The moderate- to large-amplitude free-decay oscillations of an air bubble in water, formed from the coalescence of two parent bubbles, are studied experimentally and by numerical simulation. Magnetic levitation is used to suspend the air bubble, with a diameter of approximately $6\mathrm{mm}$, within the liquid as if under weightless conditions. We find that the method does not significantly distort the shape of the air bubble, facilitating direct comparison with theoretical predictions of oscillations from an assumed spherical equilibrium shape. The coalescence of two equal-sized parent bubbles produces a single bubble undergoing freely decaying nonlinear shape oscillations dominated by the two-lobed shape mode, approximating the problem considered theoretically by Tsamopoulos and Brown, who obtained the corrections to the shapes and frequencies of the linear modes of oscillation to second and third order in amplitude, respectively. The frequency of the two-lobed oscillations decreases with the square of the amplitude, as predicted, but with a coefficient smaller in magnitude than expected. Coalescence of two unequal-sized bubbles, differing in diameter by a factor 1.54, produced a bubble oscillating with comparable contributions from two- and three-lobed shapes. Here the quadratic coefficient is the same (within uncertainty) as that observed in the symmetric case. However, there is also a significant dependence of the frequency on the fourth power of the amplitude in this case, and the quadratic coefficient of the three-lobed mode is approximately three times larger than predicted, which we attribute to coupling between the two- and three-lobed modes. The magnitudes of the various surface harmonics contributing to the shape of the two-lobed mode agree well with Tsamopoulos and Brown's prediction at second order in amplitude and with our calculations at third order. Results from simulation are consistent with those from experiment.

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 propose a novel method for model-based time super-sampling of turbulent flow fields. The key enabler is the identification of an empirical Galerkin model from the projection of the Navier-Stokes equations on a data-tailored basis. The basis is obtained from a Proper Orthogonal Decomposition (POD) of the measured fields. Time super-sampling is thus achieved by a time-marching integration of the identified dynamical system, taking the original snapshots as initial conditions. Temporal continuity of the reconstructed velocity fields is achieved through a forward-backwards integration between consecutive measured Particle Image Velocimetry measurements of a turbulent jet flow. The results are compared with the interpolation of the POD temporal coefficients and the low-order reconstruction of data measured at a higher sampling rate. In both cases, the results obtained show the ability of the method to reconstruct the dynamics of the flow with small errors during several flow characteristic times.

Cilia are cell organelles acquired by eukaryotes more than a billion years ago that induce flow in the surrounding fluid by periodically beating in waves. From a viewpoint of biofluid mechanics, cilia perform four major functions: swimming, feeding, pumping, and sensing. In this paper, we describe the flow produced by cilia and its biological functions. First, the speed and efficiency of ciliary swimming are discussed. It is shown that the friction between cilia and the cell surface is extremely high, with more than 90% of the mechanical power input into the fluid being dissipated by viscous friction within the ciliary layer. Our analysis reveals that swimming efficiency is highest when the number of cilia increases in proportion to the square of the body length, which is consistent with scaling in nature. Next, the swimming and feeding of the colony of choanoflagellates are discussed. The choanoflagellates turn their flagella inwards when exposed to light and flip their flagella outwards when it is dark. Our analysis illustrates that the inward flagellar flow is advantageous for feeding, whereas the outward flagellar flow is advantageous for swimming. Due to their morphological similarities, the pumping function of a choanocyte chamber of a sponge is also addressed. Finally, we discuss nodal flow in mouse embryos, the direction of which determines the left-right axis of the body. The strength of the nodal flow generated by the motile cilia acts equally on the immotile cilia located at the left and right edges of the nodal cavity. Therefore, in order to create a left-right asymmetry, the immotile cilia must sense the direction of the flow, which has been confirmed experimentally. These studies demonstrate that ciliary flow gives rise to a variety of biological functions and that fluid dynamics can provide valuable insights into biology.

