Low Reynolds number flight frequently involves aggressive maneuvers or rotating wings at a high angle of attack. In these conditions a leading-edge vortex (LEV) forms, augmenting the force produced by the wing. To better understand how the LEV grows during its initial formation and to be able to compare across different conditions, it is important to have a normalization method that is grounded in the governing equations for vorticity. The result of an integral analysis of the vorticity equation for a general unsteady motion is a linear relationship between normalized circulation, $\frac{\mathrm{\Gamma }}{u\left(t\right)c}$, and the number of chord lengths traveled. To determine the validity of this analysis, planar particle image velocimetry measurements of the flow on three different wing motions were analyzed. Surging wing data from prior work, an impulsively started rotating wing, and a pitching wing were the three cases used in this study. For all of these cases, the relationship derived in the integral analysis accurately described how the normalized circulation grows with the number of chords traveled for a period from 0.01 to at least 1.6 chords traveled, with a modification to the distance traveled normalization for pitching wings to include the effect of angle of attack.

Recently, new models of the boundary condition for the Boltzmann equation were proposed on the basis of a kinetic model of gas-surface interactions [K. Aoki et al., Phys. Rev. E 106, 035306 (2022)]. In the present paper, the kernel representations of the models are given, and the models are applied to some basic problems of a rarefied gas between two parallel plates. To be more specific, the heat transfer between the plates with different temperatures, plane Couette flow, and plane Poiseuille flow driven by an external force are numerically investigated by using the Bhatnagar-Gross-Krook model of the Boltzmann equation and the new models of the boundary condition. The results are compared with those based on the conventional Maxwell-type boundary condition. It is shown that when the interaction of gas and solid molecules is strong, the results based on the new models tend to approach those based on the diffuse reflection. However, when the interaction is not strong, the former results deviate from those based on the Maxwell-type condition with a constant accommodation coefficient.

The identification of cells and particles based on their transport properties in microfluidic devices is crucial for numerous applications in biology and medicine. Neutrally buoyant particles transported in microfluidic channels migrate laterally toward stable locations due to inertial effects. However, the effect of the particle and flow properties on these focusing positions remain largely unknown. We conduct large scale simulations with dissipative particle dynamics, demonstrating that freely moving particles exhibit significant differences in their focusing patterns from particles that are prevented from rotation. In circular pipes, we observe drastic changes in rotating versus nonrotating focusing positions. We demonstrate that rotation-induced lateral lift force is significant, unlike previously believed, and is linearly dependent on the rotation magnitude. A simple phenomenological explanation extending existing theories is presented, that agrees well with our numerical findings. In square ducts, we report four face-centered stable positions for rotating particles, in accordance with experimental studies on a range of Reynolds numbers $50\le \text{Re}\le 200$. However, nonrotating particles stay scattered on a concentric one-dimensional annulus, revealing qualitatively different behavior with respect to the free ones. Our findings suggest new designs for microparticle and cell sorting in inertia-based microfluidics devices.

The levitating Leidenfrost (LF) state of a droplet on a heated substrate is often accompanied by fascinating behaviors such as star-shaped deformations, self-propulsion, bouncing, and trampolining. Here, we report on the intermittent trampolining events at specific drop sizes over the entire lifespan of an evaporating LF droplet. Between the trampolining events, the droplet exhibits decreased amplitude bouncing or quiescent hovering. We show that the reemergence of trampolining behavior of the droplet at specific radii is triggered by parametric resonance between the intervening vapor layer oscillation and the droplet, where the oscillations in the droplet subharmonically excite increased amplitude oscillations in the vapor. The trampolining events are observed when the ratio of the natural frequency of the vapor layer and Rayleigh frequency corresponds to the instability zones on the corresponding Mathieu's chart. This model even explains the observation of trampolining from a quiescent hovering state of the droplet. The proposed mechanism of resonance-driven trampolining of LF droplets is observed to be applicable for different liquids irrespective of the initial volume and substrate temperatures, thus indicating a universality of the behavior.

