Pressure-driven flow of a dilute polymer solution has been numerically observed to possess a form of elastic turbulence which is organized around the interactions of localized versions of two-dimensional (2D) “arrowhead” traveling waves [J. Page et al. Phys. Rev. Lett. 125, 154501 (2020)]. As a step to confirming this theoretically, we identify spanwise-localized arrowhead traveling waves by tracking a symmetry-breaking bifurcation of the known spanwise-invariant (2D) arrowhead to a spanwise-periodic state and then discovering a secondary modulational instability to a spanwise-localized traveling wave. Spanwise-symmetric and -asymmetric localized arrowheads exist with the latter having a phase speed slightly inclined to the streamwise direction. Computations capture the flow randomly switching between spanwise local and global arrowhead states in a streamwise-restricted domain, suggesting they form the building blocks of the chaos. Splitting events are also seen, in which a single localized state spawns multiple arrowheads. However, both cross-shear and spanwise velocities are small, suggesting that this elastic turbulence will not be a good mixer.

Hydrogels are soft, poroelastic solids, comprising hydrophilic polymer scaffold surrounded by adsorbed water that is free to move through the pore spaces. Hydrogels are typically biocompatible, and are therefore used in a wide variety of medical contexts. For instance, they are used to make soft contact lenses, and have potential as advanced wound dressings, targeted drug delivery devices, and deployable intestinal stents. In all these applications, the hydrogel tends to be confined by or adhered to its surroundings, and while hydrogel dynamics has received increasing mathematical attention recently, most studies have focused on free swelling. In this paper, we mathematically analyze the swelling and deswelling behavior of a hydrogel confined between two plates, in both the case where the hydrogel can slip parallel to the wall and the case where it cannot. In the slip case, we numerically solve for a full nonlinear solution based on uniaxial deformation. In the adhered case, focusing on small deformation, we find that the gel may swell either completely or incompletely (i.e., the water only penetrates partially though the gel). We give a leading-order closed-form solution for the evolution of the porosity, and thus the force on the two plates, in both cases. The partial swelling may greatly impact the efficacy of hydrogels as actuators for deployable medical devices, so may need to be a consideration in design.

Hydrodynamic interactions (HI) between segments of a polymer have long been known to strongly affect polymer stretching in laminar viscometric flows. Yet the role of HI in fluctuating turbulent flows remains unclear. Using Brownian dynamics simulations, we examine the stretching dynamics of bead-spring chains with interbead HI, as they are transported in a homogeneous isotropic turbulent flow (within the ultradilute, one-way coupling regime). We find that the effects of HI are negligibly small for dumbbells but become increasingly prominent as the polymer model is refined, i.e., as the number of beads are increased. HI-endowed chains exhibit a steeper coil-stretch transition as the elastic relaxation time is increased, i.e., HI cause less stretching of stiff polymers and more stretching of moderately elastic polymers. The probability distribution function of the end-to-end extension is also modified, with HI significantly limiting the range of extensions over which a power-law range appears. On quantifying the repeated stretching and recoiling of chains by computing persistence time distributions, we find that HI delays migration between stretched and coiled states. These effects of HI, which are consistent with chains experiencing an effective conformation-dependent drag, are sensitive to the level of coarse graining in the bead-spring model. Specifically, an HI-endowed dumbbell, which cannot form a physical coil, is unable to experience the hydrodynamic shielding effect of HI. Our results highlight the importance of incorporating an extension-dependent drag force in dumbbell-based simulations of turbulent polymer solutions. To develop and test such an augmented dumbbell model, we propose the use of a time-correlated Gaussian random flow, in which the turbulent stretching statistics are shown to be well approximated.