Controllable swarms of active particles are considered prospective for object manipulation in general and as payload carriers in fluidic microenvironments in particular. However, a theoretical description of finite-sized swarms is missing, as opposed to continuous fields of active particles. Here, we thus develop a torque dipole-based hydrodynamics with spin model for the motion of active particle swarms in an external magnetic field. We apply the developed model to swarms of magnetotactic bacteria. We experimentally observe the motion of magnetotactic bacteria swarms perpendicular to the applied in-plane magnetic field. We use our model to explain that the swarms move according to the left-hand rule in combined vertical and lateral magnetic fields and that this movement originates from hydrodynamic interactions within the torque dipole ensembles. We also report the linear scaling of the swarm motion velocity with the driving magnetic field magnitude, and are able to derive the propulsion torque of the active particles from the experiments. Our results are applicable to other types of active particles and driving fields, and will pave the way for further research into harnessing active particle swarms as collective robots.

This paper investigates one- and two-point correlations conditioned to the turbulent/nonturbulent interface (TNTI) of a planar turbulent temporal jet. A classical average, which is taken with respect to a spatially averaged TNTI location, is compared to two types of conditional averages, which are conditioned with respect to the instantaneous TNTI. We show that the two conditional averages differ from the classical average, especially in the TNTI region and over a distance that is comparable to the standard deviation of the instantaneous TNTI location. All correlations scale in a self-similar manner with time when normalized with a characteristic jet width calculated from integral quantities of momentum and volume fluxes. This paper presents a two-dimensional framework of separation between the correlation points and physical position from the TNTI to show interesting behavior related to the location, size, and intensity of velocity fluctuations with respect to the TNTI. We observe that the conditional velocity correlation functions exhibit distinct peaks at well-defined separations, indicating the typical scales of turbulent motions influenced by the TNTI. The values of the relevant peaks clearly demonstrate that, even when studied in a conditional framework, the dynamics of the velocity fluctuations with respect to, for example, the enstrophy, shows the presence of length scales that are very large with respect to the width of the turbulent region. Interesting results emerge when the correlation where one point is always fixed on the TNTI and the other interrogates the turbulent zone is considered. This observable investigates the turbulent dynamics inside the turbulent zone with respect to the TNTI. We show that the peak correlations are in line with the standard deviation of the TNTI, suggesting a connection to the scale of the turbulent motions attached to the TNTI. These features are not captured in classical statistics or in prior TNTI studies relying solely on one-point quantities.

When turbulent boundary layer flows encounter abrupt roughness changes, an internal boundary layer (IBL) forms. Equilibrium theory breaks down in the nonequilibrium IBL, which may extend O(10) km for natural atmospheric flows. Here, we find that the IBL possesses a characteristic time scale associated with the IBL height, ${\delta }_i$. We show that ${\delta }_i$ and the edge velocity set the scales of the mean and defect velocity profiles within the IBL, for simulation and experimental data covering a multitude of roughness transition types. For the flow within the IBL, this scaling is more appropriate than more classic scaling parameters—such as viscous and outer ones—providing an alternative scaling for this intermediate region. We present a nontrivial extension of equilibrium theory to the dynamically adjusting IBL, which can be useful for modeling a range of environmental and industrial flows.

Direct numerical simulations have been conducted to investigate a zero-pressure-gradient boundary layer flow over a single deep circular dimple with a depth $d$ of $0.1D$ and a Reynolds number ${\text{Re}}_D$ (based on the dimple diameter $D$ and freestream velocity $U$) of 20 000. This is a sequel to the earlier study on flow over a significantly shallower dimple with $d/D=0.05$ [Zhu et al., Phys. Fluids 36, 023608 (2024)]. The effect of inlet boundary layer thickness $\delta$ is explored by considering values ranging from $0.07D$ to $0.1D$. The flow features a tornado-like vortex pair within the dimple, followed by a quasiperiodically shedding hairpin vortex street downstream of the dimple. The peak frequency of the vortex shedding increases from $1.05U/D$ to $1.41U/D$ as $\delta /D$ decreases. The tornado-like vortex pair exhibits a transition from a symmetric pattern to an asymmetric pattern and finally to a quasiperiodic spanwise meandering pattern as $\delta /D$ decreases to 0.07. Both sinuous and varicose streak instabilities emerge downstream, with sinuous instabilities showing notably lower frequencies. It is found that the formation of the primary hairpin vortex downstream of the dimple is initiated by the varicose instability, which triggers the shedding of the shear layer near the downstream edge of the dimple. This shed shear layer then connects with the tornado-like vortex pair, forming a complete hairpin vortex. The sinuous instability results in visible periodic meandering of the tornado-like vortex pair at $\delta /D=0.07$, leading to an early transition to turbulence far downstream of the dimple, manifested by hairpin vortex packets.

