Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session G13: Drop Interactions 
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Chair: Michael Rother, University of Minnesota, Duluth Room: Georgia World Congress Center B218 
Monday, November 19, 2018 10:35AM  10:48AM 
G13.00001: Gravitational Interactions of Small Contaminated Drops ina Temperature Gradient at Finite Stokes Numbers Michael Rother Relative trajectories are calculated for two sedimenting spherical drops in the presence of a vertical temperature gradient with exact methods for determining the hydrodynamic forces at finite Stokes number and low Reynolds number. The drops are covered with incompressible surfactant, and thermal convection and Brownian motion are negligible. When the Reynolds number is small, fluid inertia is negligible, and the hydrodynamic forces are linear functions of the translational velocities of the drops. However, at nonzero Stokes numbers, drop inertia must be taken into account, and the hydrodynamic forces do not balance the applied forces. For drops in close approach, lubrication forces and attractive molecular forces are considered. In the absence of attractive molecular forces, inertia leads to asymmetry in the drops’ relative trajectories. Interesting behavior, such as two drops moving in stable, tandem motion with a finite gap, is possible in the dimensionless parameter space. Moreover, retrograde motion is observed in the numerical results, depending on the relative strength of the thermocapillary and gravitational driving forces. An important application is to raindrop growth, where the model is applicable to water droplets with radii between 10 and 30 μm. 
Monday, November 19, 2018 10:48AM  11:01AM 
G13.00002: Spin lattices of walking droplets Pedro J Saenz, Giuseppe Pucci, Alexis Goujon, Rodolfo R Rosales, Jorn Dunkel, John Bush We present experiments that demonstrate the spontaneous emergence of collective behavior in spin lattices of droplets walking on a vibrating fluid surface. Circular wells at the bottom of the fluid bath encourage individual droplets to walk in clockwise or counterclockwise direction along circular trajectories centered at the lattice sites. A thin fluid layer between the wells enables wavemediated interactions between neighboring walkers resulting in coherent rotation dynamics across the lattice. When the paircoupling is sufficiently strong, interactions between neighboring droplets may induce local spin flips leading to ferromagnetic or antiferromagnetic order. Results for different lattice geometries are discussed. 
Monday, November 19, 2018 11:01AM  11:14AM 
G13.00003: Oscillations of a hydrodynamic crystal lattice Stuart J Thomson, Miles MP Couchman, John Bush When brought into close proximity, two or more droplets bouncing on a vertically vibrating fluid bath exhibit a rich spectrum of dynamical behaviour. In particular, pairs of such droplets have been shown to destabilize into oscillatory, orbiting, and promenading modes, while a collection of multiple droplets can form crystallike lattices with highly regular structure. In this talk, we present the results of a combined experimental and theoretical study in we characterize and rationalize the behaviour of a circular chain of bouncing drops, reminiscent of a onedimensional crystal lattice. As the vibrational forcing is increased, the stationary chain first destabilizes into an oscillatory mode and then into a striking solitonlike disturbance, before ``melting'' at sufficiently high acceleration of the bath. Similarities with models such as the Toda lattice, used to model crystal vibrations in solidstate physics, are discussed. 
Monday, November 19, 2018 11:14AM  11:27AM 
G13.00004: Nonkeplerian orbits of drops levitating on a cryogenic bath Anais Gauthier, Guillaume Lajoinie, Devaraj R.M. Van Der Meer, Jacco Snoeijer An “inverse Leidenfrost” state is observed when ambient temperature drops are deposited on a liquid nitrogen bath: fast evaporation of the pool is sufficient to generate and sustain a vapor film that keeps the drops in levitation. Isolated suspended drops then move in straight lines with nearzero friction. Here, we discuss the case of two gliding drops approaching each other. Each drop locally deforms the surface of the bath to balance its weight, and interaction between the two menisci generates mutual attraction. This is a frictionless version of the socalled “Cheerios effect”. In first approach, such a twobody system shares similarities with gravitational attraction between planets. However, the fundamental difference in the nature of the attractive potential gives rise to a set of trajectories quite distinct from the classical Keplerian orbits (ellipse, parabola or hyperbola). We first reconstruct the Cheerios attractive potential from experimental measurement of the drops motion, and then, by pushing the comparison further, we use the reconstructed potential to predict the most unusual trajectories that were experimentally observed . Finally, this approach enables us to determine the necessary conditions to obtain closed orbits. 
