Session Q12: Drops: Impact on Surfaces II

Self-similar dynamics of inertia-driven drop impacts

We investigate the dynamics of inertia-driven drop impacts on solid surfaces. By synchronizing high-speed imaging with fast force measurements, we simultaneously measure the shape and impact force of impacting drops and demonstrate the existence of self-similar inertial fronts during the initial impact of liquid drops at short times. With the propagation speed six times faster than the impact speed of liquid drops, the inertial front gives rise to a maximal impact force that is important for living organisms and soil and architectural surfaces exposed to the elements. Moreover, we find an exact closed-form self-similar solution for the inertia-driven drop spreading following the initial impact, which quantitatively predicts the shape of spreading drops. Our study reveals hidden self-similarity and illustrates its importance in determining the dynamics of drop impact processes.   

Analytical consideration of droplet impingement behavior on solid surfaces

Current knowledge of the detailed behaviour of droplet impingement has improved gradually with advancements in experimental technology. On the other hand, theoretical approaches employ models that attempt to predict maximum spreading diameter of droplet based on energy balance, momentum balance, and empirical considerations. However, most models have an applicability limit with respect to impingement velocity for predicting the spreading diameter of the droplet. In this study, analytical model is developed on the basis of an energy balance approach to predict the maximum spreading diameter. In the model, the adhesion energy at the contact line in the vertical direction in addition to the horizontal direction are considered. The developed equation can quantitatively predict the maximum spreading diameter in a wide range of the impingement velocity without the use of arbitrary fitting parameters.   

Shaping drops with textured surfaces

When a drop impacts a substrate, it can behave differently depending on the nature of the surface and of the liquid (spreading, bouncing, resting, splashing…). Understanding these behaviors is crucial to predict the drop morphology during and after impact. Whereas surface wettability has extensively been studied, the effect of surface roughness remains hardly explored. In this work, we consider the impact of a drop in a pure non-wetting situation by using superheated substrates i.e. in the Leidenfrost regime. The surface texture consists of a well-controlled microscopic defect shaped with photolithography on a smooth silicon wafer. Different regimes are observed, depending on the distance between the defect and the impact point and the defect size. Comparing the lamella thickness versus the defect height proves relevant as the transition criteria between regimes. Others characteristics of the drop behavior (direction of satellite droplet ejection, lamella rupture) are also well captured by inertial/capillary models. Drop impacts on multiple defects are also investigated and drop shape well predicted considering the interactions between the local flow and the defects.   

Is drop impact the same for both moving and inclined surfaces?

Drop impact is an important phenomenon in a wide variety of applications. Researchers have largely examined drop impact onto a moving surface, and an inclined surface separately. Given that in both systems the impact phenomenon is influenced by tangential and normal velocity components, the question remains, if these two systems are essentially equivalent or gravity and boundary layer effects are such that the outcomes will be different. Experiments have been performed by varying liquid surface tension, viscosity and both normal and tangential velocities (0.3 to 2.9 m/s). The desired velocity components were achieved by changing the height where drop is released, the surface inclination angle for inclined system, and the horizontal velocity for the moving surface. To compare the systems, spreading was analyzed by measuring the width and length of the lamella at various time intervals; for splashing, top view images were compared to see the extent of splashing at initial stage. The data suggests that, for the given velocity, neither the boundary layer differences between the two systems nor the gravity play a role on spreading and splashing of the drop, as such one system can replace the other for future studies.   

Drop impact on a solid surface at reduced air pressure

When a drop approaches a solid surface at atmospheric pressure, the lubrication pressure within the air forms a dimple in the bottom of the drop resulting in the entrainment of an air disc upon impact. Reducing the ambient air pressure below atmospheric has been shown to suppress splashing [1] and the compression of the intervening air could be significant on the air disc formation [2]; however, to date there have been no experimental studies showing how the entrainment of the air disc is affected by reducing the ambient pressure. Using ultra-high-speed interferometry, at up to 5 Mfps, we investigate droplet impacts onto dry solid surfaces in reduced ambient air pressures with particular interest in what happens as rarified gas effects become important, i.e. when the thickness of the air layer is of the same magnitude as the mean free path of the air molecules. Experimental data will be presented showing novel phenomena and comparisons will be drawn with theoretical models from the literature. [1] Xu, L., Zhang, W.W. and Nagel, S.R. "Drop splashing on a dry smooth surface." \emph{Phys. Rev. Lett.} 94, 184505 (2005). [2] Mandre, S., Mani, M. and Brenner, M.P. "Precursors to splashing of liquid droplets on a solid surface." \emph{Phys. Rev. Lett.} 102, 134502 (2009).   

Partitioning of a Falling Droplet's Energy After Surface Impact

Understanding energy partitioning post-impact is a first step to understanding immersive flow-forming processes. Here we investigate the partitioning of kinetic energy into surface energies for capillary water droplets falling onto homogeneous prepared hydrophilic, hydrophobic and super-hydrophobic surfaces. We analyze high-speed images of the impact event. Pre-impact Weber numbers range from 0-15. After impact and initial spreading, the droplet's contact line pins. After pinning, there is a slow decay to the rest state. During this underdamped decay, the droplet's remaining kinetic energy partitions into a linear combination of mode shape energies. These mode shapes and their frequencies correspond to those of pinned sessile droplets from theory. The influence of impact energy on modes excited will be discussed.   