We numerically study the rotational flow-induced vibrations (FIV) of an inverted cylinder-plate, consisting of a rigid circular cylinder and an attached splitter plate on its windward side. A torsional spring mounted at the center of the cylinder facilitates a one degree-of-freedom flow-induced rotational motion. While splitter plates are conventionally utilized to suppress the vibrations of bluff bodies, the present study demonstrates the opposite effect of enhancing the vibrations. We employ an in-house, sharp-interface immersed-boundary-method-based flow solver, which is one-way coupled to a forced torsional harmonic oscillator equation. Our two-dimensional simulations at a Reynolds number of 100 show the existence of several FIV regimes as a function of reduced velocity, namely, initial excitation, intermediate and final symmetry breaking, large-amplitude oscillations, and chaos. We demonstrate the presence of harmonic lock-in during large-amplitude oscillations through frequency synchronization and enhanced energy exchange between structure and fluid. Leading-edge vortices (LEVs) form during the large-amplitude oscillation and symmetry-breaking regimes and create large negative pressure zones that drive the cylinder-plate to undergo significant displacements. The splitter plate length influences the LEV formation and the strength of LEVs diminishes for shorter plates, resulting in a significant drop in amplitude. As the structure-to-fluid density ratio increases, the range of reduced velocity over which the regimes are observed becomes broader. Synchronized oscillations of the cylinder-plate with fluid forcing indicate vortex-induced vibrations as the driving mechanism. This is further confirmed through dynamic mode decomposition of the vorticity field, which reveals that the dominant vortex-shedding mode remains synchronized with the cylinder-plate oscillations across the regimes.

Active particles in anisotropic, viscoelastic fluids experience competing stresses which guide their trajectories. An aligned suspension of particles can trigger a hydrodynamic bend instability, but the elasticity of the fluid can drive particle orientations back towards alignment. To study these competing effects, we examine a dilute suspension of active particles in an Ericksen-Leslie model nematic liquid crystal. An anchoring strength linking the active and passive media tunes the system between active suspension theory in Newtonian fluids in one limit and active nematic theory in another. For extensile active stresses, beyond a critical active Ericksen number or particle concentration, the suspension first comes into alignment, then buckles via a classical bend instability. Rather than entering the fully developed roiling state observed in isotropic fluids, the development is arrested into a steady, flowing state by fluid elasticity. Arrested states of higher wave number appear at yet larger extensile activity, and a phase transition is identified at finite anchoring strength. If the active particles are motile, the particles can surf along the bent environment of their own creation. More exotic states are also observed, including a oscillatory “thrashing” mode. Moment equations are derived, compared to kinetic theory simulations, and analyzed in asymptotic limits which admit exact expressions for the traveling wave speed and both particle orientation and director fields in the first arrested state.

