Violent respiratory events such as coughs and sneezes play a key role in transferring respiratory diseases between infectious and susceptible individuals. We present the results of a combined experimental and theoretical investigation of the fluid dynamics of such violent expiratory events. Direct observation of sneezing and coughing events reveals that such flows are multiphase turbulent buoyant clouds with suspended droplets of various sizes. Our observations guide the development of an accompanying theoretical model of pathogen-bearing droplets interacting with a turbulent buoyant momentum puff. We develop in turn discrete and continuous models of droplet fallout from the cloud in order to predict the range of pathogens. According to the discrete fallout model droplets remain suspended in the cloud until their settling speed matches that of the decelerating cloud. A continuous fallout model is developed by adapting models of sedimentation from turbulent fluids. The predictions of our theoretical models are tested against data gathered from a series of analogue experiments in which a particle-laden cloud is ejected into a relatively dense ambient. Our study highlights the importance of the multiphase nature of respiratory clouds, specifically the suspension of the smallest drops by circulation within the cloud, in extending the range of respiratory pathogens.

Water striders Gerridae are insects of characteristic length 1 cm and weight 10 dynes that reside on the surface of ponds, rivers, and the open ocean. Their weight is supported by the surface tension force generated by curvature of the free surface, and they propel themselves by driving their central pair of hydrophobic legs in a sculling motion. Previous investigators have assumed that the hydrodynamic propulsion of the water strider relies on momentum transfer by surface waves. This assumption leads to Denny's paradox: infant water striders, whose legs are too slow to generate waves, should be incapable of propelling themselves along the surface. We here resolve this paradox through reporting the results of high-speed video and particle-tracking studies. Experiments reveal that the strider transfers momentum to the underlying fluid not primarily through capillary waves, but rather through hemispherical vortices shed by its driving legs. This insight guided us in constructing a self-contained mechanical water strider whose means of propulsion is analogous to that of its natural counterpart.

We present the results of a combined experimental and theoretical investigation of droplets walking on a vertically vibrating fluid bath. Several walking states are reported, including pure resonant walkers that bounce with precisely half the driving frequency, limping states, wherein a short contact occurs between two longer ones, and irregular chaotic walking. It is possible for several states to arise for the same parameter combination, including high- and low-energy resonant walking states. The extent of the walking regime is shown to be crucially dependent on the stability of the bouncing states. In order to estimate the resistive forces acting on the drop during impact, we measure the tangential coefficient of restitution of drops impacting a quiescent bath. We then analyse the spatio-temporal evolution of the standing waves created by the drop impact and obtain approximations to their form in the small-drop and long-time limits. By combining theoretical descriptions of the horizontal and vertical drop dynamics and the associated wave field, we develop a theoretical model for the walking drops that allows us to rationalize the limited extent of the walking regimes. The critical requirement for walking is that the drop achieves resonance with its guiding wave field. We also rationalize the observed dependence of the walking speed on system parameters: while the walking speed is generally an increasing function of the driving acceleration, exceptions arise due to possible switching between different vertical bouncing modes. Special focus is given to elucidating the critical role of impact phase on the walking dynamics. The model predictions are shown to compare favourably with previous and new experimental data. Our results form the basis of the first rational hydrodynamic pilot-wave theory.

We consider the hydrodynamics of creatures capable of sustaining themselves on the water surface by means other than flotation. Particular attention is given to classifying water walkers according to their principal means of weight support and lateral propulsion. The various propulsion mechanisms are rationalized through consideration of energetics, hydrodynamic forces applied, or momentum transferred by the driving stroke. We review previous research in this area and suggest directions for future work. Special attention is given to introductory discussions of problems not previously treated in the fluid mechanics literature, with hopes of attracting physicists, applied mathematicians, and engineers to this relatively unexplored area of fluid mechanics.

The variability of bird beak morphology reflects diverse foraging strategies. One such feeding mechanism in shorebirds involves surface tension-induced transport of prey in millimetric droplets: By repeatedly opening and closing its beak in a tweezering motion, the bird moves the drop from the tip of its beak to its mouth in a stepwise ratcheting fashion. We have analyzed the subtle physical mechanism responsible for drop transport and demonstrated experimentally that the beak geometry and the dynamics of tweezering may be tuned to optimize transport efficiency. We also highlight the critical dependence of the capillary ratchet on the beak's wetting properties, thus making clear the vulnerability of capillary feeders to surface pollutants.

Yves Couder, Emmanuel Fort and coworkers have recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. We review experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. We then review theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantum-like behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, while multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. We attempt to assess the potential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics, more closely related to de Broglie's original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through workers in stochastic electrodynamics.

The current revival of the American economy is being predicated on social distancing, specifically the Six-Foot Rule, a guideline that offers little protection from pathogen-bearing aerosol droplets sufficiently small to be continuously mixed through an indoor space. The importance of airborne transmission of COVID-19 is now widely recognized. While tools for risk assessment have recently been developed, no safety guideline has been proposed to protect against it. We here build on models of airborne disease transmission in order to derive an indoor safety guideline that would impose an upper bound on the “cumulative exposure time,” the product of the number of occupants and their time in an enclosed space. We demonstrate how this bound depends on the rates of ventilation and air filtration, dimensions of the room, breathing rate, respiratory activity and face mask use of its occupants, and infectiousness of the respiratory aerosols. By synthesizing available data from the best-characterized indoor spreading events with respiratory drop size distributions, we estimate an infectious dose on the order of 10 aerosol-borne virions. The new virus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) is thus inferred to be an order of magnitude more infectious than its forerunner (SARS-CoV), consistent with the pandemic status achieved by COVID-19. Case studies are presented for classrooms and nursing homes, and a spreadsheet and online app are provided to facilitate use of our guideline. Implications for contact tracing and quarantining are considered, and appropriate caveats enumerated. Particular consideration is given to respiratory jets, which may substantially elevate risk when face masks are not worn.

Yves Couder and coworkers have demonstrated that millimetric droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic quantum realm, including single-particle diffraction, tunneling, quantized orbits, and wave-like statistics in a corral. We here develop an integro-differential trajectory equation for these walking droplets with a view to gaining insight into their subtle dynamics. The orbital quantization is rationalized by assessing the stability of the orbital solutions. The stability analysis also predicts the existence of wobbling orbital states reported in recent experiments, and the absence of stable orbits in the limit of large vibrational forcing. In this limit, the complex walker dynamics give rise to a coherent statistical behavior with wave-like features. We characterize the progression from quantized orbits to chaotic dynamics as the vibrational forcing is increased progressively. We then describe the dynamics of a weakly-accelerating walker in terms of its wave-induced added mass, which provides rationale for the anomalously large orbital radii observed in experiments.