The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. Using an active liquid crystal model, we employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. We also extend our theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. Our results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and the cell nucleus.

We present a data- and first-principles-driven method for inferring the shape of a solid obstacle and its flow field in three-dimensional steady-state supersonic flows. The proposed method combines the optimizing a discrete loss (ODIL) technique with the automatically differentiable JAX-Fluids computational fluid dynamics (CFD) solver to study the joint reconstruction of flow fields and obstacle shapes. ODIL minimizes the discrete residual of the governing partial differential equation (PDE) by gradient descent-based algorithms. The ODIL framework inherits the characteristics of the chosen numerical discretization of the underlying PDE, including its consistency and stability. Discrete residuals and their automatic differentiation gradients are computed by the JAX-Fluids solver, which provides nonlinear shock-capturing schemes and level-set-based immersed solid boundaries. We use synthetic data to validate this approach on challenging inverse problems, including the shape inference of a solid obstacle in three-dimensional steady-state supersonic flow. Specifically, we study flows around a cylinder, a sphere, and an ellipse. We investigate two distinct approaches for the obstacle shape representation: (1) parametric shape representation, where the obstacle is described by a small set of parameters (e.g., the radius of the cylinder and the sphere) that are optimized together with the flow field, and (2) free shape representation, where the level-set function is directly optimized at each point of the computational mesh, without relying on predefined shapes. For the former, a thorough comparison with physics-informed neural networks is provided. We show that the nonlinear shock-capturing discretization in combination with the level-set-based interface representation allows for accurate inference of the obstacle shape and its flow field for the ODIL method. The proposed approach opens new avenues for solving complex inverse problems in supersonic aerodynamics.

Particles in a sufficiently strong electric field spontaneously rotate, provided that charge relaxation is slower in the particle than in the suspending fluid. It has long been known that drops also exhibit such “Quincke rotation,” with the electrohydrodynamic flow induced by electrical shear stresses at the interface leading to an increased critical field. However, the hysteretic onset of this instability, observed for sufficiently low-viscosity drops, has so far eluded theoretical understanding—including simulations that have struggled in this regime owing to charge-density steepening driven by surface convection. Here, we conduct a numerical study of the leaky-dielectric model in a simplified two-dimensional setting involving a circular drop, considering arbitrary viscosity ratios and field strengths. As the viscosity of the drop is decreased relative to the suspending fluid, the pitchfork bifurcation marking the onset of drop rotation is found to transition from supercritical to subcritical, giving rise to a field-strength interval of bistability. In this subcritical regime, the critical field is always large enough that, at the bifurcation, the symmetric base-state solution exhibits equatorial charge-density blowup singularities of the type recently described by Peng et al. [Phys. Rev. Fluids 9, 083701 (2024)]. As the rotation speed increases along the initially unstable solution branch from the bifurcation, the singularities gradually shift from the equator and ultimately disperse once the rotational component of the flow is strong enough to eliminate the surface stagnation points.

We examine the fundamental fluid dynamical mechanisms dictating the generation of bioaerosols in the human trachea during intense respiratory events such as coughing and sneezing, with an emphasis on the role played by the mucosalivary fluid viscoelasticity. An experimental investigation of the shear-induced fragmentation of a mucosalivary-mimetic fluid in a confined geometry reveals that viscoelastic liquids undergo atomization in a manner akin to Newtonian liquids—via the formation of baglike structures—which ultimately rupture through the appearance of retracting holes on the bag surface. Droplets are produced via the unstable retraction of liquid rims bounding these holes. However, in comparison to Newtonian liquids, viscoelastic bags inflate to larger sizes—implying thinner sheets and, consequently smaller droplets upon rupture. Numerical simulations support that the smaller droplets can be attributed to the thinner sheets, with a more uniform thickness, for viscoelastic bags prior to rupture. Hence, we highlight the role of the viscoelasticity in determining the thickness of the intermediate baglike structures, which, in turn, govern the droplet size distribution of the expelled aerosol.

