary droplets in certain directions which are associated with the lattice. Directional splashing can be suppressed to a gentle spreading by decreasing the periodicity of the lattice and, furthermore, can be tuned to a completely-wetting splashing in the diagonal directions of the lattice by a larger periodicity, offering opportunities to control the wetting process. Finally, the elimination of directional splashing by reducing air pressure suggests that the underlying air is squeezed outwards by the falling droplet upon the solid boundary whereby the air flow is affected, leading to different splashing behavior.

Impact of water droplets on a flat, solid surface was studied using both experiments and numerical simulation. Liquid-solid contact angle was varied in experiments by adding traces of a surfactant to water. Impacting droplets were photographed and liquid-solid contact diameters and contact angles were measured from photographs. A numerical solution of the Navier-Stokes equation using a modified SOLA-VOF method was used to model droplet deformation. Measured values of dynamic contact angles were used as a boundary condition for the numerical model. Impacting droplets spread on the surface until liquid surface tension and viscosity overcame inertial forces, after which they recoiled off the surface. Adding a surfactant did not affect droplet shape during the initial stages of impact, but did increase maximum spread diameter and reduce recoil height. Comparison of computer generated images of impacting droplets with photographs showed that the numerical model modeled droplet shape evolution correctly. Accurate predictions were obtained for droplet contact diameter during spreading and at equilibrium. The model overpredicted droplet contact diameters during recoil. Assuming that dynamic surface tension of surfactant solutions is constant, equaling that of pure water, gave predicted droplet shapes that best agreed with experimental observations. When the contact angle was assumed constant in the model, equal to the measured equilibrium value, predictions were less accurate. A simple analytical model was developed to predict maximum droplet diameter after impact. Model predictions agreed well with experimental measurements reported in the literature. Capillary effects were shown to be negligible during droplet impact when We much greater than Rel(1/2). (C) 1996 American Institute of Physics.

In industrial applications involving spray-cooling, combustion, and so on, prediction of the maximum spreading diameter of a droplet impinging on a solid surface permits a quantitative estimation of heat removal and energy consumption. However, although there are many experimental studies regarding droplet impingement behaviour, theoretical models have an applicability limit for predicting the maximum spreading diameter. In the present study, we have developed an analytical model for droplet impingement based on energy conservation that considers adhesion energy in both horizontal and vertical directions at the contact line. The theory is validated by our experiment and existing experimental data possessing a wide range of Weber numbers. We demonstrate that our model can predict尾m(i.e., the maximum spreading diameter normalised in terms of initial droplet diameter) for various Newtonian liquids ranging from micro- to millimetre-sized droplets on different solid surfaces and can determine the transition between capillary and viscous regimes. Furthermore, theoretical relations for scaling laws observed by many researchers are derived.

Abstract The spread and rebound of droplets upon impact on flat surfaces at room temperature were studied over a wide range of impact velocities (0.5–6 m/s), viscosities (1–100 mPa.s), static contact angles (30–120°), droplet sizes (1.5–3.5 mm), and surface roughnesses using a fast-shutter-speed CCD camera. The maximum spread of a droplet upon impact depended strongly on the liquid viscosity and the impact velocity. The tendency of a droplet to deposit or to rebound is determined primarily by the liquid viscosity and the liquid/substrate static contact angle. A model more broadly applicable than existing models was developed to predict maximum spread as a function of the Reynolds number, the Weber number, and the static contact angle. Based on the conservation of energy, a rebound model is proposed that predicts the tendency to rebound as a function of maximum spread and static contact angle. The maximum-spread model prediction agrees to within 10% with more than 90% of the experimental data from different sources. In the current study, the rebound model successfully predicts the tendency of a droplet to rebound.

Finite-amplitude, axially symmetric oscillations of small (0.2 mm) liquid droplets in a gaseous environment are studied, both experimentally and theoretically. When the amplitude of natural oscillations of the fundamental mode exceeds approximately 10% of the droplet radius, typical nonlinear effects like the dependence of the oscillation frequency on the amplitude, the asymmetry of the oscillation amplitude, and the interaction between modes are observed. As the amplitude decreases due to viscous damping, the oscillation frequency and the amplitude decay factor reach their asymptotical values predicted by linear theory. The initial behaviour of the droplet is described quite satisfactorily by a proposed nonlinear inviscid theoretical model.

