The Leidenfrost state is typically studied by placing droplets on flat or slightly curved surfaces. Here this phenomenon is investigated by depositing water in hot conical bowls. We found that this phase exists even for large amounts of liquid in very narrow cones without considerable effect of the confinement on the Leidenfrost transition temperature $T_L$. At a fixed temperature, $T>T_L$, the total evaporation time $\tau$ has a nonmonotonic dependence on the angle of confinement $\theta$: for large volumes $(\sim 20$ ml) on flat surfaces $\left(\theta \sim 0^{\circ }\right)$, vapor chimneys appear and accelerate the evaporation rate, their frequency diminishes as $\theta$ augments and becomes zero at a certain angle ${\theta }_c$, at which $\tau$ reaches its maximum value; then, $\tau$ decreases again at larger angles because the vapor layer holding up the water becomes thinner due to the increase of hydrostatic pressure and because the geometry facilitates the vapor expulsion along the conical wall. For small volumes $(\sim 1$ ml), surface tension mainly determines the drop curvature and the lifetime is practically independent of $\theta$. Different chimney regimes and oscillation patterns were observed and summarized in a phase diagram. Finally, we developed a simple model to decipher the shape adopted by the liquid volume and its evolution as a function of time, and the predictions are in good agreement with the experimental results.

Reynolds averaged Navier-Stokes models represent the workhorse for studying turbulent flows in academia and in industry. Such single-point turbulence models have limitations in accounting for the influence of the nonlocal physics and flow history on turbulence evolution. In this context, we investigate the sensitivity inherent in such single-point models due to their characterization of the internal structure of homogeneous turbulent flows solely by the means of the Reynolds stresses. For a wide variety of mean flows under diverse conditions, we study the prediction intervals engendered due to this coarse-grained description. The nature of this variability and its dependence on parameters such as the mean flow topology, the initial Reynolds stress tensor, and the relative influence of linear contra nonlinear physics is identified, analyzed, and explicated.

Hypersonic boundary layer flows over a circular cone at moderate incidence angle can support strong crossflow instability in between the windward and leeward rays on the plane of symmetry. Due to more efficient excitation of stationary crossflow vortices by surface roughness, such boundary layer flows may transition to turbulence via rapid amplification of the high-frequency secondary instabilities of finite-amplitude stationary crossflow vortices. The amplification characteristics of these secondary instabilities are investigated for crossflow vortices generated by an azimuthally periodic array of roughness elements over a 7° half-angle circular cone in a Mach 6 free stream. The analysis is based on both quasiparallel stability theory in the form of a partial-differential-equation-based eigenvalue analysis and plane marching parabolized stability equations that account for the effects of the nonparallel basic state on the growth of secondary disturbances. Depending on the local amplitude of the stationary crossflow mode, the most unstable high-frequency disturbances either originate from the second (i.e., Mack) mode instabilities of the unperturbed boundary layer or correspond to genuine secondary instabilities that reduce to stable disturbances at sufficiently small amplitudes of the stationary crossflow vortex. The predicted frequencies of the dominant secondary disturbances of either type are similar to those measured during wind tunnel experiments at Purdue University and the Technical University of Braunschweig, Germany. Including transverse surface curvature within the quasiparallel predictions does not alter the topology of the unstable modes; however, the resulting changes in both mode shape and disturbance growth rate are rather significant and curvature can be either stabilizing or destabilizing depending on the disturbance frequency and mode type. Nonparallel effects are shown to be strongly destabilizing for secondary instabilities originating from both Mack modes and instabilities of the inclined shear layer bounding the crossflow vortex. Consequently, the two types of instabilities are found to achieve logarithmic amplification factors of up to $N=10$ and $N=7$, respectively. Results also reveal possible phase synchronization between a pair of modes that may have a significant influence on their overall amplification.

For wall-bounded flows, the model of Marusic et al. [Science 329, 193 (2010)] allows one to predict the statistics of the streamwise fluctuating velocity in the inner region, from a measured input signal in the logarithmic region. Normally, a user-defined large-scale portion of the input forms the large-scale content in the prediction by scaling its amplitude, as well as temporally shifting the signal to account for the physical inclination of these scales. Incoherent smaller scales are then fused to the prediction via universally expressed fluctuations that are subject to an amplitude modulation. Here we present a refined version of the model using spectral linear stochastic estimation, which eliminates a user-defined scale separation of the input. Now, an empirically derived transfer kernel comprises an implicit filtering via a scale-dependent gain and phase; this kernel captures the coherent portion in the prediction. An additional refinement of the model embodies a relative shift between the stochastically estimated scales in the prediction and the modulation envelope of the universal small scales. Predictions over a three-decade span of Reynolds numbers, ${\text{Re}}_{\tau }\sim O\left({10}^3\right)$ to $O\left({10}^6\right)$, highlight promising applications of the refined model to high-Reynolds-number flows, in which coherent scales become the primary contributor to the fluctuating energy.

Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.

Active matter is a new class of intrinsically out-of equilibrium material with intriguing properties. The recent upsurge of studies in this field has mostly focused on the spontaneous behavior of these systems. Yet, many systems evolve under external constraints and driving forces, being subjected to both flow and various taxis. We present a new experimental system based on the directional control of magnetotactic bacteria which enables quantitative investigations to complement the challenging theoretical description of such systems. We explore the behavior of self-propelled magnetotactic bacteria as a particularly rich and versatile class of driven matter, whose behavior can be studied under a range of hydrodynamic and magnetic field stimuli. In particular we demonstrate that the competition between cell orientation toward a magnetic field and hydrodynamic flow lead not only to jetting, but to a new pearling instability. This model system illustrates new structuring capabilities of driven active matter.

Oscillatory flows are commonly experienced by swimming micro-organisms in the environment, industrial applications, and rheological investigations. We characterize experimentally the response of the alga Dunaliella salina to oscillatory shear flows and report the surprising discovery that algal swimming trajectories orient perpendicular to the flow-shear plane. The ordering has the characteristics of a resonance in the driving parameter space. The behavior is qualitatively reproduced by a simple model and simulations accounting for helical swimming, suggesting a mechanism for ordering and criteria for the resonant amplitude and frequency. The implications of this work for active oscillatory rheology and industrial algal processing are discussed.

Understanding the conformational dynamics of polymers in time-dependent flows is of key importance for controlling materials properties during processing. Despite this importance, however, it has been challenging to study polymer dynamics in controlled time-dependent or oscillatory extensional flows. In this work, we study the dynamics of single polymers in large-amplitude oscillatory extension (LAOE) using a combination of experiments and Brownian dynamics (BD) simulations. Two-dimensional LAOE flow is generated using a feedback-controlled stagnation point device known as the Stokes trap, thereby generating an oscillatory planar extensional flow with alternating principal axes of extension and compression. Our results show that polymers experience periodic cycles of compression, reorientation, and extension in LAOE, and dynamics are generally governed by a dimensionless flow strength (Weissenberg number $\text{Wi})$ and dimensionless frequency (Deborah number $\text{De})$. Single molecule experiments are compared to BD simulations with and without intramolecular hydrodynamic interactions (HI) and excluded volume (EV) interactions, and good agreement is obtained across a range of parameters. Moreover, transient bulk stress in LAOE is determined from simulations using the Kramers relation, which reveals interesting and unique rheological signatures for this time-dependent flow. We further construct a series of single polymer stretch-flow rate curves (defined as single molecule Lissajous curves) as a function of $\text{Wi}$ and $\text{De}$, and we observe qualitatively different dynamic signatures (butterfly, bow tie, arch, and line shapes) across the two-dimensional Pipkin space defined by $\text{Wi}$ and $\text{De}$. Finally, polymer dynamics spanning from the linear to nonlinear response regimes are interpreted in the context of accumulated fluid strain in LAOE.

The turbulent Rayleigh-Taylor system in a rotating reference frame is investigated by direct numerical simulations within the Oberbeck-Boussinesq approximation. On the basis of theoretical arguments, supported by our simulations, we show that the Rossby number decreases in time, and therefore the Coriolis force becomes more important as the system evolves and produces many effects on Rayleigh-Taylor turbulence. We find that rotation reduces the intensity of turbulent velocity fluctuations and therefore the growth rate of the temperature mixing layer. Moreover, in the presence of rotation the conversion of potential energy into turbulent kinetic energy is found to be less effective, and the efficiency of the heat transfer is reduced. Finally, during the evolution of the mixing layer we observe the development of a cyclone-anticyclone asymmetry.

We show that a volatile liquid drop placed at the surface of a nonvolatile liquid pool warmer than the boiling point of the drop can be held in a Leidenfrost state even for vanishingly small superheats. Such an observation points to the importance of the substrate roughness, negligible in the case considered here, in determining the threshold Leidenfrost temperature. A theoretical model based on the one proposed by Sobac et al. [Phys. Rev. E 90, 053011 (2014)] is developed in order to rationalize the experimental data. The shapes of the drop and of the liquid substrate are analyzed. The model notably provides scalings for the vapor film thickness profile. For small drops, these scalings appear to be identical to the case of a Leidenfrost drop on a solid substrate. For large drops, in contrast, they are different, and no evidence of chimney formation has been observed either experimentally or theoretically in the range of drop sizes considered in this study. Concerning the evaporation dynamics, the radius is shown to decrease linearly with time whatever the drop size, which differs from the case of a Leidenfrost drop on a solid substrate. For high superheats, the characteristic lifetime of the drops versus the superheat follows a scaling law that is derived from the model, but, at low superheats, it deviates from this scaling by rather saturating.

