Spatially nonuniform structural properties in aquatic animals, together with their active stiffness-modulation behavior, have inspired bioinspired designs that can now be emulated using smart materials capable of dynamic stiffness changes. This study numerically investigates the propulsion performance of a self-propelled swimmer in which variable stiffness is achieved through spatially nonuniform modulus distributions, dynamically varying patterns, or a combination of both. Three spatial modulus distributions are examined, namely uniform, growing (S↑), and declining (S↓). Three dynamic modulus variation modes are also considered, namely constant, increasing with activation intensity (D↑), and decreasing with activation intensity (D↓). The results show that spatial variation mainly affects external performance. The S↑ mode enhances the fluid moment at the tail, leading to the highest cruising speed and power consumption but the lowest efficiency, while the S↓ mode exhibits the opposite trend. Comparisons of bending energy reliably predict the relative swimming speeds among different modes. Dynamic variation primarily influences the internal actuation requirements by altering the cycle-averaged equivalent stiffness. Under the D↓ mode, this reduction in effective stiffness lowers the intensity of the active bending-moment input and suppresses head deformation. Moreover, when the degree of variation is large, the D↑ mode can achieve a higher swimming speed without sacrificing efficiency. Combining spatial and dynamic variation affects both external and internal performance, with the S↓ plus D↓ configuration achieving higher efficiency at lower actuation input and the S↑ plus D↑ configuration delivering higher swimming speeds. These findings offer guidance for designing efficient and high-performance bioinspired underwater vehicles.

This study investigates the characteristics of detonation structure and droplet behavior in $n$-heptane spray detonations where droplets experience a thermodynamic critical event. Using a one-dimensional Eulerian-Lagrangian simulation, this investigation seeks to understand the influence of droplet criticality on spray detonation dynamics. When a droplet reaches the critical point, it transitions into a combustible flow, strengthening the detonation by reducing evaporation time and shortening both the induction zone length and post-detonation dispersion distance. The thermophysical critical event is identified when the initial pressure ($p_0$) exceeds 0.5 atm, and the initial droplet diameter ($d_0$) exceeds 1 µm. At $p_0=0.5$ atm, where droplets cannot reach the critical state, a longer time is required to stabilize the detonation. Evaluation of the critical droplet fraction reveals that droplet criticality contributes substantially to detonation in off-stoichiometric mixtures compared to stoichiometric ones. This liquid-to-gas transition at the critical point generates locally high $n$-heptane mass fraction, elevates the heat release rate, and creates a criticality-induced shock (CIS). The CIS causes noticeable fluctuations in the induction zone length and post-detonation dispersion distance, particularly at $d_0=30\mu \mathrm{m}$. A critical droplet diagram is constructed, showing that the droplet thermophysical critical event is observed for $d_0$ ranging from 5 to 100 µm and $p_0$ between 1.0 and 1.5 atm.

Wind farm parameterizations are crucial for quantifying the wind farm atmosphere interaction, where wind turbines are typically modeled as elevated momentum sinks and sources of turbulence kinetic energy (TKE). These quantities must be properly distributed to the mesoscale grid and integrated into the governing equations. Existing parameterizations use a single-column method solely based on the relationship between the coordinates of the rotor center and the mesoscale grid. However, this method fails to account for the effects of different wind turbine positions within the grid, particularly neglecting the contributions of other turbines located in close proximity to grid boundaries. This can easily lead to errors of the spatial distribution of the sink and source, thereby impacting the accuracy of mesoscale flow simulations. To this end, we propose a multicolumn spatial distribution method based on the Gaussian function. This method distributes the sink and source to multiple vertical grid columns based on the grid weights, which are analytically determined by integrating the two-dimensional Gaussian function over the mesoscale grid. We have applied this approach to the classic Fitch model, proposed as the improved Fitch-Gaussian model, and integrated it into the mesoscale Weather Research and Forecasting model. The validation results demonstrate that when turbines are situated near grid boundaries, the proposed method captures the spatial distribution of the sink and source terms more accurately, exhibiting a higher correlation coefficient and a lower normalized root–mean–square error. For turbines located near the grid center, the performance of the proposed method is virtually identical to that of the single–column approach. However, due to the inherent limitations of the Fitch model, the Fitch-Gaussian model still faces challenges in accurately predicting the magnitude and streamwise evolution of the momentum sink, velocity deficit, and added TKE in wind farm wakes. Nevertheless, the Fitch-Gaussian model better captures their overall spatial distribution patterns. Therefore, the proposed Gaussian-based multicolumn spatial distribution method is recommended for future mesoscale wind farm simulations, especially in cases where the influence of the wind turbine rotor spans multiple mesoscale grid columns.