Bubbles stabilised by colloidal particles can find applications in advanced materials, catalysis and drug delivery. For applications in controlled release, it is desirable to remove the particles from the interface in a programmable fashion. We have previously shown that ultrasound waves excite volumetric os Soft Matter Emerging Investigators 2017

This paper deals with air bubbles rising in purified water in the range of equivalent diameters where surface oscillations appear on the interface. The shape of the bubbles including these capillary distortions is recorded by taking a large number of high speed pictures for each spiraling or zigzagging bubble trajectory. In analogy with surface harmonics, the oscillations are indicated as (2,0) axisymmetric and with wavelength equal to the distance from pole to pole and (2,2) nonaxisymmetric and with wavelength equal to one-half of the length of the equator. In the second series of experiments, the phenomena in the wakes of rising bubbles are made visible by using Schlieren optics, which are applicable because a temperature gradient is applied to the water. The frequencies of vortex shedding correspond to the (2,0) mode of surface oscillation, whereas in other works reported in the literature, they correspond to twice the frequency of the spiraling or zigzagging bubble paths. By measurements and by analysis, it is shown here that the latter is due to contamination of surfactants.

Microbubbles – gas bubbles of diameter less than 1mm – became currently of considerable importance for chemical and process engineering applications, mainly because of the recent discovery of an energetically efficient method of their generation with a fluidic oscillator in the gas supply into an aerator. The oscillation should be applied at the microbubble resonant conditions, about which there has been so far known very little. The key problem is the unknown and difficult to evaluate extent of the surrounding liquid that takes part in the microbubble oscillatory motions and represents the inertia term in the governing equation. The oscillation of microbubbles also influences their ascent, which is slow and puts them often into mutual proximity causing their conjunctions. Author evaluated basic data on oscillating microbubbles from high-speed camera frames and used them to setup a simple model, suitable for engineering design purposes.

The objective of this work is to determine the effect of the rising motion on the dynamics of inertial shape oscillations of drops and bubbles. We have carried out axisymmetric direct numerical simulations of an ascending drop (or bubble) using a level-set method. The drop is initially elongated in the vertical direction and therefore performs shape oscillations. The analysis is based on the decomposition of the interface into spherical harmonics, the time evolutions of which are processed to obtain the frequency and the damping rate of the oscillations. As the drop accelerates, its shape flattens and oscillations no longer take place around a spherical equilibrium shape. This causes the eigenmode of oscillations to change, which results in the appearance of spherical harmonics of high order that all oscillate at the same frequency. For both drops and bubbles, the frequency, which remains controlled by the potential flow, slightly decreases with the rising velocity. The damping rate of drops, which is controlled by the dissipation within boundary layers at the interface, strongly increases with the rising velocity. At terminal velocity, the damping rate of bubbles, which results from the dissipation by the potential flow associated with the oscillating motion, remains close to that of a non-rising bubble. During the transient, the rate of deformation of the equilibrium shape of bubbles can be comparable to the oscillation frequency, which causes complex evolutions of the shape. These results extend the description of shape oscillations to common situations where gravity plays a role. In particular, the present conclusions are useful to interpret experimental results where the effect of the rising motion is often combined with that of surfactant.

An inviscid spherical liquid drop held by surface tension exhibits linear oscillations of a characteristic frequency and mode shape (Rayleigh oscillations). If the drop is pinned on a circle of contact the mode shapes change and the frequencies are shifted. The linear problem of inviscid, axisymmetric, volume-preserving oscillations of a liquid drop constrained by pinning along a latitude is solved here. The formulation gives rise to an integrodifferential boundary value problem, similar to that for Rayleigh oscillations, and for oscillations of a drop in contact with a spherical bowl [M. Strani and F. Sabetta, J. Fluid Mech. 141, 233 (1984)], only more constrained. A spectral method delivers a truncated solution to the eigenvalue problem. A numerical routine has been used to generate the eigenfrequencies/eigenmodes as a function of the location of the pinned circle of constraint. The effect of pinning the drop is to introduce a new low-frequency eigenmode. The center-of-mass motion, important in application, is partitioned among all the eigenmodes but the low-frequency mode is its principal carrier.