Transonic buffet is a class of shock wave–boundary layer interaction known to exhibit self-sustained two-dimensional (2D) chordwise shock wave oscillations (Strouhal number $\mathrm{St}\approx 0.05–0.1$), and three-dimensional (3D) spanwise-modulated flow separation and reattachment $(\mathrm{St}\approx 0.2–0.4)$. Due to computational cost, scale-resolving simulations of span-periodic configurations to date have been limited to narrow airfoils (aspect ratio $AR=L_z/c\approx 0.05–0.25$, for span width $L_z$ and chord $c$). These ratios are insufficient to accommodate the 3D “buffet cell” instability reported in low-fidelity simulations and experiments. In this work, implicit large-eddy simulations and modal analysis are performed on infinite wings up to $AR=3$ with sweep angles between $\lambda =[0^{\circ },{35}^{\circ }]$. The sensitivity of the 2D and 3D modes to crossflow is detailed. Two flow conditions are examined, corresponding to minimally and largely separated mean flow at the shock location. For the minimally separated case, the shock dynamics remain essentially spanwise uniform (quasi-2D), with only weak and intermittent separation cells confined to the trailing edge region and exhibiting negligible interaction with the shock. In contrast, increased mean separation leads to the emergence of pronounced 3D buffet cells with a characteristic spanwise wavelength ${\lambda }_z\approx 1–1.5c$. Spectral proper orthogonal decomposition reveals that a quasistationary low-frequency 3D separation mode previously identified on unswept wings $(\mathrm{St}\approx 0.02)$ becomes a spanwise traveling mode as sweep is imposed, shifting monotonically to intermediate frequencies $(\mathrm{St}=0.06–0.35)$. The 2D shock mode is largely insensitive to sweep, whereas the frequency and energy content of the 3D mode increase with sweep while its wavelength remains unchanged. The results demonstrate that transonic buffet on infinite wings arises from the superposition of distinct but coexisting 2D shock motion and separation-driven 3D instabilities, with mean flow separation at the shock identified as a necessary condition for dominant 3D buffet dynamics to emerge.

The objective of this study is to elucidate the physical mechanisms by which the Marangoni number Ma influence the stability of thick liquid film flow with insoluble surfactants on a vertical fiber. Through nondimensionalization and the long-wave approximation, the original two-dimensional model is successfully reduced to a one-dimensional simplified model whose validity is verified by high consistency with fully linearized results in the long-wave region. Linear stability analysis reveals three stability mechanisms governed by Ma. The Rayleigh–Plateau instability mode dominates at low Ma, Marangoni instability mode prevails at high Ma, and complete stability is exhibited at intermediate Ma. The nonlinear numerical method reveals that the competition between Marangoni convection and the difference between the interface velocity and the wave speed $c_w$ results in diverse outcomes at different Ma values. At low Ma, the effect of advection by $c_w$ is much greater than that of Marangoni convection, such that Marangoni convection primarily serves to mitigate the Rayleigh–Plateau instability. At high Ma, Marangoni convection becomes stronger and induces Marangoni convection instability.

We present a unified theoretical and numerical study of dual bubble ripening on flat substrates under constant contact angle conditions. A theoretical framework is established by deriving the bubble growth rate $k_{\theta }$ and the kinetic equation for the curvature radius $R_B$, showing that $k_{\theta }$ decreases with contact angle yet remains positive, in agreement with simulations by lattice Boltzmann method (LBM). For dual bubbles on both homogeneous and heterogeneous substrates, the evolution of $R_B$ modeled by LBM follows the classical Ostwald ripening, independent of contact angles, and matches our theoretical predictions across a wide range of surface wettabilities. The normalized interfacial area change also follows a Gibbs free energy minimization mechanism. Furthermore, for heterogeneous substrates with different bubble contact angles, we find that the “reversed volume ripening” occurs when $\frac{R_1}{R_2}\in (1,\sqrt{\frac{{\theta }_2-sin{\theta }_{2}cos{\theta }_2}{{\theta }_1-sin{\theta }_{1}cos{\theta }_1}})$, i.e., the bubble with smaller volume grows at the expense of that with larger volume. For both ripening cases, they strictly follow the governing rule that ripening is driven by the chemical potential difference induced by curvature difference, regardless of different volume evolution mechanisms. Our work provides new insights into the interplay between interfacial kinetics and substrate wettability of constrained bubble ripening.

