We develop a nonlinear model for electroosmotic transport through a constricted microchannel with a rigid curved upper wall and a compliant lower wall. The framework couples Helmholtz-Smoluchowski slip under a globally constrained electric field, lubrication hydrodynamics, quasistatic Kirchhoff-Love wall bending, and Derjaguin-Landau-Verwey-Overbeek disjoining pressure. The response is governed by wall stiffness, geometric curvature, surface conduction, and the strengths of the repulsive and attractive intermolecular interactions. Asymptotic analysis and fully coupled Chebyshev-collocation computations reveal three regimes: a stiff-wall regime with negligible deformation, a compliance-limited regime in which localized throat narrowing suppresses throughput, and a small-gap saturation regime in which further thinning becomes progressively slower because of the coupled elastic, hydrodynamic, and disjoining-pressure response. In the strong-constriction limit, geometric focusing amplifies the electric field and produces a sublinear increase of throughput with curvature, whereas in the localized-throat limit the deformation and compliance-induced flux reduction are organized by the effective stiffness $\mathcal{B}{C}^2$. The results provide compact, design-oriented scaling laws for compliant electroosmotic constrictions and clarify how stiffness, curvature, surface conduction, and minimum-gap interactions regulate transport in soft microfluidic, biosensing, drug-delivery, and iontronic systems.

An analytical theory is developed for the deformation of a viscous ferrofluid droplet subject to a uniform magnetic field together with a linear background flow. Under weak flow conditions ($\text{Ca}\ll 1$), we apply the method of domain perturbation to compute ellipsoidal corrections to the droplet shape up to $O\left({\text{Ca}}^2\right)$ in the capillary number. The resulting small-deformation equations show that droplet deformation and breakup depend strongly on both the direction and the strength of the imposed magnetic field as demonstrated in existing computational studies. Steady-state bifurcation analysis is used to determine droplet breakup and the critical capillary number as functions of the flow type and magnetic-field orientation. We then analyze the rheology of a dilute ferrofluid emulsion by extending the classical approach of Batchelor [J. Fluid Mech. 41, 545 (1970)] to compute the emulsion extra stress and the associated rheological material functions (e.g., shear and extensional viscosities). The existence of a nonsymmetric stress tensor, reported by previous computational studies, is demonstrated and the extra torque in the suspension is calculated. Analytical expressions for rheological properties of bulk emulsions are derived up to $O\left(\text{Ca}\right)$.

Taking advantage of the recently developed Linearized Arbitrary Lagrangian-Eulerian framework [Sierra-Ausin et al., Phys. Rev. Fluids 7, 113603 (2022)], we characterize the linear dynamics of an incompressible gas bubble immersed in a biaxial straining flow. We show that the system undergoes a saddle-node bifurcation with strongly different equilibrium shapes when varying the Ohnesorge number, $\text{Oh}$, which compares viscous and capillary effects. Equilibrium shapes are found to be oblate for sufficiently large $\text{Oh}$ while, counterintuitively, they are prolate for low-enough $\text{Oh}$. The bifurcation diagram is found to contain also two sets of disconnected branches that cannot be obtained by continuation starting from a spherical shape. One set corresponds to bubble shapes expected to be unstable, while the second set comprises a wide region exhibiting stable shapes that might be observed experimentally. We then characterize the linear stability of the various branches. In addition to the unstable axisymmetric mode arising at the saddle-node bifurcation, two nonoscillating drift modes are also identified, together with two unstable modes with azimuthal wave number $m=2$ and two oscillating modes with $m=3$ that appear on oblate bubbles in the presence of large inertial effects. Present results lead to conclusions that may be relevant in the context of bubble breakup in turbulence. In particular, they show that bubbles are much more stable in the biaxial flow geometry than in the uniaxial one. This presumably explains why turbulent breakup mostly happens in uniaxial regions, although biaxial regions are significantly more frequent.