Deformations of drops and bubbles opposed by surface tension and driven by radiation stresses at the interface are calculated using spherical harmonic expansions for the radial and tangential stresses. Superimposed acoustic waves produce stresses which oscillate at the difference frequency ω of the waves in addition to static stresses. When the effects of viscosity on the acoustic waves are omitted, the tangential radiation stress vanishes; a procedure is proposed for calculating the radial stresses from the theory for ’’Acoustic Radiation Pressure on a Compressible Sphere’’ [K. Yosioka and Y. Kawasima, Acustica 5, 167–173 (1955)]. The calculation of the response assumes incompressible second‐order flow and omits the body forces which are normally asociated with acoustic streaming. Resonance phase shifts and enhancements of the response should occur when ω is close to the natural oscillation frequency of a mode. Quadrupole resonance phase shifts and enhancements have been observed by the author [J. Acoust. Soc. Am. 67, 27–37 (1980)]. Diverse applications of the theory include the possibilities of: inference of the interfacial tension from the response; emulsification by exciting large amplitude oscillations; and deformation or splitting of bubbles by radiation stresses. The decay time of free oscillation is also calculated; a new term is found which is small but significant for drops surrounded by a liquid and supplements the theory for ’’The Oscillations of a Fluid Droplet Immersed in Another Fluid’’ [C. A. Miller and L. E. Scriven, J. Fluid Mech. 32, 417–435 (1968)].

The small-amplitude oscillations of constrained drops, bubbles, and plane liquid surfaces are studied theoretically. The constraints have the form of closed lines of zero thickness which prevent the motion of the liquid in the direction normal to the undisturbed free surface. It is shown that, by accounting explicitly for the singular nature of the curvature of the interface and the force exerted by the constraint, methods of analysis very close to the standard ones applicable to the unconstrained case can be followed. Weak viscous effects are accounted for by means of the dissipation function. Graphical and numerical results for the oscillations of constrained drops and bubbles are presented. Examples of two- and three-dimensional gravity-capillary waves are treated by the same method. A brief consideration of the Rayleigh-Taylor unstable configuration shows that the nature of the instability is not affected, although its growth rate is decreased.

The impact of molten tin droplets (0.6 mm diameter) on solid surfaces was observed for a range of impact velocities (10–30 m/s), substrate temperatures (25–200 °C) and substrate materials (stainless steel, aluminum and glass). The substrate was mounted on the rim of a rotating flywheel and the collision of single droplets with the moving substrate was photographed. Droplet impact Reynolds number ranged from 2.2 × 10 4 to 6.5 × 10 4 and Weber number from 8.0 × 10 2 to 7.2 × 10 3. On a hot surface there was no splashing and droplets spread to form disk-like splats with smooth edges. Solidification around the edges of droplets spreading on cold surfaces created a solid rim that obstructed flow and triggered splashing. An analytical model was developed to predict the transition temperature at which splashing disappeared by assuming that the thickness of the solid layer had to equal that of the splat in the time the droplet spread to its maximum extent in order to obstruct liquid flow. The model predicted the transition temperature for aluminum and stainless steel surfaces, assuming that thermal contact resistance between the droplet and substrate varied between 10 616 and 10 617 m 2 K/W. The model also predicted that tin droplets would not splash on glass surfaces maintained at or above room temperature, and this was confirmed by experiments.

We study the spreading characteristics of a reactive-wetting system of mercury (Hg) droplets on silver (Ag) films in room temperature. This is done using our recently developed method for reconstructing the dynamical three-dimensional shape of spreading droplets from two-dimensional microscope images [A. Be'er and Y. Lereah, J. Microsc. 208, 148 (2002)]. We study the time evolution of the droplet radius and its contact angle, and find that the spreading process consists of two stages: (i) the "bulk propagation" regime, controlled by chemical reaction on the surface, and (ii) the "fast-flow" regime, which occurs within the metal film as well as on the surface and consists of both reactive and diffusive propagation. We show that the transition time between the two main time regimes depends solely on the thickness of the Ag film. We also discuss the chemical structure of the intermetallic compound formed in this process.

The spreading of a small mercury droplet (150 μm) on thin gold films is studied, using an optical microscope enhanced with a differential interference contrast system. The growing interfaces are analyzed in order to determine the roughness ( α) and growth ( β) exponents. For gold film thickness of 1500 A 06 we find that α=0.88±0.03 and β=0.76±0.03, while for gold thickness of 3000 A 06, α=0.96±0.04 and β=1.00±0.04. Both sets of exponents satisfy the scaling relation α+ α/ β=2. In both systems the roughness exponent α crosses over to a value close to 0.5 in the final stages of the experiment and for relatively long length scales (order of a few microns).

