We present an experimental study of capillary surfers, a new fluid-mediated active system that bridges the gap between dissipation- and inertia-dominated regimes. Surfers are wave-driven particles that self-propel and interact on a fluid interface via an extended field of surface waves. A surfer's speed and interaction with its environment can be tuned broadly through the particle, fluid, and vibration parameters. The wave nature of interactions among surfers allows for multistability of interaction modes and promises a number of novel collective behaviors.

Before a droplet can contact a surface during impact, it must first displace the air beneath it. Over a wide range of impact velocities, the droplet first squeezes the air into a thin film, enhancing its resistance to drainage; this slows the progress of the liquid toward the surface. Indeed, below a critical impact velocity, the air film remains intact, and the droplet rebounds off of the air film without making contact. For impact velocities exceeding this critical impact velocity, the droplet always makes contact. The initiation of contact formation requires a topological transition, whereby the initially connected gas domain is ruptured and a liquid capillary bridge forms, binding the droplet to the surface. Here we probe this transition in detail around the critical impact velocity using calibrated total internal reflection microscopy to monitor the air film thickness and profile at high speed during the impact process. Two air film rupture modalities are observed: nucleated contacts, which are isolated and do not correspond to the global minimum air film thickness, and spontaneous contacts, which occur always on a ring centered upon the impact axis where the air film reaches its global minimum. Our measurements show that for impact velocities exceeding the critical velocity for contact initiation, the air film ruptures at a nearly identical height $h_{min}\approx 20$ nm, for two fluids: silicone oil and a water-glycerol mixture. The height and time duration of the air film prior to contact are presented for over 180 droplet impact experiments. Impact events of water solution droplets show statistics for contact nucleation different from those for the silicone oil; this suggests that another mechanism may dominate contact nucleation during impact of the solution. Nevertheless, a critical impact velocity above which contact always occurs is identifiable for both liquids.

Internal waves are ubiquitous in the ocean and play an essential role in the transport of energy and mixing. Their peculiar reflection enables the concentration of energy on a limit cycle. With wave beams viewed as rays, this reflection on an inclined slope shrinks its width and generically brings closer two initially different trajectories eventually reaching a limit cycle called an attractor. Following previous studies, a ray-tracing algorithm is used to track the convergence of wave beams onto such a structure in a 3D axisymmetric domain. This information is used to design experiments using a truncated conical shaped tank in order to form an inertia-gravity waves attractor in a 3D axisymmetric geometry. By increasing the amplitude of the forcing, an evolution of the attractor characteristics can be observed. The occurrence of waves at frequencies lower than the forcing frequency ${\omega }_0$ suggests triadic resonant instability in a rotating or in a stratified case. Experiments performed in a stratification-only or a rotation-only case indicate two distinct behaviors. The existence of easily excited standing waves, resonant modes of the tank, at frequencies lower than the forcing one enables sharp triadic resonance instability for internal gravity waves, which is not possible for inertial waves. The effect of the symmetry axis is also investigated by adding a cylinder of sufficient diameter at the center of the domain for the wave to reflect on and thereby avoid the interaction on the singularity. Without it, the large amplitude of the waves on the axis triggers nonlinear effects and mixing, denying the access to the wave turbulence regime.

From microfluidics to fog-harvesting applications, tiny droplets are transported along various solid substrates including hairs, threads, grooves, and other light structures. Driven by gravity, a droplet sliding along a vertical fiber is a complex problem since it is losing volume and speed as it goes down. With the help of an original setup, we solve this problem by tracking in real-time droplet characteristics and dynamics. Single fibers as well as multiple fiber systems are studied to consider the presence of grooves. On both fibers and grooved threads, droplet speed and volume are seen to decay rapidly because the liquid entity is leaving a thin film behind. This film exerts a capillary force able to stop the droplet motion before it is completely drained. A model is proposed to capture the droplet dynamics. We evidence also that multiple vertical fibers are enhancing the droplet speed while simultaneously promoting increased liquid loss on grooves.