With the increasing demand for thermal management in electronic devices, microscale film transportation has become a research focus in recent years. This study numerically investigates the working mechanism of two-phase micro-electrohydrodynamic (EHD) conduction pumping. Simulations were performed with the open-source platform OpenFOAM based on the finite volume method. The volume of fluid method was utilized to track the air-liquid interface. A two-dimensional flush electrode configuration with a typical size of $240\mu \mathrm{m}$ was considered. Results show that the flow system is controlled by three charge structures. The heterocharge layer generates the main driving force in the liquid bulk, and its transportation ability is limited by the film thickness. The interface charge layer can induce an additional electric force on the film's top surface, resulting in flow strength enhancement and interface deformation. The electric double layer (EDL) can enhance the asymmetry of the overall electric field and electric force distribution, thus improving or suppressing the pump flow rate depending on the zeta potential polarity. In addition, the effects of the interface charge and the EDL are weakened with an increase in film thickness. Insights provided by the present study will be helpful to researchers in designing an EHD-based two-phase heat transfer system.

We present a low-dimensional model that explains the coupled dynamics of floating boundaries that interact with turbulent flows in thermal convection. The model consists of Langevin-type, stochastic differential equations, which captures the deterministic and stochastic movements of boundaries shown in an earlier experiment J.-Q. Zhong et al. [Phys. Rev. E 75, 055301(R) (2007)]. From the displacement, speed, and acceleration of the boundaries, we construct the force potentials that underlie two distinct boundary-size-dependent behaviors. Namely, we find a repulsive potential (when the boundary is small) that leads to an oscillatory state and an attractive potential (when the boundary is large) that leads to a trapped state. The boundary movements, which are subject to thermal convection underneath, also inform us of the mean speed and turbulent fluctuations of the flows.

Breath figures are the complex patterns that form when water vapor condenses into liquid droplets on a surface. The primary question concerning breath figures is how the condensing vapor is allocated between the growth of existing droplets and the nucleation of new ones. Although numerous theoretical studies have concentrated on scenarios resulting in highly polydisperse droplet ensembles, a companion paper [Bouillant et al., Phys. Rev. Lett. 134, 188204 (2025)] demonstrates that nearly monodisperse patterns can be achieved on defect-free substrates in a diffusion-controlled regime. The objective of this work is to present a theoretical framework that elucidates the formation and evolution of nearly monodisperse patterns in breath figures. We discover that, following a short nucleation phase, the number of droplets remains constant over an extensive range of timescales due to collective effects mediated by the diffusion of vapor. The spatial extent of these diffusive interactions is identified through asymptotic matching, based on which we provide an accurate description of breath figures through a mean-field model. The model accounts for the subdiffusive growth of droplets as well as for the arrest of nucleating new droplets, and reveals the scaling laws for the droplet density observed in experiments. Finally, droplets expand and ultimately coalesce, which is shown to trigger a scale-free coarsening of the breath figures.

In recent experiments [M. Ceccaldi et al., Phys. Rev. Fluids 8, 024302 (2023); Phys. Rev. Fluids 9, 074003 (2024)], it was shown that the permeability of foam-filled granular packings is strongly influenced by the ratio of bubble size to grain size. This effect appears to be primarily driven by geometric factors and is independent of interfacial mobility. It was suggested that the liquid from the foam introduced into a granular medium redistributes toward the grain surfaces and the contact points between grains, contributing to the drying of the foam and significantly reducing its hydraulic permeability. To investigate this phenomenon in detail, we developed a numerical model of foam within a granular medium, which describes the liquid distribution within the pores and allows to calculate the liquid permeability. This model offers improved predictions of liquid redistribution compared to existing analytical models and closely matches permeability measurements. Moreover, our results quantify the contributions to permeability of all liquid components formed within the pores, particularly bulk and wall foam liquid channels.