We study the dynamics of sail membranes during a model of a tacking maneuver, when the sail angle of attack is reversed in order to sail upwind. In successful tacking the sail flips to the mirror-image shape, while in unsuccessful tacking the sail remains stuck in a metastable state close to the initial shape. We investigate whether the sail flips, and if so, how long it takes and the subsequent dynamics, over a parameter space that describes the sail membrane properties and the kinematics of tacking. We find that the “steady” parameters—stretching rigidity, pretension, and angle of attack—mostly determine whether a membrane flips or not. Flipping is more likely with larger values of the stretching rigidity, pretension, and angle of attack. The dynamical parameters—membrane mass density, concavity of angle-of-attack transition kinematics, and time length of the tacking maneuver—mainly affect how long flipping takes. With large membrane mass the membrane can maintain the momentum from the tacking motion long enough to reach the flipped state, but it may also take longer to converge to a steady shape. Concave-down angle-of-attack profiles and small tack times are generally associated with shorter flip times but a few exceptions exist, because these kinematics can also give a larger acceleration to the fluid-sail system that persists for longer times. We also investigate slack sails and find that they are more difficult to flip.

Many complex wetting behaviors of fibrous materials are rooted in the behaviors of individual droplets attached to pairs of fibers. Here, we study the splitting of a droplet held between the tips of two cylindrical fibers. We discover a sharp transition between two post-rupture states, navigated by changing the angle between the rods, in agreement with our bifurcation analysis. Depinning of the bridge contact line can lead to a much larger asymmetry between the volume of liquid left on each rod. This second scenario enables the near-complete transfer of an aqueous glycerol droplet between two identical vinylpolysiloxane fibers. We leverage this response in a device that uses a ruck to pass a droplet along a train of fibers, a proof-of-concept for the geometric control of droplets on deformable, architected surfaces.

We study experimentally a symmetrical rigid foil performing pitching oscillations around a mean incidence angle (${\alpha }_m$) with respect to an incoming flow in a hydrodynamic channel at a constant velocity where the Reynolds number based on the chord of the foil is ${\mathrm{Re}}_c=\rho U_{\infty }c/\mu =14400$. The problem is inspired by the pumping maneuver used by athletes on the new hydrofoil-based windsurf boards. In windsurfing, the pumping mode is used by athletes to produce unsteady propulsion. Because of the complex kinematics and the sail's position relative to the perceived wind, the sail produces thrust or drag, and lift. In sailing, the wind perceived by the sail is not parallel to the mean chord. Even if the sail is in a steady mode, it can propel the board by adjusting the mean incidence angle. Few studies investigate the impact of ${\alpha }_m$ on the mean values of aerodynamic force. The goal of this study is to quantify the forces on this configuration by varying the pitching kinematics characterized by the Strouhal number (${\text{St}}_A=fA/U_{\infty }$, with $f$ and $A$ the frequency and amplitude of pumping, respectively, and $U_{\infty }$ the wind velocity perceived by the sail) from 0 to 0.27, and the mean incidence angle ${\alpha }_m$, from 0° to ${30}^{\circ }$, of the foil. The force measurements show a high lift production and the delay of the stall angle according to ${\text{St}}_A$ which can be linked to previous studies about the generation of vortices at the trailing edge. A general trend of decrease is observed for the drag force coefficient in pitching compared to the static case. For the highest Strouhal numbers tested, the drag coefficient can become negative (thrust) in a range of ${\alpha }_m$ up to ${15}^{\circ }$ in specific cases. By using a sport-mimetic approach, we transform the measured lift and drag forces into propulsive and drifting forces, which are the decomposition of the aerodynamic force in the board frame. It is the reference frame in sailing to characterize and optimize physical parameters of the boat such as speed and trajectory. We investigate the impact of unsteady propulsion in upwind conditions. Doing so allows us to investigate race strategies because the generation of propulsion resulting from the drive force is linked to a sideways motion caused by the drift force. We also discuss the impact of using the pumping maneuver rather than the steady propulsion and show several behaviors that could help athletes with decision making.

