Session J31: Drops: Impact, Bouncing, Wetting and Spreading II

Absence of diffusion in pilot-wave hydrodynamics: A classical analog of Anderson localization

A self-propelled particle in heterogeneous media may undergo diffusive motion when its energy is comparable to the average potential barrier of the random background. The evolution of an ensemble of such particles may thus be described by the diffusion equation, leading to a uniform spatial distribution in the long-time limit. In this talk, we will introduce a hydrodynamic pilot-wave system in which particles instantaneously exhibit diffusive motion, yet their position histogram becomes localized. The constituents of this hydrodynamic pilot-wave system are millimetric liquid droplets that may walk across the surface of a vibrating fluid bath, self-propelled through a resonant interaction with their own wave fields. By virtue of the coupling with their wave fields, these walking droplets, or 'walkers', extend the range of classical mechanics to include certain features previously thought to be exclusive to the microscopic, quantum realm. Through experiments and mathematical modeling, we investigate the motion of walkers over submerged random topographies. For sufficiently shallow liquid layers, the walker trajectory becomes chaotic due to scattering from random features at the bottom of the bath. Nevertheless, consideration of an ensemble of drop trajectories reveals that our hydrodynamic pilot-wave system displays localized statistics in the particle position histogram, an effect strongly reminiscent to the so-called Anderson localization. Particular attention is given to characterizing the influence of the submerged topography on the emergent particle dynamics and long-time probability distributions. The localized statistics are rationalized in terms of a wave-mediated scattering mechanism.   

Mechanism for orbital quantization of walking droplets in a rotating frame

Millimetric liquid droplets may walk on the surface of a vibrating fluid bath thanks to a resonant interaction with their self-excited wave field. This system constitutes a macroscopic realization of particle-wave duality, exhibiting a range of exotic behaviors previously thought exclusive to quantum particles. In particular, placing walking droplets, or `walkers', in a rotating frame to mimic the effect of a magnetic field leads to quantized circular orbits, with radii taking on values in a discrete set. Though captured by numerical simulations, a theoretical identification of the precise mechanism responsible for the walkers' orbital quantization remains elusive. We here use asymptotic methods to rigorously demonstrate that, owing to wave interference, the force responsible for orbital quantization originates from stationary points on the walker's past trajectory. Moreover, we derive a new minimal quantization model that contains the essential ingredients to reproduce orbital quantization and examine its validity in a wide parameter regime. We discuss the potential of our minimal model to rationalize the mechanism of other hydrodynamic quantum analogs.   

Impact craters: experiments with Carbopol and non-Newtonian simulations

The impact of drops or solid spheres on solid surfaces, fluid films, or deep pools are processes widely studied using Newtonian fluids and granular media, and less often non-Newtonian fluids. The present work is motivated by planetary impact cratering, a geological process that shapes the surface of planetary bodies. In this process the strength of the impactor and target plays a role in the morphology and scale of the resulting crater.  Our experiments use Carbopol gel, a yield-stress fluid, for both the spherical impactor and the target pool. We employ a high-speed camera to record the cavity evolution through a transparent cubic tank following impact. Studying the transient part of the process, we find an energy balance of kinetic, potential, elastic and yield energy and using these findings we explain the size and shape of the transient cavities. Simulations are performed using OpenFOAM with the aim of reproducing the experimental impacts using non-Newtonian fluid models. By varying the models’ parameters, we explore the influence of each of them on the resulting craters. By comparing these results with the experimental ones we disentangle the complex nature of the material we use.

    

Retraction Dynamics of Droplets Impacting on Mask Surfaces

Phenomena of droplet impact on solid surfaces are ubiquitous in nature and have been widely explored for industrial applications, such as inkjet printing systems, anti-icing, and spray cooling. Recently, droplet impact on a face mask has been considered since COVID-19 pandemic. In this study, we experimentally studied the retraction dynamics of droplets impact on mask surfaces with different roughness. We firstly focused on understanding the relationship between retraction phase and the final impingement mode. During inertia-dominant retraction regime, the kinetic energy was investigated to analyze the retraction dynamics. We observed that the retraction kinetic energy determined the final impingement mode. Secondly, in order to investigate the effect of surface roughness on the droplet behavior, we monitored the retraction dynamics of the droplet upon each surface by high-speed imaging. The results showed that the rough rim pattern formed upon the rough surface decreased the retraction kinetic energy. This study provides a better understanding of retraction dynamics by developing a theoretical energy model to predict the final behavior of the droplet. We also discussed the mask roughness for minimizing disease transmission with a good breathable performance.   

