Session T12: Drops: Impact, Bouncing, Wetting and Spreading III

Impact Dynamics of Water Droplets on Suspended Ultrathin Layers of Oil

The findings on droplet impact dynamics can help in determining careful applications of droplets such as spray cooling, oil spill control, emulsion formation, etc. The current study investigates water droplet impingement on a deep pool of water covered with a suspended ultrathin layer of silicone oil. Changing the size and velocity of the impacting droplets as well as the viscosity of the suspended oil layers affect the characteristics of the formed craters and follow-up jets. It was observed that when the viscosity of the oil layers decreased to a minimum of 1 cSt, the jet height and crater dimensions (width and depth) reached to their extreme values.  The characteristic dimensions of craters and jets were the highest for droplet sizes of around 4.2 mm and release heights of 750 mm, which translates to We number of nearly 710. The impact dynamics were also characterized qualitatively through specifying the type of crown/crater formation, jet pinch-off modes, and the number of secondary droplets. It was seen that top pinch-off modes were likely to occur when large (4.2 mm in diameter) droplets impact 1 cSt oil layers released from a height of 750 mm (We ≈ 710, Re ≈ 15500). The impact dynamics of immiscible fluids could be used as a basis for understanding droplet interactions in applications such as water in oil emulsion formation.   

Oil droplet impacting on the water surface: jet dynamics depending on the oil viscosity

We investigate the evolution of Worthington jet and secondary droplets, driven by the oil droplet impacting on the water surface, while varying its viscosity. In detail, the silicon oil viscosity was varied in the range of 0.65-100 cP, and the droplet (the diameter of 1.5 - 2.3 mm) was dropped at different height from the water surface to achieve the impact velocity of 1.5 - 3.5 m/s. During the impact of oil droplet onto the surface, the resulting interface deformation, with a focus on the jet dynamics (the maximum height of the jet, the pinch-off time, and the height and number of secondary droplets, and so on), was measured with a high-speed camera at the speed of 4000-5000 fps. Interestingly, we found that the number of secondary droplets and their occurrence height was varied depending on the oil viscosity and the impact velocity of the droplet. With lower viscosity, the number of secondary droplets increased as the impact velocity decreases, and vice versa when the oil viscosity is higher. We will discuss further the mechanism of this phenomena.   

Mocha Diffusion: viscous fingering during drop spreading on miscible fluids

Mocha diffusion is a well-known technique for generating beautiful, flower-like patterns on ceramic surfaces. A thin coating of wet, clay "slip" is first applied to the surface, followed by drops of dark ink with additives such as ethanol or vinegar. The result is a complex fingering pattern resembling viscous fingering in a Hele Shaw cell. In the laboratory, we use shear-thinning solutions of sodium alginate or clay and water as the sub-fluid, and drops of food coloring containing water and propylene glycol as the spreading fluid. Crucially, the spreading fluid must be a mixture of two fluids with different surface tensions to help drive the flow through Marangoni forces. Of equal importance is the rheology of the subfluid. A shear thinning fluid promotes fingering through less resistance to fast moving fingers. Surprisingly though, we also find fingering patterns on Newtonian fluids such as thick, sucrose solutions. In this case, the sucrose concentration is so high that the addition of a spreading water layer can drastically lower the local viscosity, enhancing the fingering instability. 

    

Author not Attending

The impact of liquid droplets onto liquid films plays an important role in a wide variety of natural systems and industrial processes, which include raindrop-assisted soil erosion, oil-water emulsions, spray deposition and coating and chemical dispersant application on oil spills. This work investigates the oil drops impacting on stratified oil-water layers with the aid of two high-speed video cameras, using different magnifications to capture both the initial details and overall evolution of the splash at later times. We show that the droplet velocity, the thickness of the silicone oil surface layer and its viscosity have substantial impact on the crown formation and the creation of a bubble canopy that sends liquid jets upwards and downwards from its radially collapsing apex. The results obtained with high-speed visualization provide new insights into the evolution of the liquid jet emerging from the bubble canopy. The effects of key parameters including Weber number, Ohnesorge number, viscosity ratio and the dimensionless film thickness are carefully examined to elucidate the crown formation and the jet breakup.   