Monday, November 19, 2018 11:27AM  11:40AM 
G13.00005: Printing wetonwet: attraction and repulsion of drops on a viscous film Michiel A. Hack, Maxime Costalonga, Tim Segers, Stefan A. Karpitschka, Herman Wijshoff, Jacco H. Snoeijer Wetonwet printing is frequently used in inkjet printing for graphical and industrial applications, where substrates can be coated with a thin liquid film prior to ink drop deposition. Two drops placed close together are expected to interact via deformations of the thin viscous film, but the nature of these capillary interactions is unknown. Here we show that the interaction can be attractive or repulsive depending on the distance separating the two drops. The distance at which the interaction changes from attraction to repulsion is found to depend on the thickness of the film, and increases over time. We reveal the origin of the nonmonotonic interactions, which lies in the appearance of a viscocapillary wave on the thin film induced by the drops. Using the thinfilm equation we identify the scaling law for the spreading of the waves, and demonstrate that this governs the range over which interaction is observed. 
Monday, November 19, 2018 11:40AM  11:53AM 
G13.00006: Abstract Withdrawn

Monday, November 19, 2018 11:53AM  12:06PM 
G13.00007: Attraction of sessile pure droplets evaporating into air Hosein Sadafi, Sam Dehaeck, Alexey Rednikov, Pierre Colinet Two pure droplets of the same perfectly wetting volatile liquid are seen to attract when deposited nearby on a flat horizontal substrate in the ambient atmosphere. The phenomenon is studied in detail using interferometry for a number of liquids. Possible driving factors behind the interaction, acting through the gas phase and the substrate are being investigated both experimentally and theoretically. To predict the velocity of attraction, a model will be presented and verified against the experimental data obtained in this work. The influence of the initial distance between the drops, and the physical properties of vapor, liquid, and solid will be investigated. 
Monday, November 19, 2018 12:06PM  12:19PM 
G13.00008: Drop Squeezing through Interparticle Constrictions with Insoluble Surfactant Jacob R Gissinger, Alexander Z Zinchenko, Robert Davis Despite the prevalence of surfactants in confined biological and subsurface settings, their 
Monday, November 19, 2018 12:19PM  12:32PM 
G13.00009: Improving Binary Droplet Collision Model Prediction of the Bouncing Regime Karrar AlDirawi, Andrew Bayly In this work, we experimentally investigate binary droplet collisions of identical droplets of 2%, 4%, and 8% of hydroxypropyl methylcellulose (HPMC) solutions in water. Monodisperse nozzles were used to generate the droplets, while the collisions events were captured using a highspeed camera. The collisions outcomes  namely bouncing, coalescence, reflexive separation, and stretching separation  were mapped in the parameter space of Weber number and the impact parameter for the three solutions. These studies were consistent with published studies and confirmed that existing models poorly predict the boundary of the bouncing regime at low impact parameter. We attribute this to modelling assumptions that are related to the considered kinetic energy and the surface area at the maximum deformation of the droplets. Therefore, a new model was developed by redefining the surface area at the moment of the maximum deformation of the droplets and making it a function of the impact parameter. The new model shows a striking improvement in the prediction of the bouncing boundary, where the main absolute error was reduced by a factor of 9 compared to the existing models. 
Monday, November 19, 2018 12:32PM  12:45PM 
G13.00010: Noncontinuum hydrodynamic interactions between settling inertial droplets Melanie Li Sing How, Anubhab Roy, Donald L Koch, Lance R Collins As cloud droplets coalesce, the air squeezed out of the gap gives rise to a continuum lubrication force that diverges with decreasing separation, thus preventing collisions from taking place. For separations comparable to the mean free path of the gas, the noncontinuum nature of the force leads to collisions in finite time. This work is a continuation of Sundararajakumar & Koch (J.Fluid M.313:283308,1996) who analyzed the noncontinuum lubrication force for the normal motion of two spheres. We extend that work to include tangential motions over the full range of Knudsen numbers (ratio of the gas meanfree path to the average droplet radius) as a function of the gap thickness. The hydrodynamic resistivity functions are obtained using a uniformly valid approximation that includes noncontinuum lubrication forces at small separations and continuum hydrodynamic interactions at larger separations. These hydrodynamic forces are used to calculate the collision rate of inertial droplets settling without a background flow. Using trajectory analysis, the collision efficiency is found for different droplet size ratios, Knudsen numbers and Stokes numbers. Eventually, this analysis will be combined with direct numerical simulations to incorporate the effects of fluid turbulence. 
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