In bubbly turbulent flows, the deformation of the bubble is known to play an important role in the interaction between the carrier phase and the dispersed phase. In the present paper, we experimentally study an idealized version of the problem where we look at the interaction of a deforming air bubble (nonzero Weber number) and a rigid buoyant particle (zero Weber number) with a single vortex ring (in water) for a large range of ring-circulation-based Reynolds numbers ($\text{Re}=\mathrm{\Gamma }/\nu$=6000–67 300; $\mathrm{\Gamma }$=ring circulation, $\nu$=kinematic viscosity of water). We are able to obtain the particle to fluid density ratio (${\rho }_{\text{particle}}/{\rho }_{\text{water}}\approx 0.008$) to be very low and of the same order as that of the bubble (${\rho }_{\text{bubble}}/{\rho }_{\text{water}}\approx 0.001$), with the main difference being the distinct difference in their deformability. The buoyant low density (rigid) particle and the deforming bubble are directly engulfed into the core of the vortex ring and enable measurements of the effects of particles or bubbles on the vortex ring. On the particle (and bubble) dynamics side, distinct differences can be seen right from the capture phase, as unlike the rigid particle, the bubble undergoes a large axial elongation and, consequently, a quicker capture than the particle. After capture by the ring, the bubble experiences an azimuthal pressure gradient, which leads to its elongation into a thin long bubble whose diameter is relatively small compared to the vortex core size. In sharp contrast, the particle does not deform and remains effectively localized along the rings azimuthal direction. These differences in the shape of the bubble and particle within the ring lead to distinct differences in the ring's convection speed, azimuthal vorticity, and enstrophy at later times. In particular, the measurements indicate that the localized large perturbation to the vorticity in the rigid particle case (an equivalent of a rigid bubble, zero Weber number) leads to a larger disruption of the vortex ring as seen in terms of higher reduction in the rings convection speed and azimuthal enstrophy than for the deforming bubble (nonzero Weber number) case. These results could have implications in bubbly turbulent flows such as in bubble drag reduction (BDR), where many studies [like Van Gils et al., J. Fluid Mech. 722, 317 (2013)] indicate that deforming bubbles are better for drag reduction than nondeforming bubbles at higher flow Re, where the dominant mechanism is the lifting of structures away from the wall. The present results suggest that in cases where vortex disruption is the primary mechanism for BDR [for example, at lower flow Re, Sugiyama et al., J. Fluid Mech. 608, 21 (2008)], better drag reduction would occur with nondeforming bubbles. The current study thus brings us insight into the role of deformability in the interaction of bubbles with a vortical structure, which could be important in helping us model and understand bubble-turbulence interactions.

The pinch-off dynamics of a liquid thread has been studied through numerical simulations and theoretical analysis. Occurring at small length scales, the pinch-off dynamics admits similarity solutions that can be classified into the Stokes regime and the diffusion-dominated regime, with the latter being recently experimentally observed in aqueous two-phase systems [Phys. Rev. Lett. 123, 134501 (2019)]. Derived by applying Onsager's variational principle, the Cahn–Hilliard–Navier–Stokes model is employed as a minimal model capable of describing the interfacial motion driven by not only advection but also diffusion. By analyzing the free energy dissipation mechanisms in the model, a characteristic length scale is introduced to measure the competition between diffusion and viscous flow in interfacial motion. This length scale is typically of nanometer scale for systems far from the critical point, but can approach micrometer scale for aqueous two-phase systems close to the critical point. The Cahn–Hilliard–Navier–Stokes model is solved by using an accurate and efficient spectral method in a cylindrical domain with axisymmetry. Ample numerical examples are presented to show the pinch-off processes in the Stokes regime and the diffusion-dominated regime respectively. In particular, the crossover between these two regimes is investigated numerically and analytically to reveal how the scaling behaviors of similarity solutions are to be qualitatively changed as the characteristic length scale is inevitably accessed by the pinching neck of the interface. Discussions are also provided for numerical examples that are performed for the breakup of long liquid filaments and show qualitatively different phenomena in different scaling regimes.