We perform an unstable periodic orbit (UPO) analysis of moderately developed Couette turbulence with large-eddy simulations (LES) using a static eddy viscosity model. The UPOs extracted here are invariant solutions to the LES dynamical system, and their instability characterizes the dynamics of large-scale motions resolved by LES, providing insights into the mechanisms underlying Navier-Stokes turbulence. We find that spanwise vortices, stretched between streamwise rolls, approach the walls, over which new spanwise vortices are generated. The stretching of these vortices is driven by strong shear layers induced by the streamwise rolls. This vortex-generation mechanism, as revealed by the LES UPOs, is a significant dynamical process in LES turbulence at high Reynolds numbers. By computing local Lyapunov exponents, which quantify the least stable perturbation growth rates along the UPOs, we show that the stretching process amplifies their growth. The corresponding Lyapunov vectors highlight the instability of prominent shear layers through which the stretched spanwise vortices emerge between the rolls. Our results suggest that high-strain-rate structures in developed turbulence play a central role in shaping the geometrical structure of turbulent orbits in phase space.

The final states of freely decaying two-dimensional (2D) topographic turbulence consist of a background flow and localized vortices. While the background flow satisfies a linear potential vorticity (PV)–stream-function relation, the vortex structures remain poorly understood. To address this gap and ensure oceanic relevance, we examine quasistationary final states of 2D turbulence over a sinusoidal topography featuring a bump and a dip, where two oppositely signed vortices are locked to the topographic extrema. After subtracting the background flow, the vortices exhibit a “$sinh$”-like PV–stream-function relation, as observed in flat-bottom turbulence. Motivated by Gaussian vortex profiles in flat-bottom turbulence, we propose an empirical model combining the background flow with Gaussian vortices centered at the topographic extrema. This model accurately reproduces quasistationary states and yields locally stationary solutions to the inviscid governing equation. We further test the model under complex topography and high-energy conditions, confirming that the “$sinh$”-like trend and Gaussian profiles are robust features of localized vortices. Linear stability analyses of these stationary vortex solutions reveal background flow-dependent stability: cyclone-elevation and anticyclone-depression configurations are stable at low background energy, while anticyclone-elevation and cyclone-depression configurations are stable at high background energy. These findings align with vortex-topography correlations observed in simulations across energy regimes. Our results provide explicit vortex solutions for quasistationary final states of 2D topographic turbulence and elucidate the mechanism underlying vortex-topography correlations through stability analyses of vortices embedded in topographic background flows.

We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first- and second-order sensitivity analysis. Building on the standard adjoint formulation, which relates multiple measurements to external sources through a linear duality relation, we first introduce a linear positional embedding that identifies the source location by aligning the measurement vector with the embedding. To capture weakly nonlinear effects that arise when the source intensity is finite, we then incorporate a quadratic correction represented as a symmetric bilinear operator and approximated via a truncated eigen-expansion obtained with Krylov subspace iterations. This yields quadratic positional embeddings that augment the linear adjoint field, enabling measurement data to be projected onto a higher-dimensional hyperplane, spanned by the linear and quadratic embeddings. A source search algorithm is formulated based on principal angle minimization between this hyperplane and the observation vector, providing a natural probabilistic interpretation of source location. The method operates in a one-shot fashion without iterative updates of candidate source positions, and it can be readily extended to scenarios involving multiple sources. Demonstrations on benchmark inverse problems include perturbation-source identification in the viscous Burgers equation and heat-source detection in a two-dimensional laminar stratified channel. The results with quadratic embeddings show significant improvements in localization accuracy compared with linear adjoint-based sensitivity methods, especially in the region where linear adjoint sensitivity vanishes.

Over the past decade, autophoretic colloids have emerged as a prototypical system for studying self-propelled motion at microscopic scales, with promising applications in microfluidics, micromachinery, and therapeutics. Their motion in a viscous fluid hinges on their ability to induce surface slip flows that are spatially asymmetric from self-generated solute gradients. Here we demonstrate theoretically that a straight elastic filament with homogeneous surface chemical properties—which is otherwise immotile—can spontaneously achieve self-propulsion by experiencing a buckling instability that serves as the symmetry-breaking mechanism. Using efficient numerical simulations, we characterize the nonlinear dynamics of the elastic filament and show that, over time, it attains distinct swimming modes such as a steadily translating “$\mathsf{U}$” shape and a metastable rotating “$\mathsf{S}$” shape when semiflexible, and an oscillatory state when highly flexible. Our findings provide physical insight into future experiments and the design of reconfigurable synthetic active colloids.