Author not Attending

Here we analyze the splash transition of drops of liquids with different viscosities impacting normally over different types of rough superhydrophobic substrates, finding that the velocity for the splash transition, V^*, increases for increasing values of the liquid viscosity and also when the proportion of air entrapped at the substrate corrugations decreases. Our experimental results also reveal that the amount of air entrapped between the substrate and the wall increases with the value of the relative roughness ϵ = ε/R, with ε and R indicating the amplitude of the corrugations and the radius of the drop, respectively. We show that our experimental values of V^*, as well as those reported in similar contributions in the literature, can be predicted using the splashing model presented in Quintero, Riboux & Gordillo (J. Fluid Mech., vol. 870, 2019, 175−188) once the liquid shear stress at the wall is expressed as a decreasing function of ϵ namely, of the proportion of air entrapped at the substrate.

    

Impact Dynamics of Hollow Droplets

The impact of droplets on rigid substrates is accompanied by the outward spreading of the liquid on the substrate, forming a lamella. Here, we report on the impact dynamics of an air-in-liquid hollow droplet on a rigid substrate. We show that during the impact of a hollow droplet (HD), the formation of the lamella is accompanied by the formation of a central jet of liquid moving upwards against the direction of impact. The liquid jet is referred to as the counterjet (CJ) and comprises 30 – 60% of the volume of the liquid in the HD. The volume of the liquid entering the CJ during the impact of a HD with a given liquid volume is observed to be independent of the impact height and increases with the volume of air encapsulated in the HD. Interestingly, even though almost half of the liquid in the droplet goes into forming the counterjet, the maximum spread of a HD is almost similar to that of a simple droplet with liquid volume and height of impact same as that of the HD. We establish that there exists an energy transfer from the liquid in the CJ to the liquid in the lamella and that the viscous loss during impact of a HD is relatively less compared to that of a simple droplet.

    

Compressibility Effects in High-speed Droplet Impact

The role of compressibility on impacts produced by high-speed (supersonic/hypersonic) liquid droplets is not well understood. The development of hypersonic projectiles requires a better understanding of the forces imparted on the object and the consequences of impact.  Droplet impact may create a water hammer effect that can lead to damage and alter the flow around the high-speed object. In this work, the impact of a 2D circular water droplet at Mach numbers greater than 2 on a rigid wall is investigated through numerical simulations. The simulations are compared against theory and approximation equations that account for compressibility. Numerical simulations are performed using a high-order accurate, shock- and interface-capturing, solution-adaptive discontinuous Galerkin method with the five-equations compressible multiphase model. As the speed of the droplet increases, the role of compressibility becomes increasingly important. The relationship between pressure and initial velocity is determined and compared to water hammer theory.

    

Experimental investigation of droplet impact on dry surface in a variable ambient pressure environment.

In this study, the effects of the ambient pressure on the dynamics of the impact of a Newtonian droplet on a dry surface are investigated using high-speed photography. Video acquisition of droplet impact was performed at 20,000 frames per second in a transparent chamber pressurized up to 4 atm using water droplets with a 3 mm diameter at an impact velocity of approx. 3 m/s.

Previous studies demonstrate that reducing the ambient pressure can suppress splash on a dry surface due to the lack of entrapment of the ambient gas between the droplet and the surface. These studies implemented sub-atmospheric ambient pressures to reduce the trapped gas bubble and suppress the formation of the secondary droplet formation. The present study further examines the effect of changes in pressure on bubble entrapment on droplet impact by analyzing droplet impact on a dry surface in a super-atmospheric pressure environment.