Droplet impact on immiscible liquid pool: Multi-scale dynamics of entrapped air cushion at short timescales

We have detected unique hydrodynamic topology in thin air film surrounding the central air dimple formed during drop impact on an immiscible liquid pool. The pattern resembles spinodal and finger-like structures typically found in various thin condensed matter systems. However, similar structures in thin entrapped gas films during drop impacts on solids or liquids have not been reported to date. The thickness profile and the associated dewetting dynamics in the entrapped air layer are investigated experimentally and theoretically using high-speed reflection interferometric imaging and linear stability analysis. We attribute the formation of multi-scale thickness perturbations, associated ruptures, and finger-like protrusions in the draining air film as a combined artifact of thin-film and Saffman–Taylor instabilities. The characteristic length scales depend on the air layer dimensions, the ratio of the liquid pool to droplet viscosity, and the air–water to air–oil surface tension.   

Droplet impact dynamics on shallow pools

High-speed droplet impact onto shallow pools can be seen throughout industry and nature: rain-induced icing, spray cooling, raindrops impinging onto puddles, and agricultural sprays coating plants – to name just a few examples. However, it is only in the last decade or so that the importance of a thin jet of fluid (ejecta sheet) during the first millisecond of impact on the subsequent dynamics has been appreciated. Using a combination of experiments and numerical simulations, we will explain the effect of pool depth, impact velocity, and the surrounding gas properties on ejecta sheet dynamics. These parameters will all be shown to have consequences for the satellite droplets generated. We will also discuss the 3D dynamics that result from breaking axisymmetry with pool base topology.   

Gunwale bobbing and the quantum canoe

Recently, various authors have shown experimentally that droplets, bouncing in a liquid bath, can be made to 'walk' at constant horizontal velocity, and in so doing exhibit a wealth of analogous quantum phenomena. A life-size application of this phenomena takes the form of a person, or many people, jumping up and down on a canoe to achieve forward motion through the surfing of their own wave field, a sport known to those who have found themselves up the lake without a paddle as gunwale bobbing. After an initial transient, the canoe achieves a cruising velocity which satisfies a balance between the thrust generated from pushing downwards into the surface gradients of the wave-field and the resistance due to a combination of skin, form and wave drag. By superposing the linear wave theories of Havelock (1919) for steady cruising and Helmholtz for a bouncing source we demonstrate that such a balance can be sustained, and calculate the optimal parameter values to achieve maximum canoe velocity. A comparison is made to accelerometer data taken from an enthusiastic Gunwale bobber, and various perspectives are discussed, including possible analogies with quantum systems.   

Mechanism of secondary entrapment of bubble.

When a drop strikes the water's free surface, a cavity forms beneath the surface. During the collapse of this cavity, a bubble entrapment is observed and this is generally called a "secondary bubble entrapment" or "irregular entrapment," since bubble formation may or may not occur under the same impact conditions. The mechanism of this secondary bubble entrapment differs slightly from the mechanism of the primary bubble entrapment (regular entrapment) mechanism. This is due to an increase in the Weber number and Froude number, which increases the maximum cavity depth and changes the cavity shape. This bubble formation is only possible if the crown collapse causes wavefronts to travel down the cavity walls at the same speed. These wavefronts arrest the cavity retraction slightly above the maximum cavity depth, steepen the cavity walls, and transform the cavity base into a single stepped cone. When the wavefronts converge near the cavity's axis of symmetry, the single stepped cone base pinches off as a bubble and leaves the cavity as a truncated cone. The speed of the wavefronts traveling down the cavity walls would probably depend on the drop shape at the time of impact on the free surface of the water.