To predict the growth rates of spikes and those of bubbles at a Richtmyer-Meshkov unstable interface between two fluids of arbitrary density ratios and over the entire nonlinear evolution stage is very important. So far most theories are applicable to bubbles only. There are no accurate theories available in the literature for spikes in systems with finite density ratios. In this paper, we present a theory that is applicable to both spikes and bubbles. Our theoretical predictions are in good agreement with numerical data for both spikes and bubbles over a wide range of density ratios and with various initial conditions. The theoretical predictions also agree well with experimental results.

We investigate the performance of active swimmers in a strongly heterogeneous two-dimensional weakly turbulent flow. The flow is heterogeneous in Reynolds number along one direction. Using a hybrid experimental-numerical model, we demonstrate that there are three regimes of preferential transport for rodlike swimmers as the swimmers' intrinsic speed increases. Using Lagrangian statistics along swimmers' trajectories, we reveal that the three regimes are due to the relative strengths of three different effects: the intrinsic speed of the swimmers, the reorientation ability of the shear layer at the interface of two flow regions, and the attracting Lagrangian coherent structures of the flow field. Our results elucidate the mechanism of preferential transport for swimmers in heterogeneous flow. We hope to raise researchers' attention to the dynamics of swimmers in strongly heterogeneous flow environments.

The propagation of horizontal dam-break flows induced by the release of a rectangular column of a liquid phase into a negligible ambient fluid is investigated by combining numerical simulations and laboratory experiments. Varying both the geometry of the initial column and liquid properties, the parameter space covered allows the investigation of the transition from inertial to viscous slumping barely considered so far. In light of the Reynolds number $\mathrm{Re}$ based on the initial parameters of the fluid column, we report a newly investigated transient regime following the inertial slumping regime and prior to the viscous-dominated one. The transient intermediate regime is shown (i) to only exist for $\mathrm{Re}\gtrsim 10$ and (ii) to be characterized by an inertial overshoot followed by a strong deceleration of the front position accompanied by an excess and a deficit of fluid at the front and at the origin, respectively, with respect to the expected theoretical prediction of the viscous-dominated regime. Beyond the intuitive idea of an adaptive transition from the inertial to fully viscous slumping, these results highlight and quantify the influence of initial inertia on the spreading of a liquid, which may be particularly useful for modeling industrial and geophysical applications.

Motivated by astrophysical and geophysical applications, the classical problem of rotating Rayleigh-Bénard convection has been widely studied. Assuming a classical Fourier heat law, in which the heat flux is directly proportional to the temperature gradient, the evolution of temperature is governed by a parabolic advection-diffusion equation; this, in turn, implies an infinite speed of propagation of information. In reality, the system is rendered hyperbolic by extending the Fourier law to include an advective derivative of the flux—the Maxwell-Cattaneo (M-C) effect. Although the correction (measured by the parameter $\mathrm{\Gamma }$, a nondimensional representation of the relaxation time) is nominally small, it represents a singular perturbation and hence can lead to significant effects when the rotation rate (measured by the Taylor number $T$) is sufficiently high. In this paper, we investigate the linear stability of rotating convection, incorporating the M-C effect, concentrating on the regime of $T\gg 1, \mathrm{\Gamma }\ll 1$. On increasing $\mathrm{\Gamma }$ for a fixed $T\gg 1$, the M-C effect first comes into play when $\mathrm{\Gamma }=O\left(T^{-1/3}\right)$. Here, as in the classical problem, the preferred mode can be either steady or oscillatory, depending on the value of the Prandtl number $\sigma$. For $\mathrm{\Gamma }>O\left(T^{-1/3}\right)$, the influence of the M-C effect is sufficiently strong that the onset of instability is always oscillatory, regardless of the value of $\sigma$. Within this regime, the dependence on $\sigma$ of the critical Rayleigh number and of the scale of the preferred mode are explored through the analysis of specific distinguished limits.

