In this work, we investigate the effects of impurity particles on the flow slip at nanogrooved superhydrophobic surfaces through many-body dissipative particle dynamics (MDPD) simulations. The local slip velocity, local slip length, and effective slip length are calculated by varying the surface wetting properties, concentration, mass, and size of the impurity particles. It is found that impurity particles greatly reduce the flow slip at the fluid-groove interface. Specifically, the slip velocity and the slip length decrease as the wetting property of the particle surface is enhanced. Furthermore, particle concentration also plays an important role in affecting the flow slip. The slip velocity and slip lengths decrease as the particle concentration is increased. The dependence of the effective slip length on the particle concentration follows the Philip model. In contrast, particle mass and size exhibit minor effects on the flow slip. The results in this work provide helpful information for regulating flow slip in fluidic systems containing impurity particles.

Precise, localized flow control in microfluidic devices remains a difficult challenge. In this paper we demonstrate, theoretically, how active droplets might be harnessed to overcome this challenge. Active droplets are produced along the microchannel wall via stimulation of a responsive hydrogel, and the ensuing phoretic slip flows drive transport and mixing in the microfluidic device. We find optimal transport times for particles traversing the channel, and show that, by switching between two droplet configurations, chaotic mixing can be achieved.

A dynamic averaging algorithm combined with a high-order spectral (HOS) model is introduced for wave reconstruction and prediction using radar data from stationary or moving ships. The algorithm enables gradual reconstruction of waves entering the radar's blind zone and improves accuracy by reducing the effects of shadowing modulation, particularly under steep wave conditions. The effects of nonlinearity on wave prediction accuracy are examined across a range of sea states with varying wave steepness and directional spreading angles. Results show that the HOS model, which includes third-order nonlinear effects, outperforms both linear and second-order models. Its advantage is especially clear in steep or narrowly spread wave fields, where simpler models fail to accurately predict the timing and height of large waves, leading to wave prediction errors at the ship's position up to three times higher than those from the HOS model. Additionally, when the ship slows down in head waves or speeds up in following waves, the relative velocity between the waves and the ship decreases. This reduction in relative speed extends both the time required for accurately reconstructing waves in the blind zone and the length of the predictable wave field ahead of the ship.

Results are presented for the explosive blast-driven instability of a stratified interface in a diverging cylindrical geometry using high-speed optical diagnostics. Specifically, the perturbation growth was studied using the qualitative Mie scattering technique, and the velocity, mixing transition, and vorticity characteristics are studied to investigate the behavior of the interface using planar particle image velocimetry (PIV). The role of density contrast is studied using ${\mathrm{CO}}_2$-air (low Atwood number, $A$) and ${\mathrm{SF}}_6$-air (high-$A$) interfaces. The perturbation growth $h\sim t^{\theta }$ was studied, where the decay parameter $\theta$ was found for $A\sim 0.22$ and $A\sim 0.68$ to be 0.34 and 0.50, respectively. Using velocity information from PIV, it was found that the initial vorticity deposition from the pressure impulse can accurately be estimated using known models previously developed for Richtmyer-Meshkov instability. There is a significant addition to the interface circulation by the long pressure decay phase of the blast wave, which gives rise to a variable acceleration Rayleigh-Taylor instability contribution. The high-$A$ case showed a prolonged increase in circulation, plausibly due to higher inertia. This trend was also supported by variations in peak turbulence intensity, where a sharp increase at early times quickly decays with increased mixing between the two fluids. Finally, the interface Reynolds number of the higher $A$ was found to exceed all criteria for the mixing transition (also indicated by the qualitative observations of the mixing in spike-structures in the Mie scattering images).

We develop data-driven models to predict the dynamics of a freely settling sphere in a quiescent Newtonian fluid using experimentally obtained trajectories. Particle tracking velocimetry was used to obtain a comprehensive dataset of settling motions, which we use to train neural networks that model the spatial evolution of a spherical particle without explicitly resolving the surrounding fluid dynamics. We employ deterministic neural ordinary differential equations (NODEs) and stochastic neural stochastic differential equations (NSDEs) to reconstruct the sphere's trajectory and capture key statistical features of the settling process. The models are evaluated based on short- and long-time dynamics, including ensemble-averaged velocity evolution, settling time distributions, and probability density functions of the final settling positions. We also examine the correlation between lateral displacement and streamwise velocity and assess the impact of dataset size on predictive accuracy. While NODEs excel in trajectory reconstruction and generalization across different initial conditions, NSDEs effectively capture statistical trends in the long-time behavior but are more sensitive to data availability. Acceleration profiles computed via second-order finite difference schemes confirm that both approaches accurately capture long-time dynamics, although short-time transients pose challenges.