Solute transport in porous media is strongly influenced by both hydrodynamic instabilities and physicochemical interactions, such as adsorption. In this study, we investigate the coupled dynamics of a finite solute blob subjected to Langmuir type nonlinear adsorption and viscous fingering (VF) instabilities during miscible displacement. To resolve the complex interplay between adsorption and instability, we solved the governing equations using a high-resolution Fourier pseudospectral method. While linear adsorption leads to symmetric blob spreading, the nonlinear Langmuir regime exhibits highly asymmetric solute profiles characterized by the formation of a rear rarefaction wave and a sharp leading shock layer. Additionally, the net advection of the blob is noticeably reduced in the upstream direction as the Langmuir adsorption parameter $b$ increases. We have found that for the range of adsorption parameters for a given suitable log mobility ratio, the VF instability was suppressed and introduced a new comet shape structure. Furthermore, we examine the impact of adsorption on mixing by tracking the degree of mixing over time. Interestingly, we observe a nonmonotonic dependence of mixing on the Langmuir parameter for a suitable log mobility ratio. The coupled effect of VF at the rear interface and of Langmuir adsorption provides a powerful mechanism to enhance or reduce the mixing and VF depending on the need of the application.

We study the evaporation dynamics of spray lamellae—the paradigm of dense sprays evaporation—injected into a quiescent dry environment from an oscillating source. Lamellae are made of a collection of densely packed microns in size droplets of liquids with different volatilities, initially in equilibrium with their vapor. Building on an earlier study [de Rivas et al., Phys. Rev. Fluids 1, 014201 (2016)], we confirm that the lifetime of an individual droplet embedded in such a spray is much larger than expected from the usual d-squared law describing the fate of a single isolated droplet evaporating in a quiescent environment. By analogy with the way mixing times of scalars are understood from the coupling between stretching and diffusion, we show that the boundary between the spray and the diluting environment is slaved to the dynamics of its saturating vapor concentration field as envisaged in Villermaux et al. [Phys. Rev. Fluids 2, 074501 (2017)], thus explaining the very substantial evaporation delay of the liquid phase in spite of its division into fine droplets. We quantify the evaporation time for the stirring protocol of an undulating lamellae as well as, thanks to unique in situ measurements, the concomitant evolution of the droplets number, and size distribution in the spray.

The collision kernel of droplets in warm clouds is a crucially important quantity for the parametrization of precipitation in weather and climate models. Nevertheless, its accurate representation remains a challenge, specifically in the bottleneck range $15\mu \mathrm{m}<r<40\mu \mathrm{m}$, within which turbulence is believed to substantially contribute to droplet growth. In this work, we address this problem by performing direct numerical simulations of polydisperse inertial particles suspended in three-dimensional turbulence at Reynolds number up to ${\text{Re}}_{\lambda }=418$. Collision statistics are compiled for droplet pairs across the Stokes number range $\text{St}\in [0.02,2]$, yielding comprehensive bidisperse maps of collision kernels, radial relative velocities, and radial distribution functions at contact. Our analysis reveals that polydispersity enhances collisions between light droplets through differential sampling, but attenuates collisions at larger Stokes numbers by rapidly reducing the spatial overlap of droplet clusters. By benchmarking existing models, we show that dominant bidisperse errors arise from overpredicted cross-species clustering. In light of these results, we propose an adapted model for the bidisperse radial distribution function, as well as a novel parametrization for the associated collision kernel, applicable to the smallest droplets in the bottleneck range with small settling velocities. Finally, we study the broadening of the droplet size distribution due to collision-coalescence and demonstrate that droplet growth is markedly accelerated in parcels of large local dissipation rate, supporting the hypothesis that turbulent intermittency may help overcome the bottleneck barrier.

