We show that when a drop of water is maintained in its Leidenfrost regime, a sound in the form of periodic beats emits from the drop. The process of beat emission involves two distinct frequencies. One component is the frequency of beats itself, and the second is the frequency of sound in every beat which is emitted when one oscillation in the drop occurs. Experiments were performed by placing a drop of water over a concave metallic surface, and the beats of the drop were recorded by fixing a microphone above the drop. A video camera was also fixed above the drop to record its oscillations. Simple analytical techniques like Fourier and wavelet transforms of the audio signals and image processing of the videos of the drop were used to gain insight into the mechanism of the beat emission process. This analysis also helped us in studying the dependence of frequencies, if any, on the radius of the drop and the substrate temperature.

The influence of inertial migration of neutrally buoyant particles on inertial flow transitions in Taylor-Couette (TC) flow of a suspensions is studied; this work considers primarily transitions associated with the circular Couette flow (CCF) and Taylor vortex flow (TVF) regimes. A concentric cylinder Taylor-Couette device with a stationary outer cylinder and rotating inner cylinder is considered. The device has an inner to outer radius ratio of $\eta =d_i/d_o=0.877$, where $d_i$ and $d_o$ are the inner and outer diameters of the flow annulus. The ratio of the axial length to the radial gap of the annulus $\mathrm{\Gamma }=L/\delta =20.5$, where $\delta =(d_o-d_i)/2$. The ratio of radial gap $\delta$ and the particle diameter $d_p$ is $\alpha =\delta /d_p=30.4$ and the particle volume fraction considered in this work is $\varphi =0.10$. A flow structure (CCF or TVF) near the transition boundary with either uniform distribution across the annular region or fully migrated concentration profile is established. The Reynolds number (Re) is subjected to a rapid step change to study the effect of the concentration profile on the flow transition Re and resulting flow structure evolution; here the Reynolds number is $\text{Re}=\delta d_i{\omega }_i\rho /2{\mu }_s$, where ${\omega }_i$ is the rotation rate of the inner cylinder and $\rho$ and ${\mu }_s$ are the density and effective viscosity of the suspension. Our results show that, relative to uniform concentration, the particle distribution following inertial migration destabilizes the CCF state near the CCF-nonaxisymmetric flow transition boundary. In contrast to this destabilizing effect in CCF, migration of particles in the TVF regime has a stabilizing effect on the TVF-wavy Taylor vortex and TVF-nonaxisymmetric flow transition boundaries. The transition away from the TVF exhibits clear hysteresis associated with migration, as once initiated TVF could be sustained below and above the transition boundaries observed for suspension TC flow with uniform concentration.

The settling behavior of small inertial particles in turbulent convection is a fundamental problem across several disciplines, from geophysics to metallurgy. In a geophysical context, the settling of dense crystals controls the mode of solidification of magma chambers and planetary scale magma oceans, while rising of light bubbles of volatiles drives volcanic outgassing and the formation of primordial atmospheres. Motivated by these geophysical systems, we perform a systematic numerical study on the settling rate of particles in a rectangular two-dimensional Rayleigh-Bénard system with Rayleigh number up to ${10}^{12}$ and Prandtl number from 10 to 50. Under the idealized condition of spherically shaped particles with small Reynolds number, two limiting behaviors exist for the settling velocity. On the one hand, Stokes law applies to particles with small but finite response time, leading to a constant settling rate. On the other hand, particles with a vanishing response time are expected to settle at an exponential rate. Based on our simulations, we present a physical model that bridges the gap between the above limiting behaviors by describing the sedimentation of inertial particles as a random process with two key components: (i) the transport of particles from vigorously convecting regions into sluggish, low-velocity “piles” that naturally develop at the horizontal boundaries of the system, and (ii) the probability that particles escape such low-velocity regions without settling at their base. In addition, we identify four distinct settling regimes and analyze the horizontal distribution of sedimented particles. For two of these regimes settling is particularly slow and the distribution is strongly nonuniform, with dense particles being deposited preferentially below major clusters of upwellings. Finally, we apply our results to the crystallization of a magma ocean. Our prediction of the characteristic residence times is consistent with fractional crystallization, i.e., with the efficient separation of dense crystals from the residual lighter fluid. In absence of an efficient mechanism to reentrain settled particles, equilibrium crystallization appears possible only for particles with extremely small density contrasts.