Understanding the rheological properties of the air-water interface is critical for applications across soft matter, biological systems, and microfluidics. In this study, we used dynamic colloidal-probe atomic-force microscopy to investigate the viscoelastic response and interfacial mobility of air-water interfaces in the presence of trace surfactant contaminants. By analyzing frequency-dependent hydrodynamic forces acting on an oscillating microsphere near the interface, we quantify both the viscous drag and elastic restoring forces arising from Marangoni stresses and interfacial deformation. To rationalize these observations, we further develop a disk-bubble analogy, which yields analytical expressions for the interfacial impedance and provides a simple model to connect slip boundary conditions with capillary elasticity. Our experimental observations reveal a pronounced coupling between hydrodynamic stresses and capillary deformation, accurately described by a Kelvin-Voigt rheological model. We demonstrate how minute surfactant contamination significantly reduces hydrodynamic drag and induces a restoring force, immobilizing the interface through Marangoni-driven rigidity, and how the capillarity responds to the hydrodynamic pressure at small gap distances. The findings provide crucial insights into interfacial mechanics, highlighting the delicate interplay between impurity-induced stresses, capillary deformation, and fluid mobility, and paving the way for advanced interfacial characterization methods in microfluidic and biomedical applications.

Turbulent flows laden with small bubbles are ubiquitous in many natural and industrial environments. From the point of view of numerical modeling, to be able to handle a very large number of small bubbles in direct numerical simulations, one traditionally relies on the one-way coupling paradigm. There, bubbles are passively advected and are noninteracting, implicitly assuming dilute conditions. Here, we study bubbles that are four-way coupled, where both the feedback on the fluid and excluded-volume interactions between bubbles are taken into account. We find that, while the back reaction from the bubble phase onto the fluid phase remains energetically small under most circumstances, the excluded-volume interactions between bubbles can have a significant influence on the Lagrangian statistics of the bubble dynamics. We show that as the volume fraction of bubbles increases, the preferential concentration of bubbles in filamentary high-vorticity regions decreases as these strong vortical structures get filled up; this happens at a volume fraction of around one percent for ${\text{Re}}_{\lambda }=\mathcal{O}\left({10}^2\right)$. We furthermore study the influence on the Lagrangian velocity-structure function as well as pair dispersion, and find that, while the mean dispersive behavior remains close to that obtained from one-way coupling simulations, some evident signatures of bubble collisions can be retrieved from the structure functions and the distribution of the dispersion, even at very small volume fractions. This work not only teaches us about the circumstances under which four-way coupling becomes important, but also opens up new directions towards probing and ultimately manipulating coherent vortical structures in small-scale turbulence using bubbles.

We report a stress-focusing phenomenology occurring in shear-thickening suspensions. Dragging a rod in a two-dimensional layer of suspension with a high force triggers jamming rays, i.e., narrow intermittent jammed strips, which propagate stress anisotropically over long distances and set the drag on the rod. These jamming rays share similarities with previously reported jamming fronts, however, some of their key features, such as their strongly anisotropic propagation, trigger force, and characteristic width, challenge the current knowledge on shear-thickening suspensions.

We investigated the Rayleigh-Plateau instability at the interface between two immiscible liquids of equal viscosity using molecular dynamics simulations. Two types of initial conditions were considered, one with an imposed single-mode perturbation at the interface and the other without any imposed perturbation. Under the single-mode perturbation, the growth rate deviated from the theoretical prediction for small cylinder radii, but progressively approached and agreed with classical macroscopic theory as the radius increased. In contrast, for the unperturbed initial condition, we found a systematic relationship between the breakup time and the minimum radius, in which the power-law exponent increased with increasing radius. These results demonstrate that, even in extremely microscopic systems with cylinder radii on the order of only about fifteen atomic diameters, the growth of the instability can follow macroscopic theoretical predictions when appropriate conditions are imposed, and that the influence of thermal fluctuations on the breakup dynamics becomes increasingly significant as the system radius decreases.