We present an experimental study of penetrative convection in gases, which allows reaching a lower Prandtl number $\mathrm{Pr}=0.7$ than classical water experiments. A heavy gas (${\mathrm{SF}}_6$) fills the bottom of a meter-sized rectangular tank. Diffusion of ${\mathrm{SF}}_6$ in air establishes a stratified vertical profile in part of the domain. Electric resistors heat the bottom plate of the tank up to a chosen temperature while water circulation fixes the top plate temperature at room temperature. After a short transient, the ${\mathrm{SF}}_6$-rich lower layer convects and progressively invades the upper stably-stratified layer while exciting propagating internal gravity waves. Density and particle image velocimetry (PIV) measurements are performed, allowing us to follow the growth of the convective region as well as the characteristics of the internal waves and convective fields. While mixing at the interface is often modeled in classical penetrative convection with an eddy diffusivity, we find that the convective layer growths here quadratically in time, which contradicts a stationary and homogeneous turbulent diffusion. The analysis of the wave spectra in the stratified domain reveals a peak frequency at the buoyancy frequency, with a clear cutoff above. Running PIV in both layers simultaneously allows us to compute the kinetic energy transfer from the convective zone into the stratified one, which amounts to about $4\%$. We also define a scaling law for the erosion rate as a function of the Froude number.

The triple decomposition of a velocity gradient tensor, which extracts local fluid motions of shear, rigid-body rotation, and irrotational strain, is extended to the decomposition of velocity vectors into shear and nonshear components. The present approach adapts the Biot-Savart law to reconstruct shear and nonshear velocities from the vorticity vectors of shear and rigid-body rotation, respectively. These velocities are related to the flows induced by small-scale shear layers or vortex tubes. The decomposed velocities are investigated with direct numerical simulations of isotropic turbulence and temporally evolving planar jets. The r.m.s. values of shear and nonshear velocities are about $70\%$ and $30\%$ of the r.m.s. value of total velocity fluctuations, and shear layers have a greater contribution to velocity fluctuations than vortex tubes. The shear and nonshear velocities are positively correlated at large scales, and the momentum transfer due to their interaction actively occurs at scales greater than 20 times the Kolmogorov scale. The contributions of shear and nonshear velocities to the Reynolds stress hardly depend on flows. The energy spectra of these velocities collapse well at small scales under Kolmogorov normalization. The present analysis of the turbulent jet confirms that shearing motion has dominant contributions to the production and diffusion of turbulent kinetic energy and the turbulent transport of a passive scalar. In addition, the energy transfer across scales is shown to be dominated by the large-scale velocity gradients arising from shearing motion and the small-scale stresses due to the shear velocity and its interaction with the nonshear component.

While various aerodynamic noise generation mechanisms and characteristics have been extensively studied for drone research, the noise features during the descending flight state have not been well addressed. In this work, we investigate the aerodynamics and aeroacoustics of a two-bladed drone rotor operating in descent using both experimental and numerical approaches. First, we measure the rotor thrust and torque in an anechoic wind tunnel at various rotational speeds and descent rates. The results reveal a significant loss of mean thrust and strong thrust fluctuations with the increase of descent rates due to the formation of highly unsteady vortex rings. The measured acoustic spectra show multiple humps occurring at the blade passing frequency and its harmonics. Next, we perform numerical simulations based on the delayed detached eddy simulations to gain more understanding of the noise generation mechanisms. The computed integrated aerodynamic forces and acoustic spectra agree well with the experimental results. We present nearfield flow structures that demonstrate the gradual formation process of the vortex ring and the complex turbulent wake structures. Notably, the computed aeroacoustic characteristics exhibit a similar tendency with respect to the descent rate to the experimental results. Moreover, the simulation results suggest that the additional noise has a radiation directivity in the axial direction perpendicular to the rotation plane. Finally, we conduct a noise source analysis on the blade surface based on the simulation results, revealing that the strong leading-edge sources are likely related to the blade-wake interaction process during descending flight.

