Droplets bouncing on a vibrated liquid bath open ways to methods of manipulating droplets, creating double emulsion and performing pilot wave model experiments. In this work, we focus on the role of the droplet deformations in the vertical bouncing dynamics by neglecting the deformation of the surface of the bath. To be under this favorable conditions, low viscous oil droplet are dropped over a highly viscous oil bath. These droplets bounce vertically on the surface of the bath and exhibit many periodic trajectories and resonant modes when tuning the forcing parameters, i.e. the oscillation of the bath. This complex dynamics emphasizes the interplay between elastic energy storage and energy dissipation in droplets at each bounce. We propose to model droplets using a bouncing mass-spring-damper system that mimics a deformable droplet bouncing on a non-deformable liquid bath. From the experimental measurements, we constructed bifurcation diagrams of the bouncing trajectories and challenged our bouncing spring model. The agreement between experiment and the spring model reveals that this model can be used to rationalize and predict a variety of bouncing droplets behaviors involving multi-periodicities.
When placed onto a vibrating liquid bath, a droplet may adopt a permanent bouncing behavior, depending on both the forcing frequency and the forcing amplitude. The relationship between the droplet deformations and the bouncing mechanism is studied experimentally and theoretically through an asymmetric and dissipative bouncing spring model. Antiresonance effects are evidenced. Experiments and theoretical predictions show that both resonance at specific frequencies and antiresonance at Rayleigh frequencies play crucial roles in the bouncing mechanism. In particular, we show that they can be expl…
We numerically investigate bouncing and non-bouncing of droplets during isothermal impact on superhydrophobic surfaces. An in-house, experimentally-validated, finite-element method based computational model is employed to simulate the droplet impact dynamics and transient fluid flow within the droplet. The liquid-gas interface is tracked accurately in Lagrangian framework with dynamic wetting boundary condition at three-phase contact line. The interplay of kinetic, surface and gravitational energies is investigated via systematic variation of impact velocity and equilibrium contact angle. The …
Droplets can self-propel when immersed in another liquid in which a concentration gradient is present. Here we report the experimental and numerical study of a self-propelling oil droplet in a vertically stratified ethanol/water mixture: At first, the droplet sinks slowly due to gravity, but then, before having reached its density matched position, jumps up suddenly. More remarkably, the droplet bounces repeatedly with an ever increasing jumping distance, until all of a sudden it stops after about 30 min. We identify the Marangoni stress at the droplet/liquid interface as responsible for the j…
Over the past few decades, superhydrophobic materials have attaracted a lot of interests, due to their numerous practical applications. Among various superhydrophobic materials, carbon nanotube arrays have gained enormous attentions simply because of their outstanding properties. The impact dynamic of water droplet on a superhydrophobic carbon nanotube array is shown in this fluid dynamics video.
We experimentally investigate impact dynamics of a microliter water droplet on a hydrophobic microgrooved surface. The surface is fabricated using photolithography and high-speed visualization is employed to record the time-varying droplet shapes in transverse as well as longitudinal direction. The effect of the pitch of the grooved surface and Weber number on droplet dynamics and impact outcome are studied. At low pitch and Weber number, the maximum droplet spreading is found to be greater in the longitudinal direction than the transverse direction to the grooves. The preferential spreading i…
This is an entry for the Gallery of Fluid Motion of the 65st Annual Meeting of the APS-DFD (fluid dynamics video). This video shows the motion of levitated liquid droplets. The levitation is produced by the vertical vibration of a liquid container. We made visualizations of the motion of many droplets to study the formation of clusters and their stability.
In 2005, Couder, Protiere, Fort and Badouad showed that oil droplets bouncing on a vibrating tray of oil can display nonlocal interactions reminiscent of the particle-wave associations in quantum mechanics; in particular they can move, attract, repel and orbit each other. Subsequent experimental work by Couder, Fort, Protiere, Eddi, Sultan, Moukhtar, Rossi, Molacek, Bush and Sbitnev has established that bouncing drops exhibit single-slit and double-slit diffraction, tunnelling, quantised energy levels, Anderson localisation and the creation/annihilation of droplet/bubble pairs. In this paper w…
In this video, Ray-tracing data visualization technique was used to obtain realistic and detailed flow motions during droplet collision. The differences of collision outcome between Newtonian and non-Newtonian were compared. Various types of droplet collision were presented, including bouncing, coalescence, and stretching separation. Because of the reducing of equivalent viscosity caused by shear stress, the gas film between shear-thinning droplet is thinner than Newtonian liquid. Since thinner gas film promotes coalescence, shear thinning liquid has smaller area of bouncing regime in the diag…
Chemically-active droplets exhibit complex avoiding trajectories. While heterogeneity is inevitable in active matter experiments, it is mostly overlooked in their modelling. Exploiting its geometric simplicity, we fully-resolve the head-on collision of two swimming droplets of different radii and demonstrate that even a small contrast in size critically conditions their collision and subsequent dynamics. We identify three fundamentally-different regimes. The resulting high sensitivity of pairwise collisions is expected to profoundly affect their collective dynamics.