The mean radial component of relative velocity (MRV) between pairs of inertial particles is studied, where the particles are advected by turbulent flow and undergo collision and coalescence. The direct numerical simulation (DNS) is conducted to illustrate the relationship between the DNS-produced MRV and particle or turbulent parameters. The results show that for particles with near-zero Stokes numbers (St), the MRV is roughly independent of St. The MRV for particles of this St range is mainly related to the characteristics of local velocity difference of turbulent flow at particle diameter scale. This conclusion holds for small St particles $(\text{St}<0.1)$ in turbulent flow with different Reynolds number. At larger St, the magnitude of MRV increases with St, and this change is most pronounced when $\text{St}>0.2$. Using the fact that the turbulent velocity difference increases with length scale and assuming that the relative velocities of the colliding particle pairs are derived from fluid velocity differences associated with a nominal resonant length scale, we propose an empirical relation between this resonant scale and Stokes number such that the resonant scale has the form $d+\alpha {\text{St}}^{\beta }$, and we found by curve fitting that $\beta \approx 1.86$. By studying the MRV under different Reynolds numbers $({\text{Re}}_{\lambda }=84,124,189)$, we find that for particles with $\text{St}>0.1$, ${\text{Re}}_{\lambda }$ dependence is observed such that the coefficients $\alpha$ and $\beta$ decrease with ${\text{Re}}_{\lambda }$.

This study investigates the influence of the Kelvin-Helmholtz (KH) instability at the base of a mixed layer on the settling and dispersion of small inertia particles in comparison to their classic Stokes settling in a quiescent environment. We use direct numerical simulations of the flow field coupled with Lagrangian tracking of point particles to examine the settling and trajectories of heavy particles ranging between 20 and $100\mu \mathrm{m}$ in diameter. Particles are initially positioned slightly above the center of the shear layer and inserted into the simulation immediately before the onset of the roll-up of the billow. For this initial positioning of particles, we find that the settling of particles $\ge 40$ $\mu \mathrm{m}$ is slower than their Stokes settling because when trapped within the KH billow, these particles preferentially sample the upward moving regions of the flow. This effect diminishes for particles larger than 80 $\mu \mathrm{m}$ as the particle and flow interactions become less strong due to fast particle settling. Conversely, small particles (20 $\mu \mathrm{m}$) exhibit enhanced settling in the presence of KH billows; their instantaneous vertical velocities are up to seven times faster than Stokes settling because they preferentially sample the downward moving portion of the billow. Particle dispersion induced by the KH flow is strongly influenced by the duration for which particles remain within the mixed layer in relation to the timing of the different phases of the KH flow development and decay. As larger particles leave the mixed layer earlier, their interaction with the KH flow becomes more limited, and this encounter time is also influenced by the initial particle position. The spanwise dispersion of the particles, and the drift of particle trajectories from twodimensional, decreases with increasing particle size. Conversely, the vertical dispersion of the particles is larger for larger particles as their early settling through the two-dimensional growth phase of the KH flow facilitates sampling of more inhomogeneous vertical velocities. This research offers new insights into the interactions between the KH instability and settling Lagrangian particles, highlighting the significant role of the instability in altering sediment transport in sheared, stratified flows for a range of tested conditions. Further investigation is necessary to understand the interaction between shear instabilities and particles over a broader range of parameters.

This study investigates the impact of drag coefficient intermittency near the drag crisis on the vertical motion of a smooth sphere falling freely through quiescent air. Using a stochastic two-state model for the drag coefficient, we show that the temporal evolution of the sphere's velocity becomes intrinsically unpredictable, requiring a statistical description of the coupled friction and gravity forces. Numerical simulations as well as a stochastic model reveal broad distributions, with relative dispersions reaching up to 50% of the mean velocity under certain conditions. These findings suggest that drag crisis intermittency can significantly affect the predictability of falling-body trajectories, with implications for both fundamental fluid dynamics and applied contexts such as ballistics or sports aerodynamics.

Experimental high-speed visualization techniques are evolving rapidly and provide valuable tools for learning about ultrafast bubble dynamics that cause unwanted but also desirable damage, such as cavitation and acoustically driven bubbles and droplets relevant for biomedical applications. This article offers my personal perspective on the quest to illuminate the hidden physics of externally stimulated bubbles that have a remarkable ability to focus energy.