In this paper, numerical simulations are conducted of flow past a circular cylinder confined symmetrically in a channel. The effects of upstream turbulence on wake properties are studied with upstream conditions assumed to be a canonical turbulent channel flow. Simulations have been conducted at blockages of $\beta =0.3$, 0.5, and 0.7, where blockage is defined as the ratio of cylinder diameter to channel height. It is found for the lowest blockage, $\beta =0.3$, turbulence trips the shear layers separating off the cylinder, forming Kelvin-Helmholtz vortices which rapidly roll-up and form Kármán vortices further downstream. This mechanism prevents merging of Kelvin-Helmholtz vortices, evidenced by a lack of a subharmonic peak in spectra of probes placed in the shear layer. For $\beta =0.5$, acceleration of fluid through the gap between the cylinder and channel wall partially relaminarizes the flow, reducing turbulence. Despite this, the surviving turbulence still trips the cylinder shear layer, causing it to break down. Finally, for $\beta =0.7$, a large change in wake dynamics is found to occur. Relaminarization again occurs through the gap, but is insufficient to suppress all turbulence. Hence, tripping the cylinder shear layer and breaking it down before wake bias could occur. This therefore results in the time- and spanwise-averaged flow being symmetric, unlike its laminar upstream counterpart. Spectral analysis also finds a strong subharmonic peak, indicating merging of Kelvin-Helmholtz vortices for $\beta =0.5$ and 0.7.

The low-frequency unsteadiness of turbulent separation bubbles is manifested in a contraction and expansion of the reverse-flow region. This study shows that, in a pressure-gradient-induced turbulent separation bubble developing in a half-diffuser, the dominant long-time behavior follows nonlinear stochastic dynamics. Planar time-resolved particle image velocimetry reveals a spanwise-organized coherent structure with anticorrelated core and sidewall regions. Its temporal evolution is quantitatively described using a Langevin equation, modeling both the deterministic drift and stochastic forcing of the dynamical system. This model suggests that the low-frequency unsteadiness may arise from stochastic forcing, resulting in transitions between two equilibrium states. The methodology and findings documented in the present paper therefore constitute a significant step toward understanding turbulent separation bubbles as probabilistic dynamical systems.

Waves refract when traveling over water of variable depth, and the theory of radiation stress implies consequent forces imparted to the bottom topography. Such forces may be relevant for deformable boundaries and submerged objects that are free to move, but such wave-structure interactions have yet to be experimentally observed nor utilized in applications. Here we demonstrate such effects at the laboratory scale by introducing experimental techniques for studying the movements of submerged structures due to water waves. Asymmetrically shaped bodies are shown to move perpendicularly to plane traveling waves, and visualizations of the distorted wave fields are consistent with a mechanism based on refraction in the shallow layer over the structure. Further, we show how this effect can be exploited to stably position or "tweeze" objects within focused wave fields. Simplified calculations suggest that refractive redirection of momentum flux can explain these outcomes, and the form of the wave field and geometry of the body can be used to control forces. The systems presented here are hydrodynamic analogs to acoustic and optical transport and trapping, suggesting generalizations that could guide further strategies for wave-based motion control.

We demonstrate the feasibility of a closure model for large-scale eddies in the energy-containing range of turbulence. To this end, we construct a data-driven closure model for the largest eddies in turbulence driven by the steady Taylor-Green force in a periodic cube, and thoroughly evaluate its stability and accuracy. A recurrent neural network is employed to autoregressively predict the temporal evolution of low-wave-number components of the Fourier coefficients of vorticity with a prediction interval $\mathrm{\Delta }{t}_{\mathrm{p}}$. The key factors for successful modeling are not only spatial low-pass filtering to construct the closure model, but also preprocessing the training data with a temporal low-pass filter. More concretely, an appropriate cutoff frequency, which is inversely proportional to $\mathrm{\Delta }{t}_{\mathrm{p}}$, is needed for stable and accurate reproduction of the dynamics and statistics of the largest eddies. Without this preprocessing, the model exhibits steady or periodic behavior and fails to reproduce the chaotic dynamics of the largest eddies.

