Session P12: Drops: Impact, Bouncing, Wetting and Spreading V

Multi-physics modeling of air entrapment during drop impact onto solid hydrophobic surfaces

Controlled drop deposition onto a dry surface is important for various technologies such as spray cooling/painting, inkjet printing/coating, pesticide deposition, etc. During these processes air might be entrapped between the liquid and the solid layers leading to detrimental effects. We have developed a multi-physics modeling approach based upon the phase-field modeling (PFM) and Navier-Stokes equations to simulated air bubble formation during the drop impact onto solid surfaces. The PFM is validated against our own experimental measurements in terms of maximum spreading and rebound height. Then, several cases with varying Weber and Froude numbers are considered to study air entrapment. The PFM results reveal that air may be entrapped under water droplet during the initial deposition as well as retraction after maximum spreading. The volume of the entrapped air bubble varies during both processes, significantly influencing drop spreading and rebound height. Furthermore, the simulation results reveal a significant pressure build up in the entrapped air (up to an order of magnitude higher than in the surrounding water phase), which has a detrimental influence on the process of drop impact and spreading. Based upon our predictions and experimental results a contour map (the Weber vs. the Froude numbers) of the air entrapment is created and discussed.   

Suppression of air bubble entrainment during drop impact on smooth surfaces

When a drop impacts on a surface, it can entrain a central air bubble, undesirable in processes such as spray coating and inkjet printing. This air bubble is caused by a combination of the pre-contact drop-air interfacial deformation and the post-contact contact line dynamics. The volume of the entrained air bubble is maximal when the pressure within the interstitial air layer between the drop and the surface is less than the liquid inertial pressure and greater than the Laplace pressure due to the interfacial curvature. The approaches used in the past to suppress air bubble entrainment have been either by reducing the ambient pressure or by increasing the liquid inertia. Here, we present theory and experiments on drop impacting a smooth surface to achieve complete suppression of bubble entrainment at ambient pressure and low liquid inertia. We use the recently reported dimple mode of drop-surface contact to initiate contact at the center and the subsequent radial contact line propagation to suppress bubble entrainment. Several Newtonian and non-Newtonian liquids are used to study the effect of liquid rheology on the air bubble suppression mechanism, thereby providing insights on improving technologies such as inkjet printing, spray coating, and others.   

Not Participating

The complete interface shape of sessile liquid drops is measured using a stereoscopic imaging technique. The approach records surface speckle patterns that refract across the liquid/gas interface and compares these patterns to control images with no drop present. Various interface shape candidates options are evaluated using a nonlinear optimization technique in order to reconstruct the drop shape that produced the particular surface speckle pattern. Earlier work (DFD Z04.00003, 2020) provided a proof-of-concept of the stereoscopic approach. The present effort refines the technique and provides extensive validation for drops on horizontal and inclined surfaces. Validation is provided by comparing reconstructed drop shapes to side-view drop profiles and applied drop volumes as well as by comparing estimated contact-line pinning force to downhill gravity forcing of the pinned drops.    

Prediction of air bubble entrapment during drop impact on solid hydrophobic surface: Combined machine learning and experimental validation

One of the fundamental requirements of painting and coating technologies is the controlled deposition onto the solid surface. However, an uncontrolled air bubble entrapment under the liquid layer could deteriorate the quality of the aforementioned process. Here, we present a deep-learning approach using both simulated and experimental images to detect air bubble formation during drop impact on solid parafilm (hydrophobic) surface. The simulation is performed using the phase-field modeling (PFM) approach. Several cases with varying drop diameters and impact velocities are considered to study air entrapment both numerically and experimentally. Using the simulated and the experimental results (top and side views), we have developed a deep learning approach based upon the VGG16 convolutional neural network (CNN) to predict bubble entrapment. The CNN, trained based on the experimental images, reveals better predicting capabilities than the one trained based on the simulated images. Also, for both data sets the prediction is more accurate when training the model using the side rather than the top views. The results allow for a fast and precise prediction of air bubble entrapment.   

How does relative humidity affect the way water droplets contact a surface?

Droplet impacts on a solid surface play an important role in many natural and industrial processes, including ink-jet printing, anti-icing, and spray coating. In this study, we set up several experiments focusing on the effect of relative humidity on drop contact dynamics. We began with building a chamber in which we could manipulate the relative humidity by introducing either dry or moist air and aligning the chamber with a novel optical imaging setup containing environmental controls. We completed two sets of experiments, one in which the relative humidity inside the chamber was approximately 5% (low humidity) and one in which it was close to 95% (high humidity). At each of these humidity levels, we completed a series of trials in which we changed the Weber number of the water droplet. The completed experiments show that the lifetime of the droplet is shorter at high humidity in comparison to low humidity. Based on the results of our experiments, we see that relative humidity plays an important role in drop contact dynamics which will apply to many industrial and biological processes.   

Spreading of a compound drop upon impact on a solid surface

The impact of liquid drops on solid substrates is extensively studied due to its wide range of industrial and natural applications. Recently, attention is paid to impact of ‘compound drops’ i.e., drops made of two immiscible liquids in core-shell configuration. To date the effect of the viscosity on the spreading of such drops is not investigated fully. The core and encapsulating shell liquid layers used in the impact experiments are Newtonian with a range of viscosities, and core to shell size ratios. We will present our findings regarding spreading behaviour and its morphology as a function of relative viscosity, and volume ratio of two liquids. A regime map based on non-dimensional impact parameters will be discussed from first principles. A comparison with simple drops impact events is also provided.   