Self-organized branching instabilities in fluids arise from the interplay of rheology, interfacial forcing and boundary constraints. We investigate the morphologies that develop when a liquid is injected into a Hele-Shaw cell filled with a yield-stress fluid, with outflow constrained to a single point sink. A transition in branching morphodynamics emerges: at low injection rates, a single finger dominates breakthrough, whereas at high rates, arborized structures form and reorganize upon reaching the sink. We explain this sudden shift as a function of the fluid's switchlike local response to dynamical stresses and the role of out-of-plane confinement, and show that at the transition, breakthrough occurs with minimal injected fluid. Furthermore, the emergence of different breakthrough morphologies between the source and sink shows a trade off between speed and accuracy in these arborization patterns. Overall, our study highlights how the interplay between local material response and global constraints determines branching morphodynamics.

The dynamics of a spherical particle undergoing Quincke electrorotation in the vicinity of a planar electrode are investigated. Using a multipole representation of the electric field, the influence of the electrode is incorporated through the method of images. Starting from the Taylor–Melcher leaky dielectric model and enforcing conservation of linear and angular momentum, we derive the evolution equations for the electric multipole moments and the particle trajectory. As the first step, a simplified scenario that neglects motion normal to the electrode is considered. Linear stability analysis of this reduced model reveals that the presence of the nearby boundary raises the threshold for Quincke electrorotation and the onset of chaotic dynamics. Numerical simulations of the simplified setting reveal that increasing the electric field induces a transition from steady rolling to periodic and then chaotic oscillations, with the onset threshold depending on the particle–surface gap and particle inertia. Full simulations that also allow normal motion of the particle show that electrostatic attraction reduces the gap, which in turn suppresses chaotic behavior and reestablishes a steady rolling state.

We analyze the stability of the tip streaming coflow configuration, in which a conical liquid meniscus emits a thin liquid thread due to the viscous force exerted by an outer stream. The experiments and global stability analysis show that the emitted jet always destabilizes before the tapering conical meniscus becomes unstable. This implies that the parameter conditions at which polydisperse microdripping arises cannot be determined from the linear stability analysis of the steady jetting mode. Transient simulations show that the linear superposition of decaying eigenmodes triggered by an initial perturbation can lead to the jet breakup. The breakup process significantly depends on the initial perturbation. These results question the validity of the (asymptotic) linear stability analysis as applied to the coflowing and other similar configurations.

Simulating massively separated turbulent flows over bodies is one of the major applications for large-eddy simulation (LES). In the current work, we propose a machine-learning-based LES framework for the rapid simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator (HUFNO) framework. The newly proposed HUFNO model integrates the strengths of both the convolutional neural network (CNN) and Fourier neural operator (FNO) in a way that the FNO is applied in the periodic directions of the flow field, while the nonperiodicity is handled by the CNN-based U-Net framework. In the numerical tests, compared to the original FNO and the U-Net framework, the HUFNO model shows a higher accuracy in the predictions of the velocity field and Reynolds stresses. Further numerical experiments in the LES show that the HUFNO framework outperforms the traditional Smagorinsky (SMAG) model and the wall-adapted local eddy-viscosity (WALE) model in the predictions of the turbulence statistics, the energy spectrum, the invariant characteristics of velocity gradients, the wall stresses, and the flow separation structures, with much lower computational cost. Importantly, the accuracy and efficiency are transferable to unseen initial conditions, Reynolds number, and hill shapes, underscoring its great potential for the fast prediction of strongly separated turbulent flows over curved boundaries.

A fundamental question in the physics of droplet–fiber interactions is: What is the maximum droplet volume a fiber can retain? While this problem has been studied for horizontal fibers and at the apex $\mathrm{\Lambda }$-shaped bent fibers, it remains less explored for V-shaped bent fibers, despite their demonstrated advantages in engineering applications such as fog harvesting. This work investigates the capability of V-shaped fibers with opening angle $\alpha$ in retaining droplets against gravity. An analytical model to predict the maximum droplet volume on V-shaped fibers is developed based on free energy analysis, and validated against experimental data from five liquid–fiber pairs. We found that the dependence of the maximum droplet volume on $\alpha$ can be reasonably captured by the function $cos\beta /cos(\beta -\alpha /2)$, where $\beta$ denotes the droplet's off-axis angle. As $\alpha$ increases from $0^{\circ }$ to ${180}^{\circ }$, the maximum droplet volume slightly decreases before entering a broad transition region around $\alpha \approx {40}^{\circ }\text{–}{100}^{\circ }$, and then increases at larger $\alpha$. In this transition region, droplets detachment is facilitated, resulting in reduced liquid hold-up and clogging, which are critical to the performance of condensers and fog-harvesting systems.

