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.

One mechanistic interpretation of baroclinic instability is that of mutual constructive interference of Rossby edge waves. The suppression of baroclinic instability over slopes has been widely established, where previous research argues that a sloping boundary modifies the properties of these Rossby edge waves, but does not provide a mechanistic explanation for the suppression that is valid over all parameter space. In the context of an Eady problem modified by the presence of a sloping boundary, we provide a mechanistic rationalization for baroclinic instability in the presence of slopes that is valid over all parameter space, via an equivalent formulation explicitly in terms of Rossby edge waves. We also highlight the differences between edge-wave phase shifts and normal-mode phase tilts, showing that the edge-wave phase shifts should be the ones that are mechanistically relevant, and normal-mode phase tilt is a potentially misleading quantity to use. Further, we present evidence that the edge-wave phase shifts but not normal-mode phase tilts are well correlated with geometric quantities diagnosed from an analysis framework based on eddy variance ellipses. The result is noteworthy in that the geometric framework makes no explicit reference to the edge-wave structures in its construction, and the correlation suggests the geometric framework can be used in problems where edge-wave structures are not so well defined or readily available. Some implications for parametrization of baroclinic instability and relevant eddy-mean feedbacks are discussed. For completeness, we also provide an explicit demonstration that the linear instability problem of the present modified Eady problem is parity-time symmetric, and speculate about some suggestive links between parity-time symmetry, shear instability, and the edge-wave interaction mechanism.

In this study, we introduce a comprehensive theoretical model for viscous liquid systems exhibiting Rayleigh-Plateau instability, accommodating cases both with and without a solid fiber. Employing the lubrication approach and implementing the hydrodynamic interaction at the solid-liquid interface, we formulate one-dimensional evolution equations for the breakup of viscous liquid threads and films on a fiber. Through several validations, we showed that our model exhibits a good agreement with experimental results in comparison to numerical simulations. Finally, our model, which incorporates the flow effect from the inner boundary condition by reconsidering the ansatz of a conventional long-wave approximation, provides a necessary condition for satellite droplet formation and determines the most unstable mode proportional to ${k^{*}}^2$, where $k^{*}$ is the most unstable wavenumber. In addition, we observed that the volume of the satellite droplets exponentially decays depending on the wavenumber. Moreover, our single model integrates the findings of Goren's liquid film on a fiber and Rayleigh's viscous liquid thread, demonstrating its versatility and relevance to a wide range of systems.

Heat transfer in wind turbulence over breaking waves is studied through direct numerical simulations. The air-water system is simulated on an Eulerian grid with the interface between the two phases captured by a coupled level set and volume-of-fluid method. To examine the effect of wave age, different cases representing slow, intermediate, and fast waves are considered for the scenario of air temperature being higher than the water temperature. The results show that the evolution of mean temperature profile responds nonmonotonically to the increasing wave age. At a small wave age, the mean temperature near the water surface increases after wave breaking. At intermediate and large wave ages, however, the temperature decreases after wave breaking, while the decrement magnitude is larger at the intermediate wave age. An investigation of the temperature fluctuation flux indicates that a combined effect of wave-coherent flux and turbulence-induced flux leads to a large magnitude of temperature decrement at the intermediate wave age. A further analysis of the production term in the transport equation of the turbulence-induced temperature flux elucidates the mechanism underlying the generation of the turbulence-induced flux at the intermediate wave age. The findings of the present study suggest that temperature responds in a more complex manner to wave age than velocity does and this phenomenon should be considered in models for air-sea interaction and weather forecasting.