The interaction between two passive human swimmer scale models is investigated both experimentally and numerically. The Froude number, comparing the swimming velocity to the characteristic wave velocity, is conserved in the study. The interaction is quantified for a large range of relative positions and for three speeds corresponding to cruising, average, and sprint swimming. The associated computational fluid dynamics study using OpenFoam allows us to determine the relative positions that optimize the drafting during an open-water race: just behind a lead swimmer or at the level of the hip of a neighbor, with reductions of drag of 40% and 30%, respectively.

We analyze the effects of the fine structure of the electric double layer and of the electrode reaction rate upon wavelength selection of the growing perturbation mode in morphological instability in cathodic electrodeposition from a dilute electrolyte solution. The metal cathode is modeled as a cation exchanger with a fixed charge density equal to the average concentration of free electrons that is several orders of magnitude higher than the typical ionic concentration in a solution. This invokes the need to consider the steric modifications in the modeling of the electric double layer at the solution/electrode interface. Accordingly, the results for Bikerman's steric model are compared to those for the classical Nernst-Planck-Poisson-Stokes model valid for pointlike ions. For both models, the diffuse electric double layer splits into a thin inner portion commensurate with the width of the Stern layer and the steric exclusion width, and a much thicker outer portion scaling with the Debye length. For quiescent cathodic electrodeposition, this fine structure combined with a finite electrode reaction rate regularizes the short-wave singularity in morphological instability of the electrodeposition front. This regularization selects a finite range of unstable perturbation modes, with critical wavelength corresponding to the fastest-growing mode. This wavelength scales with the geometric average of the width of the highly charged inner portion of the electric double layer and the reaction–diffusion length, defined as the ratio of cation diffusivity to the electrode reaction rate. The fluid flow induced by the motion of the solid/liquid interface has a negligible effect on morphological instability. At the same time, the emerging electroconvective (electroosmotic) flow in the nonequilibrium regime with its related electroosmotic instability, has a major effect, selecting the width of the cathodic diffusion layer as the dominant length scale for morphological instability and the emerging dendrites. It is observed that the steric correction considerably lowers the voltage threshold for the onset of the nonequilibrium electroosmotic instability.

This paper is devoted to a specific motion observed for glycerin droplets sliding on a horizontal hydrophobic substrate under the influence of a shear flow. In this regime, the droplet elongates in the flow direction, adopting a rivulet shape. Waves develop on the droplet sheared surface, resulting in a wavy contracting and stretching motion mechanism, similar to the movement of a caterpillar. If long enough, the droplet can break up into several droplets that can be submitted to a pearling instability. Furthermore, these droplets can also coalesce.

We study the drag on a centimetric sphere in a uniform flow in the presence of a free surface as a function of submergence depth. Through direct force measurements in a custom benchtop recirculating flume, we demonstrate that the drag can significantly exceed the corresponding drag in a single-phase flow and achieves a peak at submergence depths just prior to complete immersion. The additional drag in the partially immersed state is rationalized by considering hydrostatic effects associated with the asymmetric surface height profile induced by the obstacle in the flow direction which persists for flow speeds below the minimum capillary-gravity wave speed. At these scales, the sphere's wettability plays a pronounced role in determining the maximum possible drag and results in hysteretic behaviors near touchdown and complete immersion. The influence of flow speed, sphere size, and surface tension on the drag characteristics are additionally explored through a combination of experiments and numerical simulations.

When two bubbles submerged in a liquid are brought closely together, the intermediate liquid film separating the bubbles begins to drain. Once the film ruptures, the bubbles coalesce and form a neck that expands with time. The dynamics of the neck growth are well understood in the context of pure, Newtonian liquids. Yet much less is known about the dynamics of this singularity when the surrounding liquid contains long flexible polymers, which provide viscoelastic characteristics to the liquid's properties. Here we experimentally study the coalescence of bubbles surrounded by polymer solutions. In contrast to drop coalescence, and in spite of the singular stretching of polymers, we find that the presence of the dissolved polymers does not at all affect the coalescence dynamics at early times. The polymer elasticity is found to slow down the flow only during the later stages of coalescence. These observations are interpreted using an asymptotic solution of the Oldroyd-B model, which predicts a strong stress singularity near the extremity of the neck. However, the polymer stress turns out to diverge only in the azimuthal direction, which can explain why elastic effects remain subdominant during the initial stages of coalescence.

