Session H12: Drops: Impact, Bouncing, Wetting and Spreading III

Underdamped dynamics of a droplet deposited onto a fluid bath

The deposition of droplets on a fluid interface is studied both experimentally and theoretically. Millimetric drops impact a deep bath of the same fluid and are generated using a custom syringe pump connected to a vertically-oriented needle. Measurements of the droplet trajectory are compared directly to the predictions of a quasi-potential model, as well as fully resolved unsteady Navier-Stokes direct numerical simulations. Both models resolve the time-dependent bath interface shape, droplet trajectory, and droplet deformation. In the quasi-potential model, the droplet and bath shape are decomposed using orthogonal function decompositions leading to a set of coupled damped linear oscillator equations solved using an implicit numerical method. The underdamped dynamics of the drop are directly coupled to the response of the bath through a single-point kinematic match condition which we demonstrate to be an effective and efficient model in certain parameter regimes.  Specific scenarios where the oscillations of the droplet and bath play a significant role in the overall dynamics will be highlighted. Ongoing and future work will be discussed.   

Mesler entrainment-like microbubble entrainment underneath drop impact on immiscible thin liquid films

The impact of a water droplet on an oil film substrate causes microbubble entrainment consistent across multiple drop sizes and velocities. The experiment was conducted by studying the impact of a water droplet on a glass slide oriented at 45 degrees and coated with a thin film of silicone oil. In order to further understand how the microbubble entrainment forms under different conditions, the height at which the drop was released was changed as well as the size of the drop. Using backlighting and high speed camera techniques, the impact trend was observed similar to the Mesler entrainment. However, an unexpected trend was also observed, in which the number of bubbles as well as the area of the entrainment did not follow a steady decline with an increase in drop size and in velocity, but rather, the number of bubbles and the area increased and peaked in the lower ends of the drop velocity experiments before decreasing. This trend was consistent across all drop sizes and velocities.   

Effect of surface irregularities on sphere settling through a liquid-liquid interface

In this study, we investigate experimentally how surface irregularities will affect the gravitational settling of a sphere through an interface of two immiscible fluids. We consider different configurations of sharp spikes of varying length scale and radii of curvature uniformly distributed over the sphere surface. Spiky spheres of different size and density fall through a layer of silicone oil at their terminal velocity and approach an interface above an aqueous solution. Depending on the solid-liquid density ratio and the Bond number, a smooth sphere may either float or sink, entraining and trapping a volume of lighter silicone oil into the heavier aqueous solution. It is hypothesized that for an appropriate range of length scale and radius of curvature(sharpness), the spikes will break the thin film of oil surrounding the sphere and induce sinking. To investigate the dynamics in detail, the sphere motion is quantified using high-speed imaging. The parameter space includes the Bond number (based on liquid-liquid density difference and the sphere radius) in the range of 0.2-4 and fluid-fluid viscosity ratios in the range of 0.05-15.   

Engulfment of a drop on solids coated by thin and thick fluid films

We investigate the dynamics of an aqueous droplet as it becomes engulfed by an oil film coating a solid substrate. This process is simulated by the conservative phase-field equation and pressure-velocity formulation using the lattice Boltzmann method, which capture the interface dynamics and the flow momentum for the ternary flow system. Through numerical simulations, we characterize how the droplet engulfment dynamics is affected by the thickness of the fluid film coating the substrate as a function of the  Ohnesorge number. The simulation results imply that when the fluid film thickness is four times or more than four times of the droplet radius, the influence of fluid film thickness can be neglected. Different regimes are identified and described by scaling analysis.   

Droplet impact onto pools of finite depth

Droplet impacts onto finite-depth liquid layers can be seen throughout industry and nature, from raindrops impinging onto puddles to pesticide sprays coating plants. We present an integrated high-speed imaging and numerical investigation of droplets impacting perpendicularly onto finite-depth pools and thin films, elucidating the post-impact dynamics and secondary droplet formation in this regime. In particular, we explore the rich behaviour and transitions that arise when varying the pool depth and liquid fluid properties, from inherently 3D-effects including "crown collapse", to variations in the generation of an axisymmetric Worthington jet. The complementary strengths of experiments and numerical simulation are exploited throughout in order to constructively explore the physical mechanisms underpinning the exciting dynamics observed.   

