Session S04: Drops: Multiple Drop Interactions (5:45pm - 6:30pm CST)

Vibrational instabilities of bound aggregates of bouncing droplets

Millimetric droplets bouncing on the surface of a vibrating fluid bath may interact through a shared wavefield to form a variety of quantized bound states. We present the results of a combined experimental and theoretical investigation investigating the rich variety of instabilities that may arise in droplet pairs, rings, and lattices as the bath’s vibrational acceleration is increased progressively. Particular attention is given to a linear stability analysis of two-dimensional Bravais lattices of bouncing droplets that allows us to discern the most unstable wave mode as a function of the initial lattice geometry and inter-drop spacing. Connections with collective vibrations in solid-state crystalline lattices are discussed.   

Coffee-Stain Deposits from Multiple Evaporating Droplets

We build on the recent theoretical work of Wray et al. [J. Fluid Mech. 884 A45 (2020)] concerning the competitive diffusion-limited evaporation of multiple thin, sessile droplets in proximity to each other. We obtain analytical predictions for the density of the contact-line deposits ("coffee-stains") left on the substrate when (initially uniformly dispersed) particles are advected by the evaporation-induced flow. Neighbouring droplets undergoing diffusion-limited evaporation interact via their vapour fields, competing to evaporate, which results in a nonlocal ``shielding'' effect, reducing the rate of evaporation. In particular, our theory confirms that in regions where evaporation is reduced by shielding, the deposition is also reduced. We give explicit results describing the deposits from a pair of identical interacting droplets, and demonstrate the excellent quantitative agreement with experimental findings of Pradhan and Panigrahi [Coll. Surf. A 482 562 (2015)]. We also give corresponding predictions for the case of three droplets arranged in an equilateral triangle.   

Resonance, Instability and Dynamical Stabilization in Bouncing Droplet Chains

The bouncing droplet system has attracted recent interest because it exhibits behaviors similar to those previously observed only in the microscopic quantum realm. We present the results of a theoretical investigation of one-dimensional chains of bouncing droplets, with particular attention to the case in which the drop at one end of the chain is oscillated periodically. We demonstrate the existence of resonant forcing frequencies, and our predictions based on linear theory compare favorably with numerical simulations. We also demonstrate a dynamical stabilization of the chain into a new bouncing state for sufficiently high forcing frequencies. Our results highlight the role of temporally nonlocal interactions in the dynamics of this unique system.   

Measurement of near-contact motion of cloud-sized droplets

The growth of cloud droplets from about 15 to 30 microns in radius is not well-understood. Turbulence drives collisions for droplets in this size range, but experiments to date have been unable to reliably measure the motions of particles when the separations between them are close to the size of the particles. In this near-contact regime, the effect of one droplet on the motions of the other due to hydrodynamic interactions cannot be ignored. We present measurements of the motions of droplet pairs in quiescent air with both colliding and nearly-colliding trajectories of approximately 25-micron water droplets when the distance to contact is less than the average radius of the droplets and initial impact parameter is between 0 and 6. We show that the behavior of the droplets is sensitive to the size ratio between the pair. We also show that droplet rotation induced by interactions between the droplets can lift both off their previous streamlines, a potential new mechanism to drive collisions in systems of three or more droplets. The data were acquired in part in collaboration with A. Dubey and B. Mehlig at the University of Gothenburg.   

Drops within drops within drops

We consider a nested set of axisymmetric viscous drops in Stokes flow. First, we derive the system of equations governing the motion of n nested drops and of the fluid between them. Then, we apply the result to compute the motion of n nested initially concentric drops in a strainfield. Here we are interested in the dependence of the strainrate in the innermost drop on the n fluid viscosities. Finally, we present the equations for a set of nested drops in a constrained geometry bounded by walls, and apply them to compute the evolution of double drops moving through a constriction.