When polydisperse granular systems are sheared, the transverse dynamics is characterized by the interplay of size segregation and diffusion. Segregation in nonuniform and confined shearing flows is studied using annular shear cell experiments complemented with discrete numerical simulations of bidisperse, inelastic, and frictional spheres under gravity. We explored the role of shear localization, granular temperature, boundaries, and mixture properties in the evolution of the segregation rate and the maximum degree of segregation achieved by a bidisperse granular system in the steady state. A faster segregation process and a more developed degree of segregation is observed for bidisperse mixtures with a larger size ratio and a higher proportion of large particles. Normally, in the presence of gravity, size segregation induces large particles to rise and small particles to sink. However, two additional complex segregation patterns were found: inverse segregation and horizontal segregation. The first might be related to the kinematics of the flow, while the second is a geometrical effect. This additional segregation mechanism, in addition to diffusion fluxes and high confining pressure, hampers complete segregation in the steady state, where some degree of mixing always persists.

Microscale cilia play a vital role in mucociliary clearance (MCC) in the human respiratory airways. In this numerical study, we examine fluid transport driven by the active beating of a single filament immersed in a three-dimensional two-phase flow. The cilium is modeled as an elastic filament actuated by a time-varying basal angle. The two-phase flow is resolved using the Shan-Chen model in a lattice Boltzmann solver, while the two-way coupling between the filament and the fluid is treated by the immersed boundary method. Pathological conditions such as cystic fibrosis and chronic obstructive pulmonary disease are associated with drastic alterations of MCC properties, including changes in periciliary layer (PCL) thickness and the viscosity ratio between the PCL and the mucus layer. Here, we systematically investigate the effects of these parameters along with filament bending stiffness on the beating pattern and fluid transport. Within the parameter ranges investigated, a moderate PCL thickness and viscosity ratio, together with high bending stiffness, tend to yield higher net flow rate and transport efficiency. The underlying hydrodynamic mechanisms are characterized through analyses of the beating pattern, filament dynamics, energy partition, and flow-field evolution. Two competing mechanisms are identified: the drag-elastic force balance and the viscous diffusion of momentum. Furthermore, quantitative relationships are established between flow rate and beating pattern, expressed in terms of tip amplitude and beating asymmetry.

A stratified and rotating, ideal (i.e., inviscid and nondiffusive) fluid, contained in a box subject to meridional differential heating (“forcing”), is described by two state vectors. These represent (1) the three-dimensional center-of-mass (COM) location relative to the basin center and (2) the nonlinearly coupled basin-averaged angular momentum vector, associated with overturning circulations in zonal, meridional, and horizontal directions. Without wind, horizontal circulation (associated with the vertical component of the basin-averaged angular momentum) is absent. The COM displacements can be likened to the motion of a "fluid pendulum." In addition to the two angles characterizing the motion of a spherical pendulum relative to the vertical and zonal directions, a stratified fluid's "pendulum length"—proportional to the fluid's stratification strength—is changing dynamically too. In this ideal fluid setting, in the absence of forcing or rotation, the remaining equations, though nonlinear, are integrable, and circulation and COM motion are periodic. When rotation and forcing (i.e., differential heating in the meridional plane) are both present, assuming the rotation axis to be antiparallel to gravity, direct integration of the governing equations reveals that the dynamics is inconclusive: both periodic and aperiodic state trajectories are observed. This is attributed to the fact that the resulting two-degrees-of-freedom Hamiltonian system is subject to the Kolmogorov-Arnold-Moser (KAM) theorem. The latter predicts that some of the periodic orbits that occur without rotation or forcing are replaced by chaotic orbits. As this Hamiltonian system, including gyroscopic terms, can be rewritten as a forced, complex Duffing equation, these results demonstrate the presence of Hamiltonian chaos in this type of Duffing equation.