Lifting surfaces in aerospace and power industry applications produce tonal noise at low-to-medium Reynolds number, significantly contributing to global noise annoyance. The dominant noise frequency depends on the freestream velocity, angle of attack, and surrounding environment. This work reports that the frequency spectra can exhibit different behavior at the same flow condition, which constitutes the hysteresis phenomenon. Time-resolved particle image velocimetry (PIV) of boundary-layer flows near the trailing edge and far-field noise measurements are performed simultaneously and synchronously. Two branches of experiments are conducted with the freestream velocity increasing and decreasing, respectively. Results are analyzed from the perspective of modern dynamical systems. The boundary layer is viewed as the forced oscillator, with the acoustic waves being the forcing mechanism. Both the bifurcation theory and the Poincaré section are introduced to investigate the dynamic process when freestream velocity changes. Typically, the dominant frequency of acoustic waves matches that of the most amplified disturbances in the boundary layer, which is consistent with existing literature on the same noise generation mechanism. However, dual peaks can be observed at specific freestream velocities: one matches the natural frequency of the current flow state while the other matches that of the previous state. The associated transitions between periodic and quasiperiodic oscillations constitute the hysteresis phenomenon.

Recent developments of the weak turbulence theory applied to internal waves exhibit a power-law solution of the kinetic energy equation close to the oceanic Garrett-Munk spectrum, confirming weakly nonlinear wave interactions as a likely explanation of the observed oceanic spectra. However, finite-size effects can hinder wave interactions in bounded domains, and observations often differ from theoretical predictions. This paper studies the dynamical regimes experimentally developing in a stratified fluid forced by internal gravity waves in a pentagonal domain. We find that by changing the shape and increasing the dimensions of the domain finite-size effects diminish and wave turbulence is observed. In this regime, the temporal spectra decay with a slope compatible with the Garrett-Munk spectra. Different regimes appear by changing the forcing conditions, namely, discrete wave turbulence, weak wave turbulence, and strongly stratified turbulence. The buoyancy Reynolds number ${\text{Re}}_b$ marks well the transitions between the regimes, with weak wave turbulence occurring for $1\lesssim {\text{Re}}_b\lesssim 3.5$ and strongly nonlinear stratified turbulence for higher ${\text{Re}}_b$.

When attracted by a stimulus (light), microswimmers can build up very densely at a constriction and thus cause jamming. The microalga Chlamydomonas Reinhardtii is used here as a model system to study this phenomenon. Its negative phototaxis makes the algae swim away from a light source and go through a microfabricated bottleneck-shaped constriction. Successive jamming events interspersed with bursts of algae are observed. A power-law decrease describes well the distribution of time lapses of blockages. Moreover, the evacuation time is found to increase when increasing the swimming velocity. These results are reminiscent of crowd dynamics and, in particular, what has been called the faster is slower effect in the dedicated literature. It also raises the question of the presence of tangential solid friction between motile cells densely packed. Furthermore, we demonstrate the existence of a transition from a jammed phase described by a power-law decrease to an uninterrupted phase described by an exponential decay, we characterize such a transition as a function of door size and swimming velocity. Interestingly, the exponential flowing regime shows what might be referred to as “a faster is faster” regime.

Formation of a splash crown and a cavity following the impact of a sphere on a body of liquid is a classical problem. In the related problem of a droplet splashing on a flat surface, it has been established that the properties of the surrounding gas can influence the splashing threshold. At lower impact speeds, this is due mainly to the influence of gas kinetic effects, since the height of the gas lubrication film which is displaced during dynamic wetting is often comparable to the mean free path of the gas. At higher Weber and Reynolds numbers, on the other hand, inertial effects dominate and the density of the gas becomes important in determining whether a splash occurs. In this article, sphere impacts on a liquid body are investigated in a rarefied atmosphere using high-speed photography. It is found that the threshold entry speed for cavity formation is influenced by the density of the surrounding gas, whereas changing the mean free path of the gas has no effect. We attribute this phenomenon to the gas slowing the sealing of the thin crown sheet behind the sphere. This assertion is supported with experimental measurements of the liquid sheet thickness. In the range of parameters considered, the splash crown influences the movement of the contact line.

