A crumpled sheet of paper displays an intricate pattern of creases and point-like singular structures, termed d-cones. It is typically assumed that elongated creases form when ridges connecting two d-cones fold beyond the material yielding threshold, and scarring is thus a by-product of the folding dynamics that seek to minimize elastic energy. Here we show that rather than merely being the consequence of folding, plasticity can act as its instigator. We introduce and characterize a different type of crease that is inherently plastic and is formed by the propagation of a single point defect. When a pre-existing d-cone is strained beyond a certain threshold, the singular structure at its apex sharpens abruptly. The resulting focusing of strains yields the material just ahead of the singularity, allowing it to propagate, leaving a furrow-like scar in its wake. We suggest an intuitive fracture analogue to explain the creation of furrows.
Drops are well known to rebound from superhydrophobic surfaces and from liquid surfaces. Here, we show that drops can also rebound from a superhydrophilic solid surface such as an atomically smooth mica sheet. However, the coefficient of restitution CR associated with this process is significantly lower than that associated with rebound from superhydrophobic surfaces. A direct imaging method allows us to characterize the dynamics of the deformation of the drop in entering the vicinity of the surface. We find that drop bouncing occurs without the drop ever touching the solid and there is a nanometer-scale film of air that separates the liquid and solid, suggesting that shear in the air film is the dominant source of dissipation during rebound. Furthermore, we see that any discrete nanometer-height defects on an otherwise hydrophilic surface, such as treated glass, completely inhibits the bouncing of the drop, causing the liquid to wet the surface. Our study adds a new facet to the dynamics of droplet impact by emphasizing that the thin film of air can play a role not just in the context of splashing but also bouncing, while highlighting the role of rare surface defects in inhibiting this response.
The application of an electric field to a suspension of charged particles can lead to the formation of patterns due to electrohydrodynamic instabilities which remain poorly understood. We elucidate this behavior by visualizing the dynamics of charged carbon black particles suspended in a nonpolar solvent in response to an electric field. As the particles are transported across a microfluidic channel, an instability occurs in which the initially uniform, rapidly advancing particle front develops fingers. Furthermore, when the direction of the applied field is repeatedly switched, the particles localize into a remarkably well-defined periodic pattern which reflects an interplay between the fingering instability and particle diffusion.
We directly measure the rapid spreading dynamics succeeding the impact of a droplet of fluid on a solid, dry surface. Upon impact, the air separating the liquid from the solid surface fails to drain and wetting is delayed as the liquid rapidly spreads outwards over a nanometer thin film of air. We show that the approach of the spreading liquid front toward the surface is unstable and the spreading front lifts off away from the surface. Lift-off ensues well before the liquid contacts the surface, in contrast with prevailing paradigm where lift-off of the liquid is contingent on solid-liquid contact and the formation of a viscous boundary layer. Here we investigate the dynamics of liquid spreading over a thin film of air and its lift-off away from the surface over a large range of fluid viscosities and find that the lift-off instability is dependent on viscosity and occurs at a time that scales with the viscosity to the power of one half.
Many bacteria organize themselves into structurally complex communities known as biofilms in which the cells are held together by an extracellular matrix. In general, the amount of extracellular matrix is related to the robustness of the biofilm. Yet, the specific signals that regulate the synthesis of matrix remain poorly understood. Here we show that the matrix itself can be a cue that regulates the expression of the genes involved in matrix synthesis in Bacillus subtilis. The presence of the exopolysaccharide component of the matrix causes an increase in osmotic pressure that leads to an inhibition of matrix gene expression. We further show that non‐specific changes in osmotic pressure also inhibit matrix gene expression and do so by activating the histidine kinase KinD. KinD, in turn, directs the phosphorylation of the master regulatory protein Spo0A, which at high levels represses matrix gene expression. Sensing a physical cue such as osmotic pressure, in addition to chemical cues, could be a strategy to non‐specifically co‐ordinate the behaviour of cells in communities composed of many different species.
The commonly accepted description of drops impacting on a surface typically ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air breaks down as the fluid wets the surface via a spinodal-like mechanism. Our results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms.