The flow over a circular cylinder is numerically studied at $\mathrm{Re}=220$ (mode-A instability) by varying the computational domain size in the spanwise direction from $L_z=0$ to $252d$ ($d$ is the cylinder diameter) with a periodic spanwise boundary condition to investigate its effect on the flow structures and mean flow quantities. For a large spanwise domain size ($L_z=252d)$, the instantaneous flow fields reveal large-scale flow structures extending over approximately $45d$ in the spanwise direction (significantly exceeding the characteristics wavelength of $4d$ associated with the mode-A instability), accompanying vortex dislocation and alternating parallel and oblique shedding, whereas parallel shedding is mostly observed for $L_z\le 12d$. The necessity of large spanwise domains to capture these structures is further confirmed through the spanwise wave-number power spectrum and the spanwise two-point correlation of the sectional lift force. Since the vortex shedding phase varies along the spanwise direction at large $L_z$'s, the root-mean-square (rms) lift coefficient decreases towards zero with increasing $L_z$. However, when the sectional lift coefficient is introduced, its rms value converges to a certain value for $L_z\ge 24d$, and other mean flow statistics similarly reach convergence beyond this threshold. We also consider the Reynolds number of $\mathrm{Re}=300$ corresponding to mode-B instability. At this Reynolds number, vortex dislocation and oblique vortex shedding do not occur even at large $L_z$'s, and flow structures and mean flow quantities are accurately obtained for $L_z\ge 6d$.

When a chordwise Reynolds number (Re) falls below about ${10}^5$ the performance of wings and aerodynamic sections become sensitive to viscous phenomena, including boundary layer separation and possible reattachment. Here, detailed measurements of the flow inside the boundary layer on the suction surface are shown for an aspect ratio 3 wing with wall boundaries. The separation lines and recirculation zones are shown on the wing and on the wall junction as Re and angle of incidence ($\alpha$) are varied. There is good agreement on the lowest Re case which has also been computed in direct numerical simulation. Though the flow at midspan may sometimes be described as two-dimensional, at $\alpha \le 6^{\circ }$ it is unrepresentative of the remainder of the wing, and the influence of the wall is seen in strong spanwise flows aft of the separation line. The geometry of the NACA 65(1)-412 section, used here, promotes a substantial chord length for the development of the recirculating regions behind separation making it apt for their study. However, the phenomena themselves are likely to be found over a wide range of airfoils/wings with moderate thickness at moderate $\alpha$.

In this study, the dynamics of droplet impact onto hydrophobic and superhydrophobic spherical surfaces are experimentally investigated, with the particle-to-droplet diameter ratio ($\mathrm{\Omega }$) ranging from 1.04 to 2.08. We analyze the transient deformations of water droplets on these surfaces and discover new impact regimes, referred to as ring rebound and claw rebound. At high Weber numbers, when $\mathrm{\Omega }>1.7$, the ring and claw rebound regimes are observed, triggered by Kelvin-Helmholtz instability. The causes of the claw rebound are examined, considering the influences of $\mathrm{\Omega }$, Weber number ($We$), and surface wettability. We identified the crucial factors contributing to regime formation—maximum spreading angle ${\beta }_{\max }$. A semiempirical formula is proposed to estimate the time required for a droplet to reach its maximum spreading state. Additionally, a theoretical model based on energy conservation laws and semiempirical formulations is developed, which can accurately predict regime transitions and maximum spreading behavior.

We present numerical investigations of flow-acoustic resonances in deep and inclined cavities using wall-resolved large-eddy simulations. The cavity geometry has a fixed aspect ratio of $D/L=2.632$, subjected to two Mach numbers of 0.2 and 0.3 at three different angles of inclination ($\alpha ={30}^{\circ }, {60}^{\circ }$, and ${90}^{\circ }$). Fully turbulent boundary layers generated from independent precursor simulations are employed upstream of the cavities. The simulation results show significant differences in aeroacoustic response between inclined and orthogonal cavities, particularly at $M_{\infty }=0.3$, where the inclined cavities exhibit stronger resonances (by more than a 20 dB) at a lower peak frequency ($\mathrm{St}=0.276$) than the orthogonal cavity, whose peak occurs at $\mathrm{St}=0.849$. Acoustic modal analysis identifies these frequencies as the first and second eigenmodes, respectively. Further analysis shows that the difference in mode selection is linked to the hydrodynamic modes that couple with the acoustic modes. In the orthogonal cavity, the second hydrodynamic mode prevails, in which two relatively small vortices travel across the cavity opening simultaneously. In the inclined cavities, however, a single large-scale rollup vortex corresponding to the first hydrodynamic mode is generated owing to strong Kelvin-Helmholtz instability in the shear layer. More importantly, this vortex spends much of its lifetime growing in size rather than traveling rapidly downstream, resulting in a longer crossing time per cycle that correlates with the first acoustic eigenmode frequency ($\mathrm{St}=0.276$). In addition, aeroacoustic resolvent analysis indicates that inclined cavities amplify acoustic responses more effectively and exhibit weaker source-sink cancellation than the orthogonal cavity. These mechanisms are identified as the primary contributors to the enhanced aeroacoustic response of the inclined cavities. Finally, it is proposed that the ratio of acoustic particle displacement to momentum thickness can be used as a criterion for predicting the onset of deep cavity resonance associated with the distinctive vortex dynamics identified in this paper.

