Controlling water motion on surfaces is critical for applications ranging from thermal management to passive water harvesting to self-cleaning coatings. Yet stabilizing continuous water films, desirable for their high surface coverage and drainage capacity, remains challenging with pure water, due to its high surface tension. Existing strategies rely on extreme wettability achieved by coating or fine-scale patterning, which are costly, fragile, or complex to scale. A robust, purely geometric solution is still lacking. We demonstrate that a pair of laser-engraved grooves on a moderately hydrophilic vertical substrate can laterally anchor water and stretch a continuous thin film, without any other surface treatment. Once stabilized, the film extends vertically over 100 capillary lengths ($>30\mathrm{cm}$), with thickness tunable via both flow rate and groove geometry. At the groove extremities, the end of anchoring triggers a cyclic instability, characterized by film rupture, retraction, and droplet release. The thickness of the film and retraction height obey predictive models, while droplet mass varies systematically with spacing and surface tension. This groove-based method offers a straightforward and scalable approach to creating, sustaining, and controlling thin water films. It opens new directions for passive liquid control in condensation, surface cleaning, and 2D millifluidic systems.

The ability to trap a single cell or microparticle in three dimensions is important for biomedical and microfluidic applications. Single-beam acoustic tweezers based on focused waves offer a compact and biocompatible solution with their high spatial resolution and intensity gradient. However, the three-dimensional (3D) trapping remains limited because the weak axial restoring radiation forces cannot always surpass the pushing drag force from the acoustic bulk streaming (ABS), particularly at high frequencies. The combined effect of the acoustic radiation force (ARF, $F_{\mathrm{rad}}$) and the drag force ($F_{\mathrm{drag}}$) induced by the ABS on a microparticle has not yet been studied in the free space. It is known that the ARF depends on the square of the pressure amplitude at the focus as $p_{\text{foc}}^2$, whereas the drag force induced by the ABS remains an open question with respect to $p_{\text{foc}}$ at different flow conditions. In this study, we propose a unified theoretical-numerical framework to compare the contribution of the ARF and the drag force by the ABS, and we systematacially derive an explicit scaling law for the streaming velocity $U_0\sim p_{\text{foc}}^n$ with the hydrodynamic flow from the viscous to the inertial regimes. It is found that the exponential power $n$ of $p_{\text{foc}}$ is bounded by $n=2$ for the viscous limit (the flow Reynolds number ${\text{Re}}_{\lambda }\ll 1$) and by $n=4/3$ for the inertial limit (${\text{Re}}_{\lambda }\gg 1$), and $n\in (4/3,2)$ throughout the transition regime (${\text{Re}}_{\lambda }\sim 1$). In addition, the Schiller-Naumann model is introduced to facilitate a more accurate estimation of the drag force compared to the Stokes model. Based on the combined effect, we find that the trap ratio of the axial ARF over the drag force can vary nonmonotonically with $p_{\text{foc}}$, which contradicts the conventional expectation of the monotone increase. This work provides a theoretical foundation for the 3D trapping of a single cell with single-beam acoustical tweezers and guidance for the optimized parameters.

We report the first direct numerical simulations using a recently introduced exact director-based formulation of the equations of motion for inertial spheroids in turbulence. The simulations consider homogeneous isotropic flow across a broad range of particle aspect ratios (from disklike to rodlike) and Stokes numbers (masses), both with and without gravity. The results reveal that particle shape and finite inertia induce complex, nonmonotonic trends in preferential clustering. Gravity markedly alters these dynamics, enhancing small-scale clustering for rod- and disklike particles while suppressing clustering for nearly spherical particles; we propose an explanation for this behavior. We confirm that at weak inertia, rodlike spheroids tend to align with the flow's major stretching direction, whereas disklike spheroids align with its major shrinking direction. We derive a generalization to the case of finite inertia, establishing preferred alignment directions that do not coincide with the flow's principal Lagrangian stretching or shrinking axes, and provide preferential alignment directions across all examined Stokes numbers and gravity conditions. We also confirm that gravity makes the symmetry axis of disklike particles orient preferentially horizontally. Finally, we introduce an efficient framework for computing Lyapunov exponents and their generalizations for inertial particles. Given its superior efficiency and ability to unify previously disparate data, we believe our approach should serve as a foundation for future simulations and a powerful tool for both theoretical and numerical studies of spheroids in turbulence.