The nearly frictionless flow of water in narrow carbon nanotubes is a genuine nanofluidic phenomenon with many prospects of applications in membrane technology. When inner dissipation is vanishing, the limiting factor to high flux lies in the viscous dissipation occurring at the tube mouth. As shown by Gravelle et al. [Gravelle, Joly, Detcheverry, Ybert, Cottin-Bizonne, and Bocquet, Proc. Natl. Acad. Sci. USA 110, 16367 (2013)], these so-called end effects can be reduced by adding a conical entrance. In this work, we take a step further and search for the optimal entrance shape. We use finite element calculations to compute the hydrodynamic resistance of a frictionless tube with superellipse-shaped entrances and propose an approximate analytical model. If perfect slip applies on its wall, an optimal entrance which is only 10 tube radii in length is sufficient to reduce end effects by an order of magnitude, a performance almost three times better than the optimal cone. In the case of partial slip, the resistance decreases with the entrance length before reaching a plateau at an optimal length controlled by liquid-solid slip. Our results are discussed in connection with biological and artificial systems.

Intense recurring bursts of turbulence on a long time scale are observed in direct numerical simulations (DNSs) of channel flow subject to rapid spanwise rotation for a range of Reynolds numbers and rotation speeds. A necessary condition for manifestation of cyclic turbulent bursts is that the Reynolds number and rotation speed are sufficiently high. The principal cause of turbulent bursts is a linearly unstable Tollmien-Schlichting-like wave with a wave vector normal to the rotation axis. This exponentially growing wave breaks down through a secondary instability when its amplitude is large causing a burst of turbulence. A new instability develops once turbulence has subsided leading to a continuous and self-sustained cycle of bursts. In several DNSs a recurring instability happens despite the flow being strongly and continuously turbulent in a part of the channel while in other DNSs turbulence is mostly weak between bursts. DNS observations have been compared to linear stability theory using the spatially averaged velocity of the DNS as base flow. Analysis shows that Tollmien-Schlichting waves are linearly unstable if Reynolds number and rotation speed are sufficiently high and bursts are observed. In several cases a good agreement between predicted and observed growth rate and eigenfunction of the instability is found, but in other cases the growth rate is overpredicted by linear stability theory and in some cases a Tollmien-Schlichting instability is predicted but not observed. Further study indicates that when observations and predictions differ turbulence or other modes alter the unstable wave, thereby reducing its ability to extract energy from the mean flow. In none of the analyzed DNSs was a significant nonlinear energy transfer from the unstable mode to other modes noted. Inclusion of an eddy viscosity in linear stability theory did not notably improve correspondence with DNSs.

Stability of flow around a rotating, semi-infinite cylinder placed in an axial stream is investigated. Assuming large Reynolds number, the basic flow is computed numerically as described by Derebail Muralidhar et al. [Proc. R. Soc. London, Ser. A 472, 20150850 (2016)], while numerical solution of the local stability equations allows calculation of the modal growth rates and hence determination of flow stability or instability. The problem has three nondimensional parameters: the Reynolds number $\mathrm{Re}$, the rotation rate $S$, and the axial location $Z$. Small amounts of rotation are found to strongly affect flow stability. This is the result of a nearly neutral mode of the nonrotating cylinder which controls stability at small $S$. Even small rotation can produce a sufficient perturbation that the mode goes from decaying to growing, with obvious consequences for stability. Without rotation, the flow is stable below a Reynolds number of about 1060 and also beyond a threshold $Z$. With rotation, no matter how small, instability is no longer constrained by a minimum $\mathrm{Re}$ nor a maximum $Z$. In particular, the critical Reynolds number goes to zero as $Z\to \infty$, so the flow is always unstable at large enough axial distances from the nose. As $Z$ is increased, the flow goes from stability at small $Z$ to instability at large $Z$. If the critical Reynolds number is a monotonic decreasing function of $Z$, as it is for $S$ between about 0.0045 and 5, there is a single boundary in $Z$, which separates the stable from the unstable part of the flow. On the other hand, when the critical Reynolds number is nonmonotonic, there can, depending on the choice of $\mathrm{Re}$, be several such boundaries and flow stability switches more than once as $Z$ is increased. Detailed results showing the critical Reynolds number as a function of $Z$ for different rotation rates are given. We also obtain an asymptotic expansion of the critical Reynolds number at large $Z$ and use perturbation theory to further quantify the behavior at small $S$.

