We propose a theory of shear flow in dense granular materials. A key ingredient of the theory is an effective temperature that determines how the material responds to external driving forces such as shear stresses and vibrations. We show that, within our model, friction between grains produces stick-slip behavior at intermediate shear rates, even if the material is rate-strengthening at larger rates. In addition, externally generated acoustic vibrations alter the stick-slip amplitude, or suppress stick-slip altogether, depending on the pressure and shear rate. We construct a phase diagram that indicates the parameter regimes for which stick-slip occurs in the presence and absence of acoustic vibrations of a fixed amplitude and frequency. These results connect the microscopic physics to macroscopic dynamics, and thus produce useful information about a variety of granular phenomena including rupture and slip along earthquake faults, the remote triggering of instabilities, and the control of friction in material processing.
We monitor the stick-slip displacements of a very slowly driven moveable perforated top plate which interacts via shearing with a packing of identical glass beads confined in a tray. When driven at a constant stress rate, the distributions of large event displacements and energies triggered by the stick-slip instabilities exhibit power law responses reminiscent of the Gutenberg-Richter law for earthquakes. Small events are quasi-size independent, signaling crossover from single-bead transport to collective behavior.
We present results from a physical experiment which demonstrates that a sheared granular medium behaves in a manner analogous to earthquake activity. The device consists of an annular plate rotating over a granular medium in a stick-slip fashion. Previous observations by us include a bounded critical state with a power law distribution of event energy consistent with the Gutenberg-Richter law, here we also reveal stair-case seismicity, clustering, foreshocks, aftershocks and seismic quiescence. Subcritical and supercritical regimes have also been observed by us depending on the system configur…
Recent experiments suggest that shear-enhanced growth of concentration fluctuations in polymer solutions is strongly influenced by solid boundaries. We analyze the dynamics of a model of a sheared polymer solution, accounting for the effect of stress variations on mass flux and for wall-slip. If (and only if) these effects are present, the flow exhibits a boundary-localized instability consistent with experimental observations. Even in the absence of flow instability, thermally-driven concentration fluctuations are significantly enhanced near the boundary.
The unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at t…
We have developed a dynamic self-consistent field theory, without any adjustable parameters, for unentangled polymer blends under shear. Our model accounts for the interaction between polymers, and enables one to compute the evolution of the local rheology, microstructure and the conformations of the polymer chains under shear self-consistently. We use this model to study the interfacial dynamics in sheared polymer blends and make a quantitative comparison between this model and Molecular Dynamics simulations. We find good agreement between the two methods.
We consider the classical problem of the stick-slip dynamics observed when peeling a roller adhesive tape at a constant velocity. From fast imaging recordings, we extract the dependencies of the stick and slip phases durations with the imposed peeling velocity and peeled ribbon length. Predictions of Maugis and Barquins [in Adhesion 12, edited by K.W. Allen, Elsevier ASP, London, 1988, pp. 205--222] based on a quasistatic assumption succeed to describe quantitatively our measurements of the stick phase duration. Such model however fails to predict the full stick-slip cycle duration, revealing …
Shear banding and stick-slip instabilities have been long observed in sheared granular materials. Yet, their microscopic underpinnings, interdependencies and variability under different loading conditions have not been fully explored. Here, we use a non-equilibrium thermodynamics model, the Shear Transformation Zone theory, to investigate the dynamics of strain localization and its connection to stability of sliding in sheared, dry, granular materials. We consider frictional and frictionless grains as well as presence and absence of acoustic vibrations. Our results suggest that at low and inte…
We propose a generic model to describe the mechanical response and failure of systems which undergo a series of stick-slip events when subjected to an external load. We model the system as a bundle of fibers, where single fibers can gradually increase their relaxed length with a stick-slip mechanism activated by the increasing load. We determine the constitutive equation of the system and show by analytical calculations that on the macro-scale a plastic response emerges followed by a hardening or softening regime. Releasing the load, an irreversible permanent deformation occurs which depends o…
We develop the theory for stick-slip motion in ultra-thin liquid films confined between two moving atomically-flat surfaces. Our model is based on hydrodynamic equation for the flow coupled to the dynamic order parameter field describing the ``shear melting and freezing'' of the confined fluid. This model successfully accounts for observed phenomenology of friction in ultra-thin films, including periodic and chaotic sequences of slips, transitions from stick-slip motion to steady sliding.