The problem of inertia-gravity waves excited by harmonic flow over topography is often simplified by the traditional approximation, which neglects the horizontal component of the Coriolis force. We consider waves forced by a two-dimensional tidal potential in a finite-depth domain, considering the full (nontraditional) Coriolis force, nonhydrostatic effects, and contribution from higher-order harmonics. We provide formulas for the vertical velocity, form drag, and conversion rate of inertia-gravity waves. Overall, including the nontraditional Coriolis force enhances the conversion rate and torque of inertia-gravity waves and extends the range of latitudes that can support them. Inertia-gravity waves under nontraditional rotation exhibit weaker suppression of the conversion rate in the low-depth limit, and weaker nonacoustic effects in the rapidly rotating limit at low latitudes.

Inertia-gravity waves present in a wide range of fluid dynamical contexts, necessitating a generalized and adaptable theory to accurately describe their behavior. We provide an analytical solution for form drag and velocity, in addition to the energy conversion rate of such waves excited by harmonic flow over a topographic source. Our analysis extends the investigations of Bell et al. [J. Fluid Mech. 67, 705 (1975)] and Llewellyn Smith et al. [J. Phys. Oceanogr. 32, 1554 (2002)] to consider a finite depth ocean without the hydrostatic or acoustic approximations. Eschewing these approximations enables consideration of waves in subinertial contexts (e.g., weak stratification, diurnal tides, or flow at high latitudes). The nonhydrostatic solution supports any waves forced at frequency $\omega$ between the stratification $N$ and Coriolis $f$ frequencies. The nonacoustic solution does not neglect the tidal excursion length and thereby enables superharmonics $n\omega$ ($n>1$) to lie within the aforementioned interval, even when the fundamental frequency does not. The finite depth of the domain is found to suppress inertia-gravity wave power when the distance between reflections of the wave approaches the thickness of the wave beam. This suppression is enhanced in strongly nonacoustic contexts.

We investigate the fragmentation dynamics of acoustically levitated microemulsion droplets subjected to laser irradiation. The influence of irradiation intensity and emulsion composition on bubble dynamics and subsequent breakup characteristics is investigated. Our findings demonstrate an inverse relationship between irradiation intensity and the onset of vapor bubble nucleation, which is consistent with theory. Depending on the composition and irradiation intensity, distinct regimes of bubble growth are revealed. The growth and collapse of these bubbles result in droplet fragmentation via ligament-mediated breakup and sheet breakup. These breakup modes are governed by interfacial instabilities, including Faraday, Rayleigh-Taylor, and Plateau-Rayleigh mechanisms. The bubble growth and collapse events are quantified using a breakup impact parameter ($\beta$), which, in turn, reveals the onset of instability triggering droplet breakup. Consequently, the variations in ligament dynamics [using Weber number (We)] are explained and correlated to the respective bubble growth and collapse events. In particular, our experimental data show that small-sized bubbles (lower value of $\beta$) typically result in the ejection of high-momentum ligaments (larger We). Finally, we report the growth and collapse dynamics of a highly viscous bubble that forms toward the end of the droplet lifetime due to the high concentration of nonvolatile surfactant.