A flow of a slightly rarefied gas driven by a uniform external force within an infinitely long square duct is considered based on the kinetic theory. The steady behavior of the gas is investigated based on the Bhatnagar–Gross–Krook model of the Boltzmann equation and the diffuse reflection boundary condition. A systematic asymptotic analysis of the system for small Knudsen numbers is carried out, and a set of fluid-dynamic-type equations and their boundary conditions that describe the behavior of the gas are derived. The obtained momentum equation in the cross-sectional directions includes the thermal stress term. This is a rarefaction effect associated with the nonuniform temperature field developed by heating due to viscous dissipation of the main axial flow. Because of the thermal stress, the flow is not strictly unidirectional, and a slow secondary flow of the order of the Knudsen number is induced within the cross section. This secondary flow, through convection, has finite effects on the leading-order axial flow and temperature fields. Numerical examples illustrating these features are presented.

Coarsening is a crucial phenomenon in bubbly media through which bubbles grow over time. In the capillary regime, i.e., when the surrounding fluid is a simple liquid, the cube of the bubble radius grows linearly with time. What happens when the simple liquid is replaced by a complex elastoplastic fluid? To answer this question, we perform two experiments with a foamed concentrated emulsion: one investigates the growth law over long durations with an emulsion having a constant yield stress, while in the other the emulsion yield stress continuously increases until coarsening arrests. Our results show that for Bingham capillary numbers (Bi), comparing yield stress to capillary effects, greater than approximately 0.1, plastic stresses slow down coarsening. We extend the growth law to capture this effect by introducing a damping factor dependent on the critical value ${\mathrm{Bi}}^{*}$, which marks the arrest of coarsening; it allows us to describe all our bubble growth data for liquid fractions ranging from 58% to 96%. Furthermore, we explain the evolution of ${\mathrm{Bi}}^{*}$ as a function of the liquid fraction using the effective yield stress of the bubbly emulsion. This work provides insights into the design of stable porous materials by demonstrating how matrix plasticity can be leveraged to control microstructure evolution, with implications for materials requiring optimized mechanical response.

We present a numerical model of fractal-structured aggregates in low-Reynolds-number flows. Assuming that aggregates are made of cubic particles, we first use a boundary integral method to compute the stresses acting on the boundary of the aggregates. From these external stresses, we compute the stresses within the aggregates to gain insights on their breakup, or disaggregation. We focus on systems in which aggregates are either settling under gravity or subjected to a background shear flow and study two types of aggregates, one with fractal dimension slightly less than two and one with fractal dimension slightly above two. We partition the aggregates into multiple shells based on the distance between the individual cubes in the aggregates and their center of mass and observe the distribution of internal stresses in each shell. Our findings indicate that large stresses are least likely to occur near the far edges of the aggregates. We also find that, for settling aggregates, the maximum internal stress scales as about 7.5% of the ratio of an aggregate's apparent weight to the area of the thinnest connection, here a single square. For aggregates exposed to a shear flow, we find that the maximum internal stress scales roughly quadratically with the aggregate radius. In addition, after breaking aggregates at the face with the maximum internal stress, we compute the mass distribution of subaggregates and observe significant differences between the settling and shear setups for the two types of aggregates, with the low-fractal-dimension aggregates being more likely to split approximately evenly. Information obtained by our numerical model can be used to develop more refined dynamical models that incorporate disaggregation.