We demonstrate the capability to experimentally measure fluctuations of the convective heat transfer coefficient at the wall in a turbulent boundary layer. To achieve this, we measure two-dimensional fields of wall-temperature fluctuations beneath a zero-pressure-gradient turbulent boundary layer at two moderate friction Reynolds numbers (${\text{Re}}_{\tau }\approx 990$ and ${\text{Re}}_{\tau }\approx 1800$). Spatiotemporal data of wall temperature are acquired by means of a heated-thin-foil sensor as sensing hardware and an infrared camera as a temperature detector. At the lower ${\text{Re}}_{\tau }$ condition, the fields of Nusselt number fluctuations (${\text{Nu}}^{\prime }$) exhibit elongated features comprising streamwise and spanwise length scales comparable to those of near-wall streaks. At higher ${\text{Re}}_{\tau }$, the effective width and length of the streaks of Nu fluctuations increase. These findings are based on two-point correlations as well as streamwise-spanwise energy spectra of Nu fluctuations at the wall. The convective velocities of the Nu fluctuations are also computed using the available temporal resolution. This allows for resolving the multiscale nature of convective footprints of wall-bounded turbulence: Our experimental data reflect that larger streaks in the footprint convect at velocities in the order of the free-stream velocity, whereas more energetic smaller-scale features move at velocities in the order of $10u_{\tau }$. Measurements of the kind presented here offer a promising method for wall-based sensing of turbulence and thus for usage as input to flow control systems.

Natural transition in high-speed boundary layers is initiated by the exponential amplification of infinitesimal instability waves. Once these waves reach appreciable amplitudes, their evolution becomes nonlinear and they subsequently break down to turbulence. Assuming the availability of wall-pressure signals within the nonlinear flow regime, we attempt to predict the boundary-layer instability waves that led to the wall-pressure data. This data-assimilation (DA) problem is formulated as a nonlinear optimization: We search for the upstream disturbance parameters that reproduce the measurements, by minimizing a cost function defined in terms of the difference between the estimated and true wall-pressure data. The optimization is challenging due to the sparsity of measurements and the computational cost of evaluating the wall-pressure data from each estimate of the instability waves during the iterative procedure. Each iteration of the Bayesian approach identifies a new estimates of the control vector that can potentially minimize the DA cost function. This procedure requires a statistical model, and therefore repeated evaluations of the cost function, for which direct numerical simulations (DNS) are not practical. We therefore adopt a deep operator network (DeepONet) surrogate for the compressible Navier-Stokes equations, which is efficient and sufficiently accurate. Using an ensemble of DeepONets, we can evaluate the expectation of the cost function and its uncertainty, to inform the Bayesian optimization. Once the new estimate of the control vector is identified, a single DNS is performed, the accuracy of the DA solution is evaluated against a convergence criterion, and the DNS data are added to the training data of the DeepONet model. This procedure is then repeated to convergence. We demonstrate the Bayesian optimization with DeepONet (BO-DeepONet) by predicting the frequency and amplitude of the incident primary instability wave, and its phase shift relative to the subharmonic mode, from wall-pressure data in the nonlinear flow regime.

The fluid dynamics community has increasingly adopted machine learning to analyze, model, predict, and control a wide range of flows. These methods offer powerful computational capabilities for regression, compression, and optimization. In some cases, machine learning has even outperformed traditional approaches. However, many fluid mechanics problems remain beyond the reach of current machine learning techniques. As the field moves from its current state toward a more mature paradigm, this article offers a critical assessment of the key challenges that must be addressed. Tackling these technical issues will not only deepen our understanding of flow physics but also expand the applicability of machine learning beyond fundamental research. We also highlight the importance of community-maintained datasets and open-source code repositories to accelerate progress in this area. Furthermore, the future success of machine learning in fluid dynamics will depend on effective training—not only for the next generation of researchers but also for established fluid mechanicians adapting to this evolving landscape. Data-driven fluid dynamics is in its critical transitional state over the next few years to shape its future. This perspective article aims to spark discussions and encourage collaborative efforts to advance the integration of machine learning in fluid dynamics.