Two-dimensional (2D) turbulence, despite being an idealization of real flows, is of fundamental interest as a model of the spontaneous emergence of order from chaotic flows. The emergence of order often displays critical behavior with the involvement of a broad range of spatial and temporal scales. Here, we experimentally study turbulence in periodically driven nanofluidic channels with a high aspect ratio using superfluid helium. We find a multistable transition behavior resulting from cascading bifurcations of large-scale vorticity and critical behavior at the transition to quasi-2D turbulence consistent with phase transitions in periodically driven many-body systems. We demonstrate that quasi-2D turbulent systems can undergo an abrupt change in response to a small change in a control parameter, consistent with predictions for large-scale atmospheric or oceanic flows.

The influence of the Soret effect and a uniform magnetic field on the dynamic behavior of vertical convection are investigated using a high-accuracy numerical method. The effects of the Soret number ($\text{Sr}$, which quantifies the direction and magnitude of species migration relative to the temperature gradient; positive $\text{Sr}$ denotes migration toward hotter regions, negative toward cooler regions) on flow, heat and mass transfer, and flow transition in the presence of a magnetic field are analyzed. The results reveal that, for a given magnetic field strength, positive and negative Soret effects have significantly different influences on heat and mass transfer as well as on flow structure. For a high Rayleigh number ($\text{Ra}$, vigor of the buoyancy) and a small magnetic field, the heat transfer initially decreases and then increases with increasing Soret number, while the mass transfer consistently decreases. In cases where temperature is dominant, heat transfer for $\text{Sr}=-1$ exceeds that for $\text{Sr}=0$ by $24\%$, while mass transfer with $\text{Sr}=-1$ exceeds that for $\text{Sr}=0$ by $85\%$. When concentration is dominant, heat transfer reaches a minimum at $\text{Sr}=0$, whereas mass transfer peaks at $\text{Sr}=-1$, corresponding to an approximate $71\%$ increase over heat transfer at $\text{Sr}=0$, and around a $210\%$ increase in mass transfer. Additionally, the flow exhibits greater complexity when the Soret number is negative than when it is positive. When the magnetic field is weak, the temperature-dominated flow changes from chaotic to periodic with increasing Soret number and eventually returns to a chaotic state. When the magnetic field is strong, the flow transitions from chaotic to periodic and finally to a steady state. The transition route involves two types of periodic flow: a simple periodic flow with an integer multiple of the fundamental frequency, and a complex periodic flow with multiple lower-frequency subharmonic waves. Furthermore, as the strength of the magnetic field increases, the flow in the rectangular enclosure is gradually inhibited, leading to a reduction in the influence of the Soret number on the flow structure and on heat and mass transfer.

This study examines transient spray cooling of a heated substrate under a single nozzle, a situation commonly encountered in spray cooling or quenching applications. The temperature range is such that the cooling process goes through the three cooling regimes in time—film boiling, transitional boiling, and nucleate boiling. The heat transfer associated with each drop impact is computed using validated theoretical expressions for each of the boiling regimes. These theoretical expressions and limits for delineating the three boiling regimes are taken from literature. The principle of superposition is then applied, using the local number flux of impacts on the surface, to compute the rate of heat transfer from the substrate. The simulation is performed over time as a full conjugate heat transfer problem, with the temperature decrease in the substrate being computed using a finite difference method. This predictive approach is validated using existing experimental results and then used to investigate the influence of various spray parameters on the cooling performance of a flat plate.