Shear-thickening suspensions of non-Brownian polydisperse particles are simulated in two dimensions using a lubrication flow-discrete element method-based algorithm at high packing fractions ($\varphi$) and large nondimensional stresses ($\sigma$). Rigidity analysis of the stress-induced particle clusters is carried out using pebble game algorithm for polydisperse suspensions and compared with the statistically equivalent bidisperse systems. A critical value of the packing fraction, ${\varphi }_c$, close to the shear-jamming transition, ${\varphi }_J^{\mu }$, (${\varphi }_c<{\varphi }_J^{\mu }$) is obtained where rigid particle clusters begin to grow sharply. The growth is found to be characterized by a critical transition of an order parameter ($f_{\text{rig}}$), defined by the fraction of particles in rigid clusters, which scales as $f_{\text{rig}}\sim {(\varphi -{\varphi }_c)}^{\beta }$ for $\varphi >{\varphi }_c$, and by the susceptibility scaling, ${\chi }_{\text{rig}}\sim {|\varphi -{\varphi }_c|}^{-\gamma }$, with exponents having values consistent with the critical exponents in two-dimensional (2D) percolation transition. The variations of $f_{\text{rig}}$ and ${\chi }_{\text{rig}}$ in polydisperse suspensions are found to be identical to that of the statistically equivalent bidisperse suspensions. Finite-size-scaling analysis shows a divergence of correlation length near ${\varphi }_{c_{\infty }}$ following critical exponent $\nu \approx 1.33$, in agreement with the 2D percolation theory. Furthermore, ${\varphi }_c$ and ${\varphi }_J^{\mu }$ are found to vary nonmonotonically with polydispersity index and depend on the particle stiffness.

We develop a reduced-order theoretical framework for inertial spheroidal particles in turbulent Navier-Stokes flow, representing their orientation with a single unit vector (the director) instead of using a full rotation matrix. This symmetry-based simplification, analogous to Jeffery's classical description of neutrally buoyant spheroids, yields a compact set of evolution equations with fewer degrees of freedom. In the limit of small inertia, the director obeys Jeffery's equation which we consider as the equation on direction of distance between two infinitesimally close trajectories of a chaotic system. This implies that the particle's director is uniquely determined by its position, defining a director field that, in turn, induces a smooth, weakly compressible effective flow through which the spheroids move. This effective flow is distinct from the underlying incompressible turbulent flow, thereby generalizing Maxey's result for spheres. In homogeneous, anisotropic turbulence with zero mean fluid flow, the effective particle flow can acquire a nonzero mean; for example, in rotating turbulence, particles drift uniformly along the rotation axis. We show analytically that prolate spheroids align with the major Lagrangian stretching direction of the turbulent flow, whereas oblate spheroids align with the major Lagrangian compression direction. In spatially inhomogeneous flows (e.g., a wall-bounded channel flow), particle anisotropy can alter turbophoretic drift, possibly reversing the usual migration toward quiescent regions. We also show that inertial spheroids exhibit preferential concentration. Finally, when gravity is included, we derive analytic expressions for the mean settling velocity in the weak-gravity regime. This settling velocity increases monotonically with the particle aspect ratio, from $8/9$ of the Stokes settling velocity of an equivalent sphere for disklike particles to $4/3$ for rodlike particles. In the strong-gravity limit, the driving of spheroids by the Navier-Stokes turbulence can be effectively described as white noise. We show that very small oblate spheroids settle edge-first, but small ones settle broadside-on. The orientation-dependent settling velocity field is spatially varying and weakly compressible, providing a new mechanism for multifractal preferential concentration. Thus, this director-based framework provides a unified, physically transparent generalization of Jeffery's and Maxey's theories, yielding multiple new analytical predictions for the transport of nonspherical particles in isotropic, anisotropic, and stratified turbulent flows and environments.