Internal gravity waves propagating within homogeneous stratified turbulence are the subject of the present study. A spatiotemporal analysis is carried out on the results of direct numerical simulations including a forcing term, with the aim of showing the energy content of the simulations as a function of frequency, $\omega$, and wave-vector inclination to the horizontal, $\theta$. Clear signatures of the dispersion relation of internal gravity waves, $\omega =\pm Ncos\theta$, where $N$ is the Brunt-Väisälä frequency, are observed in all our simulations, which have low Froude number, ${\text{Fr}}_h\ll 1$, and increasing buoyancy Reynolds number up to ${\text{Re}}_b\approx 10$. Interestingly, we observe the presence of high-frequency waves with $\omega \sim N$ and a corresponding low-frequency vortex mode, both containing a non-negligible amount of energy. These waves are large-scale waves, their energy signature being found at scales larger than the forcing scales. We also observe the growth of energy in the shear modes, constituting a horizontal mean flow, and we show that their continuous growth is due to an upscale energy transfer, from the forcing scales to larger horizontal as well as vertical scales. These shear modes are found to be responsible for Doppler shifting the frequency of the large-scale waves. When considering the wave energy across the simulations at varying ${\text{Re}}_b$, such energy is seen to reduce as ${\text{Re}}_b$ is increased and the flow enters the strongly stratified turbulence regime. The classical wave-vortex decomposition, based on a purely spatial decomposition of instantaneous snapshots of the flow, is analyzed within the current framework and is seen to correspond relatively well to the “true” wave signal identified by the spatiotemporal analysis, at least for the large-scale waves with $\omega \sim N$. Distinct energy peaks in $\theta \text{−}\omega$ space highlight that the waves have preferential directions of propagation, specifically $\theta ={45}^{\circ }$ and $\theta \approx {55}^{\circ }$, similar to observations in studies of wave radiation from localized regions of turbulence. This suggests that the same wave-generation mechanisms may be relevant for homogeneous and inhomogeneous stratified turbulent flows.

Active navigation relies on effectively extracting information from the surrounding environment, and often features the tracking of gradients of a relevant signal—such as the concentration of molecules. Microfluidic networks of closed pathways pose the challenge of determining the shortest exit pathway, which involves the proper local decision-making at each bifurcating junction. Here, we focus on the basic decision faced at a T-junction by a microscopic particle, which orients among possible paths via its sensing of a diffusible substance's concentration. We study experimentally the navigation of colloidal particles following concentration gradients by diffusiophoresis. We treat the situation as a mean first passage time (MFPT) problem that unveils the important role of a separatrix in the concentration field to determine the statistics of path taking. Further, we use numerical experiments to study different strategies, including biomimetic ones such as run and tumble or Markovian chemotactic migration. The discontinuity in the MFPT at the junction makes it remarkably difficult for microscopic agents to follow the shortest path, irrespective of adopted navigation strategy. In contrast, increasing the size of the sensing agents improves the efficiency of short-path taking by harvesting information on a larger scale. It inspires the development of a run-and-whirl dynamics that takes advantage of the mathematical properties of harmonic functions to emulate particles beyond their own size.

Traditional models of electrokinetic transport in porous media are based on homogenized material properties, which neglect any macroscopic effects of microscopic fluctuations. This perspective is taken not only for convenience but also motivated by the expectation of irrotational electro-osmotic flow, proportional to the electric field, for uniformly charged surfaces (or constant $\zeta$ potential) in the limit of thin double layers. Here, we show that the inherent heterogeneity of porous media generally leads to macroscopic vortex patterns, which have important implications for convective transport and mixing. These vortical flows originate due to competition between pressure-driven and electro-osmotic flows, and their sizes are characterized by the correlation length of heterogeneity in permeability or surface charge. The appearance of vortices is controlled by a single dimensionless control parameter, defined as the ratio of a typical electro-osmotic velocity to the total mean velocity.