Faults are intrinsically heterogeneous with common occurrences of jogs, edges and steps. We therefore explore experimentally and theoretically how fault edges may affect earthquake and slip dynamics. In the presented experiments and accompanying theoretical model, shear loads are applied to the edge of one of two flat blocks in frictional contact that form a fault analog. We show that slip occurs via a sequence of rapid rupture events that initiate from the loading edge and are arrested after propagating a finite distance. Each successive event extends the slip size, transfers the applied shear across the block, and causes progressively larger changes of the contact area along the contact surface. Resulting from this sequence of events, a hard asperity is dynamically formed near the loaded edge. The contact area beyond this asperity is largely reduced. These sequences of rapid events culminate in slow slip events that precede a major, unarrested slip event along the entire contact surface. We suggest that the 1998 M5.0 Sendai and 1995 off-Etorofu earthquake sequences may correspond to this scenario. Our work demonstrates, qualitatively, how the simplest deviation from uniform shear loading may significantly affect both earthquake nucleation processes and how fault complexity develops.
Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes. Such manipulation of collective modes may be generally relevant to extended nonlinear systems driven near to criticality.
Bacillus subtilis is able to form architecturally complex biofilms on solid medium due to the production of an extracellular matrix. A master regulator that controls the expression of the genes involved in matrix synthesis is Spo0A, which is activated by phosphorylation via a phosphorelay involving multiple histidine kinases. Here we report that four kinases, KinA, KinB, KinC, and KinD, help govern biofilm formation but that their contributions are partially masked by redundancy. We show that the kinases fall into two categories and that the members of each pair (one pair comprising KinA and KinB and the other comprising KinC and KinD) are partially redundant with each other. We also show that the kinases are spatially regulated: KinA and KinB are active principally in the older, inner regions of the colony, and KinC and KinD function chiefly in the younger, outer regions. These conclusions are based on the morphology of kinase mutants, real-time measurements of gene expression using luciferase as a reporter, and confocal microscopy using a fluorescent protein as a reporter. Our findings suggest that multiple signals from the older and younger regions of the colony are integrated by the kinases to determine the overall architecture of the biofilm community.
Natural faults are intrinsically heterogeneous where jogs, edges and steps are common. We experimentally explore how fault edges may affect earthquake and slip dynamics by applying shear to the edge of one of two flat blocks in frictional contact. We show that slip occurs via a sequence of rapid rupture events that arrest after a finite distance. Successive events extend the slip size, transfer the applied shear across the block, and cause progressively larger changes of the contact area along the contact surface. Each sequence of events dynamically forms an asperity near the edge and largely reduces the contact area beyond. These sequences of rapid events all culminate in slow slip events that lead to major, unarrested slip along the entire contact surface. These results show that a simple deviation from uniform shear loading configuration can significantly and qualitatively affect both earthquake nucleation processes and the evolution of fault complexity.
The evolution of frictional strength has great fundamental and practical importance. Applications range from earthquake dynamicsto hard-drive read/write cycles. Frictional strength is governed by the resistance to shear of the large ensemble of discrete contacts that forms the interface that separates two sliding bodies. An interface’s overall strength is determined by both the real contact area and the contacts’ shear strength. Whereas the average motion of large, slowly sliding bodies is well-described by empirical friction laws3,8,9,10, interface strength is a dynamic entity that is inherently related to both fast processes such as detachment/re-attachment and the slow process of contact area rejuvenation. Here we show how frictional strength evolves from extremely short to long timescales, by continuous measurements of the concurrent local evolution of the real contact area and the corresponding interface motion (slip) from the first microseconds when contact detachment occurs to large (100-second) timescales. We identify four distinct and inter-related phases of evolution. First, all of the local contact area reduction occurs within a few microseconds, on the passage of a crack-like front. This is followed by the onset of rapid slip over a characteristic time, the value of which suggests a fracture-induced reduction of contact strength before any slip occurs. This rapid slip phase culminates with a sharp transition to slip at velocities an order of magnitude slower. At slip arrest, ‘ageing’ immediately commences as contact area increases on a characteristic timescale determined by the system’s local memory of its effective contact time before slip arrest. We show how the singular logarithmic behaviour generally associated with ageing is cut off at short times16. These results provide a comprehensive picture of how frictional strength evolves from the short times and rapid slip velocities at the onset of motion to ageing at the long times following slip arrest.
Understanding the dynamics of frictional motion is essential to fields ranging from nano-machines to the study of earthquakes. Frictional motion involves a huge range of time and length scales, coupling the elastic fields of two blocks under stress to the dynamics of the myriad interlocking microscopic contacts that form the interface at their plane of separation. In spite of the immense practical and fundamental importance of friction, many aspects of the basic physics of the problem are still not well understood. One such aspect is the nucleation of frictional motion commonly referred to as the transition from static to dynamic friction. Here we review experimental studies of dynamical aspects of frictional sliding. We focus mainly on recent advances in real-time visualization of the real area of contact along large spatially extended interfaces and the importance of rapid fracture-like processes that appear at the onset of frictional instability.