Here we analyze the splash transition of drops of liquids with different viscosities impacting normally over different types of rough superhydrophobic substrates, finding that the velocity for the splash transition, $V^{*}$, increases for increasing values of the liquid viscosity and also when the proportion of air entrapped at the substrate corrugations decreases. Our experimental results also reveal that the amount of air entrapped between the substrate and the wall increases with the value of the relative roughness $\epsilon =\varepsilon /R$, with $\varepsilon$ and $R$ indicating the amplitude of the corrugations and the radius of the drop, respectively. We show that our experimental values of $V^{*}$, as well as those reported in similar contributions in the literature, can be predicted using the splashing model presented by Quintero, Riboux, and Gordillo [J. Fluid Mech. 870, 175 (2019)], once the liquid shear stress at the wall is expressed as a decreasing function of $\epsilon$, namely, of the proportion of air entrapped at the substrate.

Mean-flow measurements of turbulent boundary layers over porous walls (permeable and rough) with varying pore size ($s$), permeability ($K$) and thickness ($h$) are presented across a wide range of friction Reynolds numbers (${\text{Re}}_{\tau }\approx 2000–18000$) and permeability based Reynolds numbers (${\text{Re}}_K\approx 1.5–60$). The mean wall shear stress was determined using a floating element drag balance and the boundary layer profiles were acquired using hot-wire anemometry. Substrate permeability is shown to increase the magnitude of the mean velocity deficit. The use of a modified indicator function, assuming “universal” values for von Karman constant $(\kappa =0.39$) supports previous results where a strongly modified logarithmic region was observed. The indicator function was also used to estimate the zero-plane displacement ($y_d$), the roughness function ($\mathrm{\Delta }{U}^{+}$), and equivalent sandgrain roughness ($k_s$). At high Reynolds numbers, the roughness function data collapses on to the Nikuradse's fully rough asymptote. However, at low roughness Reynolds numbers ($k_s^{+}<100$), we observe the flow to be transitionally rough, evolving with Nikuradse-type behavior. The equivalent sandgrain roughness $k_s$ for each substrate appears to include roughness and permeability contributions. These two contributions can be separated using data obtained from the same substrates with different thickness. This may allow us to model the porous wall as a combination of rough and permeable wall.

A model of the bronchioles lined by the airway surface liquid is employed to investigate the Plateau-Rayleigh instability that can lead to the occlusion of the airways. This physiologically relevant phenomenon is normally occurring in distal airways, i.e., in the bronchioles from the seventh generation on. Special attention is paid to the effect of surfactant dispersed in the liquid phase and along the liquid-gas interface. A single-layer Newtonian film is simulated in a rigid capillary pipe in order to isolate the impact of the surfactant and unravel their complex dynamics coupled with the multiphase liquid-gas dynamics. Apart from the primary instability leading to airway closure, we focus on the postcoalescence wall stresses and stress gradients produced by the bifrontal plug growth. With our model, we demonstrate that increasing the surfactant concentration and their strength, the airway closure slows and the wall stresses are reduced up to 20%. Within the physiological application intended for our model, we study the stability of the multiphase system. We predict the generation at which airway closure will occur depending on the liquid lining thickness and the initial surfactant concentration.

In adopting a poroelastic model for a hydrogel, one views its constituent fluid and solid phases as interpenetrating continua, thereby erasing the pore-scale geometry. This gives rise to the need for additional boundary conditions (BCs) at the interface between a hydrogel and a clear fluid to supplement the momentum equations for the fluid and solid phases in the hydrogel. Using a thermodynamic argument on energy dissipation, we propose three sets of BCs for the gel-fluid interface that link the normal and tangential velocity jumps across the interface to the normal and tangential stresses on either side of the interface. Using several flow problems—one-dimensional compression, two-layer Couette and Poiseuille shear flows, and deformation of a gel particle by a planar extension flow—as tests, we compare the predictions of these three BCs with that of a previously proposed BC. Some differences are stark and reveal flaws in certain BCs. Others are subtler and will require quantitative experimental data for validation. Based on these results, we recommend one set of BCs over the other three for computing the flow and deformation of hydrogels in contact with a clear fluid. In addition, we suggest benchmark experiments to validate the BCs and our recommendation.