This study introduces biodegradable particles as a sustainable, low-cost, and effective alternative to synthetic tracers for flow visualization of biological and underwater systems using particle image velocimetry (PIV). Biodegradable alternatives address critical challenges associated with conventional synthetic tracers (e.g., silver-coated glass beads), such as potential environmental impact, toxicity, and high costs. We characterized various biodegradable particles to determine their density, size, and light-scattering properties. Corn and arrowroot starch emerged as the most promising candidates, with densities closely matching deionized and artificial seawater (35 ppt), minimizing buoyancy effects. Both particles exhibited uniform size distributions, with mean diameters of 10.9 (corn) and $8.7\mu \mathrm{m}$ (arrowroot). PIV experiments using a translating airfoil, live brine shrimp, and live jellyfish confirmed that starch particles accurately visualized velocity and vorticity fields, effectively capturing flow structures in brine shrimp and jellyfish swimming. The nontoxic, digestible nature of starch makes them ideal for biological and ecological studies, minimizing risks to live organisms and the environment. Thus, we highlight the potential of natural starch as an eco-friendly replacement for synthetic tracers in PIV experiments, promoting sustainable and frugal practices in flow visualization without compromising performance.

We propose a sensor-restrained model for the shear viscosity term within the localized artificial diffusivity (LAD) scheme to stabilize compressible large-eddy simulations with low-pressure-core vortical structures. LAD methods are used in numerical solvers based on spectral-like compact finite-difference schemes. While high-order-accurate numerical schemes with proper discretization guarantee physical fidelity, the LAD role is to suppress nonphysical oscillations arising in compressible flow simulations near shock waves and other sharp gradients. LAD is a cost-effective approach that adds artificial shear and bulk viscosities, and thermal conductivity and thermal conductivity to their physical counterparts. However, an unrestricted added diffusivity may lead to poorly resolved coherent structures and undesirable turbulence statistics. To prevent excessive numerical diffusion in compressible shear flows, the artificial shear viscosity term can be disabled in cases where the simulation is already stable. However, in flow simulations where vortices emerge within a low-pressure region, a strong pressure decay may lead to instabilities that make the simulation unstable. For such cases, adding artificial shear viscosity is necessary to maintain numerical stability, as this issue is unaddressed by the artificial bulk viscosity and thermal conductivity alone. Our approach integrates a sensor into the standard LAD formulation, particularly in the artificial shear viscosity, which reduces the added diffusivity while preserving numerical stability. This advancement is possible by adding the shear diffusivity only in localized flow regions consisting of low-pressure core vortices, and it enables stable and accurate large-eddy simulations (LES) of compressible vortex-dominated flows, such as those encountered in separated flows and bluff-body wakes.

The sticky fluids found in pitcher plant traps leave behind dendritic, treelike filaments when the liquid dewets from a substrate. To understand the origin of these filaments, we investigate the retreating thin-film dynamics of aqueous glycerol and polyethylene oxide solutions on partially wetting polydimethyl siloxane substrates, conditionally generating regularly spaced filaments. We show that during the early-stage dynamics of these films, there is a critical average film thickness, $h_f$ (governed by the interplay between van der Waals and capillary forces), below which the film will be unstable, giving rise to filaments. Conversely, filaments are not formed when the average film thickness $\overline{h}$ exceeds $h_f$. Experiments probing the conditions when filaments are formed and not formed show good agreement with the theory. After the early stage, filament dynamics enter an intermediate stage governed by a Plateau-Rayleigh instability. In this stage, the key scaling relation is ${\lambda }_f\eta /\gamma \propto {\widehat{\text{Ca}}}^s$ with $s\approx 1$, where ${\lambda }_f$ is the average spacing between filaments, $\eta$ and $\gamma$ the viscosity and surface tension of the fluid, and $\widehat{\text{Ca}}$ is the capillary number (given by $\eta U/\gamma$; $U$ is the receding contact line velocity). The evolution of the thin-film shape is modeled numerically to show that the formation of filaments arises because the thin-film equation numerically hints at a singular solution after certain time $t_f$ and when the thin-film thickness is below $h_f$.