The electrophoretic mobility of a microparticle with a small $\zeta$ potential attached to a fluid interface is studied analytically in the limit of two fluids with vanishing viscosity and permittivity ratios under the assumption of a weak applied electric field. The analysis is based on perturbation expansions in the capillary number, the electric capillary number, and in the deviation of the contact angle on the particle surface from ${90}^{\circ }$. For the case of a very thin electric double layer (EDL), the Smoluchowski limit for the electrophoretic mobility is recovered. For arbitrary values of the EDL thickness, a spherical particle is considered. In that case the electrophoretic mobility is a function of the EDL thickness and the contact angle at the particle surface. Hydrophobic particles have a higher mobility than hydrophilic ones. The deformation of the fluid interface is shown to be separable into a dynamic and static part. The motion of the particle (dynamic part) does not contribute to the interfacial deformation in the case of a small capillary number, even for arbitrary EDL thickness. The static interfacial deformation due to electric stresses, known as electrodipping, is examined for spherical particles and shown to be independent of the first-order perturbation in the contact angle. The limits of validity of our theory and possible applications are discussed.

The relationship between the state of the plastron, slip velocity, and drag of a superhydrophobic surface in contact with a turbulent boundary layer was investigated. The experiments were carried out using a body of revolution which was spray coated with a superhydrophobic layer and tested in a water tunnel at velocities ranging from 0.98 to 2.92 m/s (Reynolds number from $5.0\times {10}^5$ to $1.5\times {10}^6$ based on the length of the model). Visualization of the plastron and particle-tracking velocimetry (PTV) of the near-wall boundary layer was carried out using a long-range microscope with backlight illumination. The model was also equipped with a load cell to simultaneously measure the drag force. The load measurement showed a 36.4% reduction in drag at the lowest Re of $5.0\times {10}^5$, which decreased to 5.6% at the highest Re of $1.5\times {10}^6$. The microscopic PTV showed an increase in the slip velocity from 0.131 to 0.602 m/s, and a relatively constant slip length (85–66 μm) over the superhydrophobic surface (SHS) as Re increased from $5.0\times {10}^5$ to $1.5\times {10}^6$. The wall-normal gradient of mean velocity in the linear viscous sublayer showed smaller viscous wall shear stress over the SHS compared with the smooth baseline surface for Re smaller than $1.0\times {10}^6$. At a larger Re of $1.2\times {10}^6$, drag reduction diminished with an increase of relative roughness. The visualizations of the surface showed frequent appearance of a full air plastron with average thickness of $\sim 10\mu \mathrm{m}$ at the two lowest Re of $5.0\times {10}^5$ and $7.0\times {10}^5$. The air-water interface of the plastron had a transient behavior due to low-wave-number ripples, which leads to thickness variation. This full plastron was essential for obtaining a considerable drag reduction ($>16\%$). At the three higher Re with smaller drag reduction ($<8\%$), the plastron demonstrated isolated menisci of air, pinned between the tip and the valley of large roughness protrusions.

In addition to mass, energy, and momentum, classical dissipationless flows conserve helicity, a measure of the topology of the flow. Helicity has far-reaching consequences for classical flows from Newtonian fluids to plasmas. Since superfluids flow without dissipation, a fundamental question is whether such a conserved quantity exists for superfluid flows. We address the existence of a “superfluid helicity” using an analytical approach based on the symmetry underlying classical helicity conservation: the particle relabeling symmetry. Furthermore, we use numerical simulations to study whether bundles of superfluid vortices which approximate the structure of a classical vortex recover the conservation of classical helicity and we find dynamics consistent with classical vortices in a viscous fluid.

This paper is associated with a video winner of a 2017 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, https://doi.org/10.1103/APS.DFD.2017.GFM.V0020

This paper is associated with a video winner of a 2017 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, https://doi.org/10.1103/APS.DFD.2017.GFM.V0052

This paper is associated with a video winner of a 2017 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, https://doi.org/10.1103/APS.DFD.2017.GFM.V0080

This paper is associated with a poster winner of a 2017 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, https://doi.org/10.1103/APS.DFD.2017.GFM.P0030

This paper is associated with a poster winner of a 2017 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, https://doi.org/10.1103/APS.DFD.2017.GFM.P0026

This paper is associated with a poster winner of a 2017 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, https://doi.org/10.1103/APS.DFD.2017.GFM.P0018

This paper is associated with a video winner of a 2017 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.V0098