Coalescence of two liquid drops falling in a liquid pool: Interaction of capillary waves

When a small liquid drop comes into contact with a free surface of a liquid pool, the drop undergoes either spreading as it drains completely inside the pool or undergoes partial coalescence dynamics as a satellite drop pinches off depending on its impacting velocity and size, as well as the fluid properties of the liquid. At low impact velocity, the primary drop injected from a needle floats on the free surface while the trapped air between the drop and the free surface drains out. Subsequently, the drop comes in contact with the free surface at a point, and due to high capillary pressure, it undergoes rapid spreading. This in turn generates upward-moving capillary waves that form a liquid column. At this stage, the bottom of the liquid column is squeezed due to the competition between the vertical and horizontal collapses resulting from the upward moving capillary waves and the surface tension force. When the horizontal collapse overcomes the vertical collapse, a liquid column is detached from the free surface as a daughter drop. Subsequently, the daughter drop completely drains in the liquid pool via a coalescence cascading cycle. As the generation of capillary waves plays an important role, we investigate the interaction of the capillary waves generated due to the simultaneous impact of multiple drops on the free surface of a liquid pool. The Navier-Stokes equations are solved in the finite-difference framework and a coupled-level-set-volume-of-fluid (CLSVOF) method is used to track the interface and the interaction of capillary waves generated due to the simultaneous impact of the droplets on the liquid pool. The influence of various parameters, such as the separation distance between the droplets, impact velocity and the size of the droplets has been investigated.    

Impact, expansion and retraction of drops of complex fluids

In many situations, one wishes to control the outcome of a drop impact on a surface, in order to minize fouling, prevent rebound, or optimize deposition. For this purpose, surfactants and polymers are often added to the impacting liquid. However the details of the interaction of such complex fluid drops with surfaces remain incompletely understood. I will show that for the case of surfactants, it is the dynamic surface tension (DST) at very short time scales that controls the outcome of the drop impact event. I will show how the DST at the time scale of the impact can be measured, since this quantity is not normally measurable with exisiting techniques. Knowing this, we can relate it to the outcome of a spraying test using surfactants.  For polymeric liquids, non-Newtonian effects become important. We provide a quantitative understanding of the expansion of the drops, that turns out to be similar to that of Newtonian fluids. However for the drop retraction, non-Newtonian normal stresses slow down the retraction and can be used to optimize deposition.   

On the structure of the air disk surrounding the central air bubble : Droplet impact on immiscible liquid pool

In this work, we probe the structure and fluid dynamics of the peripheral air disk surrounding the central air dimple beneath an impacting water droplet on an immiscible liquid pool of silicone oil. For the first time, we report the detection of hydrodynamic instability signature in the air disk. We studied low impact energies with Weber-number in the range of 2 - 20. The instability patterns in the air disk were similar in signature to thin-film and Saffman Taylor instability. The air disk undergoes rupture due to thin-film instability and entraps the central air bubble. We provide a detailed mechanistic view of the rupture process experimentally using high-speed reflection interferometric imaging and theoretically using scaling analysis. The central bubble and Messler entrainment found during drop impact on liquid pools result from the air-disk rupture.   

Marangoni flowers when drop impacts on a miscible liquid film

Interfacial flows driven by the Marangoni effect are common in daily life, such as tears of wine, coffee rings, and flow-patterns in soap bubbles. In this work, we investigate the various flower-like patterns which form when a water drop impacts a glycerol film at different speeds, where the Marangoni instability plays an essential role. Through high-speed imaging, we observed the formation of flowers is determined by surface tension instability at the air-liquid interfaces where present unsteady concentrations of glycerol and water after drop impact. Intense vortices inside the water layer are driven by the spatial variations of surface tension, which interacts with the evolution of glycerol-water concentration. At the same time, the impact patterns of drops at different speeds can tune the initial contact modes and therefore vary the final flower patterns.