The reconnection of two interacting vortex tubes is a fundamental process in fluid mechanics, which, at very high Reynolds numbers, is associated with the formation of intense velocity gradients. Reconnection is usually studied using two antiparallel tubes which are destabilized via the long-wavelength Crow instability, leading to a very symmetric configuration and to a strong flattening of the cores into thin sheets. Here, we consider the interaction of two initially straight tubes at an angle of β and show that by relaxing some symmetries of the problem, a rich phenomenology appears. When the angle between the two tubes is close to β=90∘, their interaction leads to pairing of small portions of antiparallel tubes, followed by the formation of thin and localized vortex sheets as a precursor of reconnection. The subsequent breakdown of these sheets involves a twisting of the paired sheets, followed by the appearance of a localized cloud of small-scale vortex structures. By decreasing β, we show that reconnection involves increasingly larger portions of tubes, whose cores are subsequently destabilizing, leaving behind more small-scale vortices. At the smallest values of the angle β studied, the two vortices break down through a mechanism, which leads to a cascadelike process of energy conveyance across length scales similar to what was found for previous studies of antiparallel vortex tubes (β=0) which imposed no symmetries. While, in all cases, the interaction of two vortices depends on the initial condition, the rapid formation of fine-scale vortex structures appears to be a robust feature, possibly universal at very high Reynolds numbers.

Optical  fluorescencemicroscopy  is  shown  to  enable  both  highspatial  and  temporal  resolution  of  redox-dependent  fluorescencein  flowing  electrolytes.  We  report  the  use  of  fluorescence  micro-scopy coupled with electrochemistry to directly observe the reac-tion and transport of redox-active quinones within porous carbonelectrodesin  operando.  We  observe  surprising  electrolyte  chan-neling features within several porous electrodes, leading to spatiallydistinguishable  advection-dominated  and  diffusion-dominated  re-gions. These results challenge the common assumption that trans-port in porous electrodes can be approximated by a homogeneousDarcy-like permeability, particularly at the length scales relevant tomany  electrochemical  systems  such  as  redox  flow  batteries.  Thiswork  presents  a  new  platform  to  provide  highly  resolved  spatialand   temporal   insight   into   electrolyte   reactions   and   transportbehavior within porous electrodes.

As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility. Experiments have shown that the total crease length accrues logarithmically when repeatedly compacting and unfolding a sheet of paper. Here, we offer insight to this unexpected result by exploring the correspondence between crumpling and fragmentation processes. We identify a physical model for the evolution of facet area and ridge length distributions of crumpled sheets, and propose a mechanism for re-fragmentation driven by geometric frustration. This mechanism establishes a feedback loop in which the facet size distribution informs the subsequent rate of fragmentation under repeated confinement, thereby producing a new size distribution. We then demonstrate the capacity of this model to reproduce the characteristic logarithmic scaling of total crease length, thereby supplying a missing physical basis for the observed phenomenon.

The axial buckling capacity of a thin cylindrical shell depends on the shape and the size of the imperfections that are present in it. Therefore, the prediction of the shells buckling capacity is difficult, expensive, and time consuming, if not impossible, because the prediction requires a priori knowledge about the imperfections. As a result, thin cylindrical shells are designed conservatively using the knockdown factor approach that accommodates the uncertainties associated with the imperfections that are present in the shells; almost all the design codes follow this approach explicitly or implicitly. A novel procedure is proposed for the accurate prediction of the axial buckling capacity of thin cylindrical shells without measuring the imperfections and is based on the probing of the axially loaded shells. Computational and experimental implementation of the procedure yields accurate results when the probing is done in location of highest imperfection amplitude. However, the procedure overpredicts the capacity when the probing is done away from that point. This study demonstrates the crucial role played by the probing location and shows that the prediction of imperfect cylinders is possible if the probing is done at the proper location.

From soda cans to space rockets, thin-walled cylindrical shells are abundant, offering exceptional load carrying capacity at relatively low weight. However, the actual load at which any shell buckles and collapses is very sensitive to imperceptible defects and cannot be predicted, which challenges the of such structures. Consequently, probabilistic descriptions in terms of empirical design rules are used and designing reliable structures requires the use of conservative strength estimates. We introduce a nonlinear description where finite-amplitude perturbations trigger buckling. Drawing from the analogy between imperfect shells which buckle and imperfect pipe flow which becomes turbulent, we experimentally show that lateral probing of cylindrical shells reveals their strength nondestructively. A new ridge-tracking method is applied to commercial cylinders with a hole showing that when the location where buckling nucleates is known we can accurately predict the buckling load of each individual shell, within ±5%. Our study provides a new promising framework to understand shell buckling, and more generally, imperfection-sensitive instabilities.

The real area of contact of a frictional interface changes rapidly when the normal load is altered, and evolves slowly when the normal load is held constant, aging over time. Traditionally, the total area of contact is considered a proxy for the frictional strength of the interface. Here, we show that the state of a frictional interface is not entirely defined by the total real area of contact but depends on the geometrical nature of that contact as well. We directly visualize an interface between rough elastomers and smooth glass and identify that normal loading and frictional aging evolve the interface differently, even at a single contact level. We introduce a protocol wherein the real area of contact is held constant in time. Under these conditions, the interface is continually evolving; small contacts shrink and large contacts coarsen.