Owing to the spatially local nature of the constitutive equations typically used to model polymeric stresses, the differential operators governing the linearized dynamics of bounded viscoelastic shearing flows have singular points. As a result, the eigenspectra of such shearing flows contain, in addition to discrete eigenvalues, continuous spectra (CS) comprising singular eigenfunctions. On account of the singularity, numerical methods capture these spectra only as extended balloons that slowly converge to the theoretical loci. A clear understanding of the theoretical CS loci is crucial in discriminating physically genuine (discrete) eigenvalues from the poorly approximated numerical CS. This is especially important because, when a parameter such as the Weissenberg number $\left(\text{Wi}\right)$ is varied, discrete eigenvalues can emerge from or disappear into the CS, as the latter are often branch cuts in the complex spectral plane. For rectilinear shear flows of Oldroyd-B fluids, the CS are a pair of line segments, with lengths equal to the base-state range of velocities. In this study, we provide the first comprehensive account of the nature of the CS for both rectilinear and curvilinear shearing flows of the FENE-P fluid. The FENE-P model is one of the most widely used constitutive equations for dilute polymer solutions, and predicts both shear thinning of the polymer viscosity and the first normal stress coefficient. In stark contrast to the CS for the Oldroyd-B fluid mentioned above, we show analytically that there are up to six distinct continuous spectra for shearing flows of FENE-P fluids. Further, owing to shear thinning, and due to the highly coupled nature of the linearized equations, these spectra possess nontrivial structures in the complex plane. When the finite extensibility parameter $L$ is greater than 50, as appropriate for large molecular weight polymers used in experiments, three of the CS are nearly identical, and independent of the solvent-to-solution viscosity ratio $\left(\beta \right)$. The other three CS are $\beta$-dependent, with one of them being the analog of the solvent (viscous) continuous spectrum in the Oldroyd-B fluid. The remaining two $\beta$-dependent CS are novel features of the FENE-P spectrum, and can have phase speeds outside the base range of velocities, including negative ones. For nonlinear shearing flows subjected to streamwise invariant disturbances, the latter two CS have a novel “winglike” structure in the complex plane, symmetric about the imaginary axis. All but two of the theoretical CS are shown to collapse onto master curves for different $(\text{Wi},L)$ pairs, with $\text{Wi}/L$ fixed, a feature not shared by the discrete spectrum. The location and structure of the theoretical CS are broadly in accord with their numerical approximations obtained using the spectral method. The complexity of the CS predicted here, for shearing flows of FENE-P fluids, is expected to carry over to other nonlinear viscoelastic models that exhibit a shear-thinning rheology. Our analytical predictions for the CS will therefore be helpful in identifying physically genuine, discrete eigenvalues in the numerically computed spectra.

We investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. Extending classical studies of vortex nucleation around smooth obstacles, we focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, we show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. For both wall and well configurations, we identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding excellent agreement between the theory and our numerical simulations. Our results provide a simple framework for understanding superflow stability past finite-size obstacles with sharp features, and they are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems.

Slender floaters drifting in propagating gravity waves slowly rotate towards a preferential state of orientation with respect to the angle of incidence. This angular drift arises from a wave-induced, second-order mean yaw moment. We develop a diffractionless, hydroelastic theory to compute this mean yaw moment for a thin, flexible structure whose width and thickness are small compared with the wavelength. For floater lengths smaller than half the wavelength, we derive a simple, predictive criterion for the preferred orientation: Soft, short, and heavy floaters prefer the longitudinal state, while stiff, long, and light floaters prefer the transverse state. For floaters longer than the wavelength, the orientational dynamics become more intricate and may exhibit multiple equilibrium states. We discuss the implications of the model for flexible floating structures such as pontoons and inflatable structures.