The dynamics of frictional motion have been studied for hundreds of years, yet many aspects of these important processes are not understood. First described by Coulomb and Amontons as the transition from static to dynamic friction, the onset of frictional motion is central to fields as diverse as physics, tribology, mechanics of earthquakes, and fracture. We review recent studies in which fast (real-time) visualization of the true contact area along a rough spatially extended interface separating two blocks of like material has revealed the detailed dynamics of how this transition takes place. The onset of motion is preceded by a discrete sequence of rapid cracklike precursors, which are initiated at shear levels that are well below the threshold for static friction. These precursors systematically increase in spatial extent with the applied shear force and leave in their wake a significant redistribution of the true contact area. Their cumulative effect is such that, just prior to overall sliding of the blocks, a highly inhomogeneous contact profile is established along the interface. At the transition to overall motion, these precursor cracks trigger both slow propagation modes and modes that travel faster than the shear wave speed. Overall frictional motion takes place only when either the slow propagation modes or additional shear cracks excited by these slow modes traverse the entire interface. Surprisingly, in the resulting stick–slip motion, the surface contact profile retains the profile built up prior to the first slipping event. These results suggest a fracture-based mechanism for stick–slip motion that is qualitatively different from other descriptions.
We present a visualization of the predicted instability in ionic conduction from a binary electrolyte into a charge selective solid. This instability develops when a voltage greater than critical is applied to a thin layer of copper sulfate flanked by a copper anode and a cation selective membrane. The current-voltage dependence exhibits a saturation at the limiting current. With a further increase of voltage, the current increases, marking the transition to the overlimiting conductance. This transition is mediated by the appearing vortical flow that increases with the applied voltage.
We measure the spatial and temporal behavior of the true contact area A along a rough spatially extended interface between two blocks in frictional contact. Upon the application of shear the onset of motion is preceded by a discrete sequence of cracklike precursors, which are initiated at shear levels that are well below the threshold for static friction. These precursors arrest well before traversing the entire interface. They systematically increase in length with the applied shear force and significantly redistribute the true contact area along the interface. Thus, when frictional sliding occurs, the initially uniform contact area along the interface has already evolved to one that is highly nonuniform in space.
We perform real-time measurements of the net contact area between two blocks of like material at the onset of frictional slip. We show that the process of interface detachment, which immediately precedes the inception of frictional sliding, is governed by three different types of detachment fronts. These crack-like detachment fronts differ by both their propagation velocities and by the amount of net contact surface reduction caused by their passage. The most rapid fronts propagate at intersonic velocities but generate a negligible reduction in contact area across the interface. Sub-Rayleigh fronts are crack-like modes which propagate at velocities up to the Rayleigh wave speed, VR, and give rise to an approximate 10% reduction in net contact area. The most efficient contact area reduction (~20%) is precipitated by the passage of ‘slow detachment fronts’. These fronts propagate at ‘anomalously’ slow velocities, which are over an order of magnitude lower than VR yet orders of magnitude higher than other characteristic velocity scales such as either slip or loading velocities. Slow fronts are generated, in conjunction with intersonic fronts, by the sudden arrest of sub-Rayleigh fronts. No overall sliding of the interface occurs until either of the slower two fronts traverses the entire interface, and motion at the leading edge of the interface is initiated. Slip at the trailing edge of the interface accompanies the motion of both the slow and sub-Rayleigh fronts. We might expect these modes to be important in both fault nucleation and earthquake dynamics.
We perform quantitative measurements of the actual area of contact, A, formed by two rough solids that are subjected to different normal loading protocols. We show that microscopic motion, induced by Poisson contraction or expansion, produces a strong memory dependence of A on the loading history with a large corresponding influence on the system’s frictional strength. These effects, together with accompanying transient dynamics, are independent of humidity, loading rates, and material contrast across the interface.
The dynamics of friction have been studied for hundreds of years, yet many aspects of these everyday processes are not understood. One such aspect is the onset of frictional motion (slip). First described more than 200 years ago as the transition from static to dynamic friction, the onset of slip is central to fields as diverse as physics, tribology, mechanics of earthquakes and fracture. Here we show that the onset of frictional slip is governed by three different types of coherent crack-like fronts: these are observed by real-time visualization of the net contact area that forms the interface separating two blocks of like material. Two of these fronts, which propagate at subsonic and intersonic velocities, have been the subject of intensive recent interest. We show that a third type of front, which propagates an order of magnitude more slowly, is the dominant mechanism for the rupture of the interface. No overall motion (sliding) of the blocks occurs until either of the slower two fronts traverses the entire interface.