Archetypal falling behaviors of impervious objects are classified into four modes: fluttering, tumbling, steady descent, and chaotic motion. The classical scenario predicts these behaviors to be affected by three dimensionless quantities: thickness-to-width ratio, dimensionless inertia, and Reynolds number. In this article we explore experimentally the effect of permeability and porosity on the falling regimes of porous plates. By drilling several hole distributions in rectangular plates, both permeability and porosity are varied systematically. We discover that the introduction of porosity affects the stability of the falling regimes eliminating tumbling. Using a phenomenological model we show that a decrease in circulation induced by the introduction of holes is the primary mechanism for stabilizing the plates' trajectories.

Contact time of bouncing drops is one of the most essential parameters to quantify the water repellency of surfaces. Generally, the contact time on superhydrophobic surfaces is known to be Weber number independent. Here, we probe an additional characteristic time, transition time, inherent in water drops impacting on superhydrophobic surfaces, marking a switch from a predominantly lateral motion to an axial motion. Systematic experiments and numerical simulations show that the transition time is also Weber number independent and accounts for half the contact time. Additionally, we identify a Weber-independent partition of volume at the maximum spreading state between the rim and the lamella and show that the latter contains 1/4 of the total volume of the drop.

An experimental investigation of the Richtmyer-Meshkov instability is conducted in spherical geometry, where convergence effects are more pronounced and the vorticity distribution is specific to the geometry. The gas lens technique is employed within a conical chamber to generate a spherical converging shock wave. This shock wave triggers the instability at a single-mode $\mathrm{air}/{\mathrm{SF}}_6$ interface for two different initial amplitudes. The displacement and the growth of the perturbations at the interface are monitored using a high-speed Mie-scattering laser tomoscopy method, and the results are compared to numerical simulations and new theoretical predictions. The instability amplitude initially grows, stabilizes, and then reduces before the arrival of the reflected shock wave. Numerical simulations demonstrate good agreement with the experiments, and they indicate a weak effect of the installed grid materializing the perturbation. In addition to the experimental and numerical results, the theoretical model developed here agrees well with the experiments, although a time shift is observed between theory and experiments in the stabilization regime. A comparison to other models available in the literature shows that, in the studied configurations, compressibility has a negligible effect on the development of the instability. Our model demonstrates that convergent Rayleigh-Taylor effects are the main stabilizing mechanisms in these configurations.

In this study, we investigated the dynamics of a droplet impacting and oscillating a polycarbonate cantilever beam of nine varying lengths. We analyzed the cantilever's damping and vibration frequency in relation to a resonance length, where the frequencies of the droplet and the cantilever are equal. In shorter beam lengths, the beam vibrates at a frequency higher than that of the droplet. Upon reaching the resonance length, the frequencies of both the droplet and the cantilever align, and the cantilever is out of phase with the oscillation of the droplet's apex. This leads to increased damping rates. At this resonance length, the droplet's force and the direction of the cantilever oppose each other. When the cantilever length exceeds the resonance length, it synchronizes more with the droplet apex. This alignment allows the droplet force and the cantilever to work in phase. Our findings provide fundamental insights into the damping effect of droplet impacts on elastic surfaces around resonance.

The Faraday instability has been extensively studied in bounded containers but only recently has research on this phenomenon in flexible domains been conducted. Here, we study floating liquid droplets with Faraday waves excited on their surface, which undergo a slow time evolution toward a stable noncircular shape. We develop a theoretical model for the evolution of the boundary of the droplet, thus allowing us to simulate its full transient motion toward steady state. By changing the forcing frequency and amplitude of our system, we observe a variety of stable droplet shapes. We experimentally measure the geometrical properties of these droplets and conditions under which different shapes are stable, which match our theoretical predictions well. Interesting transient behavior such as hysteresis is also discussed, where the final droplet shape depends on its previous shape. Finally, we touch upon droplets that do not reach a steady state shape, instead oscillating periodically in time or rotating at a constant angular velocity.