The dispersion of rigid elongated particles in turbulent channel flow bounded by rough walls is examined. In particular, the interplay between particle inertia, particle length, and wall roughness characteristics in determining particle spatial distribution, preferential orientation, and alignment within the flow is analyzed. The dispersion process is investigated by performing direct numerical simulations of the turbulent flow coupled with the Lagrangian tracking of the particles, modeled as prolate ellipsoids with varying aspect ratio and inertia, under dilute flow conditions. Simulations are carried out at friction Reynolds number ${\text{Re}}_{\tau }=180$ based on the channel half height in a domain confined by walls with different two-dimensional roughness characteristics. Particle elongation is varied considering different aspect ratios (ranging from $\lambda =1$ for the reference case of spherical particles to $\lambda =10$ for the longest particle set) while particle inertia is varied considering different Stokes numbers (ranging from ${\text{St}}^{+}=1$ for the least inertial particles to ${\text{St}}^{+}=100$ for the most inertial ones), for a total of 12 different particle sets. Our results show that particles are affected by the turbulent structures that form near the rough walls in a way that is biased both by elongation, namely length, and inertia. This is not observed with smooth walls: In this case, increasing particle inertia always leads to a stronger turbophoretic particle drift to the walls. Elongation is observed to have a quantitative effect on the slip velocity statistics, particularly for particles with small Stokes number. Differences induced by a change of the aspect ratio tend to vanish as particle inertia increases, since the relative translational motion between the particles and the surrounding fluid appears to be closely connected to preferential concentration phenomena. Wall roughness modifies the overall dynamics of the particles, as well as their distribution, orientation, and alignment with flow direction, especially in the near-wall region. Roughness hinders long-term wall deposition of particles and determines a more uniform spatial distribution across the channel. In the near-wall region, elongated particles tend to align with the streamwise direction even in the presence of large-scale roughness, albeit to a lesser extent compared to the case of smooth walls. A stronger effect of roughness is noticed on the alignment along the spanwise and wall-normal directions. Such alignment, as well as preferential orientation, is hampered by the strong velocity fluctuations induced by roughness and the behavior of the ellipsoidal particles resembles again that of spherical particles.

The present study reports an original physical model for simulating pulsating heat pipes (PHPs). Their high heat performance is due to the phase change over thin liquid films. The simulation of physically correct film behavior is thus crucial. The model adopts the one-dimensional approach, which is computationally efficient yet still capable of capturing major physical phenomena. The model assumes a spatially uniform film thickness, whereas both the film thickness and length can vary over time; therefore, we call it the oscillating film thickness model. It is based on the physical analysis of liquid film deposition by the receding menisci of Taylor bubbles and of contact line dynamics. Three key phenomena are addressed: (1) film deposition, (2) contact line receding due to dewetting acceleration by evaporation, and (3) mass exchange over films and contact lines. The model is evaluated by simulating the simplest, single-branch PHP, for which detailed experimental data are available. A quantitative agreement is reached. As the model includes the wetting properties, their impact on oscillations is analyzed, and a qualitative agreement with the experiment is demonstrated.