When a slice of beet is placed on a plate with a thin layer of beet juice, one can observe a clear fringe around the beet, where the color is more translucent than the rest of the juice. The hypotheses in literature were inconsistent and limited, which motivated us to revisit this phenomenon. Using a motorized confocal displacement sensor, we measured the temporal evolution of the liquid surface profile across the fringe. Our findings suggest that a suction flow, induced by the capillary rise of the contact line, causes a dimple—a small concave depression—to form on the liquid surface. While surface tension and gravity tends to smooth out the dimple, viscous drag acts against them if the liquid film is sufficiently thin. Our scaling analysis correctly estimates the dependence of dimple lifetime on liquid properties and film thickness. We also capture the dimple formation dynamics by numerically solving the lubrication equation with the Young-Laplace equation. This work provides an interpretation for a common phenomenon.

This study examines the dynamics of roll waves that spontaneously arise in muddy debris flows, where phase separation is not observed. To this end, a set of bulk mass and momentum balance equations is derived from the depth-averaged model proposed by Meng et al. [J. Fluid Mech. 943, A19 (2022)]. The derived equations are shown to be well-posed, with the threshold Froude number for flow instability slightly exceeding the classical $2/3(1-\mathrm{\Gamma })$, which corresponds to dry granular flows on rough planes. A high-resolution shock-capturing scheme is employed to resolve the evolution of debris roll waves, which emerge from initially steady, uniform flows subjected to sinusoidal perturbations. These waves grow under the influence of inertial forces and eventually saturate into steady, traveling waveforms. A traveling-wave solution is subsequently constructed, accurately capturing the steady traveling waves observed in the simulations. This theoretical framework is further applied to natural debris roll waves observed in the Illgraben torrent, Switzerland. Simulated time series of the flow depth and wave speeds, based on the $\mu \left(I\right)$-dependent basal granular friction law, exhibit excellent agreement with field measurements. Numerical results also reveal that large-amplitude waves, which carry significant mass flux, are dynamically unstable and tend to fragment into multiple smaller-amplitude waves. These smaller waves are overtaken and merged by trailing waves with larger amplitudes and faster propagation speeds, a phenomenon consistent with field observations.

Although it is commonly expected that a metal disk placed on the surface of water will sink, our investigation has revealed a surprising phenomenon: a vertical jet directed onto the disk from above can allow it to remain afloat. This result defies intuition, as one would assume that the force of the jet's impact would cause the disk to sink. We have discovered that this phenomenon occurs as a result of water displacement from the top of the disk caused by the impacting jet, operating through a mechanism similar to the hydraulic jump. This displacement increases the effective immersed volume, resulting in an increased buoyant force that balances gravity. In contrast to the classical case, here the jump radius is fixed by the geometric parameters of a disk, a phenomenon we refer to as the boundary jump. To further explore this effect, we have presented a theoretical model based on scaling laws, which provides the conditions required for the disk to float. The prefactor was determined through an independent experiment. Finally, we conducted experiments on the disk's floating and sinking, which showed a good match with the proposed theory.

Singular or weak solutions of the incompressible Euler equations have been hypothesized to acccount for anomalous dissipation at very high Reynolds numbers and, in particular, to explain the d'Alembert paradox of nonvanishing drag. A possible objection to this explanation is the mathematical property called “weak-strong uniqueness,” which requires that any admissable weak solution of the Euler equations must coincide with the smooth Euler solution for the same initial data. As an application of the Josephson-Anderson relation, we sketch a proof of conditional weak-strong uniqueness for the potential Euler solution of d'Alembert within the class of strong inviscid limits. We suggest that the mild conditions required for weak-strong uniqueness are, in fact, physically violated by violent eruption of very thin boundary layers. We discuss observational signatures of these extreme events and explain how the small length scales involved could threaten the validity of a hydrodynamic description.