We calculate the effective slip length for a rectangularly grooved periodic surface encapsulated (i.e., fully wetted) by a lubricant fluid and subjected to exterior shear flow parallel to the grooves. Our focus is the limit of a nearly inviscid lubricant, where the ratio $\mu$ of the lubricant viscosity to that of the exterior fluid is small. This limit is singular for an encapsulated surface, indicating a dominant lubricant-flow effect—a stark contrast to superhydrophobic surfaces where the role of the lubricant is typically negligible. In addition to $\mu$, the ratio $\lambda$ of the slip length to the grooving semiperiod depends on three geometric lengths, all normalized by the semiperiod: $b$, the thickness of the lubricant films wetting the groove ridges, and $\varphi$ and $h$, the semiwidth and height of the ridges, respectively. We identify two key limits characterizing the regime $\mu \ll 1$. In the first, with $b$ held fixed, we find $\lambda \sim {\mu }^{-1}\tilde{\lambda }(b,\varphi ,h)$, where the rescaled slip length $\tilde{\lambda }$ is determined by an interior lubricant-flow problem. In the second, with $b/\mu$ held fixed, we find $\lambda \sim \mathrm{\Lambda }(b/\mu ,\varphi )$, where $\mathrm{\Lambda }$ is governed by an exterior flow problem in which the thin lubricant films wetting the ridges are effectively replaced by a Navier-slip condition, while the rest of the interface is shear free. As $b/\mu \to 0$, the Navier-slip condition simplifies to no slip, whereby the exterior problem reduces to that for a superhydrophobic grooved surface—famously solved by Philip using complex variables [Philip, Z. Angew. Math. Phys. 23, 353 (1972)]. Asymptotic and numerical analysis of the exterior problem demonstrates (i) the transition from Philip's solution at $b/\mu \ll 1$ to an algebraic behavior $\mathrm{\Lambda }\sim b/\left(\mu \varphi \right)$ at $b/\mu \gg 1$, matching with the small-$b$ limit of the interior problem, and (ii) for $\varphi \ll 1$, the transition from a logarithmic $O(ln\varphi )$ scaling for $b\ll \mu \varphi$—familiar from the superhydrophobic case, where $\varphi$ constitutes the solid-to-air fraction—to the aforementioned algebraic regime when $\mu \varphi \ll b\ll \varphi$. As $b$ becomes comparable to $\varphi$, the exterior problem loses validity in favor of the interior problem. By analyzing the latter in the distinguished sublimit where $b$ and $\varphi$ are comparably small, we demonstrate how, as $b/\varphi$ is increased, the algebraic growth of $\lambda$ with $b/\mu$ is arrested at order ${\mu }^{-1}/lnb$.

The role of interparticle collisions in turbulent particle-laden channel flow is investigated through a detailed comparison between two-way and four-way coupled point-particle direct numerical simulations. Simulations are performed with particle Stokes number ${\mathrm{St}}^{+}$ ranging from 3 to 300, at a fixed mass loading ${\mathrm{\Phi }}_m=0.6$ and bulk Reynolds number ${\mathrm{Re}}_b=U_{b}h/\nu =5150$. It is found that interparticle collisions significantly modulate the dynamical features of both fluid and particle phases, resulting in a substantial reduction of near-wall particle concentration, enhanced turbulence attenuation, and more pronounced drag reduction especially for high ${\mathrm{St}}^{+}$ cases. These modulating effects mechanistically arise from the following two differences compared with the two-way coupling cases. First, interparticle collisions increase particle velocity fluctuations in the wall-normal direction, which enhances particle dispersion and consequently weakens near-wall particle accumulation. Second, interparticle collisions amplify the slip velocity fluctuations and thereby increase the extra dissipation, which leads to turbulence attenuation and further drag reduction. The above findings suggest that four-way coupling is of fundamental importance for accurate modeling of interphase momentum and energy dynamics in particle-laden turbulent flows.

We apply a physics-informed deep learning method to reconstruct the flow field from sparse and noisy particle tracks, focusing on accurately assimilating the global minimum pressure on a fine-grid domain from very sparse velocity data. The spatial resolution of the velocity data could be much larger than the mesh spacing of the reconstructed flow field. To address this problem, we first quantify the performance of the physics-informed neural network (PINN) model using a series of analytical vortex models. Synthetic particle data are generated using the analytical solutions of the velocities; the PINN model is trained on these sparse particle measurements, and the model then reconstructs the finer-resolution flow field within a fixed domain of interest and obtains the minimum pressure. We also investigate the effects of the reconstruction resolution, particle densities, particle distributions, incomplete measurements, velocity noise, and noise in spatial coordinates. The methodology is applied to a turbulent flow of interacting counterrotating vortices of unequal strength obtained from Large-Eddy Simulation, and the results are discussed.