We investigate active interfacial ion flux in droplet electrohydrodynamics with an emphasis on deformation, pinch-off, and recoalescence. A thermodynamically consistent phase-field framework is developed that couples Nernst–Planck–Poisson electrodiffusion with incompressible Navier–Stokes–Cahn–Hilliard flow and incorporates active interfacial ionic fluxes. In a baseline case without active interfacial transport, applied fields merely polarize the droplet, and deformation is negligible. In contrast, surface-localized active transport drives the accumulation of positive ions within the droplet, elevates the interior potential, and generates nonuniform electric fields. The resulting electric stresses stretch and displace the droplet, thin interfacial necks, and trigger pinch-off; the daughter droplets subsequently recoalesce, often after wall contact, yielding flattened remnants. In multiple-droplet configurations, charging induced by active interfacial transport produces lateral electrostatic repulsion and asymmetric deformation; under geometric confinement, crescent bending and star-like morphologies emerge. Poiseuille-flow tests further show that a droplet with active transport can be immobilized and ruptured, while a neighbor without active flux is advected downstream, suggesting a route to sorting. Together, the results establish active interfacial transport as an internal actuation mechanism that robustly controls droplet morphology and dynamics across configurations.

We study the collective sedimentation of cube-shaped particles in the Stokes regime using direct numerical simulations based on the smooth profile method. The particles, constructed as rigid assemblies of $3\times 3\times 3$ spherical beads, settle in a Newtonian fluid at Reynolds number $\mathrm{Re}=0.1$ over volume fractions $0.001\le \varphi \le 0.08$. Although orientation-dependent hydrodynamic forces at the single-particle level, the suspension recovers the classical Stokesian scaling laws traditionally associated with spherical particles. The radial distribution function exhibits a single dominant peak that grows monotonically with $\varphi$, indicating isotropic microstructural organization and progressive clustering. Orientation statistics show random alignment in dilute suspensions and a transition toward preferential alignment at ${45}^{\circ }$ with respect to gravity as concentration increases. The mean settling velocity follows the Richardson-Zaki law with exponent $n\simeq 6$, velocity fluctuations scale as ${\varphi }^{1/2}$, and relaxation timescale as ${\varphi }^{-1/2}$. Self-diffusion coefficients increase weakly with volume fraction and asymptotically approach the ${\varphi }^{1/2}$ scaling characteristic of spherical suspensions. These results demonstrate that geometric symmetry, rather than sphericity alone, governs the emergence of sphere-like collective sedimentation behavior in nonspherical particle suspensions under creeping-flow conditions.

Particle image velocimetry is the most widely used optical technique for measuring two-dimensional velocity fields in fluids. However, with the standard cross-correlation algorithm, improving the spatial resolution of instantaneous velocity fields and obtaining dense velocity fields in real time and at high frequencies remains challenging. Optical flow velocimetry (OFV) provides an alternative route to per-pixel velocimetry. In this study, we show that dense velocity fields (one vector per pixel) with high effective spatial resolution can be obtained in real time at frequencies up to kHz using an optical flow approach. First, using synthetic images on two cases (a well-defined Rankine vortex and a homogeneous isotropic turbulence DNS dataset), we show that resolving large displacement gradients down to small scales is feasible when the particle seeding is appropriately tuned. Second, we show that real-time processing rates can be achieved through algorithmic and GPU-oriented optimizations, together with appropriate choices of optical flow parameters. With this implementation, 21 Mp velocity fields are measured in real time (live) at 90 Hz, while 4 Mp velocity fields can be measured up to 460 Hz and 1 Mp velocity fields can be measured up to 1400 Hz. The approach is further validated on experimental measurements of the flow past a circular cylinder, where dense instantaneous fields are obtained and used to compute derived quantities in real time over long durations. These processing rates enable real-time computation of derived flow quantities during experiments, including long-duration monitoring, low-frequency dynamics captured from sustained high-rate acquisition, and closed-loop flow-control strategies based on OFV measurements. In addition to enabling live operation, the approach accelerates standard off-line postprocessing, reducing turnaround time and computational cost.