Simulation of High-Speed Droplet Impact Against Dry Substrates with Partial Velocity Slip

High-speed droplet impact can be used to clean substrates such as silicon wafers. Radially spreading shear flow after the impact may allow for mechanically removing contaminant particles at substrate surfaces. Since it is a big challenge to experimentally explore such complicated flow that exhibits contact line motion and water hammer, its flow feature is not well understood. Here, we aim to numerically evaluate shear flow caused by the impact of a spherical water droplet (of submillimeter sizes) at high speed (up to 50 m/s) against a dry rigid wall. We model the flow based on compressible Navier-Stokes equations with Stokes' hypothesis and solve them by a high-order-accurate finite volume method equipped with shock and interface capturing. To treat the motion of a contact line between the three phases (the droplet, the rigid wall, and the ambient air) in a robust manner, we permit velocity slip at the wall with Navier's model, for wall slip is known to come into play under steep velocity gradients that can arise from high-speed droplet impact. In our presentation, we will examine radially spreading flow after the droplet impact and the resulting wall shear stress generation from the simulation.   

Numerical study of liquid film rupture after droplet spreading on a superhydrophilic surface

When a droplet impacts onto a solid surface, different outcomes can be observed, such as rebound, spreading and splashing. We present numerical simulation results on liquid film rupture after spreading of a droplet impact on a smooth superhydrophilic surface. The Navier-Stokes equations are solved using the variable density pressure projection method and the moment-of-fluid method is used to track the droplet interface. A superhydrophilic or superwetting surface has strong affinity to liquid and we assume the contact angle between solid and liquid is almost zero degree. The droplet spreading and film rupture process occurs in two stages: the droplet first spreads onto the surface and flattens into a thin film as it reaches the maximum diameter, then the film rim becomes unstable and the film rupture initiates from the rim toward the center gradually until the entire film breaks up into secondary droplets. The duration of the film rupture stage is much shorter than the spreading stage. The simulation result is compared with experiment and good agreement is achieved. We investigate the film thickness evolution during spreading and the effect of surface wettability on film rupture.   

Dynamic Impacts of Water Droplets onto Icephobic Soft Surfaces at High Weber Numbers

An experimental investigation was performed to examine the effects of the stiffness of icephobic soft PDMS materials on the impact dynamics of water drops at high weber numbers pertinent to aircraft icing phenomena. The experimental study was performed in the Icing Research Tunnel available at Iowa State University (ISU-IRT). During the experiments, both the shear modulus of the soft PDMS surface and the Weber numbers of the impinging water droplets are controlled for the comparative study. While the shear modulus of the soft PDMS surface was changed by tuning the recipes to make the PDMS materials, the Weber number of the impinging water droplets was altered by adjusting the airflow speed in the wind tunnel. A suite of advanced flow diagnostic techniques, which include high-speed photographic imaging, digital image projection (DIP), and infrared (IR) imaging thermometry, were used to quantify the transient behavior of water droplet impingement, unsteady heat transfer and dynamic ice accreting process over the icephobic soft airfoil surfaces. The findings derived from the icing physics studies can be used to improve current icing accretion models for more accurate prediction of ice formation and accretion on aircraft wings and to develop effective anti-/de-icing strategies for safer and more efficient operation of aircraft in cold weather.   

Impact, Spreading and Splashing of Superfluid Drops

We investigate the impact of superfluid and normal liquid helium drops onto glass plates, in a custom-made optical cryostat, over a temperature range from 1.3 - 5 K. The unusual properties of liquid helium allow us to explore ranges of parameters that are difficult to obtain in conventional systems. Even in the normal state with T \textgreater 2.17K, the viscosity and surface tension of liquid helium are unusually low, so it is easy to prepare drops with Re \textgreater 30,000 and We \textgreater 500. We track the spreading radius of the fluid rim, which initially grows as a power law in time with an exponent of {\$}$\backslash $sim 0.5{\$}, while transitioning to Tanner's law at later times. In the superfluid state the rim velocity can exceed 4 m/s, which is significantly higher than the superfluid critical velocity. Here we see no splashing even at Re \textgreater 100,000. Our experiments take place in an atmosphere of helium gas [1]. In conventional impact splashing the exterior air is incondensable, while our impacts in helium involve a condensable exterior phase, so the dynamics can be expected to be quite different. We study how these differences affect the splashing. [1] J.C. Burton, J.E. Rutledge, and P. Taborek, \textit{Phys. Rev. E}, \textbf{75}, 036311 (2007).   

Numerical study of the impact of a drop containing a bubble

The impact of a drop has many applications from inkjet printing to the spreading of crops diseases. This fundamental phenomenon has therefore attracted a lot of interest from different fields. However, they have mostly focused on the simplest case of a drop containing a single fluid. In inkjet printing and in the deposition process of thermal barrier coatings, some bubbles can be present in the drop when it impacts on the solid surface. The presence of the bubble can produce some additional splashing, and affect the quality of the deposited material. Only a few studies have looked at this problem, and many questions still need to be investigated. Generally, there are three possibilities when a drop containing a bubble impacts onto a solid surface, namely the bubble stays in drop, the bubble bursts and a counter jet forms. We have performed axisymmetric numerical simulations with the open source code Gerris to study this vertical jet. We have systematically varied several parameters, including the impact velocity, the bubble size, the vertical position of the bubble, and the liquid properties. We were thus able to characterize under which condition the bubble leads to splashing and the velocity of the produced jet.