This paper is associated with a poster winner of a 2016 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.2016.GFM.P0030

This paper is associated with a video winner of a 2016 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.2016.GFM.V0095

This paper is associated with a poster winner of a 2016 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.2016.GFM.P0009

This paper is associated with a video winner of a 2016 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.2016.GFM.V0092

This paper is associated with a poster winner of a 2016 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.2016.GFM.P0028

This paper is associated with a video winner of a 2016 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.2016.GFM.V0038

This paper is associated with a poster winner of a 2016 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.2016.GFM.P0020

This paper is associated with a poster winner of a 2016 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.2016.GFM.P0012

This paper is associated with a poster winner of a 2016 APS/DFD Gallery of Fluid Motion Award. The original poster is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2016.GFM.P0044

This paper is associated with a video winner of a 2016 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.2016.GFM.V0046

This paper is associated with a video winner of a 2016 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.2016.GFM.V0076

We propose a model where a fluid drop is represented by an octahedron whose six vertices are connected by linear springs. We determine the relevant spring constants and damping coefficients by matching the oscillation modes of an octahedron to those of a perturbed spherical drop. We model bouncing on solid and liquid surfaces by dynamically imposing a contact force. We use our model to quantify the normal and tangential restitution coefficients of bouncing drops as a function of the Weber, Bond, and Ohnesorge numbers.

Suspensions of self-propelled bodies generate a unique mechanical stress owing to their motility that impacts their large-scale collective behavior. For microswimmers suspended in a fluid with negligible particle inertia, we have shown that the virial swim stress is a useful quantity to understand the rheology and nonequilibrium behaviors of active soft matter systems. For larger self-propelled organisms such as fish, it is unclear how particle inertia impacts their stress generation and collective movement. Here we analyze the effects of finite particle inertia on the mechanical pressure (or stress) generated by a suspension of self-propelled bodies. We find that swimmers of all scales generate a unique swim stress and Reynolds stress that impact their collective motion. We discover that particle inertia plays a similar role as confinement in overdamped active Brownian systems, where the reduced run length of the swimmers decreases the swim stress and affects the phase behavior. Although the swim and Reynolds stresses vary individually with the magnitude of particle inertia, the sum of the two contributions is independent of particle inertia. This points to an important concept when computing stresses in computer simulations of nonequilibrium systems: The Reynolds and the virial stresses must both be calculated to obtain the overall stress generated by a system.

Large-scale turbulence in fluid layers and other quasi-two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces a direct energy cascade, while solenoidal planar turbulence transports energy to large scales by an inverse cascade. Here, we consider turbulence at finite Mach numbers when the interaction between acoustic waves and vortices is substantial. We employ solenoidal pumping at intermediate scales and show how both direct and inverse energy cascades are formed starting from the pumping scale. We show that there is an inverse cascade of kinetic energy up to a scale $\ell$, where a typical velocity reaches the speed of sound; this creates shock waves, which provide for a compensating direct cascade. When the system size is less than $\ell$, the steady state contains a system-size pair of long-living condensate vortices connected by a system of shocks. Thus turbulence in fluid layers processes energy via a loop: Most energy first goes to large scales via vortices and is then transported by waves to small-scale dissipation.

Liquid entrapment over patterned surfaces has applications in diagnostics, oil recovery, and printing processes. Here we study the process of oil displacement upon sequential injection of water over a photopatterned structure in a confined geometry. By varying the amplitude and frequency of triangular and sinusoidal patterns, we are able to completely remove oil or trap oil in varying amounts. We present a theoretical model based on geometrical arguments that successfully predicts the criterion for liquid entrapment and provides insights into the parameters that govern the physical process.

Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in quasi-two-dimensional (Q2D) flow, while a small rotation rate allows turbulence to be three-dimensional (3D). It is found that the transition from the Q2D turbulent flow to the 3D turbulent flow and the reverse transition occur at different values of the rotation rates. At intermediate rotation rates, bistability of these two statistically steady states is observed. Such a hysteretic transition is also observed for variations of the amplitude of an external force.

