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 real area of contact of a frictional interface changes rapidly when the normal load is altered, and evolves slowly when 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 novel 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.
The essence of turbulent flow is the conveyance of kinetic 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. For nearly a century, this universal energy cascade has been the foundation of our understanding for how turbulent flows function. However, a mechanistic description of how ensembles of vortices interact to drive this energy cascade remains elusive. Here we introduce one essential mechanism for turbulence. We show that a sequence of the elliptical instability, arising from the close interaction between counter-rotating vortices, leads to the emergence of turbulent flow. We demonstrate how the nonlinear development of the elliptical instability generates an ordered array of antiparallel secondary filaments, which are perpendicular to the original vortex tubes. These secondary filaments interact with one another, leading to the generation of even smaller tertiary filaments. This iterated cascade of the elliptical instability produces vortices of smaller and smaller sizes, until viscosity damps out all motion. In our experiments and simulations, we clearly observe two and three iterations of this cascade, respectively. Our observations indicate that the elliptical instability could be a fundamental mechanism by which the turbulent cascade develops and is sustained.
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.
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.
We use experiments and numerical simulations to study the rapid buckling of thin-walled cones as they impact a solid surface at high velocities. The buildup of air pressure inside the cone localizes the deformations to the impacting interface with the solid surface, leading to the hierarchical formation of an ordered pattern of small rhomboidal cells. In contrast, when the inner air pressure is not allowed to develop, the ordered pattern is destabilized and the cone collapses in a highly disordered state on long length scales. Numerical simulations confirm that the transition between ordered and disordered crumpling is governed by the competition between the elastic deformation energy of the shells and the work required to pressurize the air. Our results show how dynamic stabilization via tensioning suppresses long wavelength subcritical instabilities in shells and leads to the localization and propagation of short wavelength patterns.
Despite the apparent ease with which sheets of paper are crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity. This arises from the infinite number of configurations that disordered, crumpled sheets can take. Here we experimentally show that key aspects of axially confined crumpled Mylar sheets have a very simple description; evolution of damage in crumpling dynamics can largely be described by a single global quantity—the total length of creases. We follow the evolution of the damage network in repetitively crumpled elastoplastic sheets, and show that the dynamics are deterministic, depending only on the instantaneous state of the crease network and not on the crumpling history. We also show that this global quantity captures the crumpling dynamics of a sheet crumpled for the first time. This leads to a remarkable reduction in complexity, allowing a description of a highly disordered system by a single state parameter.
This paper investigates issues that have arisen in recent efforts to revise long-standing knockdown factors for elastic shell buckling, which are widely regarded as being overly conservative for well-constructed shells. In particular, this paper focuses on cylindrical shells under axial compression with emphasis on the role of local geometric dimple imperfections and the use of lateral force probes as surrogate imperfections. Local and global buckling loads are identified and related for the two kinds of imperfections. Buckling loads are computed for four sets of relevant boundary conditions revealing a strong dependence of the global buckling load on overall end-rotation constraint when local buckling precedes global buckling. A reasonably complete picture emerges, which should be useful for informing decisions on establishing knockdown factors. Experiments are performed using a lateral probe to study the stability landscape for a cylindrical shell with overall end rotation constrained in the first set of tests and then unconstrained in the second set of tests. The nonlinear buckling behavior of spherical shells under external pressure is also examined for both types of imperfections. The buckling behavior of spherical shells is different in a number of important respects from that of the cylindrical shells, particularly regarding the interplay between local and global buckling and the post-buckling load-carrying capacity. These behavioral differences have bearing on efforts to revise buckling design rules. The present study raises questions about the perspicacity of using probe force imperfections as surrogates for geometric dimple imperfections.
We measure the static frictional resistance and the real area of contact between two solid blocks subjected to a normal load. We show that following a two-step change in the normal load the system exhibits nonmonotonic aging and memory effects, two hallmarks of glassy dynamics. These dynamics are strongly influenced by the discrete geometry of the frictional interface, characterized by the attachment and detachment of unique microcontacts. The results are in good agreement with a theoretical model we propose that incorporates this geometry into the framework recently used to describe Kovacs-like relaxation in glasses as well as thermal disordered systems. These results indicate that a frictional interface is a glassy system and strengthen the notion that nonmonotonic relaxation behavior is generic in such systems.