The linear stability of an elongated axisymmetric gas bubble transported by a liquid in a capillary tube is analyzed through the use of numerical simulations. The study focuses on the influence of inertia, characterized by the Reynolds number ($\mathrm{Re}$) and the imposed flow rate, characterized by a capillary number (${\mathrm{Ca}}_{\mathrm{l}}$), on the stability of the bubble tail, which exhibits ripples at high Re. The numerical approach utilizes a boundary-fitted method in a reference frame anchored to the bubble, combined with a mixed spatial discretization based on spectral collocation in the radial direction and finite differences in the axial direction. This framework enables the computation of steady nonlinear solutions through a Newton iteration scheme and facilitates the linear stability analysis of these solutions. Direct numerical simulations using the volume of fluid method in OpenFOAM are also performed to corroborate the results of the stability analysis. We perform systematic simulations for ${\mathrm{Ca}}_{\mathrm{l}}=0.005-0.04$ and observe that the system becomes unstable, with the emergence of oscillations at the rear of the bubble, when the Reynolds number grows above a critical value, designated as ${\mathrm{Re}}^{*}$; this critical value is dependent on the capillary number. The instability is due to the increased inertia of the recirculating flow in the liquid behind the bubble, which impinges its rear meniscus. A modified Weber number ${\mathrm{We}}_{\mathrm{p}}$, based on the relative velocity between the external flow and the bubble, is introduced to describe the competition between the destabilizing pressure force acting on the bubble rear and surface tension. Our results show that the bubble dynamics become unstable for a critical value, ${\mathrm{We}}_{\mathrm{p}}^{*}\approx 3.65$, which remains quite uniform across the range of capillary numbers tested, and divides the ${\mathrm{Ca}}_{\mathrm{l}}-\mathrm{Re}$ diagram into stable and unstable regimes. Our findings offer insights into the behavior of bubbles in microfluidic applications, with implications for heat transfer, mass transfer, and cleaning processes in microchannels.

In Hele-Shaw cells, pressure-driven viscous fluid motion between two closely-spaced plates gives rise to a two-dimensional potential flow with zero circulation. Here, we show how the introduction of electromagnetic effects enables the realization of potential flows with circulation. We present canonical Hele-Shaw experiments with circulation prescribed by the electromagnetic configuration, and rationalize the observed flows theoretically. We also draw an analogy between this new class of circulatory potential flows and a class of electrostatic systems.

The numerical modeling of ultrathin platelike particles in viscous flow is challenging because it requires an accurate representation of the particles' ultrathin edge. However, in many flow conditions, the effect of the edges on the flow and rheology is negligible. This paper presents a slender body theory for active or passive platelike particles in two-dimensional viscous flow. The theory simplifies the treatment of the particle geometry for the fluid-structure interaction, particularly by excluding the edge effects. The slender body theory is derived from the boundary integral formulation of the incompressible Stokes equations, which recasts the equations as an integral equation over the boundary of the particle's cross-section. By expanding the integral equation to leading order via a matched asymptotic expansion in the particle slenderness, a simplified nonlocal line integral across the central line of the particle is obtained. This integral relates the flow velocity and the hydrodynamic traction and does not depend on nontrivial edge effects. The results are validated for passive and active cases of ultrathin two-dimensional particles for which analytical results are known. The validations confirm the capability of the two-dimensional slender body theory to accurately describe the flow and rheology of passive and active ultrathin platelike particles under many flow conditions.