This study aims to evaluate the effect of freestream turbulence (FST) on wakes produced by disks with different porosity. The wakes are exposed to various freestream turbulence “flavors,” where turbulence intensity and integral length scale are independently varied. The turbulent wakes are interrogated through hot-wire anemometry from 3 to 15 diameters downstream of the disks. It is found that disks with low porosity behave similarly to a solid body, in terms of both entrainment behavior and scaling laws for the centerline mean velocity evolution. Far from the disks, the presence of FST reduces both the wake growth rate and entrainment rate, with a clear effect of both turbulence intensity and integral length scale. As porosity increases, these “solid body” FST effects gradually diminish and are reversed above a critical porosity. The entrainment behavior in disk-generated wakes is significantly influenced by the presence of large-scale coherent structures, which act as a shield between the wake and the surrounding flow, thus impeding mixing in the near wake. We found that higher porosity, turbulence intensity, or integral length scale weakens the energy content of these structures, thereby limiting their influence on wake development to a shorter distance downstream of the disk. This, in turn, potentially reduces the influence of large-scale engulfment on the overall entrainment mechanism to a shorter distance downstream of the disks as well. For low-porosity disks, freestream turbulence intensity initially promotes near-wake growth through the suppression of large-scale structures; however, farther downstream, the wakes grow faster when the background is nonturbulent.

To achieve decarbonization targets, wind turbines are growing in hub height and rotor diameter, and they are being deployed in new locations with diverse atmospheric conditions not previously seen, such as offshore. Physics-based analytical wake models commonly used for design and control of wind farms simplify atmospheric boundary layer (ABL) and wake physics to achieve computational efficiency. This is accomplished primarily through a simplified model form that neglects certain flow processes, such as atmospheric stability, and through the parametrization of ABL and wake turbulence through a wake spreading rate. In this study, we systematically analyze the physical mechanisms that govern momentum and turbulence within a wind turbine wake in the stratified ABL. We use large-eddy simulation and analysis of the streamwise momentum deficit and wake-added turbulence kinetic energy (TKE) budgets to study wind turbine wakes under neutral and stable conditions. To parse the turbulence in the wake from the turbulent, incident ABL flow, we decompose the flow into the base ABL flow and the deficit flow produced by the presence of a turbine. We then analyze the decomposed flow field budgets to study the effects of changing stability on the streamwise momentum deficit and wake-added TKE. The results demonstrate that stability changes the relative balance of turbulence and advection for both the streamwise momentum deficit and wake-added TKE primarily through the nonlinear interactions of the base flow with the deficit flow. The stable cases are most affected by increased shear and veer in the base flow and the neutral case is most affected by the increased ambient turbulence intensity. These differences in the base flow that arise from stratification are relatively more important than the buoyancy forcing terms in the wake-added TKE budget. The wake-added TKE depends on the ABL stability. An existing wake-added TKE model that neglects the effects of ABL stability yields $15–25\%$ error compared to large-eddy simulation, with errors that are higher in stable conditions than neutral. These results motivate future research to develop fast-running models of wake-added TKE that account for stability effects.

We investigate the dynamics of pendulum chains immersed in turbulent boundary layers. We combine qualitative video analysis of the artist Ned Kahn's kinetic façades of buildings, and laboratory experiments on a unidimensional weakly coupled chain of pendulums. We performed analysis of both the façades and the laboratory scale model. We show that pendulum waves traveled in the direction of the wind. These waves originate from the excitation by the spatiotemporal pressure fluctuations. We identified two dispersion relation branches. The first branch corresponds to a resonant response of each pendulum at its natural frequency of oscillations. The second branch corresponds to an excitation by the advected pressure fluctuations along the chain. Using local pressure sensors, we show a quantitative agreement between the convection velocity of the pendulum chain waves and the pressure fluctuations. Eventually, we propose a model in Fourier space to describe the magnitude of each branch. We show that at a small wind speed, the pendulum response is dominated by the resonance at their natural frequency. At larger wind speed, the response becomes dominated by the advected pressure fluctuations.