We illuminate effects of surface-charge convection intrinsic to leaky-dielectric electrohydrodynamics by analyzing the symmetric steady state of a circular drop in an external field at arbitrary electric Reynolds number ${\mathrm{Re}}_E$. In formulating the problem, we identify an exact factorization that reduces the number of dimensionless parameters from four—${\mathrm{Re}}_E$ and the conductivity, permittivity and viscosity ratios—to two: a modified electric Reynolds number $\widetilde{\mathrm{Re}}$ and a charging parameter $\varpi$. In the case $\varpi <0$, where charge relaxation in the drop phase is slower than in the suspending phase, and, as a consequence, the interface polarizes antiparallel to the external field, we find that above a critical $\widetilde{\mathrm{Re}}$ value the solution exhibits a blowup singularity such that the surface-charge density diverges antisymmetrically with the $-1/3$ power of distance from the equator. We use local analysis to uncover the structure of that blowup singularity, wherein surface charges are convected by a locally induced flow towards the equator where they annihilate. To study the blowup regime, we devise a numerical scheme encoding that local structure where the blowup prefactor is determined by a global charging-annihilation balance. We also employ asymptotic analysis to construct a universal problem governing the blowup solutions in the regime $\widetilde{\mathrm{Re}}\gg 1$, far beyond the blowup threshold. In the case $\varpi >0$, where charge relaxation is faster in the drop phase and the interface polarizes parallel to the external field, we numerically observe and asymptotically characterize the formation at large $\widetilde{\mathrm{Re}}$ of stagnant, perfectly conducting surface-charge caps about the drop poles. The cap size grows and the cap voltage decreases monotonically with increasing conductivity or decreasing permittivity of the drop phase relative to the suspending phase. The flow in this scenario is nonlinearly driven by electrical shear stresses at the complement of the caps. In both polarization scenarios, the flow at large $\widetilde{\mathrm{Re}}$ scales linearly with the magnitude of the external field, contrasting the familiar quadratic scaling under weak fields.

Surfactant-laden thin liquid films overlaid on solid substrates are encountered in a variety of industrial and biological settings. As these films reach submicron thickness, they tend to become unstable owing to the influence of long-range dispersion forces. In the current study, we investigate how gravitational drainage affects the stability attributes of such thin liquid films. Using scaling arguments, we demonstrate that gravity and dispersion forces can exert their influence simultaneously over a wide range of film thicknesses. In the lubrication limit, we carry out linear stability analysis and nonlinear simulations to understand the evolution of draining thin films. Linear stability indicates the existence of two unstable modes and two cutoff wave numbers, as opposed to a single unstable mode and a unique cutoff wave number observed in stationary films. It is also found that surfactant-laden flowing films are more stable than stationary films with surfactants as well as draining films with clean interfaces. The origin of stabilization is identified as the enhanced surfactant perturbations generated due to drainage. We demonstrate that films exhibiting intermediate levels of surfactant activity and significant drainage exhibit the lowest rates of disturbance growth, leading to extending the time of rupture.

Biofilament-motor protein complexes are ubiquitous in biology and drive the transport of cargo vital for many fundamental life processes at the cellular level. As they move, motor proteins exert compressive forces on the filaments to which they are attached. If the filament is clamped or tethered in some way, this force leads to buckling and a subsequent range of dynamics. The follower force model, in which a single compressive force is imposed at the filament tip, is a simple filament model that is becoming widely used to describe an elastic filament, such as a microtubule, compressed by a motor protein. Depending on the force value, one can observe different states including whirling, beating, and writhing, though the bifurcations giving rise to these states are not completely understood. In this paper, we utilize techniques from computational dynamical systems to determine and characterize these bifurcations. We track emerging time-periodic branches and identify quasiperiodic states. We investigate the effect of filament slenderness on the bifurcations and, in doing so, present a comprehensive overview of the dynamics which emerge in the follower force model.

The verification of whether small-scale turbulence is isotropic remains a grand challenge. The difficulty arises because the presence of small-scale anisotropy is tied to the dissipation tensor, whose components require the full three-dimensional information of the flow field in both high spatial and temporal resolution, a condition rarely satisfied in turbulence experiments, especially during field scale measurement of atmospheric turbulence. To circumvent this issue, an intermittency-anisotropy framework is proposed through which we successfully extract the features of small-scale anisotropy from single-point measurements of turbulent time series by exploiting the properties of small-scale intermittency. Specifically, this framework quantifies anisotropy by studying the contrasting effects of burstlike activities on the scalewise production of turbulence kinetic energy between the horizontal and vertical directions. The veracity of this approach is tested by applying it over a range of datasets covering an unprecedented range in the Reynolds numbers $(\mathrm{Re}\approx {10}^3–{10}^6)$, sampling frequencies (10 kHz to 10 Hz), surface conditions (aerodynamically smooth surfaces to typical grasslands to forest canopies), and flow types (channel flows, boundary-layer flows, atmospheric flows, and flows over forest canopies). For these diverse datasets, the findings indicate that the effects of small-scale anisotropy persists up to the integral scales of the streamwise velocity fluctuations and there exists a universal relationship to predict this anisotropy from the two-component state of the Reynolds stress tensor. This relationship is important towards the development of next-generation closure models of wall turbulence by incorporating the effects of anisotropy at smaller scales of the flow.