We report that an electro-osmotic instability of concentration enrichment in curved geometries for an aqueous electrolyte, as opposed to the well-known one, is initiated exclusively at the enriched interface (anode), rather than at the depleted one (cathode). For this instability, the limitation of an unrealistically high material Peclet number in planar geometry is eliminated by the strong electric field arising from the line charge singularity. In a model setup of concentric circular electrodes, we show by stability analysis, numerical simulation, and experimental visualization that instability occurs at the inner anode, below a critical radius of curvature. The stability criterion is also formulated in terms of a critical electric field and extended to arbitrary (two-dimensional) geometries by conformal mapping. This discovery suggests that transport may be enhanced in processes limited by salt enrichment, such as reverse osmosis, by triggering this instability with needlelike electrodes.

We simultaneously measure the static friction and the real area of contact between two solid bodies. These quantities are traditionally considered equivalent, and under static conditions both increase logarithmically in time, a phenomenon coined aging. Here we show that the frictional aging rate is determined by the combination of the aging rate of the real area of contact and two memory-erasure effects that occur when shear is changed (e.g., to measure static friction.) The application of a static shear load accelerates frictional aging while the aging rate of the real area of contact is unaffected. Moreover, a negative static shear-pulling instead of pushing-slows frictional aging, but similarly does not affect the aging of contacts. The origin of this shear effect on aging is geometrical. When shear load is increased, minute relative tilts between the two blocks prematurely erase interfacial memory prior to sliding, negating the effect of aging. Modifying the loading point of the interface eliminates these tilts and as a result frictional aging rate becomes insensitive to shear. We also identify a secondary memory-erasure effect that remains even when all tilts are eliminated and show that this effect can be leveraged to accelerate aging by cycling between two static shear loads.

The essence of turbulent flow is the conveyance of energy through the formation, interaction, and destruction of eddies over a wide range of spatial scales-from the largest scales where energy is injected down to the smallest scales where it is dissipated through viscosity. Currently, there is no mechanistic framework that captures how the interactions of vortices drive this cascade. We show that iterations of the elliptical instability, arising from the interactions between counter-rotating vortices, lead to the emergence of turbulence. We demonstrate how the nonlinear development of the elliptical instability generates an ordered array of antiparallel secondary filaments. The secondary filaments mutually interact, leading to the formation of even smaller tertiary filaments. In experiments and simulations, we observe two and three iterations of this cascade, respectively. Our observations indicate that the elliptical instability could be one of the fundamental mechanisms by which the turbulent cascade develops.

We report frozen ice patterns for the water droplets impacting on a cold substrate through high-speed images. These patterns can be manipulated by several physical parameters (the droplet size, falling height, and substrate temperature), and the scaling analysis has a remarkable agreement with the phase diagram. The observed double-concentric toroidal shape is attributed to the correlation between the impacting dynamics and freezing process, as confirmed by the spatiotemporal evolution of the droplet temperature, the identified timescale associated with the morphology and solidification (t(inn) similar or equal to tau(sol)), and the ice front-advection model. These results for frozen patterns provide insight into the complex interplay of the rapid impacting hydrodynamics, the transient heat transfer, and the intricate solidification process.

In a circular channel passing overlimiting current (faster than diffusion), transient vortices of bulk electroconvection are observed in a salt-depleted region within the horizontal plane. The spatiotemporal evolution of the salt concentration is directly visualized, revealing the propagation of a deionization shock wave driven by bulk electroconvection up to millimeter scales. This mechanism leads to quantitatively similar dynamics as for deionization shocks in charged porous media, which are driven instead by surface conduction and electro-osmotic flow at micron to nanometer scales. The remarkable generality of deionization shocks under overlimiting current could be used to manipulate ion transport in complex geometries for desalination and water treatment.

Granular material in a swirled container exhibits a curious transition as the number of particles is increased: At low densities, the particle cluster rotates in the same direction as the swirling motion of the container, while at high densities it rotates in the opposite direction. We investigate this phenomenon experimentally and numerically using a corotating reference frame in which the system reaches a statistical steady state. In this steady state, the particles form a cluster whose translational degrees of freedom are stationary, while the individual particles constantly circulate around the cluster’s center of mass, similar to a ball rolling along the wall within a rotating drum. We show that the transition to counterrotation is friction dependent. At high particle densities, frictional effects result in geometric frustration, which prevents particles from cooperatively rolling and spinning. Consequently, the particle cluster rolls like a rigid body with no-slip conditions on the container wall, which necessarily counterrotates around its own axis. Numerical simulations verify that both wall-disk friction and disk-disk friction are critical for inducing counterrotation.