Speech is a potent route for viral transmission in the COVID-19 pandemic. Informed mitigation strategies are difficult to develop since no aerosolization mechanism has been visualized yet in the oral cavity. Here we show with high-speed imaging how phonation of common stop consonants, found in most of the world's spoken languages, form and extend salivary filaments in a few milliseconds as moist lips open or when the tongue separates from the teeth. Both saliva viscoelasticity and airflow associated with the plosion of stop consonants are essential for stabilizing and subsequently forming centimeter-scale thin filaments, tens of microns in diameter, that break into speech droplets. Moreover, these plosive consonants induce vortex rings that drive meter-long transport of exhaled air, tying this mechanism to transport associated with speech. We demonstrate that a similar mechanism of aerosolization occurs during the vibration of reeds in wind instruments and may occur during the flapping of the glottis folds. Finally, our research suggests a mitigation of droplet production during speech by using a lip balm.

Recent experiments have shown that liquid Leidenfrost drops levitated by their vapor above a flat hot surface can exhibit symmetry-breaking spontaneous dynamics [A. Bouillant et al., Nat. Phys. 14, 1188 (2018)]. Motivated by these observations, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a simplified two-dimensional model, focusing on near-circular drops small relative to the capillary length. The model couples the equations of motion of the drop, which flows as a rigid wheel, and thin-film equations governing the vapor flow, the profile of the deformable vapor-liquid interface, and thus the hydrodynamic forces and torques on the drop. In contrast to previous analytical models of Leidenfrost drops levitating above a flat surface which predict only symmetric solutions, we find that the symmetric Leidenfrost state is unstable above a critical drop radius: $R_1$ for a free drop and $R_2>R_1$ for an immobilized drop. In these respective cases, symmetry breaking is manifested in supercritical pitchfork bifurcations into steady states of pure rolling and constant angular velocity. In further qualitative agreement with the experiments, when a symmetry-broken immobilized drop is suddenly released it initially moves at an acceleration $\alpha g$, where $\alpha$ is an angle characterizing the slope of the liquid-vapor profile and $g$ is the gravitational acceleration; moreover, $\alpha$ exhibits a maximum with respect to the drop radius at a radius increasing with the temperature difference between the surface and the drop.

We study the effect of inhomogeneous environments on the swimming direction of the microalgae Chlamydomonas reinhardtii (CR) in the presence of a light stimulus. Positive or negative phototaxis describe the ability of microorganisms to bias their swimming toward or away from a light source. Here we consider microswimmers with negative phototaxis in a microfluidic device with a microfabricated square lattice of pillars as obstacles. We measured a mean deflection of microswimmers that shows an interesting nonlinear dependence on the direction of the guiding light beam with respect to the symmetry axes of the pillar lattice. By simulating a model swimmer in a pillar lattice and analyzing its scattering behavior, we identified the width of the reorientation distribution of swimmers to be also crucial for the nonlinear behavior of the swimmer deflection. On the basis of these results we suggest in addition an analytical model for microswimmers, where the pillar lattice is replaced by an anisotropic scattering medium, that depends only on a scattering rate and the width of the reorientation distribution of swimmers. This flexible and handy model fits the experimental results as well. The presented analysis of the deflection of light guided swimmers through pillar lattice may be used for separating swimmers having different reorientation distributions.

