Upon impact on a solid surface, a drop expands into a sheet, a corona, which can rebound, stick or splash and fragment into secondary droplets. Previously, focus has been placed on impacts of single drops on surfaces to understand their splash, rebound or spreading. This is important for spraying, printing, and environmental and health processes such as contamination by pathogen-bearing droplets. However, sessile drops are ubiquitous on most surfaces and their interaction with the impacting drop is largely unknown. We report on the regimes of interactions between an impacting drop and a sessile drop. Combining experiments and theory, we derive the existence conditions for the four regimes of drop–drop interaction identified, and report that a subtle combination of geometry and momentum transfer determines a critical impact force governing their physics. Crescent-moon fragmentation is most efficient at producing and projecting secondary droplets, even when the impacting drop Weber number would not allow for splash to occur on the surface considered if the drop were isolated. We introduce a critical horizontal impact Weber number $We_{c}$ that governs the formation of a sheet from the sessile drop upon collision with the expanding corona of the impacting drop. We also predict and validate important properties of the crescent-moon fragmentation: the extension of its sheet base and the ligaments surrounding its base. Finally, our results suggest a new paradigm: impacts on most surfaces can make a splash of a new kind – a crescent-moon – for any impact velocity when neighbouring sessile drops are present.

Turbulent flows subject to solid-body rotation are known to generate steep energy spectra and two-dimensional columnar vortices. The localness of the dominant energy transfers responsible for the accumulation of the energy in the two-dimensional columnar vortices of large horizontal scale remains undetermined. Here, we investigate the scale-locality of the energy transfers directly contributing to the growth of the two-dimensional columnar structures observed in the intermediate Rossby number () regime. Our approach is to investigate the dynamics of the waves and vortices separately: we ensure that the two-dimensional columnar structures are not directly forced so that the vortices can result only from association with wave to vortical energy transfers. Detailed energy transfers between waves and vortices are computed as a function of scale, allowing the direct tracking of the role and scales of the wave–vortex nonlinear interactions in the accumulation of energy in the large two-dimensional columnar structures. It is shown that the dominant energy transfers responsible for the generation of a steep two-dimensional spectrum involve direct non-local energy transfers from small-frequency small-horizontal-scale three-dimensional waves to large-horizontal-scale two-dimensional columnar vortices. Sensitivity of the results to changes in resolution and forcing scales is investigated and the non-locality of the dominant energy transfers leading to the emergence of the columnar vortices is shown to be robust. The interpretation of the scaling law observed in rotating flows in the intermediate- regime is revisited in the light of this new finding of dominant non-locality.

Rotating homogeneous turbulence in a finite domain is studied using numerical simulations, with a particular emphasis on the interactions between the wave and zero-frequency modes. Numerical simulations of decaying homogeneous turbulence subject to a wide range ofbackground rotation rates are presented. The effect of rotation is examined in two finiteperiodic domains in order to test the effect of the size of the computational domain on the results obtained, thereby testing the accurate sampling of near-resonant interactions.We observe a non-monotonic tendency when Rossby number Ro is varied from large values to the small-Ro limit, which is robust to the change of domain size. Three rotation regimes are identified and discussed: the large-, the intermediate-, and the small-Ro regimes. The intermediate-Ro regime is characterized by a positive transfer of energy from wave modes to vortices. The three-dimensional to two-dimensional transfer reaches an initial maximum for Ro ≈ 0.2 and it is associated with a maximum skewness of vertical vorticity in favour of positive vortices. This maximum is also reached at Ro ≈ 0.2. In the intermediate range an overall reduction of vertical energy transfer is observed. Additional characteristic horizontal and vertical scales of this particular rotation regime are presented and discussed.

We consider the radially expanding sheet formed upon impact of a drop on a surface of comparable size to that of the drop. A unified self-similar solution for the unsteady radial thickness profile of the expanding sheet is derived from first principles in the inviscid limit. This unified functional form reconciles two conflicting theoretical profiles of sheet thickness proposed in the literature and allows for the collapse on a single curve direct measurements of sheet thickness profiles reported in the literature and the detailed measurements conducted herein. We show good agreement between our proposed unified thickness profile and data from our experiments for a range of surface-to-drop size ratios. We show that there is an optimal range of surface-to-drop size ratio for which the hypothesis of inviscid thin sheet expansion in the air holds. Outside of this optimal range, either insufficient vertical momentum is transferred to horizontal momentum to form an expanding sheet or viscous effects become too important to neglect. In this latter regime, the dominant effect of surface friction is to modify the velocity profile. We elucidate this effect using a Blasius-type boundary layer model. Finally, we relate the geometry of the drop in its early phase of impact to the sheet thickness profile in the air. We show that the coefficients of the proposed unified similarity thickness profile can directly be linked to volume flux conservation at early times, and to the maximum sheet thickness at the edge of the surface. Our results thus quantitatively link the fluid history on the surface to the thickness and velocity profiles of the freely expanding sheet in the air.

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.

Upon burst, surface bubbles transfer biological and chemical material from water bodies to the air we breathe via the production of droplets. An understanding of what shapes the size and payload of such droplets starts by understanding the fundamental physics of bubble birth, drainage and burst. Our combined experimental and theoretical investigation focuses on film-drop-producing surface bubbles. Controlling fluid properties such as temperature, salinity and volatility, coupled with changes of ambient air saturation, we elucidate the ageing and lifetime of bubbles. We derive and validate a generalized bubble cap drainage model accounting for both curvature-pressure-induced drainage and Marangoni flows induced by the coupling between the bubble and its surrounding air. We show that this deterministic drainage is coupled with stochastic local perturbations, both intrinsic and extrinsic, from impacts by mist droplets to microbubbles. We derive the conditions for such perturbations to be lethal to the cap film, involving the competition of mixing and drainage time scales on the bubble, the film thickness, the size of the perturbation and the local Marangoni stresses introduced. We explain how the mixing dynamics on the cap ensures that bursts mostly occur at the foot of bubbles rather than on their cap. Our study sheds light on the coupling between the deterministic cap thinning and the stochastic events leading to bubble death. We conclude that ubiquitous water contaminants enable the birth of a bubble, sustain it through its ageing, but ultimately also kill it.

Understanding what shapes the drop size distributions produced from fluid fragmentation is important for a range of industrial, natural and health processes. Gilet & Bourouiba (J. R. Soc. Interface, vol. 12, 2015, 20141092) showed that both the size and speed of fragmented droplets are critical to transmission of pathogens in the agricultural context. In this paper, we study both the size and speed distributions of droplets ejected during a canonical unsteady sheet fragmentation from drop impact on a target of comparable size to that of the drop. Upon impact, the drop transforms into a sheet which expands in the air bounded by a rim on which ligaments grow, continuously shedding droplets. We developed high-precision tracking algorithms that capture all ejected droplets, measuring their size and speed, as well as the detachment time from, and link to, their ligament of origin. Both size and speed distributions of all ejected droplets are skewed. We show that the polydispersity and skewness of the distributions are inherently due to the unsteadiness of the sheet expansion. We show that each ligament sheds a single drop at a time throughout the entire sheet expansion by a mechanism of end-pinching. The droplet-to-ligament size ratio $R\approx 1.5$ remains constant throughout the unsteady fragmentation, and is robust to change in impact Weber number. We also show that the population mean speed of the fragmented droplets at a given time is equal to the population mean speed of ligaments one necking time prior to detachment time.