Reliable description of the inflow boundary conditions of the fully developed turbulence in atmospheric boundary layers for large-eddy simulation (LES) has been a subject of significant research interest due to its considerable impact on simulation results. In existing synthetic random Fourier methods for generating inhomogeneous inflow turbulence, the inhomogeneous field can be obtained by superimposing multiple homogeneous turbulence fields, each weighted by an assigned weighting function. However, inappropriate mapping strategies may distort the spatial correlations and continuity of turbulence structures from the targeted values, which could further deteriorate the simulation results. In this study, the impacts of the weighting functions on the total-energy profiles, spatial correlations, and the continuity condition of turbulence are clarified, based on which an adaptive energy-preserving mapping (AEPM) strategy is developed. The results from a priori numerical test demonstrate that inflow turbulence fields generated by the established synthetic random Fourier framework in combination with the AEPM accurately preserve the target turbulence energy profiles while maintaining good agreement with spatial correlation properties. Furthermore, the robustness and effectiveness of the AEPM are demonstrated through three LES case studies. Case 1 and Case 2 simulate atmospheric boundary layers around an isolated rectangular building and are validated against experimental data under neutral and unstable thermal stratification, respectively. In these two cases, wall-modeled LES (WMLES) results are compared with wall-resolved LES to investigate the performance of WMLES in urban environment simulations. In Case 3, the building in Case 1 is removed to form an empty domain, in which downstream turbulence statistics are evaluated to further assess the AEPM-generated inflow.

A physics-based analysis framework is developed to characterize low-frequency unsteadiness (LFU) in separated wake flows. LFU is interpreted as an outcome of a temporal imbalance of kinetic energy within the mean recirculation region. A kinetic energy transport equation is derived from the rotational form of the Navier-Stokes equations using vorticity-based quantities, motivated by their direct connection to vortical dynamics and flow structures relevant to LFU. To isolate LFU from dominant wake motions, temporal low-pass filtering is applied together with conditioning based on a local intermittency measure, extracting intermittent fluctuations at frequencies much lower than the primary vortex shedding frequency. The framework is demonstrated for a two-dimensional laminar wake past a normal plate. The filtered drag coefficient exhibits a clear LFU signature and is strongly correlated with the net filtered kinetic energy within the mean recirculation region. Analysis of the kinetic energy budget identifies the Bernoulli energy flux and Lamb-vector transport as the dominant mechanisms governing kinetic-energy charging and discharging, respectively. Strong correlations are observed between the filtered drag and the net Lamb-vector divergence, attributed to vortex merging and intensified roll-up that redistribute the Lamb vector and reduce base pressure. The LFU frequency is estimated using dimensional scaling and a data-driven approach. The analysis highlights the central role of the Lamb-vector divergence in understanding and predicting LFU in separated wake flows. By providing a reduced, physics-based description of LFU in terms of kinetic energy dynamics, the proposed framework offers a useful tool for analyzing LFU in turbulent separated flows, where visual inspection is limited and modal decompositions remain high dimensional.

This paper studies the interrelation between the Rayleigh-Bénard and the electroconvective instability in concentration polarization during ionic dc current passage from an electrolyte solution into a charge-selective solid, such as a metal electrode, an ion-exchange membrane, or a set of nanochannels. We conclude that, whereas in the underlimiting current regime the effect of electroconvection on the onset of buoyant convection is insignificant, these two phenomena become strongly intertwined at the limiting current. In this regime, the development of the extended space charge and its related nonequilibrium electroconvective instability have a major effect upon the onset of the buoyant instability; and vice versa, buoyancy has a major effect on the features of the electroconvective instability. This includes lowering of the onset threshold and regularization of the shortwave singularity typical of electroconvective instability.

Turbulent puffs in pipe flow remain sustained for an extended period of time before abruptly transitioning to laminar flow through viscous exponential decay. During the statistically stable state, the topology of sectional streamlines reveals the presence of numerous saddle and nodal points in proximity to the wall. The number of saddle and node points decreases as relaminarization begins, and they migrate away from the near-wall region. In the final stage of relaminarization, direct numerical simulations reveal, in some cases, sequences of saddle-node bifurcations that ultimately lead to the annihilation of saddle-node pairs. The Riccati equation is proposed as a simple approach to model the motion of these pairs.