We study the retraction of a viscous liquid sheet of finite length with negligible effect of the ambient medium. Using the long-wavelength model we derive the scaling laws and similarity solution for the interface profile of the retracting sheet. Far from the tip, the similarity solution for the interface profiles converges to an asymptotic value of 1/4. Direct numerical simulations are performed to compare the theoretical results with the simulations. When the inertia is negligible, the interface profiles remain flat during the retraction process which is in agreement with the self-similar solution. Using this similarity solution we derive the expression for the temporal variation of the tip speed for finite liquid sheets. We demonstrate that unlike an infinite sheet where the sheet retracts with a steady speed (known as Taylor-Culick speed), the tip speed decreases as a function of time for a finite liquid sheet. This is true when the viscous effects are larger than or of the same order with the inertia effects. Otherwise, the sheet retracts with the formation of a bulbous tip whose speed reaches a value closer to the Taylor-Culick speed.

We present a new mesoscale model for ionic liquids based on a low Mach number fluctuating hydrodynamics formulation for multicomponent charged species. The low Mach number approach eliminates sound waves from the fully compressible equations leading to a computationally efficient incompressible formulation. The model uses a Gibbs free-energy functional that includes enthalpy of mixing, interfacial energy, and electrostatic contributions. These lead to a new fourth-order term in the mass equations and a reversible stress in the momentum equations. We calibrate our model using parameters for [$\mathrm{DMPI}+$][F6P-], an extensively studied room temperature ionic liquid (RTIL), and numerically demonstrate the formation of mesoscopic structuring at equilibrium in two and three dimensions. In simulations with electrode boundaries the measured double-layer capacitance decreases with voltage, in agreement with theoretical predictions and experimental measurements for RTILs. Finally, we present a shear electroosmosis example to demonstrate that the methodology can be used to model electrokinetic flows.

Stability analysis of gravity-driven flow of a thermoviscous liquid on the exterior surface of a uniformly heated or cooled vertical cylinder is presented. The film evolution model derived using lubrication approximation consists of four dimensionless groups, namely, Marangoni number, Biot number, Bond number, and thermoviscosity number. The viscosity of the liquid is modeled as an exponentially varying function of temperature. The thermocapillary stress significantly affects the Rayleigh-Plateau instability for flow over a nonisothermal cylinder with intricate dependence on various parameters involved. For the temporally unstable system, spatiotemporal stability analysis is performed to delineate the parameter regions for convectively and absolutely unstable systems. Brigg's criterion is employed and the critical value of a composite parameter $\beta$ is evaluated to study the transition from convective to absolute instability. A proper rescaling of the dispersion relation shows that the condition on the composite parameter is $\beta <1.507$ for the existence of absolute instability, which is consistent with an earlier work on isothermal flows. Further, an expression is found for the critical composite Marangoni number beyond which the film is always absolutely unstable independent of the Bond number. This critical value is shown to be an increasing function of thermoviscosity number. Results from the nonlinear simulations are in agreement with the predictions of the linear temporal and spatiotemporal analyses.

Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette, and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code ChannelFlow in a narrow computational domain tilted by ${24}^{\circ }$ with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances. Depending on the Reynolds number, a turbulent band can either decay to laminar flow or split into two bands. As with past studies of other wall-bounded shear flows, in most cases survival probabilities are found to be consistent with exponential distributions for both decay and splitting, indicating that the processes are memoryless. Statistically estimated mean lifetimes for decay and splitting are plotted as a function of the Reynolds number and lead to the estimation of a critical Reynolds number ${\mathrm{Re}}_{\text{cross}}\simeq 965$, where decay and splitting lifetimes cross at greater than ${10}^6$ advective time units. The processes of splitting and decay are also examined through analysis of their Fourier spectra. The dynamics of large-scale spectral components seem to statistically follow the same pathway during the splitting of a turbulent band and may be considered as precursors of splitting.

Lubrication forces depend to a high degree on elasticity, texture, charge, chemistry, and temperature of the interacting surfaces. Therefore, by appropriately designing surface properties, we may tailor lubrication forces to reduce friction, adhesion, and wear between sliding surfaces and control repulsion, assembly, and collision of interacting particles. Here, we show that variations of slippage on one of the contacting surfaces induce a lift force. We demonstrate the consequences of this force on the mobility of a cylinder traveling near a wall and show the emergence of particle oscillation and migration that would not otherwise occur in the Stokes flow regime. Our study has implications for understanding how inhomogeneous biological interfaces interact with their environment; we also propose a method of patterning surfaces for controlling the motion of nearby particles.