Soft surfaces impacted by liquid droplets trap more air underneath than their rigid counterpart. The extended lifetime of the air film not only facilitates bouncing behaviours of the impacting droplets but also increases the possibility of an interaction between the air film itself and the air cavity formed inside the droplets by capillary waves. Such interaction may cause rupture of the trapped air film by a so-called dimple inversion phenomenon and suppress bouncing. In this work, we systematically investigate the relation between air cavity collapse and air film rupture for water droplets i…
We introduce a solvable Lagrangian model for droplet bouncing. The model predicts that, for an axisymmetric drop, the contact time decreases to a constant value with increasing Weber number, in qualitative agreement with experiments, because the system is well approximated as a simple harmonic oscillator. We introduce asymmetries in the velocity, initial droplet shape, and contact line drag acting on the droplet and show that asymmetry can often lead to a reduced contact time and lift-off in an elongated shape. The model allows us to explain the mechanisms behind non-axisymmetric bouncing in t…
In a set of experiments, Couder et. al. demonstrate that an oscillating fluid bed may propagate a bouncing droplet through the guidance of the surface waves. We present a dynamical systems model, in the form of an iterative map, for a droplet on an oscillating bath. We examine the droplet bifurcation from bouncing to walking, and prescribe general requirements for the surface wave to support stable walking states. We show that in addition to walking, there is a region of large forcing that may support the chaotic bouncing of the droplet. Using the map, we then investigate the droplet trajector…
Modelling wetting-bouncing transitions of droplet impact on random rough surfaces
State Key Laboratory of Mesoscience and Engineering, Institute of Process Engineering, Chinese Academy of Sciences（中国科学院过程工程研究所介科学工程国家重点实验室）；School of Civil Engineering, University of Sydney（悉尼大学土木工程学院）；School of Chemical Engineering, University of Chinese Academy of Sciences（中国科学院大学化学工程学院）
We introduce a droplet-jumping phenomenon on a superhydrophobic surface driven by the resonant AC electrowetting. The resonant electrical actuation enables a droplet to accumulate sufficient surface energy for jumping, and superhydrophobic surface minimizes adhesion and hysteresis effects. They provide the effective energy conversion from the surface energy to the kinetic energy and improve the stability and the reproducibility of the droplet jumping. The controlled droplet jumping made by the resonant AC electrowetting could place another milestone in digital microfluidics by establishing a p…
We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm interpretation of quantum mechanics. Through numerical means we obtain single-slit diffraction and double-slit interference patterns that strongly resemble those reported in experiment and that reflect a striking resemblance to quantum diffraction and interference on a phenomenological level. We, however, identify evident differences from quantum mechanics which arise from the governing equations at the …
Two oppositely charged droplets of (say) water in e.g. oil or air will tend to drift together under the influence of their charges. As they make contact, one might expect them to coalesce and form one large droplet, and this indeed happens when the charge difference is sufficiently small. However, Ristenpart et al discovered a remarkable physical phenomenon whereby for large enough charge differentials, the droplets bounce off each other as they make contact. Explanations based on minimisation of area under a volume constraint have been proposed based on the premise that consideration of surfa…
We experimentally investigated the splashing of dense suspension droplets impacting a solid surface, extending prior work to the regime where the viscosity of the suspending liquid becomes a significant parameter. The overall behavior can be described by a combination of two trends. The first one is that the splashing becomes favored when the kinetic energy of individual particles at the surface of a droplet overcomes the confinement produced by surface tension. This is expressed by a particle-based Weber number $We_p$. The second is that splashing is suppressed by increasing the viscosity of …
The effect of pitch of the pillars and impact velocity are studied for the impact dynamics of a microliter water droplet on a micropillared hydrophobic surface. The results are presented qualitatively by the high-speed photography and quantitatively by the temporal variation of wetted diameter and droplet height. A characterization of the transient quantitative results is a novel aspect of our work. Three distinct regimes, namely, non-bouncing, complete bouncing and partial bouncing are presented. A critical pitch as well as impact velocity exists for the transition from one regime to another.…
The impact of a jet of droplets upon surfaces of varying hydrophobicity is studied via high-speed imaging. Microstructures on silicone surfaces consisting of cylindrical pillars of varying sizes and spacings are utilized to enhance hydrophobicity. Comparison of droplet motion after impact with these microstructured surfaces is contrasted with that noted for plain glass (hydrophilic) and flat silicone surfaces. Fluid dynamics videos are captured at 6000 fps and played back at 30 fps over a field of view of 1.35 cm (height) X 2.7 cm (width) that is back-illuminated with an LED array for 800-micr…
A droplet bouncing on the surface of a vibrating liquid bath can move horizontally guided by the wave it produces on impacting the bath. The wave itself is modified by the environment, and thus the interactions of the moving droplet with the surroundings are mediated through the wave. This forms an example of a pilot-wave system. Taking the Oza Rosales Bush description for walking droplets as a theoretical pilot-wave model, we investigate the dynamics of two interacting identical, in-phase bouncing droplets theoretically and numerically. A remarkably rich range of behaviors is encountered as a…