Equilibrium electroconvective instability at a perfectly charge-selective solid, such as ion-exchange membrane or metal electrode, previously deemed impossible, is possible if one takes into account finite electrical conductivity of the solid. A simple model of electroconvective diffusion of ions in the depleted diffusion layer in this system predicts a supercritical transition to instability in the vicinity of the limiting current, as opposed to the subcritical transition for the previously studied nonequilibrium instability related to the extended space charge. The linear stability analysis in this model yields the division of the parameter space into domains in which each instability mechanism with its characteristic signatures dominates. Identification of the particular instability mechanism for a given system requires a detailed experimental study of the vicinity of the instability threshold in terms of both the voltage versus current dependence and flow visualization.

As a confined long bubble translates along a horizontal liquid-filled tube, a thin film of liquid is formed on the tube wall. For negligible inertial and buoyancy effects, respectively, small Reynolds $\left(\text{Re}\right)$ and Bond $\left(\text{Bo}\right)$ numbers, the thickness of the liquid film depends only on the flow capillary number $\left(\text{Ca}\right)$. However, buoyancy effects are no longer negligible as the diameter of the tube reaches millimeter length scales, which corresponds to finite values of $\text{Bo}$. We perform experiments and theoretical analysis for a long bubble in a horizontal tube to investigate the effect of Bond number $\left(0.05<\text{Bo}<0.5\right)$ on the thickness of the liquid film and the bubble orientation at different capillary numbers ${10}^{-3}<\text{Ca}<{10}^{-1}$. We investigate several features of the lubricating film around the bubble. (i) Due to the gravitational effects, the film deposited on the upper wall of the channel is thinner than the film at the bottom wall. We extend the available theory for the film thickness at the front of the bubble in a two-dimensional geometry at low capillary numbers $\text{Ca}<{10}^{-3}$ and finite $\text{Bo}$ to account for the effect of larger $\text{Ca}$. The resulting model shows very good agreement with the present experimental measurements. (ii) Due to the asymmetry in the liquid film thickness and the consequent drainage of the liquid from the top to the bottom of the tube, the bubble is inclined relative to the channel centerline and our side-view visualizations allow direct quantification of the inclination angle, which increases with both $\text{Bo}$ and $\text{Ca}$. While the inclination angle at the top is smaller than that at the bottom of the tube, the average of these two values follows the predictions of a mass balance analysis in the central region of the bubble. (iii) The inclination of the bubble causes the thickness of the thin film at the back of the bubble to depend on the length of the bubble, whereas the thickness at the front of the bubble does not depend on the bubble length.

We consider the displacement of an inviscid fluid (air) by a viscous fluid (oil) in a narrow channel with gap-thickness modulations. The interfacial dynamics of this problem is strongly nonlocal and exhibits competing effects from capillarity and permeability. We derive analytical predictions of steady-state front morphologies, which are exact at linear level in the case of a persistent modulation in the direction of front advancement. The theoretical predictions are in good agreement with experimental measurements of steady-state front morphologies obtained in a Hele-Shaw cell with modulations of the channel depth, consisting on three parallel tracks of reduced depth, for small gap modulations. The relative average distance between theoretical and experimental fronts in the region around the central track is smaller than about $4\%$, provided that the height of the tracks is less than $13\%$ of the total channel depth and the local distortion of the front height $h$ is small enough $\left(\left|\mathbf{\nabla }h\right|<0.8\right)$ for the linear approximation to hold.

A simple analytical description for the effects of a single vortex near a turbulent/non-turbulent interface (TNTI) layer, based on a Burgers vortex (BV) model, is compared with results from direct numerical simulation (DNS) of shear-free turbulence. The BV model parameters are derived from the DNS data, and the model separates the entrainment as a two-stage process: (i) the strain imposed on the vortex draws non-turbulent fluid toward the irrotational boundary that separates the irrotational from the turbulent region, and afterwards (ii) the velocity associated with the vorticity field moves the entrained fluid toward the turbulent core region. The resulting model is able to predict the enstrophy dynamics, flow streamlines, and flow topology—such as the formation of the teardrop map in the invariants of the velocity gradient tensor—as well as the entrainment velocity. The BV model provides an interesting framework to analyze the small-scale “nibbling” eddy motions near the TNTI and allows the inclusion of the large-scale flow-dependent effects imposed by the strain rate, while it also links the entrainment characteristics to the eddy structure of the flow near TNTIs.