The multiscale structure of the respiratory organ encompasses a challenging environment to predict the transport and deposition of inhaled aerosols, whether relevant to therapeutic drug delivery or hazardous exposure assessment. While the traditional leading deposition mechanisms, foremost impaction, gravitational settling and diffusion, are generally well understood and extensively studied, the role of electrostatic charge present in aerosols generated with common inhalers remains in comparison poorly characterized. Here, we employ a so-called one-path airway model integrated into an airway-on-chip to explore the contribution of electrostatic forces to aerosol deposition along the respiratory tract. By comparing neutralized and charged particles (diameters 0.2 and 2 µm), we show that electrostatic forces significantly alter deposition patterns, foremost shifting deposition from the deep acinar region to more proximal airways in the small bronchial regions (i.e. bronchioles), in analogy to a screening phenomenon. Our experiments, complemented by nondimensional analysis, underscore conditions where electrostatics begin to dominate over traditional deposition mechanisms, thereby underlining the importance of recognizing the role of electrostatics towards pulmonary deposition.

The transient flow induced by an array of wall-mounted flexible blades performing impulsive metachronal rowing, i.e., the sudden onset of coordinated oscillations of wall-mounted flexible blades with phase differences among them in an initially quiescent fluid, is numerically investigated across a wide range of the Cauchy number ($\mathrm{Ca}$), which quantifies the ratio of fluid inertial to the blade elastic force. Two distinct flow regimes emerge depending on the ratio of the natural frequency ($f_n$) to the rowing frequency ($f$). For stiff blades ($f_n>f$), the mean deflection angle scales linearly with $\mathrm{Ca}$, and the rescaled flow rate remains high. In contrast, for soft blades ($f_n<f$), the deflection saturates, and the rescaled flow rate decays rapidly as ${\mathrm{Ca}}^{-2.35}$. The maximum fluid transport is achieved near $\mathrm{Ca}=1$ and at shorter rowing wavelength (six blades per wavelength and unit spacing), where tip-shed concentrated vortices are (1) optimally positioned to reinforce the flow around power-stroke blades and (2) subsequently captured by those blades, thereby enhancing thrust. These findings provide physical insights into the hydrodynamic optimization principles underlying bio-inspired metachronal propulsion.

Unstably stratified mixing layers laden with inertial, heated particles are investigated using Eulerian-Lagrangian direct numerical simulations, primarily aiming to account for interphasial energy transfer due to the momentum and thermal couplings between particle and fluid phases. The heated particles with Stokes numbers $\mathrm{St}=0.2$, 1.3, 8.0, 20.0, and 38.0 settling across unstably stratified mixing layers are considered. Compared with the unstably stratified mixing layers in the absence of particles, the addition of heated particles enhances turbulence and induces the faster transition from shear-driven to turbulent mixing affected by the combined buoyancy and shear. The integrated turbulent kinetic energy $E$ of fluid phase varies nonmonotonically as St increases. When the particles are initially distributed in the whole domain, the heated particles with $\mathrm{St}\approx 1$ maximize $E$ and its viscous dissipation due to the most energy injected from particles into fluid phase. Moreover, the mean kinetic energy transferred from heated particles to fluids varies nonmonotonically while the fluctuating counterpart increases with increasing St. In contrast, the interphasial heat transfer decreases with increasing St due to the larger thermal response time of large particles. Heated particles give rise to stronger flow instability and turbulence modulation when initially distributed in the upper stream, attributing to transfer of more gravitational potential energy and stronger particle-fluid interactions. Concerning the dynamics of heated particles settling across unstably stratified mixing layers, it is found that the drag force of the particles increases in the direction opposite to the shear and decreases in vertical direction, forming the vertically inclined particle streaks which contribute the enhanced buoyancy production and fluctuating power to fluid.