Machine learning has gained widespread attention as a powerful tool to identify structure in complex, high-dimensional data. However, these techniques are ostensibly inapplicable for experimental systems where data are scarce or expensive to obtain. Here, we introduce a strategy to resolve this impasse by augmenting the experimental dataset with synthetically generated data of a much simpler sister system. Specifically, we study spontaneously emerging local order in crease networks of crumpled thin sheets, a paradigmatic example of spatial complexity, and show that machine learning techniques can be effective even in a data-limited regime. This is achieved by augmenting the scarce experimental dataset with inexhaustible amounts of simulated data of rigid flat-folded sheets, which are simple to simulate and share common statistical properties. This considerably improves the predictive power in a test problem of pattern completion and demonstrates the usefulness of machine learning in bench-top experiments where data are good but scarce.

Biofilms are structured communities of bacteria that exhibit complex spatio-temporal dynamics. In liquid media, Bacillus subtilis produces an opaque floating biofilm, or a pellicle. Biofilms are generally associated with an interface, but the ability of Bacillus subtilis to swim means the bacteria are additionally able to reside within the liquid phase. However, due to imaging complications associated with the opacity of pellicles, the extent to which bacteria coexist within the liquid bulk as well as their behavior in the liquid is not well studied. We therefore develop a high-throughput imaging system to image underneath developing pellicles. Here we report a well-defined sequence of developmental events that occurs underneath a growing pellicle. Comparison with bacteria deficient in swimming and chemotaxis suggest that these properties enable collective bacterial swimming within the liquid phase which facilitate faster surface colonization. Furthermore, comparison to bacteria deficient in exopolymeric substances (EPS) suggest that the lack of a surface pellicle prevents further developmental steps from occurring within the liquid phase. Our results reveal a sequence of developmental events during pellicle growth, encompassing adhesion, conversion, growth, maturity, and detachment on the interface, which are synchronized with the bacteria in the liquid bulk increasing in density until the formation of a mature surface pellicle, after which the density of bacteria in the liquid drops.

A key difficulty to understanding friction is that many physical mechanisms contribute simultaneously. Here we investigate third-body frictional dynamics in a model experimental system that eliminates first-body interaction, wear, and fracture, and concentrates on the elastic interaction between sliding blocks and third bodies. We simultaneously visualize the particle motion and measure the global shear force. By systematically increasing the number of foreign particles, we find that the frictional dissipation depends only on the size ratio between surface asperities and the loose particles, irrespective of the particle’s size or the surface’s roughness. When the particles are comparable in size to the surface features, friction increases linearly with the number of particles. For particles smaller than the surface features, friction grows sublinearly with the number of particles. Our findings suggest that matching the size of surface features to the size of potential contaminants may be a good strategy for reliable lubrication.

The initiation of contact between liquid and a dry solid is of great fundamental and practical importance. We experimentally probe the dynamics of wetting that occur when an impacting drop first contacts a dry surface. We show that, initially, wetting is mediated by the formation and growth of nanoscale liquid bridges, binding the liquid to the solid across a thin film of air. As the liquid bridge expands, air accumulates and deforms the liquid-air interface, and a capillary wave forms ahead of the advancing wetting front. This capillary wave regularizes the pressure at the advancing wetting front and explains the anomalously low wetting velocities observed. As the liquid viscosity increases, the wetting front velocity decreases; we propose a phenomenological scaling for the observed decrease of the wetting velocity with liquid viscosity.

Many phenomena of interest in nature and industry occur rapidly and are difficult and cost-prohibitive to visualize properly without specialized cameras. Here we describe in detail the Virtual Frame Technique (VFT), a simple, useful, and accessible form of compressed sensing that increases the frame acquisition rate of any camera by several orders of magnitude by leveraging its dynamic range. VFT is a powerful tool for capturing rapid phenomenon where the dynamics facilitate a transition between two states, and are thus binary. The advantages of VFT are demonstrated by examining such dynamics in five physical processes at unprecedented rates and spatial resolution: fracture of an elastic solid, wetting of a solid surface, rapid fingerprint reading, peeling of adhesive tape, and impact of an elastic hemisphere on a hard surface. We show that the performance of the VFT exceeds that of any commercial high speed camera not only in rate of imaging but also in field of view, achieving a 65MHz frame rate at 4MPx resolution. Finally, we discuss the performance of the VFT with several commercially available conventional and high-speed cameras. In principle, modern cell phones can achieve imaging rates of over a million frames per second using the VFT.

When vortex rings collide head-on at high enough Reynolds numbers, they ultimately annihilate through a violent interaction which breaks down their cores into a turbulent cloud. We experimentally show that this very strong interaction, which leads to the production of fluid motion at very fine scales, uncovers direct evidence of an iterative cascade of instabilities in a bulk fluid. When the coherent vortex cores approach each other, they deform into tentlike structures and the mutual strain causes them to locally flatten into extremely thin vortex sheets. These sheets then break down into smaller secondary vortex filaments, which themselves rapidly flatten and break down into even smaller tertiary filaments. By performing numerical simulations of the full Navier-Stokes equations, we also resolve one iteration of this instability and highlight the subtle role that viscosity must play in the rupturing of a vortex sheet. The concurrence of this observed iterative cascade of instabilities over various scales with those of recent theoretical predictions could provide a mechanistic framework in which the evolution of turbulent flows can be examined in real time as a series of discrete dynamic instabilities.