Ring-shaped deposits can be often found after a droplet evaporates on a substrate. If the fluid in the droplet is a pure liquid and its contact line remains pinned during the process, then the mechanism behind such ring-shaped deposition is the well-known coffee-stain effect. However, adding small amounts of salt to such a droplet can change the internal flow dramatically and consequently change the deposition mechanism. Due to an increase of surface tension in the contact line region, a Marangoni flow arises which is directed from the apex of the droplet toward the contact line. As a result, particles arrive at the contact line following the liquid-air interface of the droplet. Interestingly, the deposit is also ring shaped, as in the classical coffee-stain effect, but with a radically different morphology: Particles form a monolayer along the liquid-air interface of the droplet, instead of a compact three-dimensional deposit. Using confocal microscopy, we study particle-per-particle how the assembly of the colloidal monolayer occurs during the evaporation of droplets for different initial concentration of sodium chloride and initial particle dilution. Our results are compared with classical diffusion-limited deposition models and open up an interesting scenario of deposits via interfacial particle assembly, which can easily yield homogeneous depositions by manipulating the initial salt and particle concentration in the droplet.

The undisturbed flow of a particle is of fundamental importance since it controls both the undisturbed flow force and the perturbation force (which includes quasisteady, added-mass, and history forces). Here we use the pairwise interaction extended point particle framework to evaluate the undisturbed flow of each particle through superposition of the perturbation flow induced by all its neighbors. This approach allows calculation of various statistics related to undisturbed fluid velocity under conditions of both stationary and nonstationary particles. In a random distribution of stationary particles, while the macroscale undisturbed flow is slowly varying, the microscale undisturbed flow that arises due to the perturbation flow of neighbors varies substantially from one particle to another and this in turn leads to large variation in the hydrodynamic force exerted on the particles. The effect of particle motion is generally to increase the particle-to-particle variation in the undisturbed fluid velocity of the particles. We observe that this increase is greater for the transverse component than for the streamwise component. As a result, with increasing random particle motion, the distribution of undisturbed fluid-velocity fluctuation becomes isotropic. Three different normalized forces are defined: ${\mathrm{\Phi }}^L$ is the Lagrangian normalized force on an individual particle suitable for application in a microscale-informed Euler-Lagrange simulation, ${\mathrm{\Phi }}^E$ is the Eulerian normalized average force suitable for application in an Euler-Euler simulation, and ${\mathrm{\Phi }}^{LE}$ is the Lagrangian normalized force on an individual particle suitable for application in the standard Euler-Lagrange simulation. We establish precise relations between these different definitions. The drag laws developed based on particle-resolved direct numerical simulation results and experiments are appropriate for application only as the Eulerian normalized average force. We introduce the force consistency relation and use it to obtain an expression for ${\mathrm{\Phi }}^L$, which when applied to each particle and averaged over all the particles equals ${\mathrm{\Phi }}^E$. The results are first obtained in the limit of stationary particles and then extended to the general case of nonstationary particles.

The influence of coherent turbulent structures on the entrainment characteristics of a separated shear layer in a Mach-2.49 longitudinal cylinder wake is investigated using stereoscopic particle image velocimetry (SPIV). Three thousand non-time-correlated velocity field measurements, acquired along a plane coincident with the central axis, were decomposed into modes using the snapshot proper orthogonal decomposition (POD) method. The second and third POD modes identified high-energy velocity fluctuations aligned with consistent directions in the separated shear layers, near the boundaries of the recirculation region. Previous work by the authors has demonstrated, using tomographic PIV, that these directionally consistent velocity fluctuations identified by the POD modes are caused by three-dimensional (3D) coherent upright and inverted hairpin vortex structures in this flow. The SPIV velocity field snapshots were conditionally sorted based on the value of their corresponding POD amplitude coefficients, and conditional statistics from these subsets of snapshots were used to derive results in the current work. It is demonstrated that a higher statistical prevalence of upright hairpin vortices in the shear layer directly correlates with reduced shear layer growth rates, and a subsequent increase in the reattachment length. Conversely, a higher statistical prevalence of inverted hairpin vortices correlates with increased shear layer growth rates, and a subsequent reduction in the reattachment length. Comparisons of conditional statistics for the SPIV data are drawn with previous laser Doppler velocimetry measurements acquired in a $5^{\circ }$ boat-tailed cylinder configuration of this flow. These comparisons demonstrate clear similarities of important features between the two flows, such as an increase in the reattachment length when compared to the unconditional blunt-based cylinder flow, which is indicative of higher cylinder base pressures and subsequently reduced pressure drag.