Submarine melting at ice-ocean interfaces such as at tidewater glaciers and ice shelves is influenced by physical and chemical environmental factors including salinity, water temperature, stratification, subglacial hydrology, meltwater plumes, and oceanic currents. The effect of these individual components on ice loss can be difficult to capture in common ice-melting models. In particular, turbulence, which can develop as a result of ambient meltwater plumes and subglacial discharge along ice-water interfaces, for example, can increase mixing of relatively warm or high salinity ambient water with meltwater, thus enhancing melting. To isolate and understand the fundamental effects of turbulence on ice melting, we performed experiments of an ice sphere melting in homogeneous isotropic turbulence (HIT) with negligible mean flow. This setup permits us to study melting in turbulence absent additional fluid flows such as mean shear generated by boundary flows, or density stratification due to thermal or salinity gradients. To reduce the effects of complex ice morphology, we selected an ice sphere to achieve a symmetric melting surface. Ambient water temperature was varied from 2 to $10{}^{\circ }\mathrm{C}$. Experiments were performed with both quiescent and turbulent flow surrounding the ice. For the turbulent melting cases, the turbulent kinetic energy of the flow was varied from 9.6 to $28.6{\mathrm{cm}}^2{\mathrm{s}}^{-2}$. To link turbulence metrics and flow patterns to melting, we performed particle image velocimetry to obtain measurements of the two-dimensional velocity fields surrounding the sphere and to capture melting rates in experiments in a nonintrusive manner. Here, we explore the development of convective melt plumes and boundary layer flows that develop along the ice-water interface. We present melting data as a function of turbulence metrics and ambient water temperature. Through novel parametrization of our empirical results, our findings increase the understanding of the impact of turbulence on melting rates and aim to improve predictive numerical simulations of ice loss.

Two-dimensional (2D) turbulence features an inverse energy cascade that produces large-scale flow structures such as large-scale vortices (LSVs) and unidirectional jets. We investigate the dynamics of such large-scale structures using extensive direct numerical simulations (DNS) of stochastically forced, viscously damped 2D turbulence within a periodic rectangular (Cartesian) domain $[0,L_x]\times [0,L_y]$. LSVs form and dominate the system when the domain aspect ratio $\delta =L_x/L_y\approx 1$, while unidirectional jets predominate at $\delta \gtrsim 1.1$. At intermediate values of $\delta$, both structures are metastable, and fluctuation-induced transitions between LSVs and jets are observed. Based on large-scale energy balance in the condensate, we derive and verify predictions for the dependence of the total kinetic energy and the flow polarity on the nondimensional control parameters. We further collect detailed statistics on the lifetimes of LSVs and jets from DNS runs of up to $10738$ viscous diffusive time units in length. The distribution of the lifetimes is consistent with that of a memoryless Poisson process. The data are compatible with an exponential dependence of the mean lifetime on the aspect ratio $\delta$. In addition, the mean lifetimes depend sensitively on the Reynolds number $\mathrm{Re}$: As $\mathrm{Re}$ increases, the energy gap between LSV (lower energy) and jet states (higher energy) arising from anisotropic dissipation increases, leading to an increase in lifetimes that is approximately exponential in $\mathrm{Re}$ for both LSVs and jets. Similarly, as the ratio of the forcing scale to the domain size increases, the transition rates increase sharply, confirming earlier findings. We investigate the transition dynamics in terms of kinetic energy, flow polarity, modal amplitude, and 2D phase-space diagrams, revealing that the transitions occur in two stages: In the initial stage, an efficient redistribution of kinetic energy by nonlinear triadic interactions facilitates a rapid transition from LSVs to jets and vice versa. In the second stage, the kinetic energy of the newly formed structure slowly adjusts to its associated (higher or lower) equilibrium value on a longer, viscous timescale, leading to a time delay that results in hysteretic transition behavior. Fluctuation-induced transitions may also occur between different numbers of jets. Our findings shed new light on the dynamics of coherent large-scale structures in anisotropic turbulence.