When two streams of equal densities but of unequal velocities and different flow directions come into contact, large-scale coherent structures are generated downstream of the confluence apex. They include vertical vortices inside the region of high mean shear between the fluids originating in the two tributaries [i.e., the mixing interface (MI)] and streamwise-oriented-vortical (SOV) cells inside and in the vicinity of the MI. The flow physics becomes even more complex when the bed elevations of the tributary channels are not the same as that of the downstream channel. Eddy resolving simulations are used to investigate how the gradual increase in the level of bed discordance between the minor tributary channel and the main downstream channel affect flow, turbulence structure, sediment entrainment mechanisms and mixing at an asymmetrical confluence with a confluence angle of ${70}^{\circ }$. To better isolate the effects of bed discordance, simulations are performed with idealized conditions in which the bottom surfaces of the open channels are horizontal except near the region where the minor tributary connects with the main channel. The other main flow parameter that is varied is the discharge ratio between the two streams, QR. Results show that for constant QR, the coherence of the vertical MI vortices increases with increasing bed discordance, and the wake mode becomes gradually dominant even though the velocity and momentum ratios are not close to unity. Increasing the bed discordance reduces the coherence and number of SOV cells forming on the minor tributary side of the MI and promotes the formation of a near-bed intrusion of mixed fluid into the minor tributary side of the main channel near the confluence apex. This is the main mechanism that is responsible for the increase in the rates of mixing between the two streams with increasing bed discordance for constant QR. While for small bed discordance levels, sediment entrainment inside the confluence hydrodynamic zone is driven primarily by the SOV cells, for sufficiently large bed discordance levels and QR, sediment entrainment on the minor tributary side is mainly driven by the plunging core of high free surface velocities as it enters the main channel.

We experimentally study the breakup of water-glycerol liquid bridges on nonconductive surfaces and find that spontaneous charge deposition at the receding contact line, slide electrification, can have a substantial influence. Compared to bridge breakup on conductive surfaces, electrostatic forces slow down the dynamics during, and cause spontaneous motion of satellite drops after the bridge breakup. We present a model for electrostatic contact line dissipation that aligns with our experimental observations. Our findings demonstrate that slide electrification plays an important role in dewetting beyond drop-related scenarios.

The pulsating motion of the cerebrospinal fluid in the subarachnoid space (SAS) surrounding the brain and the spinal cord is known to be affected by the presence of trabeculae, which are thin collagen-reinforced fibers that form a dispersed web-like structure stretching across the SAS. Previous analyses employed a homogenized approach comprising macroscopic conservation equations for flow and transport in porous media, an approximation justified by the disparity of scales present in the problem. Here, we assess the accuracy of these macroscopic equations by comparing their predictions with direct numerical simulations performed in a parallel-plate channel containing a random array of circular cylinders, used as a canonical representation of the SAS. The comparisons cover physiologically relevant ranges of the governing flow parameters. The results show that the unsteady Brinkman equation, when supplemented with an appropriately selected permeability, accurately captures the momentum balance. In contrast, the study of solute dispersion under the oscillatory flow conditions characteristic of the SAS demonstrates that the macroscopic transport equation for fibrous porous media—derived under the assumption of quasisteady microscopic flow—tends to overpredict streamwise dispersion while underpredicting local transverse dispersion across near-wall Stokes layers. These findings suggest that macroscopic transport models incorporating unsteady, shear-enhanced mixing effects at the microscopic scale are needed to accurately describe the influence of trabeculae on solute dispersion, with implications for intrathecal drug delivery and related clinical processes.