The spreading characteristics of a liquid GaInSn alloy droplet on a glass surface with the action of a horizontal magnetic field have been experimentally investigated in the present paper. With changing the impact velocity from 0.1 m/s to 1.2 m/s and increasing the magnetic field from 0 T to 1.6 T, we focus on studying the influence of the horizontal magnetic field on the spreading characteristics of a liquid metal droplet using the shadow-graph method. The elliptical spreading pattern of a liquid metal droplet induced by the horizontal magnetic field was discovered by experiments. By introducing a numerical method in getting the distribution of current lines and the Lorentz force inside the droplet, we give a detailed explanation on the mechanism of elliptical spreading. Furthermore, some quantitative results on a maximum spreading factor and time at moment of maximum spreading varied with the Hartmann number and Weber number are shown to give us a comprehensive understanding of the elliptical spreading. With the increasing of the magnetic field, the maximum spreading factor in the front view is reduced while that in the side view is increased, which reveals a larger deformation happened during the spreading process. While with the increasing of impact velocity, the spreading factor increased. Finally, we present a non-dimensional parameter to get scaling laws for the averaged maximum spreading factor and the aspect ratio of the maximum spreading factor; results show that the predict data can agree with experimental data in a certain degree.

We photographed the impact of molten metal droplets on a flat plate. From these images we measured droplet dimensions during spreading and counted the number of fingers around a splashing drop. Experiments were done using stainless steel substrates with average roughness of 0.06, 0.07, 0.56, and 3.45 μm respectively. The temperature of the substrate was kept at either 25 or 240 °C. Droplet diameter (2.2 mm) and impact velocity (4 m/s) were kept constant, giving a Reynolds number ( Re) of 31 135 and Weber number ( We) of 463. Raising substrate roughness from 0.06 to 0.56 μm enhanced the tendency of droplet to splash, whereas increasing roughness even further to 3.45 μm suppressed splashing. This behaviour was attributed to changes in droplet solidification rate with surface roughness. A simple model of droplet spreading was used to estimate thermal contact resistance between the droplet and surface. Increasing surface roughness was found to raise thermal contact resistance and reduce heat transfer from the droplet to the substrate, delaying the onset of solidification and reducing splashing. The number of fingers formed around a droplet splashing on a smooth surface could be predicted reasonably well by a model based on Rayleigh–Taylor instability theory. Increasing surface roughness reduced the number of fingers while enlarging their size.

GaInSn, a eutectic alloy, has been successfully used in the Magneto-Thermofluid Research Laboratory at the University of California-Los Angeles and at the Princeton Plasma Physics Laboratory for the past six years. This paper describes the handling and safety of GaInSn based on the experience gained in these institutions, augmented by observations from other researchers in the liquid metal experimental community. GaInSn is an alloy with benign properties and shows considerable potential in liquid metal experimental research and cooling applications.

We have obtained interfacial properties of Galinstan, a nontoxic liquid-metal alloy, to help replace mercury in miniature devices. To prevent formation of an oxide skin that severely hinders the fluidic behavior of small Galinstan droplets and leads to inaccurate property data, we performed our experiments in a nitrogen-filled glove box. It was found that only if never exposed to oxygen levels above 1 part per million (ppm) would Galinstan droplets behave like a liquid. Two key properties were then investigated: contact angles and surface tension. Advancing and receding contact angles of Galinstan were measured from sessile droplets on various materials: for example, 146.8 and 121.5, respectively, on glass. Surface tension was measured by the pendant-drop method to be 534.6 10.7 mN/m. All the measurements were done in nitrogen at 28 with oxygen and moisture levels below 0.5 ppm. To help design droplet-based microfluidic devices, we tested the response of Galinstan to electrowetting-on-dielectric actuation.

Liquid metals exhibit remarkable mechanical properties, in particular large surface tension and low viscosity. However, these properties are greatly affected by oxidation when exposed to air. We measure the viscosity, surface tension, and contact angle of gallium and a eutectic gallium-indium alloy while controlling such oxidation by surrounding the metals with an acid bath of variable concentration. Rheometry measurements reveal a yield stress directly attributable to an oxide skin that obscures the intrinsic behavior of the liquid metals. We demonstrate how the intrinsic viscosity can be obtained with precision through a scaling technique that collapses low- and high-Reynolds number data. Measuring surface tension with a pendant drop method, we show that the oxide skin generates a surface stress that mimics surface tension and develop a simple model to relate this to the yield stress obtained from rheometry. We find that yield stress, surface tension, and contact angle all transition from solid-like to liquid behavior at the same critical acid concentration, thereby quantitatively confirming that the wettability of these liquid metals is due to the oxide skin.

