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

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.P0048

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.P0050

This paper is associated with a video winner of a 2015 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.V0013

This paper is associated with a video winner of a 2015 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.V0087

This paper is associated with a video winner of a 2015 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.V0040

This paper is associated with a poster winner of a 2015 APS/DFD Gallery of Fluid Motion Award. The original poster is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.P0014

This paper is associated with a poster winner of a 2015 APS/DFD Gallery of Fluid Motion Award. The original poster is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.P0051

This paper is associated with a video winner of a 2015 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.V0015

This paper is associated with a video winner of a 2015 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.V0064

This paper is associated with a video winner of a 2015 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.V0088

This paper is associated with a video winner of a 2015 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion, http://dx.doi.org/10.1103/APS.DFD.2015.GFM.V0029

We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet unexplored, extension of the much studied case of small spherical particles. We show that heavy isotropic helicoids, due to the coupling between translational and rotational degrees of freedom, preferentially sample different helical regions in laminar or chaotic advecting flows. This opens the way to control and engineer particles able to track complex flow structures with potential applications to microfluidics and turbulence.