High speeds micron-sized droplets impact onto smooth substrate

The spreading-splashing transition of millimetric drops impacting over a smooth solid substrate received abundant consideration in the last decades. It is known that this transition takes place, for given material properties of both the liquid and the surrounding gaseous atmosphere, when the impact velocity V is above the critical velocity for splashing of a few meters per second. Here the transition from spreading to splashing of drops with radii R varying from millimeters to tens of microns impacting onto a smooth and dry partially wetting substrate at normal atmospheric conditions is investigated. Experiments show that the smaller R is, the larger the impact velocity V for the drop to splash needs to be but also that, unexpectedly, splash is inhibited if We_λ = ρ V² λ / σ ≧ 0.5, with σ, ρ, and λ indicating the interfacial tension coefficient, the liquid density, and the mean free path of gas molecules. The reason of this behaviour results from the fact that the thickness H_t of the thin liquid film ejected after the drop touches the substrate, under many practical conditions is H_t ≅ σ / (ρ V²) whose values becomes similar to the mean free path of gas molecules, i.e., H_t ∼ λ for sufficiently large values of the impacting velocity V.   

Drop impact on unheated and heated flat surfaces

We experimentally investigate water droplet impact dynamics on a heated flat surface using a high-speed camera, an Infrared (IR) camera, and embedded thermocouples. As the increase of surface temperature, Ts, and Weber number, We (from 1.6 to 129), four typical outcomes are observed: spreading, complete rebound, spreading with atomization, and splashing breakup with atomization. The surface temperature variation, |ΔT|, analyzed from the thermocouple measurements, is found to increase in the low-Ts regime but decrease in the high-Ts regime. At low-Ts (100 – 200 ^oC), spreading is the primary impact outcome at various We. In contrast, a total rebound occurs at high Ts ( > 350 ^oC) but low We; The droplet temperature and surface temperature are nearly unchanged because of the Leidenfrost effect with the formation of an insulating vapor layer, limiting the heat transfer. Our experimental results reveal the combining effect of fluid motion and heat transfer on impact dynamics and temperature distribution.   

A slip boundary condition for an unsteady moving contact line

Determining the correct matching boundary condition is fundamental to our understanding of several everyday problems, such as that of a moving contact line. The Navier and Maxwell slip boundary condition which is widely used to alleviate the singularity at the moving contact line are derived with the implicit assumptions of the flow being steady and having a velocity variation only in the wall-normal direction. Both of these assumptions are invalid in the case of an unsteady moving contact line. Here, by relaxing these assumptions we re-derive the slip boundary condition that shows that slip velocity is dependent on the acceleration and linear strain rate, in addition to its dependence on shear rate. This new finding is validated using molecular dynamics simulations.    

Erosion by dripping drops: the stress distribution and surface shock wave of drop impact

Drop impact causes severe surface erosion, dictating many important natural, environmental and engineering processes and calling for tremendous prevention and preservation efforts. Despite extensive studies on the kinematics of impacting drops, it is still far from clear why drop impact is so effective in erosion. Here, we develop a method of high-speed stress microscopy, which maps the shear stress and pressure distributions of drop impact—the key dynamic factors responsible for erosion—with unprecedented spatiotemporal resolutions. Our experiments reveal the fast propagation of self-similar noncentral stress maxima underneath impacting drops and quantify the shear force on impacted substrates. Moreover, we examine the deformation of impacted substrates and uncover impact-induced surface shock waves. Our study opens the door for quantitative measurements of the impact stress of liquid drops and sheds light on the origin of the superior ability of drop impact in erosion.    

Droplet dynamics under an airflow: splitting versus depinning

Partially-wetting droplets under an airflow can exhibit complex behaviors that arise from the coupling of surface tension, inertia of the airflow, and the contact line dynamics. Recent experiments by Hooshanginejad et al. (2020) have demonstrated that a water droplet may split under the jet or escape the wind by depinning to one side, depending on the magnitude and position of the jet. To rationalize these observations, we develop a 2D lubrication model that incorporates the external pressure of the airflow and capillary pressure of the droplet. Distinct from the previous model, we simulate the motion of the contact line based on a precursor film and disjoining pressure, which is required to capture depinning. The resultant simulations qualitatively reproduce the onset of splitting and depinning regimes for varying parameters, in addition to the overall speed of the moving contact line. We also obtain analytical steady-state solutions and construct the minimum criteria for splitting and depinning, respectively.    

Anomalous capillary flow of a molten metal – Ageing contact angle

An anomalous behavior of dynamic contact angle and position of contact line has been recently observed in capillary flow experiments of molten alloys. The experimental setup consists of a combination of a wetting/non-wetting solid substrate with the molten alloy attracted by the wetting wall and simultaneously repelled by the non-wetting substrate. The dynamic receding contact angle experiences a non-monotonic evolution towards its equilibrium value, i.e, it drops below the equilibrium and then it overshoots. The receding contact line moves either gradually or abruptly, in different experiments.

We postulate a novel diffusive boundary condition for the phase field model where the quasi-equilibrium contact angle changes in time, as a result of slow chemical changes at interfaces, which affect interface energies and therefore – the quasi-equilibrium contact angle. We discover two distinct topological paths: one is characterized by a coalescence of liquid-solid contact domains, the other by a contact line separation. The selection of the two paths in the configurational space depends on both contact ageing parameters and viscosity of the melt.