In this study, we conduct numerical investigations into the impact of droplet collisions on solid surfaces, with a specific focus on the influence of wettability and initial diameter. Previous studies have proposed two distinct scaling laws, namely $W{e}^{1/2}$ and $W{e}^{1/4}$, where $We$ denotes the Weber number, to describe the maximum spreading diameter ratio in the capillary regime. Our energy analysis reveals that only the $W{e}^{1/2}$ scaling accurately characterizes the capillary regime. Additionally, we elucidate that the observed data slope of $1/4$ arises from the $W{e}^{1/2}$ scaling while the initial diameter also plays a role within the low-$We$ range. To address this, we introduce a modified Weber number ($W{e}^{*}$), dependent on wettability, defined through energy conservation and accounting for the initial diameter $apriori$. Utilizing the $W{e}^{*}$, we establish a generalized scaling for the maximum spreading diameter ratio, enabling the consolidation of numerical and experimental findings onto a single curve, regardless of wettability. Furthermore, this scaling demonstrates excellent agreement with numerical results for both low and relatively high-$We$ regimes but without splashing.

We experimentally reveal that a sub-millimetric liquid jet can impact a heated substrate without making any contact with the underlying solid. These Leidenfrost jets are surfing on their own vapor layer and are observed under certain conditions related to jet radius, fluid velocity, incident angle and substrate temperature. We focus on the thickness of the vapor layer and on its typical area over which the jet bounces on the substrate. The experimental results are found to be in good agreement with models. We also observe a directed percolationlike transition appearing when the jet enters in contact boiling with the heated substrate.

The steady-state behavior of a single drop under shear flow has been extensively investigated in the limit of small deformation and negligible inertia effects. In this work, we combine the calculations proposed by Flumerfelt [R. W. Flumerfelt, J. Colloid Interface Sci. 76, 330 (1980)] for unconfined drops with interface viscosity, with those by Shapira and Haber [M. Shapira and S. Haber, Int. J. Multiphase Flow 16, 305 (1990)] for confined drops without interface viscosity. By merging these two approaches, we provide comprehensive analytical predictions for steady-state drop deformation and inclination angle across a wide range of physical conditions, from confined to unconfined droplets, including or excluding the effect of interface viscosity. The proposed analytical predictions are also robust concerning variations in the viscosity ratio, making our model general enough to include any of the above conditions.

We present experimental evidence of multiple blood flow configurations in a relatively simple microfluidic network under constant inlet conditions. We provide evidence of multistability and unsteady dynamics and find good agreement with a theoretical one-dimensional advection model for blood flow in microvascular networks that relies on the widely used laws for rheology and phase separation. We discuss the ramifications for microfluidic experiments and measurements using blood and implications for in vivo microcirculation. Our findings suggest that further modeling in microvascular networks should discard the usual assumption of unique, steady-state flow solutions, with crucial consequences regarding gas, nutrient, and waste transport.

The continued development of shallow continental shelf regions with offshore wind farm (OWF) structures raises the question of what potential hydrodynamic impacts may be expected. One such impact is a reduction in the ocean currents that results from the additional frictional drag from the turbine foundation structures. To understand this potential "blocking" effect, we construct a fluid mechanical model consisting of an idealized circular patch of OWF with increased friction. The idealized OWF is then subjected to a steady mean flow superimposed on much stronger elliptical tidal currents—a common scenario in shelf seas with OWF installations. Due to the quadratic dependence of friction on fluid velocity, the elliptical tidal currents result in a linearized friction acting on the mean flow that is no longer parallel to the mean flow. This "anisotropic" friction has the effect of deflecting, in addition to reducing, the mean flow in the region of the OWF. However, it is found that a good approximation to the reduction of flow caused by OWFs can be obtained by the simplest linear, isotropic representation of the friction, i.e., a linear drag law. The flow reduction within the OWFs is found to be primarily dependent on the ratio of the increase in drag coefficient inside the farm to that of the surroundings, with weaker dependencies on the parameters describing the tidal ellipse. The magnitudes of the flow reductions in the idealized model appear to be in approximate agreement with more realistic modeling results, and are expected to capture the basic balance of the mean flow in the blocking of ocean currents by many OWFs in the North Sea, especially with increasing size in future development scenarios.