Magnetic particles underpin a broad range of technologies, from water purification and mineral processing to bioseparations and targeted drug delivery. The dynamics of magnetic particles in high-gradient magnetic fields—encompassing both their transport and eventual capture—arise from the coupled interplay of field-driven drift, fluid advection, and particle-field feedback. These processes remain poorly captured by existing models relying on empirical closures or discrete particle tracking. Here we present a thermodynamically consistent continuum theory for collective magnetic particle transport and capture in high-gradient fields. The framework derives from a free-energy functional that couples magnetic energy, entropic mixing, and steric interactions, yielding a concentration-dependent susceptibility via homogenization theory. The resulting equations unify magnetism, mass transport, and momentum balances without ad hoc shut-off criteria, allowing field shielding, anisotropic deposition, and boundary-layer confinement to emerge naturally. Simulations predict canonical capture morphologies—axially aligned plumes, crescent-shaped deposits, and nonlinear shielding—across field strengths and flow regimes, consistent with trends reported in prior experimental and modeling studies. By organizing captured particle mass data into a dimensionless phase diagram based on the Mason number, we reveal three distinct regimes—thermodynamically controlled, transitional, and dynamically controlled. This perspective provides a predictive platform for in silico optimization and extension to 3D geometries, and informing digital twin development for industrial-scale high-gradient magnetic separation processes.

We present the results of a two-dimensional experiment designed to test mechanisms responsible for the change in shape of the surface of a saturated granular bed below a submerged, oscillating plate. During the plate's upward motion, a fraction of the grains in a region of the bed become mobilized, allowing some particles to be dragged by the fluid both vertically and horizontally through the remaining matrix of fixed particles. Because the vertical forces are stronger than the horizontal, vertical displacements are greater than horizontal, and the horizontal flow of the particle-fluid mixture is less resistant than the vertical. Consequently, when we attempt to fit the measured streamlines over many cycles to those observed in the experiment, using the pressure field in the bed that results from the solution of Darcy's equation, we must employ different horizontal and vertical permeabilities in the Darcy flow relations. Doing this, we find relatively good agreement with the predictions of the mixture flow.

This study experimentally examines the impact of spacing between two pulsed jets and their strengths on the fluid dynamics within an elastic hemispherical cavity. Such interactions between multiple pulsed jets are observed in various natural and industrial contexts, including cardiovascular flows, where they occur naturally within the atria or result from medical interventions (e.g., mitral valve repair, mechanical heart valves, paravalvular leaks) or diseases (e.g., aortic or pulmonary valve regurgitation). Fundamentally, these flows usually feature two or more pulsed jets interacting in an expanding, elastic environment. In this investigation, the experimental setup features two parallel pulsed jets entering the cavity, with jet strength varied across five formation times (1, 2, 3, 4, 5) and four spacing ratios (1.5, 2.0, 2.5, 3.0). Time-resolved particle image velocimetry is used to capture the instantaneous velocity fields. The results reveal three distinct flow regimes: short-time decay, decay at the wall, and wall rebound—with or without the formation of secondary vortices. These findings uncover rare aspects of twin vortex ring behavior, including symmetry breaking, trajectory shifts, and wall-induced rebound mechanisms, with direct relevance to cardiac fluid dynamics in both healthy and pathological conditions.

The size of a pendant drop detaching from a capillary is classically set by the balance between gravity and surface tension, as described by Tate's law, implying only a weak dependence on nozzle size. I show that purely geometric confinement provides a simple and robust means to tune the detachment volume well below this classical limit. By placing a capillary between two superhydrophobic plates forming a shallow wedge, I demonstrate experimentally that drops detach at significantly reduced volumes. A scaling argument reveals that the wedge induces a capillary pressure gradient that assists gravity, yielding a simple relation between drop volume and confinement geometry that collapses all measurements. For completeness, I also consider the complementary case of drops resting on an inclined superhydrophobic surface, which enables volumes above the classical limit through a similarly simple geometric control.