We consider a simple thermodynamically consistent model that captures the self-organized chemomechanical coupling resulting from the interplay between autocatalytically reacting surfactants, the Marangoni effect, and wetting dynamics. An ambient bath of surfactant acts as a chemostat and provides the system with chemical fuel, thereby driving it away from thermodynamic equilibrium. We find that a positive feedback loop between the local reactions and the Marangoni effect induces surface tension gradients that allow for self-propelled droplets. Besides simple directional motion, we find crawling and shuttling droplets as well as droplets performing random walks, thus exploring the entire substrate. We study the occurring chemomechanical motility modes and show how the observed dynamic states emerge from local and global bifurcations. Due to the underlying generic thermodynamic structure, we expect that our results are relevant not only to directly related biomimetic droplet systems but also to structurally similar systems like chemically active phase-separating mixtures.

The particle behavior and turbulent modulation of wall-bounded turbulent flow are analyzed by comparing a new simulation of channel turbulence with older simulation of spatially developing turbulent boundary layer at almost identical friction Reynolds number and laden particles with identical inertia and bulk volume fraction. It is found that particle locally accumulate in the wake region of the external boundary layer flow due to more pronounced turbulent/nonturbulent interface effect. Therefore, the particle-turbulence interaction in the outer layer of boundary layer results in stronger turbulent modulation than that in particle-laden channel. This influence not only makes the outer-layer structures more different but may penetrate to the near-wall region of wall turbulence, generating opposite modulation of turbulent mean velocity of the two flows. However, the modulation in second-order statistics and turbulent structures by the presence of inertial particles are qualitatively similar below the logarithmic layer. The similarities/dissimilarities are further explained by comparing the average stress, the turbulent kinetic energy budget and uniform momentum zones/quiescent core.

Hall, in his Ph.D. thesis (University of London, 1973), demonstrated that the viscous flow arising in a slender channel of slowly varying cross section subject to a purely oscillatory pressure difference between its open ends contains a steady streaming component. This study extends the analysis to channels with a porous interior. Using a homogenized flow model that incorporates a Darcy resistance term proportional to the local velocity, a closed-form solution for the streaming motion is derived in the asymptotic limit of small stroke-to-channel length ratios $\varepsilon \ll 1$. Consistent with Hall's findings, a net flow rate is seen to arise only when the channel ends have unequal widths. The presence of a porous medium significantly attenuates the streaming-flow magnitude, with the differences between porous and nonporous channels becoming more pronounced for large Womersley numbers, a limiting case considered separately. In nonporous channels with unequal end widths the streaming motion exhibits large velocities that are comparable in magnitude to those of the oscillatory flow, whereas in porous channels the streaming velocities remain a factor $\varepsilon$ smaller. Channels with equal end widths feature streaming recirculating vortices within near-wall Stokes boundary layers. Nonporous channels display additional recirculating vortices in the central core region, which are absent in porous configurations. These results provide insights into transport processes in biomedical and technological applications involving oscillatory flow in wall-bounded porous media.

In the past 15 years, flow instabilities reminiscent of the Taylor-like instabilities driven by hoop stresses have been observed in wormlike micelles based on surfactant molecules. In particular, purely elastic instabilities and turbulence have been shown to develop on top of shear banding, a type of flow specific to the semidilute and concentrated regimes. These instabilities have been identified as the origin of the large body of data showing complex spatiotemporal fluctuations, collected in shear-banded systems using multiple experimental techniques. Different categories of banding have been suggested depending on their stability, which involve intrinsic properties of the system and streamline curvature. It has been shown qualitatively that instabilities are promoted by an increase in the surfactant concentration or in the curvature of the flow geometry, while an increase in temperature stabilizes the flow. Here, using benchmark shear banding micellar systems, we quantify the effect of the streamline curvature on these flow instabilities, focusing more specifically on the transition toward purely elastic turbulence. Using various optical visualizations, we identify two transitional pathways to elastic turbulence. We construct a generic state diagram in a parameter space based on the curvature ratio and the Weissenberg number. The nature—supercritical vs subcritical—of the transition to elastic turbulence is discussed. The stress evolution is in favor of a change of nature from subcritical to supercritical transition as the curvature ratio increases. However, we show that finite size effects cannot be neglected and may artificially smooth the stress response. Furthermore, each domain of this diagram is characterized using velocimetry measurements. Finally, a scaling for the onset of elastic turbulence is determined.

