Shmuel M. Rubinstein

Detachment fronts and the onset of dynamic friction.

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.

Slip-stick and the evolution of frictional strength

The evolution of frictional strength has great fundamental and practical importance. Applications range from earthquake dynamics to 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 laws, 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 times. 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.

SKATING ON A FILM OF AIR: DROPS IMPACTING ON A SURFACE

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.

Spatial regulation of histidine kinases governing biofilm formation in Bacillus subtilis.

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.

Osmotic pressure can regulate matrix gene expression in Bacillus subtilis

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.

Visualizing stick–slip: experimental observations of processes governing the nucleation of frictional sliding

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.

Drops can bounce from perfectly hydrophilic surfaces

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.

Crack-like processes governing the onset of frictional slip

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.

Stabilizing stick-slip friction

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.

Probing phenotypic growth in expanding Bacillus subtilis biofilms

We develop an optical imaging technique for spatially and temporally tracking biofilm growth and the distribution of the main phenotypes of a Bacillus subtilis strain 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.