Hydrophobic coatings have tremendous applications in many fields of industries, and their robustness is an important subject of investigation. Here we experimentally demonstrate the detachment of hydrophobic coating and the formation of the residual deposit resulting from an evaporating drop of water. A hydrophobic octadecanethiol (ODT) coating is employed to enhance the hydrophobicity of ZnO nanowire arrays (advancing and receding contact angle of 165° and 128°, respectively). Being a model system of the unique bonding interaction between ODT and ZnO, water drop drying on the structure of ODT/ZnO is examined. Our experimental results showed the significant depression and even failure of the hydrophobicity on this composite surface resulting from collecting the deposits of ODT molecules during the drop drying. By analyzing energy criterion and force balance, surface tension at the moving contact line is identified as a dominating destructive force to unstick the coating molecules. Interestingly, a normal rinsing stream does not damage this coating to alter its hydrophobicity, but rather is overshadowed by the evaporation of the tinny water drop. The drops of rain or condensed water outdoor may thus play the same role to damage the functional coatings after their evaporation. Our findings indicate that more delicate designs are needed to prevent the destructive effects of drop evaporation on superhydrophobic surfaces.

Pressure driven flow of superfluid helium through single high-aspect-ratio glass nanopipes into a vacuum has been studied for a wide range of pressure drop (0–30 bars), reservoir temperature (0.8–2.5 K), pipe lengths (1–30 mm), and pipe radii (131 and 230 nm). As a function of pressure drop we observe two distinct flow regimes above and below a critical pressure drop $P_c$. For $P<P_c$, the critical velocity is approximately the Feynman critical velocity. As the pressure drop approaches $P_c$, there is a sudden transition to a new flow state with a critical velocity more than an order of magnitude higher. The position of the transition is explained by a simple model that accounts for the fountain pressure generated by evaporative cooling at the outlet of the nanopipe.

As a bubble bursts at a liquid-air interface, a tiny liquid jet rises and can release the so-called jet drops. In this paper the size of the top jet drop produced by a bubble bursting is investigated experimentally. We determine and discuss the first scaling law enabling the determination of the top jet drop size as a function of the corresponding mother bubble radius and the liquid properties (viscosity, surface tension, and density), along with its regime of existence. Furthermore, with the aim of decoupling experimentally the effects of bubble collapse and jet dynamics on the drop detachment, we propose a scaling providing the top drop size only as a function of the jet velocity and liquid parameters. In particular, this allows us to untangle the intricate roles of viscosity, gravity, and surface tension in the end pinching of the bubble bursting jet.

We consider the effective hydrophobicity of a periodically grooved surface immersed in liquid, with trapped shear-free bubbles protruding between the no-slip ridges at a $\pi /2$ contact angle. Specifically, we carry out a singular-perturbation analysis in the limit $\epsilon \ll 1$ where the bubbles are closely spaced, finding the effective slip length (normalized by the bubble radius) for longitudinal flow along the ridges as $\pi /\sqrt{2\epsilon }-(12/\pi )ln2+(13\pi /24)\sqrt{2\epsilon }+o\left(\sqrt{\epsilon }\right)$, the small parameter $\epsilon$ being the planform solid fraction. The square-root divergence highlights the strong hydrophobic character of this configuration; this leading singular term (along with the third term) follows from a local lubrication-like analysis of the gap regions between the bubbles, together with general matching considerations and a global conservation relation. The $O\left(1\right)$ constant term is found by matching with a leading-order solution in the outer region, where the bubbles appear to be touching. We find excellent agreement between our slip-length formula and a numerical scheme recently derived using a unified-transform method [Crowdy, IMA J. Appl. Math. 80, 1902 (2015)]. The comparison demonstrates that our asymptotic formula, together with the diametric dilute-limit approximation [Crowdy, J. Fluid Mech. 791, R7 (2016)], provides an elementary analytical description for essentially arbitrary no-slip fractions.

This paper presents a theoretical study of circulation of streamwise vortices that are generated by a hypermixer strut in a supersonic flow. By taking account of the spanwise velocity, the circulation based on the streamwise vorticity is derived from an inviscid flow around the strut. The theoretical circulations are in agreement with the values obtained from three-dimensional numerical simulations for small slope angles at a Mach number of 2.48. Therefore, the proposed circulation formula can contribute to designing struts, in that it depends only on the strut configuration and inflow conditions. This study also finds that the linear relations between circulation and angle is broken by separated flows on the slope wall with increasing angle and the maximum value in circulation is expressed as a product of the mainstream velocity and the height of the strut.

This paper is associated with a poster winner of a 2015 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.P0008