Bacterial biofilms are surface-attached microbial communities encased in self-produced extracellular polymeric substances. Here we demonstrate that during the development ofBacillus subtilis biofilms, matrix production is localized to an annular front propagating at the periphery and sporulation to a second front at a fixed distance at the interior. We show that within these fronts, cells switch off matrix production and transition to sporulation after a set time delay of ∼100 min. Correlation analyses of fluctuations in fluorescence reporter activity reveal that the fronts emerge from a pair of gene-expression waves of matrix production and sporulation. The localized expression waves travel across cells that are immobilized in the biofilm matrix in contrast to active cell migration or horizontal colony spreading. Our results suggest that front propagation arises via a local developmental program occurring at the level of individual bacterial cells, likely driven by nutrient depletion and metabolic by-product accumulation. A single-length scale and timescale couples the spatiotemporal propagation of both fronts throughout development. As a result, gene expression patterns within the advancing fronts collapse to self-similar expression profiles. Our findings highlight the key role of the localized cellular developmental program associated with the propagating front in describing biofilm growth.
Bioinspired soft machines made of highly deformable materials are enabling a variety of innovative applications, yet their locomotion typically requires several actuators that are independently activated. We harnessed kirigami principles to significantly enhance the crawling capability of a soft actuator. We designed highly stretchable kirigami surfaces in which mechanical instabilities induce a transformation from flat sheets to 3D-textured surfaces akin to the scaled skin of snakes. First, we showed that this transformation was accompanied by a dramatic change in the frictional properties of the surfaces. Then, we demonstrated that, when wrapped around an extending soft actuator, the buckling-induced directional frictional properties of these surfaces enabled the system to efficiently crawl.
We measure the response of cylindrical shells to poking and identify a stability landscape, which fully characterizes the stability of perfect shells and imperfect ones in the case where a single defect dominates. We show that the landscape of stability is independent of the loading protocol and the poker geometry. Our results suggest that the complex stability of shells reduces to a low dimensional description. Tracking ridges and valleys of this landscape defines a natural phase-space coordinates for describing the stability of shells.
We demonstrate the use of fluorescence microscopy as a tool for mapping the spatial distribution of fluid flow and electrochemical reactions in an operating aqueous quinone flow cell. 9,10-anthraquinone-2,7-disulfonic acid (AQDS) is a reversibly redox active molecule with a reduced form (H2AQDS) that fluoresces when excited by UV light. Visualization of AQDS/H2AQDS within commercial porous carbon electrode papers enables a direct comparison of their performance. In particular, this technique illuminates surprisingly large-scale heterogeneous fluid flow profiles present in several carbon papers, leaving substantial areas of the electrode mass-transport limited. In others, more homogeneous flow distribution is observed, but limitations such as low electronic conductivity and limited accessible electrode surface area limit the performance. This work provides insights into improving structural properties of porous electrodes for high-power density electrochemical flow cells.
We observe nonmonotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic nonexponential relaxation. However, when after a certain waiting time the compression is partially reduced, both systems exhibit a nonmonotonic response: the normal force first increases over many minutes or even hours until reaching a peak value, and only then is relaxation resumed. The peak time scales linearly with the waiting time, indicating that these systems retain long-lasting memory of previous conditions. Our results and the measured scaling relations are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems, suggesting that the nonmonotonic behavior may be generic and that athermal systems can show genuine glassy behavior.
When soft gels move across a hard surface, stick–slip frictional sliding is mediated by propagation of adhesion and detachment fronts. Here we experimentally investigate the sliding dynamics of an extended frictional interface between soft Silicone gel and hard PMMA and identify three distinct sliding regimes. We directly visualize the interface and show that a minute manipulation of the initial loading angle results in a sharp bifurcation between the different sliding states. The phase diagram as well as universal scaling relations governing the dynamics is presented.
We develop an optical imaging technique for spatially and temporally tracking biofilm growth and the distribution of the main phenotypes of a Bacillus subtilisstrain with a triple-fluorescent reporter for motility, matrix production, and sporulation. We develop a calibration procedure for determining the biofilm thickness from the transmission images, which is based on Beer-Lambert’s law and involves cross-sectioning of biofilms. To obtain the phenotype distribution, we assume a linear relationship between the number of cells and their fluorescence and determine the best combination of calibration coefficients that matches the total number of cells for all three phenotypes and with the total number of cells from the transmission images. Based on this analysis, we resolve the composition of the biofilm in terms of motile, matrix-producing, sporulating cells and low-fluorescent materials which includes matrix and cells that are dead or have low fluorescent gene expression. We take advantage of the circular growth to make kymograph plots of all three phenotypes and the dominant phenotype in terms of radial distance and time. To visualize the nonlocal character of biofilm growth, we also make kymographs using the local colonization time. Our technique is suitable for real-time, noninvasive, quantitative studies of the growth and phenotype distribution of biofilms which are either exposed to different conditions such as biocides, nutrient depletion, dehydration, or waste accumulation.