In this paper, we study the free streamline theory for the separating flow over a circular cylinder. The objective of this paper is twofold: (i) to demonstrate the validity of the condition of matching curvature and (ii) to obtain a reasonable estimate of the separation angle in the subcritical regime ($\text{Re}={10}^4–{10}^5$) without explicitly modeling the boundary layer, following Prandtl's conjecture in his seminal paper [L. Prandtl, in Proceedings of the Third International Mathematical Congress in Heidelberg (B. G. Teubner, Leipzig, 1904), pp. 484–491]. For the former goal, we study Roshko's free streamline model [Roshko, Tech. Rep. No. NACA-TN-3168 (NASA, Washington, D.C., 1954)]; it is an ideal flow model with sheets of discontinuities that represent the separating shear layers in the near-wake region. It is known that the model fails to predict the correct separation angle over a curved surface. Roshko attributed this discrepancy to the condition of matching curvature, deeming it invalid. This condition (known as the condition of smooth detachment) asserts that the curvature of the separating streamline at the separation point must match that of the cylinder. We show that the condition of matching curvature is legitimate and is not the real culprit for the failure of Roshko's model in predicting the correct separation angle. We also show that Roshko's model is nonunique. There are solutions in Roshko's family with matching curvature whose separation point agrees with experimental measurements. As for the second goal, we rely on the principle of minimum pressure gradient (PMPG), which asserts that an incompressible flow evolves from one instant to another in order to minimize the total magnitude of the pressure gradient over the domain. Encouraged by the fact that the flow characteristics in the range $\text{Re}={10}^4–{10}^5$ are fairly independent of $\text{Re}$, we aim to predict the separation angle in this regime without modeling the boundary layer—a task that may seem impossible, though anticipated in Prandtl's original paper that introduced the concept of boundary layer [Prandtl, Proc. Intl. Congress Math. (1904)]. Over the family of kinematically admissible equilibrium flows, we utilize the PMPG to single out the separating flow with the minimum pressure gradient cost. Interestingly, the obtained separation angles match the experimental measurements over the $\text{Re}={10}^4–{10}^5$ regime.

Turbulent flows beneath a free surface play a central role in the Earth system, yet their coupling to observable surface features remains incompletely understood. Recent studies using direct numerical simulations (DNS) have reported strong correlation between observable surface features and surface divergence as well as velocity statistics directly beneath, but were limited to Reynolds numbers ($\mathrm{Re}$) far below those typical of natural flows, and do not carry the inherent challenges of measurement and flow fidelity that real flows present. We present a laboratory study in which free-surface topology and subsurface turbulent velocity are measured simultaneously in a jet-stirred tank, extending these numerical results to the physical domain. Using a combination of particle-image velocimetry and free-surface profilometry, we access $\mathrm{Re}$ up to two orders of magnitude higher than in the DNS. A computer vision method developed for identifying turbulent imprints on the free surface is successfully applied to experimental data, enabling direct comparison with the DNS. The correlation between time series of mean-squared surface divergence and surface features is found to persist as strongly at higher Reynolds numbers, despite the increased disparity of turbulent scales. Beyond the thin viscous layer, all surface-to-bulk correlations scale with the integral length scale across both experimental and numerical cases. The normalized cross-correlation between mean-squared horizontal velocity divergence and surface area covered by structures decreases linearly with depth and remains significant even two integral scales beneath the surface, unlike point-to-point correlations which decay fast, illustrating how correlations are near-instantaneous but spatially nonlocal. These results demonstrate that visible surface features provide considerable quantitative information about energetic flow events even below the surface-influenced layer.

We investigate the rheology of biphasic fluid systems comprising an elastoviscoplastic (EVP) matrix fluid containing initially spherical, monodisperse, viscous droplets through interface-resolved numerical simulations. The interface is captured using the level-set method, and the EVP phase is modeled with the Saramito constitutive equation. We explore the effects of the volume fraction, capillary, Weissenberg, and Bingham numbers, considering both dilute and semidilute regimes (dispersed phase volume fractions from 0.16% to 20%) at two density and viscosity ratios. The constitutive curve shows a negative curvature, consistent with previous studies on emulsion rheology with coalescing drops. Increasing the capillary and Bingham numbers show qualitatively similar trends: increasing drop deformation with both results in a decrease of the system's relative viscosity. This is further supported by stress budget analysis, which shows that yield stress increases the effective viscosity of the matrix fluid, thereby increasing the effective capillary number and reducing the effective viscosity ratios. The bulk rheology shows a complex relationship with the Weissenberg number ($\text{Wi}$). In dilute systems, droplet deformation increases with $\text{Wi}$, while bubbles exhibit a nonmonotonic trend. Relative viscosity rises with $\text{Wi}$ for emulsions up to $\text{Wi}=1.75$ due to localized EVP stresses, then slightly decreases. For bubbly suspensions, the viscosity shows little variation at low $\text{Wi}$ but decreases at larger values. At semidilute concentrations, similar trends emerge with EVP stresses dictating the system's bulk rheology. At high $\text{Wi}$, increased EVP stresses, reduced coalescence, larger interfacial stress, and near-wall droplet migration collectively increase emulsion relative viscosity.