Electrokinetic transport occurs at the two-liquid interfaces due to its inevitably spontaneous charging induced by imbalanced partition and/or specific adsorption. The diffuse feature of the liquid-liquid interface is essential in interpretation of its electrokinetic behavior and the interplay of the two charging mechanisms is strongly dependent on the interfacial physicochemical properties, which are often ignored in previous studies and may lead to the impractical electrokinetic predictions. We propose a diffuse interface framework which includes a modified Boltzmann formulation, to incorporate the solvent mixing effect and unify the description of both possible charging mechanisms. The permittivity- and viscosity-related solvent mixing effects are stressed when imbalanced ion partition dominates and the viscosity ratio is large. The effects of permittivity-dependent ion partition and organic impurity ions are exhaustively discussed for nonpolar and polar organic liquids. For polar organic liquid with moderate permittivity, the water velocity presents a nonmonotonic dependency on the impurity concentration under different pHs, resulting from the competitive effect of the two charging mechanisms. A semiempirical correction formula for the sharp interface model is proposed to eliminate the modeling deviations, while the viscosity interpolation model is demonstrated to have a great impact on the interpretation of the electroosmotic velocity profile. Our work sheds light on the further studies of the complex electrokinetic multiphase flows with complex geometry, large deformation, contact line dynamics, and weak nonequilibrium transport.

When particles of a few tens of microns are spread on the surface of water, they aggregate under the action of capillary forces and form a thin floating membrane, a particle raft. In a tank with a raft made of graphite powder, we generate in the laboratory gravity surface waves, whose wavelength about 17 cm is very large compared to the thickness of the raft of order $10\mathrm{\mu }\mathrm{m}$. For a sufficiently strong wave amplitude, the raft breaks up progressively by developing cracks and producing fragments whose sizes decrease on a timescale long compared to the period of the wave. We characterize the breaking mechanisms. Then we investigate the area distribution of the fragments produced during the fragmentation process. The visual appearance of the fragments distributed in size and surrounded by open water bears a notable resemblance to the floes produced by the fracturing of sea ice by waves in the polar oceans. Fragmentation concepts and morphological tools built for sea ice floes can be applied to our macroscopic analog, on which the entire dynamic evolution is accessible. However, the mechanics of the two systems differ, as our particle raft breaks due to the viscous stresses, whereas the sea ice fractures due to its bending by the waves.

This experimental study aims to compare the role of plume dynamics and canopy-induced instabilities on the transport of inertial particles, with application to firebrand transport in spotfire spread. In an idealized “wind-driven” model system, we consider the impact of plume buoyancy, plume momentum, and canopy turbulence on the downstream transport of particles in the wake of a canopy, and in particular the mean and standard deviation of the distribution of landing sites. Experiments were conducted in a recirculating flume with model vegetation, a heated plume/jet source, and three-dimensional printed spherical plastic particles. In a first set of experiments, particles were released with a fixed starting elevation above the plumes' upper boundaries, such that the particles were not lofted by the plume. In these cases, observations suggest that plumes have a role in extending particles' streamwise transport by delaying their downward transport. The plumes also have a strong role in increasing absolute dispersion of the particles, although less so when dispersion is normalized by distance traveled. While canopy turbulence alone significantly increases particle dispersion, in the presence of the plume its impact is more limited. Canopy turbulence was also found to cause shorter mean landing positions. In a second set of experiments, particles were released at the plume source/outlet such that their initial vertical momentum was provided by the plume's momentum and buoyancy. In these cases, the impact of canopy turbulence on particle transport is observed more distinctly. The canopy coherent structures introduce a mechanical instability to the plume, which manifests as vertical oscillatory motions that lead to variability in the particles' initial conditions and, therefore, trajectories. This leads to particles settling at both shorter and longer downstream distances.