We investigate the wake structure and the three-dimensional stability of the two-dimensional von Kármán vortex street developing in the wake of a permeable circular cylinder. The flow through the porous medium, assumed homogenous and isotropic, is described by the Darcy law, with a Navier slip coupling condition at the interface with the pure fluid region. The two-dimensional and steady flow past the cylinder is initially considered. Permeability induces a downstream displacement of the recirculation region, which reduces its dimensions until it eventually disappears. Linear stability analysis shows that the flow is progressively stabilized as permeability increases. We identify a critical value of permeability beyond which the steady wake is linearly stable independently of the Reynolds number. Two-dimensional, time-dependent simulations are then carried out. A progressive downstream displacement of the region of onset of the vortex shedding is observed, together with a decrease in the oscillation frequency. Oscillations of aerodynamic forces are progressively quenched with permeability owing to the downstream displacement of the onset region of the vortex shedding. At the same time, traveling vortices are observed far downstream of the body, in opposition with the impervious case, characterized instead by the formation of two shear layers of opposite vorticity, at very large distances from the body. We perform linearized simulations for the evolution of three-dimensional perturbations on the two-dimensional von Kármán vortex street. The growth rate and the spatial structure of the perturbations are extracted from such linearized dynamics by employing a sparsity-promoting dynamic mode decomposition (SP-DMD). As permeability increases, the unsteady vortex street past the cylinder is progressively stabilized with respect to three-dimensional perturbations until the transition to three-dimensionality is prevented. We identify a critical value of the permeability beyond which the vortex shedding preserves its two-dimensionality, at least in the considered parameters space.

Diffusion-driven flow is a boundary layer flow that results from the combined influence of gravity and diffusion, which exists in density-stratified fluids whenever a gravitational field is not parallel to the solid boundary. In this paper, we investigate the unsteady diffusion-driven flows that emerge in a parallel-plate channel domain with a linear density stratification. We first compute the time-dependent diffusion-driven flows and perturbed density field using eigenfunction expansions under the Boussinesq approximation. In channel domain, the unsteady flow converges to a steady-state solution either monotonically or nonmonotonically (highly oscillatory), depending on the relation between the Schmidt number and the nondimensionalized stratified scalar diffusivity, while the flow in the half-space inclined plane problem exhibits oscillatory convergence for all parameters. To validate the Boussinesq approximation, we propose the quasi-Boussinesq approximation, which includes transverse density variation in the inertial term. Numerical solutions show that the relative difference between the Boussinesq and quasi-Boussinesq approximations is uniformly small. We also study the mixing of a passive tracer induced by the advection of the unsteady diffusion-driven flow and present the series representation of the time-dependent effective diffusion coefficient. For small Schmidt numbers, the effective diffusion coefficient induced by the unsteady flow solution can oscillate with an amplitude larger than the effective diffusion coefficient induced by the long-time-limiting steady-state flow. Interestingly, the unsteady flow solution can reduce the time-dependent effective diffusion coefficient temporally in some parameter regimes, below even that produced by pure molecular diffusion in the absence of a flow. However, at long times, the effective diffusion is significantly enhanced for large Péclet numbers.

We combine experiments and numerical computations to examine underlying fluid mechanical processes associated with bioaerosol generation during violent respiratory maneuvers, such as coughing or sneezing. Analogous experiments performed in a cough machine—consisting of a strong shearing airflow over a thin liquid film—allow us to illustrate the changes in film topology as it disintegrates into small droplets. We identify that aerosol generation during the shearing of the liquid film is mediated by the formation of inflated baglike structures. The breakup of these bags is triggered by the appearance of retracting holes that puncture the bag surface. Consequently, the cascade from inflated bags to droplets is primarily controlled by the dynamics and stability of liquid rims bounding these retracting holes. We also reveal the key role of fluid viscosity in the overall fragmentation process. It is shown that more viscous films when sheared produce smaller droplets.