In this paper, we investigate the flow of discontinuous shear-thickening fluids, which exhibit S-shaped rheology, in confined and disordered geometries such as constrictions in channels or porous media. We demonstrate that such fluids tend to limit the flow rate at a given pressure gradient. This limitation arises due to the emergence of highly viscous structures. In channel geometries with obstacles, these structures form in the most constricted regions. In porous media, they occur similarly in the narrowest pore throats. However, we show that their locations are strongly correlated in the direction transverse to the flow, effectively forming a viscous barrier. We further characterize the emergence of such barriers, whose lengths diverge as the pressure difference approaches a critical value. This behavior exhibits scaling properties reminiscent to those encountered in other critical systems, such as percolation, depinning transitions, clogging, or yield-stress fluids in porous media.

An extended body, free floating near one of the horizontal boundaries in a convective cell heated from below and cooled from above, with a suitable set of control parameters, provides the convective pendulum mode in which the body performs regular oscillatory movements from one sidewall to the other. In this paper we consider numerically, in the simplest two-dimensional formulation, a convective cell at moderate Rayleigh numbers $\mathrm{Ra}\approx (5\times {10}^5)\text{–}(5\times {10}^6)$ with two bodies (plates) floating at different depths. Two convective oscillators in one cell are subject to a complex mutual influence determined by the geometry of the cavity, the size and the depth of immersion of the plates, and the intensity of heating, leading to a wide variety of observed modes. The dynamics of large plates (of the order of half the horizontal size of the cell or more) strongly depends on the depth of immersion and includes a convective pendulum mode with regular antiphase oscillations, irregular fluctuations, full stops, and synchronized periodic movements. The dynamics of two plates of relatively small size is fundamentally different and unexpected. The complex interaction between the small plates leads to modes with a pronounced intermittent character, when intervals of quasiperiodic movements of both plates are replaced by low-amplitude oscillations against the background of random wandering throughout the cell. During full-amplitude oscillations, the plates move quasiperiodically but with a random phase shift. The very specific behavior observed during random walks, in which the plates perform small-scale chaotic oscillations, without breaking away from each other, as if they are on a flexible bundle.

In this experimental study, we introduce methods to characterize drop oscillation and shape using a two-camera setup inspired by two-dimensional video disdrometers. The two cameras maintain close proximity to the levitating drop, enabling high-fidelity three-dimensional reconstruction of drop orientation and dynamics. The prevailing drop shadow in each camera view is extracted to determine a time-averaged characteristic shape, from which a volume-equivalent characteristic diameter $D_0$ is obtained via disk integration. We find strong agreement between our measured $D_0$ and established models of axis ratio and equilibrium drop shape. A frequency analysis along the drop shadow perimeter reveals the presence of three dominant modes, i.e., axisymmetric $(2,0)$, horizontal $(2,2)$, and transverse $(2,1)$, with the axisymmetric mode the most prominent and resilient to noise. We define a nondimensional total oscillation amplitude which enables comparison of oscillation intensities across drop conditions. The addition of nanoparticles increases interfacial tension and, at low concentrations (<0.5% m/m), promotes deformation through heterogeneous distributions and interfacial instabilities. These effects enhance canting amplitude, canting angular velocity, and results in an unsteady orientation, sometimes leading to a full circulation of the drop. Beyond a nanoparticle saturation concentration (NSC) of approximately 0.5% m/m, surface-bound nanoparticles stabilize the drop, reducing canting and total oscillation amplitude. The presence of surfactant increases the NSC by capturing surface particles into micelles, delaying interfacial saturation. These findings offer different tools and insights for characterizing complex oscillation dynamics in levitated multiphase drops, with implications for raindrop physics and fluid-interface studies. Our work is an experimental validation of all the accumulated theoretical work on raindrop studies since 1879.