RESUMEN
In many physical processes, including cloud electrification, electrospray, and demulsification, droplets and bubbles are exposed to electric fields and may either remain whole or burst in response to electrical stresses. Determining the stability limit of a droplet exposed to an external electric field has been a long-standing mathematical challenge, and the only analytical treatment to date is an approximate calculation for the particular case of a free-floating droplet. Here we demonstrate, experimentally and theoretically, that the stability limit of a conducting droplet or bubble exposed to an external electric field is described by a power law with broad generality that, in practice, applies to the cases in which the droplet or bubble is pinned or sliding on a conducting surface or free floating. This power law can facilitate the design of devices for liquid manipulation via a simple formula that captures the parameter range of bubbles and droplets that can be supported on electrified surfaces.
RESUMEN
We present the results of an experimental investigation of the dynamics of droplets bouncing on a vibrating fluid bath for forcing accelerations above the Faraday threshold. Two distinct fluid viscosity and vibrational frequency combinations (20 cS-80 Hz and 50 cS-50 Hz) are considered, and the dependence of the system behavior on drop size and vibrational acceleration is characterized. A number of new dynamical regimes are reported, including meandering, zig-zagging, erratic bouncing, coalescing, and trapped regimes. Particular attention is given to the regime in which droplets change direction erratically and exhibit a dynamics akin to Brownian motion. We demonstrate that the effective diffusivity increases with vibrational acceleration and decreases with drop size, as suggested by simple scaling arguments.
RESUMEN
The walking droplet system has extended the range of classical systems to include several features previously thought to be exclusive to quantum systems. We review the hierarchy of analytic models that have been developed, on the basis of various simplifying assumptions, to describe droplets walking on a vibrating fluid bath. Particular attention is given to detailing their successes and failures in various settings. Finally, we present a theoretical model that may be adopted to explore a more generalized pilot-wave framework capable of further extending the phenomenological range of classical pilot-wave systems beyond that achievable in the laboratory.
RESUMEN
Millimetric droplets may be levitated on the surface of a vibrating fluid bath. Eddi et al. [Europhys. Lett. 82, 44001 (2008)] demonstrated that when a pair of levitating drops of unequal size are placed nearby, they interact through their common wavefield in such a way as to self-propel through a ratcheting mechanism. We present the results of an integrated experimental and theoretical investigation of such ratcheting pairs. Particular attention is given to characterizing the dependence of the ratcheting behavior on the droplet sizes and vibrational acceleration. Our experiments demonstrate that the quantized inter-drop distances of a ratcheting pair depend on the vibrational acceleration, and that as this acceleration is increased progressively, the direction of the ratcheting motion may reverse up to four times. Our simulations highlight the critical role of both the vertical bouncing dynamics of the individual drops and the traveling wave fronts generated during impact on the ratcheting motion, allowing us to rationalize the majority of our experimental findings.
RESUMEN
We report the results of a theoretical investigation of the stability of a toroidal vortex bound by an interface. Two distinct instability mechanisms are identified that rely on, respectively, surface tension and fluid inertia, either of which may prompt the transformation from a circular to a polygonal torus. Our results are discussed in the context of three experiments, a toroidal vortex ring, the hydraulic jump, and the hydraulic bump.
RESUMEN
We present the results of a combined experimental and theoretical investigation of rolling elastic ribbons. Particular attention is given to characterizing the steady shapes that arise in static and dynamic rolling configurations. In both cases, above a critical value of the forcing (either gravitational or centrifugal), the ribbon assumes a two-lobed, peanut shape similar to that assumed by rolling droplets. Our theoretical model allows us to rationalize the observed shapes through consideration of the ribbon's bending and stretching in response to the applied forcing.
RESUMEN
We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an integro-differential trajectory equation, which is found to admit steady orbital solutions. Predictions for the dependence of the orbital radius and frequency on the strength of the radial harmonic force field agree favorably with experimental data. The orbital quantization is rationalized through an analysis of the orbital solutions. The predicted dependence of the orbital stability on system parameters is compared with experimental data and the limitations of the model are discussed.
RESUMEN
Coughs and sneezes feature turbulent, multiphase flows that may contain pathogen-bearing droplets of mucosalivary fluid. As such, they can contribute to the spread of numerous infectious diseases, including influenza and SARS. The range of contamination of the droplets is largely determined by their size. However, major uncertainties on the drop size distributions persist. Here, we report direct observation of the physical mechanisms of droplet formation at the exit of the mouth during sneezing. Specifically, we use high-speed imaging to directly examine the fluid fragmentation at the exit of the mouths of healthy subjects. We reveal for the first time that the breakup of the fluid into droplets continues to occur outside of the respiratory tract during violent exhalations. We show that such breakup involves a complex cascade of events from sheets, to bag bursts, to ligaments, which finally break into droplets. Finally, we reveal that the viscoelasticity of the mucosalivary fluid plays an important role in delaying fragmentation by causing the merger of the droplet precursors that form along stretched filaments; thereby affecting the final drop size distribution farther downstream.
RESUMEN
Gas release in photic-zone microbialites can lead to preservable morphological biosignatures. Here, we investigate the formation and stability of oxygen-rich bubbles enmeshed by filamentous cyanobacteria. Sub-millimetric and millimetric bubbles can be stable for weeks and even months. During this time, lithifying organic-rich laminae surrounding the bubbles can preserve the shape of bubbles. Cm-scale unstable bubbles support the growth of centimetric tubular towers with distinctly laminated mineralized walls. In environments that enable high photosynthetic rates, only small stable bubbles will be enclosed by a dense microbial mesh, while in deep waters extensive microbial mesh will cover even larger photosynthetic bubbles, increasing their preservation potential. Stable photosynthetic bubbles may be preserved as sub-millimeter and millimeter-diameter features with nearly circular cross-sections in the crests of some Proterozoic conical stromatolites, while centrimetric tubes formed around unstable bubbles provide a model for the formation of tubular carbonate microbialites that are not markedly depleted in (13)C.