We investigate experimentally stratified turbulence forced by waves. Stratified turbulence is present in oceans and it is expected to be dominated by nonlinear interaction of internal gravity waves as described by the Garrett and Munk spectrum. To reach turbulent regimes dominated by stratification we use the Coriolis facility in Grenoble (France), where the large size enables us to reach regimes with both low Froude number and large Reynolds number. Stratification is obtained by using vertically linearly varying salt concentration and we force large-scale waves in a $6\times 6\times 1{\mathrm{m}}^3$ domain. We perform time-resolved particle image velocimetry to probe the space-time structure of the velocity field. We observe a wide band spectrum which is made of waves. Discrete modes are observed due to the square shape of the flow container as well as a continuum part which appears consistent with an axisymmetric superposition of random weakly nonlinear waves. Our observations support the interpretation of turbulence of a strongly stratified fluid as wave turbulence of internal waves although our spectrum is quite different from the Garrett and Munk spectrum. Weak turbulence proceeds down to a small cutoff length scale (the buoyancy wavelength) at which a transition to more strongly nonlinear turbulence is expected.

The behavior of flagellated bacteria swimming in non-Newtonian media remains an area with contradictory and conflicting results. We report on the behavior of wild-type and smooth-swimming E. coli in Newtonian, shear-thinning, and viscoelastic media, measuring their trajectories and swimming speed using a three-dimensional real-time tracking microscope. We conclude that the speed enhancement in Methocel solution at higher concentrations is due to shear thinning and an analytical model is used to support our experimental result. We argue that shear-induced normal stresses reduce wobbling behavior during cell swimming but do not significantly affect swimming speed. However, the normal stresses play an important role in decreasing the flagellar bundling time, which changes the swimming-speed distribution. A dimensionless number, the “strangulation number” (Str) is proposed and used to characterize this effect.

We numerically study the retraction of an axisymmetric viscous filament in a passive surrounding fluid. The analysis focuses on the evolution of the tip velocity, from the early stage of the filament retraction until it reaches its final equilibrium spherical shape. The problem is governed by two control parameters: the Ohnesorge number, Oh, which measures the relative importance of viscous and surface tension effects, and the initial aspect ratio of the filament, $\mathcal{A}$. We investigate the influence of Oh over a wide range of aspect ratios. The small-Oh regime is characterized by the occurrence of a spherical blob at the extremity of the filament. This feature has a key impact on the tip dynamics, which moves with an oscillating velocity whose mean value is close to the Taylor-Culick prediction. The oscillatory behavior of the tip velocity is explained through a simple mass-spring model. This regime is also characterized by the presence of capillary waves, with a phase velocity slightly larger than the Taylor-Culick velocity. Surface oscillations are also observed when the filament reaches its final spherical shape; the corresponding period agrees well with predictions of the linear theory. At intermediate Oh and large $\mathcal{A}$, the tip velocity reaches a value close to the Taylor-Culick prediction. However, for smaller aspect ratios, the maximum tip velocity is much smaller than this prediction, and does not exhibit any oscillation. The recoil dynamics is qualitatively and quantitatively different at high Oh. In this case, the radius of the filament grows uniformly over time and no blob forms, making the tip velocity decrease after a short transient. A self-similar solution is found to closely match the numerical results in this regime.