The impact of droplets is a ubiquitous phenomenon, and reducing the residence time of the impact process is important for many potential applications. In this study of the impact dynamics on heated surfaces, we identify a mode of droplet bouncing (bouncing-with-spray mode) that can reduce the residence time significantly compared with the traditional retraction-bouncing mode. Comparing with other strategies to reduce the residence time, this approach induced by heat is simple and reliable. The reduction in the residence time is due to the burst of vapor bubbles in the liquid film, which result…
The off-center collision of binary bouncing droplets of equal size was studied numerically by a volume-of-fluid (VOF) method with two marker functions, which has been validated by comparing with available experimental results. A non-monotonic kinetic energy recovery with varying impact parameters was found based on the energy budget analysis. This can be explained by the prolonged entanglement time and the enhanced internal-flow-induced viscous dissipation for bouncing droplets at intermediate impact parameters, compared with those at smaller or larger impact parameters. The universality of th…
Bouncing walking droplets possess fascinating properties due to their peculiar wave/particule interaction. In order to study such walkers in a 1d system, we considered the case of one or more droplets in an annular cavity. We show that, in this geometry, walking droplets form a string of synchronized bouncing droplets that share a common coherent wave propelling the group at a speed faster than single walkers. The formation of this coherent wave and the collective behavior of droplets is captured by a model.
A liquid droplet hovering on a hot surface is commonly referred to as a Leidenfrost droplet. In this study, we discover that a Leidenfrost droplet involuntarily performs a series of distinct oscillations as it shrinks during the span of its life. The oscillation first starts out erratically, followed by a stage with stable frequencies, and finally turns into periodic bouncing with signatures of a parametric oscillation and occasional resonances. The last bouncing stage exhibits nearly perfect collisions. We showed experimentally and theoretically the enabling effects of each oscillation mode a…
A new method is proposed to stop the cascade of partial coalescences of a droplet laid on a liquid bath. The strategy consists in vibrating the bath in the vertical direction in order to keep small droplets bouncing. Since large droplets are not able to bounce, they partially coalesce until they reach a critical size. The system behaves as a low pass filter : droplets smaller than the critical size are selected. This size has been investigated as a function of the acceleration and the frequency of the bath vibration. Results suggest that the limit size for bouncing is related to the first mode…
A millimetric bouncing droplet sustained on a vibrating bath becomes a moving wave source (particle) through periodically interacting with the local wave field it generates during the droplet-bath impact. By virtue of such particle-wave duality, the macroscopic hydrodynamic system imitates enigmatic behaviors of the quantum realm. Here we show that it is possible to create an integrated pilot-wave field to better prescribe the droplet trajectories, via amplified bath capillarity. This is demonstrated with a liquid metal droplet-bath system in which the local wave field generated by droplet bou…
When an oil droplet is placed on a quiescent oil bath, it eventually collapses into the bath due to gravity. The resulting coalescence may be eliminated when the bath is vertically vibrated. The droplet bounces periodically on the bath, and the air layer between the droplet and the bath is replenished at each bounce. This sustained bouncing motion is achieved when the forcing acceleration is higher than a threshold value. When the droplet has a sufficiently low viscosity, it significantly deforms : spherical harmonic \boldmath{$Y_{\ell}^m$} modes are excited, resulting in resonant effects on t…
The impact of droplets on an inclined falling liquid film is studied experimentally using high-speed imaging. The falling film is created on a flat substrate with controllable thicknesses and flow rates. Droplets with different sizes and speeds are used to study the impact process under various Ohnesorge and Weber numbers, and film Reynolds numbers. A number of phenomena associated with droplet impact are identified and analysed, such as bouncing, partial coalescence, total coalescence, and splashing. The effects of droplet size, speed, as well the film flow rate are studied culminating in the…
Effects of spinning motion on the bouncing and coalescence between a spinning droplet and a non-spinning droplet undergoing the head-on collision were numerically studied by using a Volume-of-Fluid method. A prominent discovery is that the spinning droplet can induce significant non-axisymmetric flow features for the head-on collision of equal-size droplets composed of the same liquid. Specifically, a non-axisymmetric bouncing was observed, and it is caused by the conversion of the spinning angular momentum into the orbital angular momentum. This process is accompanied by the rotational kineti…
A three dimensional small deformation theory is developed to examine the motion of a magnetic droplet in a uniform rotating magnetic field. The equations describing the droplet's shape evolution are derived using two different approaches - a phenomenological equation for the tensor describing the anisotropy of the droplet, and the hydrodynamic solution using perturbation theory. We get a system of ordinary differential equations for the parameters describing the droplet's shape, which we further analyze for the particular case when the droplet's elongation is in the plane of the rotating field…
It has been shown that a water drop can bounce persistently, when thrown on a super-hydrophobic substrate. We present here scaling arguments which allow us to predict the maximal deformation and the contact time of the drop. This approach is completed by a model describing the flow inside the drop, and by original experimental data.