The results show that, under the ambient pressure of 4 atm, small secondary droplets (~50 µm in diameter) were ejected during impact, while no secondary droplets were observed under the atmospheric ambient pressure. In the pressurized condition, the secondary droplets were ejected at approximately 0.25 µs after the droplet impact, well before the formation of the droplet corona.   

The coalescence to stretching separation transition in binary droplet collisions

The transition from coalescence to stretching separation occurs in binary droplet collisions as the collision off-set (impact parameter) is increased. This work investigates the impact of fluid viscosity on this transition for equi-diameter droplets It shows that the transition is viscosity-independent for Ohnesorge numbers spanning an order of magnitude. The maximum length of coalesced droplet ligand formed prior to stretching separation is 3.35 droplet diameters. Surprisingly this was constant for all conditions tested, i.e. independent of Weber and Ohnesorge number. This observation can be used to develop a simple, robust model of the coalescence-stretching separation transition.

    

'Cassie-Baxter to' Wenzel like transition on patterned electrodes

Hydrogen production through electrolysis is receiving widespread attention in the wake of the much-desired energy transition in our society. However, this hitherto limited to lab-scale process suffers from low productivity due to the produced hydrogen gas bubbles not 'taking off' the electrode efficiently, thereby blocking the production of the next bubble. Researchers have attempted to create patterned substrates with hydrophobic patches which would force the bubbles to limited parts of the electrode, thereby helping them take off. However, sideways movement of bubbles on these patches and subsequent coalescence between the bubbles, keep posing problems in such situations. In this work, patterned substrates have been created by photolithograhy with various hydrophobic, dielectric layers. The jump of a water droplet from the top of of a patch (a pillar) to the area next to the pillar (a valley), a phenomenon very similar to the classic Cassie-Baxter to Wenzel type transition. We observe separated regimes in the nature of the phenomenon, based on the type of dielectric layers. More importantly, the influence of an external electric potential has been investigated on the nature of the jump, since the electrodes during electrolysis also carry such potential.   

On the Shapes of Microliter Alcoholic Sessile Droplets in Normal Atmospheric Conditions

Alcoholic sessile droplets do not typically behave as pure-liquid (even volatile) ones. This is due to their hygroscopic nature and the ambient moisture present in the atmosphere. In such conditions, the absorbed water concentration near the contact line gets higher in comparison to the bulk of the droplet. This, in turn, induces strong solutal Marangoni stresses from the apex of the droplet toward its contact line, modifying the otherwise expected droplet shapes and spreading laws. Experiments have been conducted by depositing initially pure alcoholic droplets on a sapphire substrate inside a controlled cell. The relative humidity (RH) and temperature inside this cell can be modified, maintained, and monitored for a wide range. The initial volumes of these droplets are in the microliter range. At different RH, once the droplet reaches an apparent quasi-steady condition, the cross-sectional shapes of the droplet have been obtained using an interferometric technique. Finally, the measured profiles are compared with numerical calculations. This study highlights, in particular, the importance of considering the non-ideality of alcohol-water solutions for droplet regime determination.

 

    

Influence of governing dimensionless parameters on droplet impact dynamics

Droplet impacts on solid surfaces are a key element of a wide variety of phenomena encountered in technical applications, such as ink-jet printing, spray painting and coating, plasma spraying, and crop spraying, etc. The impact may result in the droplet spreading over the solid surface, receding, or rebounding which depends on numerous factors such as impact velocity, droplet size, etc. In this study, we numerically analyzed the impingement of a single droplet on a stationary surface in the regimes of deposition or rebound. We considered the effects of droplet to surface distance, Reynold number, and Weber number on the droplet dynamics, impingement outcome, spreading ratio, wetted length, maximum rebound height etc. We used Volume of Fluid approach available within commercial CFD package Ansys Fluent to conduct our numerical simulations and compared our numerical results with the literature data and found good agreement between them. Finally, using the simulation data, we developed machine learning based predictive model algorithm which can predict the impingement outcome (deposition or rebound) as well as the maximum spreading ratio based on the governing dimensionless parameters.