This paper is associated with a video winner of a 2017 APS/DFD Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.V0018

This paper is associated with a video winner of a 2017 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.V0037

This paper is associated with a video winner of a 2017 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.V0053

This paper is associated with a poster winner of a 2017 APS/DFD Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2017.GFM.P0053

We investigate the dynamics of energy cascades in quantum turbulence by directly observing the vorticity distributions in numerical simulations of the Gross-Pitaevskii equation. By Fourier filtering each scale of the vorticity distribution, we find that antiparallel vortex tubes at a large scale generate small-scale vortex tubes orthogonal to those at the large scale, which is a manifestation of the energy cascade from large to small scales. We reveal the dynamics of quantized vortex lines in these processes.

We report quantitative evidence of mixing-layer elastic instability in a viscoelastic fluid flow between two widely spaced obstacles hindering a channel flow at $\text{Re}\ll 1$ and $\text{Wi}\gg 1$. Two mixing layers with nonuniform shear velocity profiles are formed in the region between the obstacles. The mixing-layer instability arises in the vicinity of an inflection point on the shear velocity profile with a steep variation in the elastic stress. The instability results in an intermittent appearance of small vortices in the mixing layers and an amplification of spatiotemporal averaged vorticity in the elastic turbulence regime. The latter is characterized through scaling of friction factor with Wi and both pressure and velocity spectra. Furthermore, the observations reported provide improved understanding of the stability of the mixing layer in a viscoelastic fluid at large elasticity, i.e., $\text{Wi}\gg 1$ and $\text{Re}\ll 1$ and oppose the current view of suppression of vorticity solely by polymer additives.

Presented here are experiments clarifying how the deformation of cavitation bubbles affects their rebound. Rebound bubbles carry the remaining energy of a bubble following its initial collapse, which dissipates energy mainly through shock waves, jets, and heat. The rebound bubble undergoes its own collapse, generating such violent events anew, which can be even more damaging or effective than at first bubble collapse. However, modeling rebound bubbles is an ongoing challenge because of the lack of knowledge on the exact factors affecting their formation. Here we use single-laser-induced cavitation bubbles and deform them by variable gravity or by a neighboring free surface to quantify the effect of bubble deformation on the rebound bubbles. Within a wide range of deformations, the energy of the rebound bubble follows a logarithmic increase with the bubble's initial dipole deformation, regardless of the origin of this deformation.

Predicting the size of droplets that pinch off from a liquid jet is important to applications ranging from bubble-initiated atmospheric aerosols to inkjet printing. These predictions are complicated by smaller satellite drops that form when a thin liquid thread develops and breaks up faster than its ends fully retract. Typically this process is modeled by perturbing a cylindrical liquid thread with an amplitude that is small relative to the cylinder diameter. Yet early on in the pinch-off process, the ends of the liquid thread are conical and lack a characteristic length scale from which to normalize a finite perturbation. Here we numerically simulate the retraction of nearly inviscid conical filaments and introduce self-similar perturbations to drive the system into a discretely self-similar retraction that can enable breakup without biasing a particular length scale. We find that for most cone angles, the perturbation amplitude must exceed a threshold for satellite drops to form. We show that this critical perturbation amplitude depends on the cone angle and can be accurately predicted by an argument based on the static stability of the initial perturbed cone.

Creeping flow of polymeric fluid without inertia exhibits elastic instabilities and elastic turbulence accompanied by drag enhancement due to elastic stress produced by flow-stretched polymers. However, in inertia-dominated flow at high $\text{Re}$ and low fluid elasticity $El$, a reduction in turbulent frictional drag is caused by an intricate competition between inertial and elastic stresses. Here we explore the effect of inertia on the stability of viscoelastic flow in a broad range of control parameters $El$ and $(\text{Re},\text{Wi})$. We present the stability diagram of observed flow regimes in $\text{Wi}\text{−}\text{Re}$ coordinates and find that the instabilities' onsets show an unexpectedly nonmonotonic dependence on $El$. Further, three distinct regions in the diagram are identified based on $El$. Strikingly, for high-elasticity fluids we discover a complete relaminarization of flow at Reynolds number in the range of 1 to 10, different from a well-known turbulent drag reduction. These counterintuitive effects may be explained by a finite polymer extensibility and a suppression of vorticity at high $\text{Wi}$. Our results call for further theoretical and numerical development to uncover the role of inertial effect on elastic turbulence in a viscoelastic flow.