A structural uncertainty validation study for a large-scale, fire-engulfed, elevated object subjected to crosswind is presented to establish the credibility of a high-fidelity, low-Mach, turbulent reacting flow wall-modeled large-eddy simulation (WMLES) approach that includes multiphysics coupling to participating media radiation and conjugate heat transfer. To establish that WMLES can accurately predict surface quantities including drag and pressure coefficient in the low-Mach crosswind regime, a foundational elevated isothermal cylinder validation case is presented at a similar gap-to-diameter ratio of 0.25, spanning the subcritical to supercritical drag regime (${\text{Re}}_D=1.1\times {10}^5$ and $4.3\times {10}^5$, respectively). This study exercised both static and dynamic coefficient LES (Smagorinsky and $k_{\mathrm{sgs}}$) with both local and exchange-based velocity sampling. Results showcase that the drag crisis (or the sudden drop in drag coefficient at increased ${\text{Re}}_D$) is well captured when using an exchange-based dynamic coefficient WMLES methodology, while noting lack of mesh convergence and overall drag and pressure coefficient predictively when using a static coefficient, local velocity sampling WMLES. For the $\mathcal{O}\left(10\right)$ m JP-8 liquid pool fire crosswind validation study presented, two experimental crosswind configurations (2 m/s and 9.5 m/s) are showcased for a fire-engulfed mock fuselage roughly 4 m in diameter. Using the best model-form practices identified in the isothermal study, dynamic coefficient $k_{\mathrm{sgs}}$ exchange-based WMLES fire validation findings demonstrate accurate peak irradiation and skin temperature predictions as a function of crosswind magnitude. Excessive yaw in the low-crosswind fuselage configuration, consistent with experimental findings, captured a significant predicted asymmetry in flame attachment and heat flux toward the downwind cylindrical cap—indicative of axial vortex structures transporting the flame along the upper and lower fuselage leeward surface. All fire mesh resolution simulations captured the experimental finding that as crosswind increased, predicted flame shape and peak irradiation magnitude onto the fuselage transitioned from a windward to a leeward cylinder location due to the migration of the upper- to lower-shear fuel/air mixing layer thereby demonstrating the novelty, significance, and credibility of this high-fidelity WMLES reacting flow framework.

Large-eddy simulations of a utility-scale offshore wind farm were performed to study the effect of sea-surface boundary conditions on high-fidelity simulation results of turbine performance and wake recovery. The actuator line and surface models were used to model the turbine blades and nacelle, respectively. Two series of simulations were performed using wave-phase-aware and wave-phase-averaged approaches. Both simulations were compared against field LiDAR and supervisory control and data acquisition (SCADA) measurements. In the wave-phase-aware approach, the kinematics of the ocean waves were obtained using a high-order spectral method and imposed as sea-surface boundary conditions of the large-eddy simulation. This coupling was done by imposing shear stress over the bottom boundary based on wave motion and flow velocity. The wave-phase-averaged approach utilizes the log-law of the wall for sea-surface parametrization, which assumes a uniform roughness across the domain. Comparisons between the large-eddy simulations of the two approaches revealed that the wave-phase-aware model resulted in faster wake recovery compared to the wave-phase-averaged approach. Analysis of the mean kinetic energy flux indicated that the wave-phase-aware model had a flux mean-flow kinetic energy due to convection from the free flow above the wake. Furthermore, comparisons of the results of the two approaches with SCADA measurements demonstrated that the wave-phase-aware model provided greater precision in power production, with a relative error ranging from $3\%$ to $10\%$. In contrast, the wave-phase-averaged approach exhibited a higher error, between $10\%$ and $20\%,$ attributed to the larger wind shear at the rotor.

Wildfires pose an increasing threat, with spotting being a key mechanism of their spread. In this process, small pieces of burning material, known as firebrands, can travel long distances and start new fires ahead of the fire front. However, modeling and predicting the behavior of firebrands in the complex flows that typify large wildfires remains a significant challenge. To clarify the impact of the flow physics on firebrand transport, we experimentally investigated the transport of model firebrands in a controlled canopy-plume system. We examined four experimental cases, varying the canopy length and plume buoyancy. The distributions of the downstream position at which the particles land have long tails in all the experimental cases, motivating a segmentation of particle population into a population that travels a short distance and one that travels a long distance. We investigate differences in the particle trajectories in these two populations, including their maximum heights and velocities, and we consider the physical parameters that are influential in determining their landing position. We find that particles that land further downstream tend to remain within the plume for longer time periods. We also evaluate the ballistic-trajectory and terminal-velocity assumptions that are often invoked in firebrand transport models under our experimental conditions, and we find that they do not fully capture the observed dynamics in our experimental system. Finally, we run reduced-order stochastic simulations to determine if knowledge of the particle characteristics, mean flow properties, and Reynolds stresses is sufficient to capture the complex dynamics in the experimental data. We find that the simulation results lack the extreme cases of the experimental data (particles that land unusually far or unusually close to the particle release). We attribute this discrepancy to the lack of spatiotemporal coherence in the simulated flow field, and we suggest that spatiotemporal coherence is necessary to accurately model these extreme trajectories.