When a semipermeable vesicle is exposed to a solute concentration gradient, it experiences a nonuniform osmotic pressure distribution. This distribution, incompatible with static equilibrium, induces inward osmosis on the low-concentration side and outward osmosis on the high-concentration side. The resulting imbalance drives the vesicle to drift down the gradient—a phenomenon known as osmophoresis. While osmophoresis may superficially resemble other phoretic mechanisms (such as diffusiophoresis or thermophoresis) driven by scalar field gradients, it is fundamentally distinct due to its essential dependence on the absolute value of the (strictly non-negative) concentration field itself. In this work, we revisit the osmophoresis problem, identifying the appropriate limiting process that consistently represents an imposed macroscale concentration gradient, and clarifying the distinction between the concentration and pressure fields and their dynamic counterparts. Our scrutiny resolves the longstanding anomaly of significant advective transport at low Péclet numbers, as originally reported by Anderson [Phys. Fluids 26, 2871 (1983)], and yields a closed-form expression for the drift velocity, valid for all Péclet numbers. We demonstrate how previous efforts to go beyond leading-order approximation at small Péclet numbers have led to inconsistent perturbation schemes.

We present an asymptotically exact continuum formulation of finite-temperature superfluid turbulence that consistently couples quantized vortex filaments to the turbulent normal fluid across all continuum scales. The key ingredient is the explicit linear-response theory (LRT) Stokes microhydrodynamic response generated by the line-supported mutual-friction and Iordanskii forces acting on the normal fluid. This response yields hydrodynamic-interaction (HI)-resolved vortex dynamics in which the filament-sampled normal-fluid velocity includes the full disturbance flow. Analytical solutions for canonical configurations (parallel and antiparallel line pairs and a vortex ring) show that microhydrodynamic coupling renormalizes defect motion and can permit stalling and reversal phenomena excluded in freely draining defect dynamics. To bridge the prohibitive separation between microhydrodynamic and turbulent scales in practical calculations, we couple a filtered Navier-Stokes description of the normal component to a concurrent low-Reynolds-number (LRT/Stokes) microflow solver. In the filtered normal-fluid equations the LRT microflow enters in two distinct, explicit ways: (i) it generates a deterministic residual (subfilter) stress from the subcutoff microflows, and (ii) it supplies hydrodynamically consistent mutual-friction and Iordanskii forcing via the HI-resolved defect reaction forces. The resulting hydrodynamic-scale system resolves inertial turbulence down to the physical cutoff set by viscous damping and two-fluid coupling. The formulation is boundary-condition agnostic—periodic, unbounded, and wall-bounded geometries enter only through the Stokes mobility returned by the solver—and is asymptotically exact in the scale-separated limit as a consequence of the overdamped Stokes/LRT response, which relaxes rapidly compared with the smallest resolved turbulent timescales. We indicate a detailed algorithmic procedure implementing the new formulation.

Electro-vortex flows (EVF) arise in conducting fluids due to diverging/converging current lines and the nonconservative Lorentz force, resulting from the interaction of this current with its own magnetic field. They are typically characterized by the EVF parameter, defined as $S={\mu }_0{I}^2/\left(4{\pi }^2\rho {\nu }^2\right)$ (${\mu }_0$ is the magnetic permeability), where it is known that $\mathit{\text{Re}}\propto \sqrt{S}$ for large $\mathit{\text{Re}}$. However, the strength of the EVF in a confined cylindrical cell with a coaxially placed current collector (CC) depends also on the ratio of the CC radius to the cylinder radius, $K=r_0/R$, in addition to the current magnitude, $I$, fluid density, $\rho$, and kinematic viscosity, $\nu$. Using the inertia-Lorentz balance in the vorticity transport equation, we derive a theoretical estimate of the r.m.s. EVF velocity and find that $u\propto I(1-K)/\sqrt{K}$, applicable for the aspect ratio of 2 (radius equals height). Our estimate leads to a modified EVF parameter, $S_M$, that incorporates $K$. We also explore the relationship between $K$ and the curvature in Lorentz force. Three-dimensional direct numerical simulations performed with our in-house OpenFOAM code confirm the validity of the estimate, with excellent agreement observed between theory and simulations across the range $S_M\in [63,9125]\times {10}^4$. We also discuss the key EVF characteristics using the vorticity dynamics: its driving mechanism, formation, and evolution. Intriguingly, our numerical simulation results reveal distinct flow features for $K\ge 0.75$, not reported earlier in the literature. Our results suggest that the scaling relationship should actually be $\mathit{\text{Re}}\propto \sqrt{S_M}$.