We present a laboratory experiment to model convection in the atmosphere driven by latent heat of condensation (“moist convection”). The system consists of a tank filled with an aqueous solution containing a color indicator that renders the fluid yellow and transparent when acidic and blue and opaque when basic. A sodium lamp positioned above the tank serves as a heat source. Initially, the solution is entirely acidic and stably stratified in temperature. A basic layer is progressively generated at the tank's bottom through water electrolysis, forming an initially stable, blue region. This layer is internally heated by absorbing the heat from the sodium lamp, modeling the latent heat of condensation in the atmosphere. Over time, instabilities develop at the interface between the yellow and blue layers. We investigate the variation of the instability wavelength and complement our observations with a linear stability analysis to elucidate the underlying mechanisms and the process of wavelength selection. Direct numerical simulations are then employed to explore the first steps of the nonlinear regime in connection with experimental observations.

We study numerically the dynamical evolution of two different vorticity arrays with an initially uniform magnetic field in two-dimensional incompressible magnetohydrodynamics. We concentrate particularly on the role of the strength of the background magnetic field, which is always assumed weak in the sense that its energy is much less than the kinetic energy of the vortical flows. Within the context of a weak background field, we are able to identify four distinct regimes. When the field is so weak that the back-reaction of the Lorentz force can be ignored (the kinematic regime), classical flux expulsion occurs. As the field strength is increased, the first signs of the dynamical influence of the small-scale field generated is in the disruption of vortex filaments, with flux expulsion still occurring in the vortex cores. A further increase in field strength leads to the regime of vortex disruption, in which the magnetic field is expelled, but is then of sufficient strength to disrupt or destroy the vortices. For yet stronger fields, even the large-scale field can be sufficiently strong to be dynamically active; flux expulsion is then prevented, and the field is dynamically active throughout the evolution. Furthermore, in the case of a row of vortices, we show that the orientation of the background field significantly influences the evolution, especially at higher field strengths.

Breath figures are the complex patterns that form when water vapor condenses into liquid droplets on a surface. The primary question concerning breath figures is how the condensing vapor is allocated between the growth of existing droplets and the nucleation of new ones. Although numerous theoretical studies have concentrated on scenarios resulting in highly polydisperse droplet ensembles, a companion paper [Bouillant et al., Phys. Rev. Lett. 134, 188204 (2025)] demonstrates that nearly monodisperse patterns can be achieved on defect-free substrates in a diffusion-controlled regime. The objective of this work is to present a theoretical framework that elucidates the formation and evolution of nearly monodisperse patterns in breath figures. We discover that, following a short nucleation phase, the number of droplets remains constant over an extensive range of timescales due to collective effects mediated by the diffusion of vapor. The spatial extent of these diffusive interactions is identified through asymptotic matching, based on which we provide an accurate description of breath figures through a mean-field model. The model accounts for the subdiffusive growth of droplets as well as for the arrest of nucleating new droplets, and reveals the scaling laws for the droplet density observed in experiments. Finally, droplets expand and ultimately coalesce, which is shown to trigger a scale-free coarsening of the breath figures.

Understanding the dynamics of fluid transport and trapping within microscale cavities is important for a range of environmental, industrial, and research applications. Using PDMS microfluidic channels, we explore the displacement and retention of (wetting) oil by an invading flow of (nonwetting) water at low Reynolds number $(\mathrm{Re}\ll 1)$ in noncontiguous pores, and examine the influence of trapping velocity, viscosity ratio, and pore aspect ratio. We find that increasing capillary numbers lead to a greater amount of oil trapped per cavity. This is contrary to findings for interconnected porous media in which the availability of multiple pathways for fluid flow leads to more displacement with increased flow rates. This result can be attributed to a dynamic transition from a meniscus displacement to a viscous fingering displacement, by which the advancing water front shifts from a discrete triple contact line at channel walls to a continuous layer of oil enveloping the water. Data from all pore geometries can be collapsed onto a single trend by subtracting the amount of oil captured in the zero capillary number limit, indicating that increased oil retention at higher values of capillary number is not dependent on pore geometry. A model for steady-state, three-dimensional flow based on the long-wave approximation was developed to analyze the amount of fluid retained as a function of capillary number and viscosity ratio. Model predictions are qualitatively consistent with several experimental observations, including the shape of the interface of the trapped oil and the trend that increasing capillary number leads to greater oil trapping per pore. Our results highlight the need to quantitatively investigate the transient dynamics of fluid invasion in multiphase systems that exhibit localized entrapment.