    

Dual Instability in Marangoni Flows during Drop Impact

Marangoni flow, driven by spatial variations of surface tension, usually occurs where the temperature or concentration gradients are present. Here, we discovered a novel two-step instability phenomenon in the Marangoni flows when a water drop impacts a thin glycerol film. Through high-speed imaging, we observed the formation of a series of mushroom vortices at initial contact, which is determined by the undulations of the liquid interfaces and reinforced by the surface tension instability following the impact. After an intensive mixture through the initial mushroom vortices, we observed the formation of branching leaves due to Marangoni instability at the air-liquid interfaces where present unsteady concentrations of water and glycerol, and a flower pattern is formed at the final state. Through particle tracking velocimetry, we obtained velocity profiles in the mushroom vortices and later branching leaves. We found that the flow velocities in the initial mushroom vortices (~300 mm/s) are much higher than those in the branching leaves (~3 mm/s). These findings reveal that the water drop impacting a glycerol film has a dual Marangoni instability at different timescales, which provides new insight into Marangoni flows when a drop interacts with a miscible liquid film.   

The interface dynamics of drops impacting onto a different liquid

In this talk we explore drop impact onto a pool of another liquid, a scenario of relevance to many applications of interest, from inkjet printing to estimating environmental risks after oil spills. A combination of high-speed photography, high-resolution numerical simulations, and physical modelling has been used to disentangle the different roles that physical fluid properties play in determining the detailed dynamics in this multi-fluid system. Simple mechanistic models and experiments of drops impacting onto a pool of the same fluid have led to estimates of the penetration speed being half the impacting drop speed. However, this is only one small part in a rich and intricate behavior landscape once fluid properties are no longer identical - we uncover velocities between 10% and 90% of the reference initial drop velocity over a range of three orders of magnitude in density and viscosity ratios between the impacting drop and the pool, while also explaining these findings and summarizing them into one key compact predictive formula. In higher speed contexts we then shed light into changes to the splashing threshold within the more complex landscape of three-phase flows.   

Impact of droplets on surfactant-laden thin liquid films

The occurrence of drop impacts on liquid surfaces has been observed in a broad range of natural phenomena and industrial applications. Most of those streams may be contaminated with surfactants (i.e., surface-active agents), whose concentration variations lead to surface tension gradients, which in turn, results in the formation of Marangoni stresses. We study the effect of insoluble surfactants on the impact of droplets on surfactant-laden thin liquid films via a fully three-dimensional direct numerical simulations, and taking into account surfactant-ind­uced Marangoni stresses due to gradients in interfacial surfactant concentration. We focus on the "crown-splash regime", and we observe that the crown dynamics go through various stages: from the growth of linear modes (through a Rayleigh-Plateau instability) to the development of nonlinearities leading to primary and secondary breakup events (through droplet shedding modulated by an end-pinching mechanism). We show that the addition of surfactants does not affect the wave selection via the Rayleigh-Plateau instability. However, the presence of surfactants affects the late stages of the dynamics as soon as the ligaments are driven from the rim. Surfactant-induced Marangoni stresses retard the end-pinching mechanisms to result in longer ligaments prior to their capillary singularity, and promote the spanwise merging between ligaments. Additionally, we have studied the limiting ca­se of three-dimensional rim-driven retraction dynamics of thin water sheets in air.   

The Shapes of Dancing Ejecta

Splashing of impacting drops produces a myriad of secondary spray droplets, which generate aerosols during rain on the ocean and can cause health hazards during the spraying of pesticides. Determining the size and number of the finest splashed droplets is therefore of practical interest. Herein we use a novel experimental facility with a 25-meter-tall vacuum tube, to study drop impacts at velocities as high as 22 m/s, where we reach parameter regimes not studied before. The ejecta sheet emerges horizontally at a velocity an order of magnitude larger than the impact velocity. We explain how convoluted shapes are generated by the interplay between inertia, air-resistance, viscous stress, and surface tension. In particular, we identify the key role of Bernoulli pressure and confined toroidal shapes when the sheet approaches the pool or drop surfaces. We also estimate the evolution of the sheet thickness, showing it reaching sub-micron dimensions, primarily owing to the azimuthal stretching. The ejecta evolution depends strongly on the initial angle of the ejection, which causes the jet to bend down towards the pool, or upwards towards the drop. We find that the direction of this bending is determined by the viscosity ratio of the pool to drop liquids.