In this paper, we derive the general solution of the unsteady Stokes equations for an unbounded fluid in spherical polar coordinates, in both time and frequency domains. The solution is an expansion in vector spherical harmonics and given as a sum of a particular solution, proportional to a pressure gradient exhibiting power-law spatial dependence, and a solution of the vector Helmholtz equation decaying exponentially in the far field, the decomposition originally introduced by Lamb. The proposed solution representation resembles the classical Lamb decomposition of the solution of steady Stokes equations, with the series coefficients being projections of the radial component, divergence, and curl of the boundary velocity on scalar spherical harmonics. It can be applied to construct the transient exterior flow induced by an arbitrary velocity distribution at the spherical boundary, such as arising in the squirmer model of a microswimmer. The approach can also be used to construct solutions for transient flows driven by initial conditions, unbounded flows driven by volumetric forces, and disturbance to the unsteady flow due to a stationary spherical particle and to study particle-particle and particle-wall interactions in oscillatory flows. The long-time behavior of the solution is controlled by the flow component corresponding to an average (or collective) motion of the boundary. This conclusion is illustrated by the study of decay of a transversal wave in the presence of a fixed sphere. We further show that the general representation reduces to the well-known solutions for unsteady flow around a sphere undergoing oscillatory rigid-body motion. The proposed solution representation provides an explicit form of the velocity potential far from an oscillating body and high- and low-frequency expansions. The leading-order high-frequency expansion yields the well-known ideal (inviscid) flow approximation, and the leading-order low-frequency expansion yields the steady Stokes equations. We derive the higher-order corrections to these approximations and discuss the d'Alembert paradox. Continuation of the general solution to imaginary frequency yields the general solution of the Brinkman equations describing viscous flow in a porous medium.

In this combined experimental and numerical study, we film the formation of fire ant rafts to determine how they cohere together. Surprisingly, we discover that ants prioritize separation and exploration: they flail legs and bounce off neighbors when they collide. Despite the active repulsion, fire ants cohere by the Cheerios effect, a capillary force that attracts small floating objects such as breakfast cereal. Experiments reveal that rafts consisting of fewer than ten ants disintegrate within minutes. Predictions by a Langevin model reproduce the stability transition and the critical raft size, which emerges from the balance between their mutual repulsion and the Cheerios effect. This work may inspire physically grounded models for the behavior of natural swarms.

The evaporation of drops of pure water on soluble substrates of salt leads to the growth of unprecedented hollow peripheral deposits. We report here on the experimental determination and numerical simulation of the flows inside a drop in this configuration. The velocity field is measured experimentally by a microparticle image velocimetry technique and is simulated using the hydrodynamics equations solved by the finite-elements method. The flow is characterized by an inward motion at the beginning of the evaporation, that is progressively replaced by an outward motion until the end of the evaporation. The transition between the two flow regions takes the form of a stagnation line, where the radial component of the velocity vanishes. This line migrates from the periphery toward the center of the drop, inducing the progressive inversion of the flow. The comparison between the experiments and simulations leads to the following interpretation of this flow reversal. The dissolution of the substrate induces the creation of a surface tension gradient at the drop free-surface, leading to an outward Marangoni flow along the drop surface and an inward flow near the substrate. As the diffusion progressively makes the concentration more uniform, this surface-driven convection stops and is replaced by the standard coffee-stain outward capillary flow.

Bounds for the poloidal and toroidal kinetic energies and the heat transport are computed numerically for rotating convection at infinite Prandtl number with both no-slip and stress-free boundaries. The constraints invoked in this computation are linear or quadratic in the problem variables and lead to the formulation of a semidefinite program. The bounds behave as a function of Rayleigh number at fixed Taylor number qualitatively in the same way as the quantities being bounded. The bounds are zero for Rayleigh numbers smaller than the critical Rayleigh number for the onset of convection, they increase rapidly with Rayleigh number for Rayleigh numbers just above onset, and increase more slowly at large Rayleigh numbers. If the dependencies on Rayleigh number are approximated by power laws, one obtains larger exponents from bounds on the Nusselt number for Rayleigh numbers just above onset than from the actual Nusselt number dependence known for large but finite Prandtl number. The wavelength of the linearly unstable mode at the onset of convection appears as a relevant length scale in the bounds.