The normal impact of liquid drops onto solid, dry surfaces has been studied experimentally, using high-resolution digital photography. A large number of parameters were varied in a systematic manner. The focus of this paper is the quantitative determination of the influence of these parameters on the drop spreading upon impact and on the phenomenological description of the outcomes. Dimensional similarity of the spreading can only be achieved for the very early stage of the impact process. At later stages, the number of influencing factors increases, generally precluding any universal correlation. Particular emphasis is placed on the influence of the wettability and the surface roughness on spreading.

Abstract We investigate the interplay between substrate roughness and surrounding gas pressure in controlling the dynamics of splashing when a liquid drop hits a dry solid surface. We associate two distinct forms of splashing with each of these control parameters: Prompt splashing is due to surface roughness and corona splashing is due to instabilities produced by the surrounding gas. The size distribution of ejected droplets reveals the length scales of the underlying droplet-creation process in both cases.

Droplet impingement experiments were performed on grooved hydrophobic surfaces with cavity fractions of 0, 80, and 93 % using droplets of water and a 50 %/50 % water/glycerol mixture. The influence of liquid viscosity, cavity fraction, and spreading direction, relative to the surface grooves, is explored qualitatively and quantitatively. The maximum droplet spread diameter, velocity of the rebounding jet, and the time delay between droplet impact and jet emission were characterized for Weber numbers, We, based on droplet impact speed and diameter, up to 500. The unequal shear stresses and contact angles influence the maximum spread diameters in the two primary spread directions. At We > 100, the ratio of the spread diameter along the direction of the grooves to the spread diameter perpendicular to the grooves increases above unity with increasing We. The maximum droplet spread diameter is compared to recent predictive models, and the data reveal differing behavior for the two fluids considered. The results also reveal the existence of very high relative jet velocities in the range 5 les We les 15 for water droplets, while such jets were not observed for the more viscous mixture. Further, in the range 115 les We les 265, the water/glycerol jet formation dynamics are radically different from the water behavior. Most evident is the existence of two-pronged jets, which arise from the anisotropy of the surface and the unequal shear stresses and contact angles that prevail on the surfaces. It is these influences that give rise to differences in the maximum spread diameters in the two primary spread directions. Similar two-pronged jet emission was observed for water over the very narrow range of We from 91 to 96. The issuing jet velocities were also observed to increase with increasing cavity fraction for both fluids and over the entire range of We explored. Lastly, the elapsed time between droplet impact and jet emission decreased with increasing cavity fraction.

Moderate-amplitude axisymmetric oscillations of incompressible inviscid drops and bubbles are studied using a Poincaré–Lindstedt expansion technique. The corrections to the drop shape and velocity potential caused by mode coupling at second order in amplitude are predicted for two-, three- and four-lobed motions. The frequency of oscillation is found to decrease with the square of the amplitude; this result compares well with experiments and numerical calculations for drops undergoing two-lobed oscillations.

A sessile drop oscillates when an ac voltage is applied in electrowetting. The oscillation results from the time-varying electrical force concentrated on the three-phase contact line. Little is known about the feature of drop oscillation in electrowetting. In the present work, the drop oscillations are observed systematically, and a theoretical model is developed to analyze the oscillation. It is revealed that resonance occurs at certain frequencies and the oscillation pattern is significantly dependent on the applied ac frequencies. The domain perturbation method is used to derive the shape-mode equations under the assumptions of a weak viscous effect and small drop deformation. The electrical force concentrated on the three-phase contact line is approximated as a delta function, which is decomposed and substituted into each shape-mode equation as a forcing term. The theoretical results for the shape and frequency responses are compared with experimental results, which shows qualitative agreement.

An air bubble driven by ultrasound can become shape-unstable through a parametric instability. We report time-resolved optical observations of shape oscillations (mode n=2 to 6) of micron-sized single air bubbles. The observed mode number n was found to be linearly related to the ambient radius of the bubble. Above the critical driving pressure threshold for shape oscillations, which is minimal at the resonance of the volumetric radial mode, the observed mode number n is independent of the forcing pressure amplitude. The microbubble shape oscillations were also analyzed numerically by introducing a small nonspherical linear perturbation to a Rayleigh-Plesset-type equation, capturing the experimental observations in detail.