In confined rotating convection, a strong zonal flow can develop close to the side wall with a modal structure that precesses anticyclonically (counter to the applied rotation) along the side wall. It is surmised that this is a robust nonlinear evolution of the wall modes observed before the onset of bulk convection. Here, we perform direct numerical simulations of cylindrically confined rotating convection at high rotation rates and strong turbulent forcing. Through comparison with earlier work, we find a fit-parameter-free relation that links the angular drift frequency of the robust wall mode observed far into the turbulent regime with the critical wall mode frequency at onset, firmly substantiating the connection between the observed boundary zonal flow and the wall modes. Deviations from this relation at stronger turbulent forcing suggest early signs of the bulk turbulence starting to hamper the development of the wall mode. Furthermore, by studying the interactive flow between the robust wall mode and the bulk turbulence, we identify radial jets penetrating from the wall mode into the bulk. These jets induce a large-scale multipolar vortex structure in the bulk turbulence, dependent on the wave number of the wall mode. In a narrow cylinder the entire bulk flow is dominated by a quadrupolar vortex driven by the radial jets, while in a wider cylinder the jets are found to have a finite penetration length and the vortices do not cover the entire bulk. We also identify the role of Reynolds stresses in the generation of zonal flows in the region near the sidewall.

The leading-edge vortex (LEV) formation on the caudal fin (CF) has been identified as playing a key role in efficient lift-based thrust production of fish-like propulsion. The enhancement of the CF LEV through its interaction with vortices formed upstream due to a median fin with a distinct shape is the focus of this paper. High-speed, high-fidelity videos and particle imaging velocimetry (PIV) were obtained from rainbow trout during steady forward swimming to visualize the undulatory kinematics and two-dimensional flow behavior. Body kinematics are quantified using a traveling-wave formulation that is used to prescribe the motion of a high-fidelity three-dimensional surface model of the fish body for a computational fluid dynamics (CFD) study. The pressure field of the CFD result is compared and validated with the PIV result from the experiment. Using CFD, the vortex forming and shedding behaviors of the anal fin (AF) and their capturing and interaction with the trunk (TK) and the CF are visualized and examined. Coherent AF-bound LEVs are found to form periodically, leading to thrust production of the AF. The vortices subsequently shed from the AF are found to help stabilize and reinforce the LEV formation on the CF by aiding LEV initiation at stroke reversal and enhancing LEV during a tail stroke, which leads to enhancement of lift-based thrust production. The CF is found to shed vortex tubes (VTs) that create backward-facing jets, and the ventral-side VT and the associated backward jets are both strengthened by vortices shed by the AF. An additional benefit of the AF is found to be reduction of body drag by reducing the lateral crossflow that leads to loss of beneficial pressure gradient across the body. Through varying AF-CF spacing and AF height, we find that CF thrust enhancement and TK drag reduction due to the AF are both affected by the position and size of the AF. The position and area of the AF that led to the most hydrodynamic benefit are found to be the original, anatomically accurate position and size. In this paper, we demonstrate the important effect of vortex interaction among propulsive surfaces in fish-like propulsion.

When a fluid in turbulent motion is tagged by a nonuniform concentration of ideal tracers, the mean velocity of the tracers may not match with the mean velocity of the fluid flow. This implies that conventional particle tracking velocimetry will not produce the mean flow of a turbulent flow unless the particle seeding is homogeneous. In this work, we consider the problem of mean flow estimation from a set of particle tracks obtained in a situation of nonhomogeneous seeding. To compensate the bias caused by the nonhomogeneous particle seeding, we propose a modified particle tracking velocimetry method. This method is called a time-delayed velocity and considers the velocity trajectory of a given particle shifted in time with respect to its position. We first introduce our method for an ideal advection–diffusion model and then we implement it for a turbulent channel and a turbulent jet. For both situations, we find that the velocity bias caused by the nonhomogeneous tracer concentration is reduced with a time delay introduced between position and velocity of the tracer trajectories. For the turbulent channel, the error on the mean flow estimation monotonically decreases for increasing time delays. For the turbulent jet, the error on the mean flow estimation also reduces with positive time delays but the time delay should not be too large. We interpret this limitation as a consequence of the spatial dependence of the mean flow. For the turbulent channel, this limitation does not appear because the velocity for the mean flow streamlines is constant. For both flows, the optimal time delay for the velocity bias compensation is consistent with the Lagrangian timescales of the flow. This method gives promising elements to take into account inhomogeneous seedings in velocity fields measurements for all kinds of turbulent flows and interesting perspectives to understand how Lagrangian trajectories from various sources build an Eulerian mean field.