When time and velocities are dynamically rescaled relative to the instantaneous turnover time, the Sabra shell model acquires another (hidden) form of scaling symmetry. It has been previously shown that this symmetry is statistically restored in the inertial interval of developed turbulence, thereby establishing a self-similarity property derived from first principles and replacing the broken $1/3$-scaling of the K41 theory. Multifractal intermittency follows from the restored hidden symmetry, in which the anomalous scaling exponents ${\zeta }_p$ are identified as Perron-Frobenius eigenvalues. In this paper, we use the hypothesis of restored hidden symmetry to address the multi-time statistics of turbulent fluctuations. The central result is the self-similarity rule stating that any observable that is time-scale homogeneous of degree $p$ is self-similar with the Hölder exponent $h={\zeta }_p/p$. As a particular case, it yields the scaling laws for decorrelation times of fluctuations obtained previously within the phenomenological multifractal approach. As further applications, we formulate self-similarity rules for multi-time structure functions and multi-time Kolmogorov multipliers and verify them numerically.

Eddy-resolving turbulence simulations require stochastic inflow conditions that accurately replicate the complex, multiscale structures of turbulence. Traditional recycling-based methods rely on computationally expensive precursor simulations while existing synthetic inflow generators often fail to reproduce realistic coherent structures of turbulence. Recent advances in deep learning (DL) have opened new possibilities for inflow turbulence generation, yet many DL-based methods rely on deterministic, autoregressive frameworks prone to error accumulation, resulting in poor robustness for long-term predictions. In this work, we present CoNFiLD-inlet, a novel DL-based inflow turbulence generator that integrates diffusion models with a conditional neural field to produce realistic, stochastic inflow turbulence. By parametrizing inflow conditions using Reynolds numbers, CoNFiLD-inlet generalizes effectively across a wide range of Reynolds numbers (${\text{Re}}_{\tau }$ between ${10}^3$ and ${10}^4$) without requiring retraining or parameter tuning. Comprehensive validation through a priori and a posteriori tests in direct numerical simulation and wall-modeled large-eddy simulation demonstrates its high fidelity, robustness, and scalability, positioning it as an efficient and versatile solution for inflow turbulence synthesis.

Steady solutions of two-dimensional Rayleigh-Bénard convection between Navier-slip boundary (partial-slip) conditions are studied for a Prandtl number $\text{Pr}=1$ and Rayleigh numbers ranging from ${10}^4$ to ${10}^9$, which extends previous research under no-slip and free-slip conditions. This work clarifies one critical range of slip length $l_s\in [0.01,1]$ within which the Nusselt number and Reynolds numbers at a given Rayleigh number exhibit strong sensitivity to the change of $l_s$. In the channel with a fixed aspect ratio $\mathrm{\Gamma }=2$, the power-law scalings of $\text{Nu}\sim {\text{Ra}}^{\beta }$ and $\text{Re}\sim {\text{Ra}}^{\gamma }$ are observed with $\beta \approx 1/4$, $\gamma \approx 1/2$ at $l_s=0$ (no slip) and $\beta \approx 1/3$, $\gamma \approx 2/3$ at $l_s\ge 0.01$ with partial slip. The thermal boundary layer becomes thinner with the increase of $l_s$. The thickness of the viscous boundary layer clearly identifies a transitional slip length $l_s=0.01$ which distinguishes the no-slip and free-slip scenarios. Additionally, it is found that the heat-flux-maximizing aspect ratio increases with the slip length. These results suggest that the slip length can significantly influence heat transport and flow configurations, providing new perspectives for both theoretical studies and practical applications involving microstructural surfaces.