Drying of fluids undergoing sol-gel transition in porous media, a process crucial for the consolidation of damaged porous structures in cultural heritage, often leads to skin formation at the surface. This phenomenon significantly hinders evaporation, yet its precise impact on drying kinetics remains poorly understood. To uncover the governing mechanisms, we develop a novel pore network model that closely replicates quasi-two-dimensional experimental porous media in a previous paper [Le Dizès Castell et al., J. Phys. Chem. Lett. 15, 628 (2024)], incorporating spatial gradients in pore size distribution, with smaller pores near the evaporation side. We demonstrate that this pore distribution dictates the air invasion path and extends the constant-rate period of drying in Newtonian liquids, reproducing the experimental drying curves for water. We further extend our model to capture the interplay of capillary-driven liquid flows, space-dependent viscosity increases, and localized skin formation. To incorporate skin formation, we implement a viscosity-dependent vapor pressure rule derived from experimental data on evaporation-induced sol-gel transition within a capillary tube. We identify a simple relationship: vapor pressure decreases once the meniscus fluid viscosity exceeds a critical threshold. By accounting for localized skin formation through reduced evaporation pressure at high-viscosity throats, our model successfully captures the slowdown of drying kinetics, achieving remarkable agreement with experimental drying curve.

Ice melting is a complex, dynamic, and multiscale process involving many feedback effects. An essential but poorly understood factor for floating ice is the potential to overturn, as dramatically demonstrated by capsizing icebergs. Here we study the melting-induced reshaping of ice coupled to its free rotation dynamics and find that periods of stable equilibrium are punctuated by spontaneous capsize events. Laboratory experiments on floating ice show that melting produces faceted and angular shapes whose tendency to orient to the waterline is repeatedly upset by rolling over. Similar geometries and motions are reproduced in simulations that drive the shape development via differential melt rate over the surface and which solve for the rotational dynamics subject to shape-dependent forcing from gravity, buoyancy, and hydrodynamics. Melting gradually drives the structure toward postural instability while also priming other orientations that prove stable when reached by abrupt flipping. These findings show how the shape and motions of ice are inextricably linked at fundamental scales, and they reveal mechanisms that may be operative for natural conditions.

We propose a geometry-to-flow diffusion model that utilizes obstacle shape as input to predict a flow field around an obstacle. The model is based on a learnable Markov transition kernel to recover the data distribution from the Gaussian distribution. The Markov process is conditioned on the obstacle geometry, estimating the noise to be removed at each step, implemented via a U-Net. A cross-attention mechanism incorporates the geometry as a prompt. We train the geometry-to-flow diffusion model using a dataset of flows around simple obstacles, including circles, ellipses, rectangles, and triangles. For comparison, two convolutional neural network (CNN)-based models and a variational autoencoder (VAE) model are trained on the same dataset. Tests are carried out on flows around obstacles with simple and complex geometries, representing interpolation and generalization on the geometry condition, respectively. To evaluate performance under demanding conditions, the test set incorporates scenarios including crosses and the characters “PKU.” Generated flow fields show that the geometry-to-flow diffusion model is superior to the CNN-based models and the VAE model in predicting instantaneous flow fields and handling complex geometries. Quantitative analysis of the accuracy and divergence demonstrates the model's robustness.

A comprehensive Darcy-type law for viscoplastic fluids is proposed. Different regimes of yield-stress fluid flow in porous media can be categorized based on the Bingham number (i.e., the ratio of the yield stress to the characteristic viscous stress). In a recent study [Chaparian, J. Fluid Mech. 980, A14 (2024)], we addressed the yield/plastic limit (infinitely large Bingham number), namely, the onset of flow when the applied pressure gradient is just sufficient to overcome the yield-stress resistance. A purely geometrical universal scale was derived for the nondimensional critical pressure gradient, which was thoroughly validated against computational data. In the present work, we investigate the Newtonian limit (infinitely large pressure difference compared to the yield stress of the fluid—ultralow Bingham number) both theoretically and computationally. We then propose a Darcy-type law applicable across the entire range of Bingham numbers by combining the mathematical models of the yield/plastic and Newtonian limits. The Exhaustive computational data generated in this study (using an augmented Lagrangian method coupled with anisotropic adaptive mesh at the pore scale) confirm the validity of the theoretical proposed law.