An immersed-boundary method-based incompressible flow solver was used to study the vertical diamond formation that occurs within fish schools and the resulting hydrodynamic performance enhancements and wake dynamics. The vertical spacing $H$ between the top and bottom fish within the diamond was varied to understand the impact of this spatial parameter on performance enhancements. At lower $H$ spacings, thrust enhancement and drag reduction were experienced by all four fish; these effects were maximized at $H$ = 0.27 body length. At this spacing, the follower obtains the largest benefits with a 15.5% drag reduction and 6.0% thrust increase compared to solitary swimming. The top and bottom fish extract a more than 6.0% thrust increase, while a less significant drag decrease is experienced. In contrast, the leader faces an increase in thrust and decrease in drag. Power consumption of the leader and follower are reduced as well; however, the top and bottom fish power consumption is increased by more than 6.0% in this formation. By examining the vortex dynamics, pressure distribution, and wake velocity patterns, mechanisms responsible for the performance enhancements in low $H$ vertical diamonds were identified. The leader benefits were obtained through body-body interactions with positive signed pressure ahead of the top and bottom fish. The top and bottom fish extracted anterior suction, and therefore drag reduction, from the leader's vortex rings. The caudal fins of the top and bottom fish generated strong leading-edge vortices (LEVs) in the interior of the diamond, therefore, enhancing thrust. These strengthened LEVs convected downstream forming coherent vortex legs within a complex pattern of vortex rings. The wake-body interaction between the top and bottom fish vortex rings and the follower fish (i) generated strong anterior suction pressure and (ii) produced a like-signed vortex ring and boundary layer vorticity interaction resulting in a reduction of drag. Finally, the follower's caudal fin extracted a wake-fin interaction and thrust increase from spanwise-compressed vortices generated by the top and bottom fish. A Reynolds number study confirmed enhancements in the lower $H$ diamond over a sparser diamond are obtained across a range of Re from 1000 to 8000. This study revealed the complex wake dynamics and body-body, wake-body, fin-fin, and wake-fin interactions that can be leveraged for performance benefits in vertical diamond fish schools. The findings provide insights into optimizing the configurations of fish-inspired robotic swarms for greater efficiency.

Human respiratory activities induce the exhalation of a cloud of air laden with droplets. These droplets can harbor pathogens and play a role in the transmission of infectious diseases. Experimentally determining the size and velocity of these droplets, along with the properties of the exhaled air cloud, is crucial for predicting their behavior postemission and developing effective strategies to mitigate infection transmission. Despite the efforts of the scientific community, there is still a lack of comprehensive characterization of exhaled droplet size distribution, with different studies yielding significantly varied results. Additionally, while several studies have measured airflow rate and velocity, droplet velocity is rarely measured and typically only within a limited size range. In this study, we use an enhanced version of the interferometric laser imaging for droplet sizing (ILIDS) technique to simultaneously measure the size and velocity of droplets exhaled by 23 volunteers during speaking, coughing, and breathing. This method allows us to detect droplet diameters as small as $2\mu \mathrm{m}$, extending the size range reported in the literature for the coupled measure of droplet size and velocity. The ILIDS technique addresses several issues encountered in previous studies by (i) directly measuring droplets larger than $20\mu \mathrm{m}$, (ii) conducting measurements close to the mouth to reduce droplet evaporation and dilution effects, and (iii) distinguishing between ambient air dust and exhaled droplets, eliminating the need for air filtration. Additionally, this study assesses the impact of protective masks on droplet size and velocity distributions, as well as the variability of the results among different volunteers and the same volunteers repeating the tests multiple times.