Providing a sound appraisal of the nature of the relationship between flow $\left(Q\right)$ and pressure drop $\left(\mathrm{\Delta }P\right)$ for porous media is a longstanding fundamental research challenge. A wide variety of environmental, societal, and industrial issues, ranging, e.g., from water-soil system remediation to subsurface energy optimization, is affected by this critical issue. While such dependence is well represented by the Kozeny-Carman formulation for homogeneous media, the fundamental nature of such a relationship ($Q$ vs $\mathrm{\Delta }P$) within heterogeneous porous systems characterized by a broad range of pore sizes is still not fully understood. We design a set of controlled and complex porous structures and quantify their intrinsic permeability through detailed high-quality microfluidics experiments. We synthesize the results upon deriving an original analytical formulation relating the overall intrinsic permeability of the porous structure and its key features. Our formulation explicitly embeds the spatial variability of pore sizes into the medium permeability through a conceptualization of the system as a collection of smaller-scale porous media arranged in series. The resulting analytical formulation yields permeability values matching their experimentally based counterparts without the need for additional tunable parameters. Our study then documents and supports the strong role played by the microstructure on the overall medium permeability.

In recent experiments, [E. Sawaguchi et al., J. Fluid Mech. 862, 261 (2019)] directly probed the lubrication layer of air beneath a droplet levitating inside a rotating cylindrical drum. For small rotation rates of the drum, the lubrication film beneath the drop adopted a steady shape, while at higher rotation rates, traveling waves propagated along the drop's lower surface with roughly half the wall velocity. Here, we rationalize the physical origin of these waves. We begin with a simplified model of the lubrication flow beneath the droplet, and examine the linear stability of this base state to perturbations of the Tollmien-Schlichting type. Our developments lead to the Orr-Sommerfeld equation (OSE), whose eigenvalues give the growth rates and phase speeds of the perturbations. By considering wavelengths long relative to the lubrication film thickness, we solve the OSE perturbatively and so deduce the wavelength and phase velocity of the most unstable mode. We find satisfactory agreement between experiment and theory over the parameter regime considered in the laboratory.

Improved numerical methods are needed to understand the effect of surfactants in interfacial fluid mechanics, with various applications including thin films, inkjet printing, and ocean-atmosphere interactions. We provide a three-dimensional coupled volume of fluid (VoF) and phase field numerical approach to simulate the effects of insoluble surfactant-laden flows. The framework is validated against analytical cases for surfactant transport and Marangoni stresses. We then systematically investigate a single surfactant-laden rising bubble. The characteristics of a clean bubble rising in a quiescent liquid are governed by nondimensional numbers, i.e., the Galileo number $\text{Ga}$, which compares inertial and viscous effects, and the Bond number $\text{Bo}$, which compares gravitational and surface tension stresses. The effect of insoluble surfactants introduces an additional independent parameter, the Marangoni number $\text{Ma}$, comparing the change in surface tension forces due to gradients in surfactants concentration with viscous forces. We apply our numerical methods to investigate the influence of surfactants (through the Marangoni number) on rising bubbles in otherwise quiescent fluids. We observe that an increase in the Marangoni number first decreases the rise velocity before reaching a limiting value at high $\text{Ma}$. The value of $\text{Ma}$ necessary to observe a significant slowdown increases with $\text{Ga}$. We discuss the associated surfactant accumulation and the vortical dynamics when a steady state is reached. Finally, we perform three-dimensional simulations and demonstrate that Marangoni effects can induce a change in the rise trajectory from spiraling to zigzagging for set values of Bo and Ga, consistent with experimental results.

It is known that, beyond a critical speed, the straight contact line of a partially -wetting liquid destabilizes into a corner. One of the earliest theoretical works exploring this phenomenon [Limat and Stone, Europhys. Lett. 65, 365 (2004)] elicited a self-similar conical structure of the interface in the viscous regime. However, noting that inertia is not expected to be negligible at contact line speeds close to and beyond the critical value for many common liquids, we provide the leading-order inertial correction to their solution. In particular, we find the self-similar corrections to the interface shape as well as the flow field, and also determine their scaling with the capillary number. We find that inertia invariably modifies the interface into a cusplike shape with an increased film thickness. Furthermore, when incorporating contact line dynamics into the model, resulting in a narrowing of the corner as the contact line speed increases, we still observe an overall increase in the inertial contribution with speed despite the increased confinement.