Recent experiments with droplets impacting a macro-textured superhydrophobic surfaces revealed new regimes of bouncing with a remarkable reduction of the contact time. We present here a comprehensive numerical study that reveals the physics behind these new bouncing regimes and quantify the role played by various external and internal forces that effect the dynamics of a drop impacting a complex surface. For the first time, three-dimensional simulations involving macro-textured surfaces are performed. Aside from demonstrating that simulations reproduce experiments in a quantitative manner, the…
Thin, viscous liquid films subjected to impact events can deform. Here we investigate free surface oil film deformations that arise due to the air pressure buildup under the impacting and rebouncing water drops. Using Digital Holographic Microscopy, we measure the 3D surface topography of the deformed film immediately after the drop rebound, with a resolution down to 20 nm. We first discuss how the film is initially deformed during impact, as a function of film thickness, film viscosity, and drop impact speed. Subsequently, we describe the slow relaxation process of the deformed film after the…
When a free-falling liquid droplet is hit by a laser it experiences a strong ablation driven pressure pulse. Here we study the resulting droplet deformation in the regime where the ablation pressure duration is short, i.e. comparable to the time scale on which pressure waves travel through the droplet. To this end an acoustic analytic model for the pressure-, pressure impulse- and velocity fields inside the droplet is developed in the limit of small density fluctuations. This model is used to examine how the droplet deformation depends on the pressure pulse duration while the total momentum to…
We investigate the break-up of Newtonian/viscoelastic droplets in a viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes. LBM are used to model two immiscible fluids with variable viscosity ratio (i.e. the ratio of the droplet to matrix viscosity); FD schemes are used to model viscoelasticity, and the kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbe…
In the drop-on-demand (DOD) inkjet system, deformation process and the direct relations between the droplet motions and the liquid properties have been seldom investigated, although they are very critical for the printing accuracy. In this study, experiments and computational simulation regarding deformation of a single droplet driven by a piezoelectric nozzle have been conducted to address the deformation characteristics of droplets. It is found that the droplet deformation is influenced by the pressure wave propagation in the ink channel related to the driven parameters and reflected in the …
A transient analysis to quantify droplet deformation under DC electric fields is presented. The full Taylor-Melcher leaky dielectric model is employed where the charge relaxation time is considered to be finite. The droplet is assumed to be spheroidal in shape for all times. The main result is an ODE governing the evolution of the droplet aspect ratio. The model is validated by extensively comparing predicted deformation with both previous theoretical and numerical studies, and with experimental data. Furthermore, the effects of parameters and stresses on deformation characteristics are system…
The deformation and breakup of droplets in air flows is important in many applications of spray and atomization processes. However, the shear effect of airflow has never been reported. In this study, the deformation and breakup of droplets in the shear flow of air is investigated experimentally using high-speed imaging, digital image processing, and particle image velocimetry. We identify a new breakup mode of droplets, i.e., the butterfly breakup, in which the strong aerodynamic pressure on the lower part of the droplet leads to the deflection of the droplet and then the formation of a butter…
We report on experiments that consist in deforming a collection of monodisperse droplets produced by a microfluidic chip through a flow-focusing device. We show that a proper numerical modelling of the flow is necessary to access the stress applied by the latter on the droplet along its trajectory through the chip. This crucial step enables the full integration of the differential equation governing the dynamical deformation, and consequently the robust measurement of the interfacial tension by fitting the experiments with the calculated deformation. Our study thus demonstrates the feasibility…