Temperature changes as small as $3{}^{\circ }\mathrm{C}$ have been observed to significantly impact how self-propelled organisms move through their environment, especially for those inhabiting the transitional flow regime in which both viscous and inertial effects are important. Nonetheless, many oceanic species can successfully migrate across temperature changes in the order of $20{}^{\circ }\mathrm{C}$, corresponding to $40\%$ differences in viscosity, via metachronal propulsion, suggesting that this propulsion mechanism is resilient to drastic changes in water column properties. We investigate marsh grass shrimp (Palaemon vulgaris) as a model organism to explore the combined physical and physiological effects on their locomotion at natural seasonal temperature extremes ($6^{\circ }\text{–}20{}^{\circ }\mathrm{C}$). Experimentally, we manipulate temperature and viscosity independently to isolate physical and physiological effects. We then use the shrimp morphology and gait data to inform a computational fluid dynamics parametric study to estimate the force-to-power ratios of varying viscosity and beat frequencies through naturally occurring extremes. Our research demonstrates that shrimp do not modify their gait parameters to naturally occurring viscosity changes, and their swimming performance is impacted by less than $9\%$. The robustness of the metachronal gait is evidence of the ecological success of shrimp-like organisms in all climates, from the tropics to pole waters and inland freshwater.

We investigate the settling hydrodynamics of a sphere confined along the centerline of a square tube filled with active nematic fluid. The sphere is restricted from rotation and subjected to either planar or homeotropic anchoring conditions on its surface. Our study focuses on the regime where direct active forces exerted on the sphere are much weaker than the hydrodynamic or chemical forces. We find that activity can still significantly alter the settling velocity by modifying the flow structure and nematic field. We first examine the fundamental settling behavior in the absence of activity, where the sphere's velocity varies nonmonotonically with the elastic constant ($K$) but increases with the collective rotational diffusion constant (Г). Introducing activity by activity number (${\tilde{K}}^{-1/2}$) while fixing $K=0.05$, $\mathrm{\Gamma }=0.5$, and Galileo number $\left(\text{Ga}\right)=5.0$, we observe that the axisymmetric flow structure emerges at low ${\tilde{K}}^{-1/2}$, where the extensile activity squeezes the vortex and enhances settling, whereas the contractile activity expands the vortex and suppresses settling. In addition, active nematics can alter the “effective viscosity” of the local flow, which in turn affects the settling velocity. As activity increases, we found that transitions between distinct flow patterns also play a critical role in altering the settling velocity. Specifically, the flow with nonzero helicity emerges at moderate activity in extensile fluids and leads to an abrupt reduction in the sphere's settling velocity. This reduction is related to the transition in the flow pattern and a corresponding shift in the deformation of the nematic field from bend to twist. The effect is particularly pronounced with homeotropic anchoring owing to the stronger helicity of the flow.

The evaluation of added mass holds practical significance in various engineering applications dealing with flow-induced vibration and fluid-structure interaction problems. A notable situation arises when bodies oscillate in an unsteady flow, leading to a coupling mass that deviates from the conventional added mass used for assessing inertial forces on a body oscillating in a steady fluid. In this paper, we revisit a comprehensive theoretical approach initially proposed by Batchelor in 1967 for quantifying the inertial force acting on a body in an accelerating fluid. To enhance this approach, we incorporate an exact and straightforward superposition of the acceleration fields along with numerical evaluation based on the kinetic energy of potential flow. Our refined approach encompasses a wide range of body shapes, ranging from simple two-dimensional primitive shapes to intricate three-dimensional bluff bodies. The paper presents a simplified concept to clarify the relationship between added mass for an accelerating body in a stationary fluid and the acceleration coefficient of a motionless object in an unsteady flow. This method benefits fluid-structure interaction studies, including seismic design, underwater systems, and multiphase flow modeling.

This paper presents a theoretical investigation of lock-released gravity currents propagating in the inertia-buoyancy regime through channels with diverse cross-sectional shapes, incorporating the effects of entrainment and drag. The study develops a generalized model based on shallow-water equations that accounts for the effects of entrainment and drag in channels with various cross-sectional shapes, extending previous models that primarily focused on rectangular channels. The finite-difference solution of the governing equations, using realistic initial and boundary conditions, effectively predicts the evolution of current height, velocity, and concentration over time. The results indicate that entrainment and drag significantly reduce current propagation speed while increasing its height and volume, particularly in channels with nonrectangular geometries. Furthermore, a high drag-to-entrainment ratio notably decreases current speed and distance of propagation, affecting the concentration profile near the current's nose, while keeping it stable at the tail.