The Lamb vector is pivotal in elucidating the physical origin of aerodynamic forces exerted on a body, and it is intricately linked to the advancement of vortex force theory. A thorough investigation of its full-life cycle evolution can greatly enhance our understanding of fluid dynamic behavior. The asymptotic expression of the Lamb vector near the no-slip boundary has been numerically validated, revealing its formation mechanisms in the viscous sublayer of supersonic flat plate flow. The wall-normal component is governed by boundary entropy and entropy flux, while the tangential component is dominated by the divergence of boundary vorticity, skin friction and dilatation-related terms. The spatiotemporal evolution equation, derived by Stokes-Helmholtz decomposition, highlights the competition between advection, stretching-tilting of transverse components of generalized Lamb vectors, and viscosity effects. The gaps in the full-life cycle of the Lamb vector are filled by defining the weakly nonlinear midfield wake region. The Lamb vector's behavior and underlying physics within this region are examined. Spatial variations in the wall-normal component of generalized Lamb vectors and viscosity cause anisotropic exponential decay, while advection and stretching-tilting of transverse components of generalized Lamb vectors lead to a distinct banded flow structure.

Integrating floating photovoltaic (FPV) installations into offshore wind farms has been proposed as a major opportunity to scale up offshore renewable energy generation. The interaction between these hybrid wind–solar farms and the atmospheric boundary layer (ABL) is addressed in the present study. Idealized large-eddy simulations (LESs) are used to investigate the flow through both isolated wind and solar farms, as well as combined wind–solar farms, in varying configurations and under different atmospheric conditions. When the FPV modules are arranged in long strips parallel to the flow direction, secondary motions arise due to the temperature difference between the warm FPV modules and the colder sea surface, significantly affecting the horizontal distribution of mean wind speed in the ABL. Associated downdrafts between the strips increase entrainment of high-speed momentum from above, thereby increasing the wind speed at these locations. LESs of hybrid wind–solar farms reveal that this is beneficial for wind turbines when they are located between the FPV arrays, leading, for the cases that we considered, to a farm-averaged power increase of up to 30% compared to an isolated wind farm. It is shown that the ratio between inertial and buoyancy forces, quantified by a heterogeneity Richardson number ${\text{Ri}}_h$, plays a crucial role in the formation of secondary flows and the resulting wind farm power enhancement. We further show that no significant power gains, but also no losses emerge in situations when the solar panels are aligned perpendicular to the flow. Although the present results suggest a large potential for wind–solar hybridization, future research should focus on a wider range of scenarios, obtained from a realistic distribution of wind directions and speeds to quantify the potential beneficial impact on real annual wind power production.

We apply linear stability analysis to nearly incompressible flow over a two-dimensional zero-pressure-gradient boundary layer in the presence of a forward-facing step (FFS), with step height to local displacement thickness ratios between $0<h/{\delta }_s^{*}<3.2$. We employ a nominally sharp FFS with a 1 $\mu \mathrm{m}$ radius to closely resemble a prior wind tunnel experiment, but we also examine the impact of various step corner radii and slopes. The Navier-Stokes equations are solved on curvilinear grids to obtain the laminar basic states. After that, we use a combination of the harmonic linearized Navier-Stokes equations and the parabolized stability equations to compute the linear amplification of Tollmien-Schlichting instabilities. The $N$-factor envelopes for the FFS reveal crucial differences with respect to those obtained previously for backward-facing steps (BFS) with $0<h/{\delta }_s^{*}<1.3$, for which accurate predictions of transition onset could be obtained via $N$-factor correlations. As the boundary-layer flow recovers to its unperturbed state in the far wake of the BFS, the slope of the $N$-factor envelope is nearly the same as that of the unperturbed flat-plate boundary layer. In contrast, the $N$-factor envelope downstream of the FFS becomes flatter as the step height increases, i.e., $\mathrm{d}N$/$\mathrm{d}x$ becomes nearly 0, which causes the $N$-factor method to become sensitive to the prescribed value of the correlating $N$-factor value. In spite of this difficulty, the $N$-factor method still captures the overall trend associated with a progressively upstream shift in the transition location as the FFS height becomes larger. However, the critical step height corresponding to the onset of a significant upstream shift in transition location is not very well predicted when compared with the measured data. Within the framework of a variable $N$-factor method, the predicted reduction in the transition $N$-factor is given by $\mathrm{\Delta }N=1.89\arctan [(h/{\delta }_s^{*}-1.29)/0.179]-2.73$.