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…
Conventional slippery surfaces show isotropic drop mobility in all directions, but many applications require directional drop motion along a particular path only. In previous studies, researchers used topographic substrates, together with different external stimuli, to demonstrate anisotropic drop motion, which is not very efficient and cost-effective. Herein, we report a novel approach to smartly control drop motion on lubricating fluid coated chemically heterogeneous surfaces composed of alternating hydrophobic and hydrophilic stripes. Upon depositing an aqueous drop on such a surface, the u…
We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional sliding and the periodic stick-slip motion are controlled by the amount of friction-induced torque at the interface. Our model provides a general framework to understand and relate a series of recent experimental observations, in particular the nucleation location of micro-slip instabilities and the build up of an asymmetric field of real contact area.
This paper is concerned with the quasi-static rheology of packings of glass spheres of diameter d (d=0.2mm, 0.7mm or 3mm). Stick-slip behaviour is observed on small spheres, i.e d=0.2mm & 0.7mm ; one observes also in this case a weakening of the rheology as the rate of deformation increases, and the larger the rate the larger the weakening; this generates macroscopic instabilities and stick-slip. Statistics of stick-slip events have been determined, which show that the larger the sample the more regular (i.e. "periodic") the sick-slip, the faster the strain rate the less periodic the events. O…
The growth dynamics of an air finger injected in a visco-elastic gel (a PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the standard Saffmann-Taylor instability, we observe - with increasing finger velocities - the existence of two new regimes: (a) a stick-slip regime for which the finger tip velocity oscillates between 2 different values, producing local pinching of the finger at regular intervals, (b) a ``tadpole'' regime where a fracture-type propagation is observed. A scaling argument is proposed to interpret the dependence of the stick-slip frequency with the me…
The effect of random surface roughness on hydrodynamics of viscous incompressible liquid is discussed. Roughness-driven contributions to hydrodynamic flows, energy dissipation, and friction force are calculated in a wide range of parameters. When the hydrodynamic decay length (the viscous wave penetration depth) is larger than the size of random surface inhomogeneities, it is possible to replace a random rough surface by effective stick-slip boundary conditions on a flat surface with two constants: the stick-slip length and the renormalization of viscosity near the boundary. The stick-slip len…
Using a high-speed camera, we follow the propagation of the detachment front during the peeling of an adhesive tape from a flat surface. In a given range of peeling velocity, this front displays a multiscale unstable dynamics, entangling two well-separated spatiotemporal scales, which correspond to microscopic and macroscopic dynamical stick-slip instabilities. While the periodic release of the stretch energy of the whole peeled ribbon drives the classical macro-stick-slip, we show that the micro-stick-slip, due to the regular propagation of transverse dynamic fractures discovered by Thoroddse…
The capillary traction of a liquid contact line causes highly localized deformations in soft solids, tremendously slowing down wetting and dewetting dynamics by viscoelastic braking. Enforcing nonetheless large velocities leads to the so-called stick-slip instability, during which the contact line periodically depins from its own wetting ridge. The mechanism of this periodic motion and, especially, the role of the dynamics in the fluid have remained elusive, partly because a theoretical description of the unsteady soft wetting problem is not available so far. Here we present the first numerica…
Stick-slip motion, a common phenomenon observed during crawling of cells, is found to be strongly sensitive to the substrate stiffness. Stick-slip behaviours have previously been investigated typically using purely elastic substrates. For a more realistic understanding of this phenomenon, we propose a theoretical model to study the dynamics on a viscoelastic substrate. Our model based on a reaction-diffusion framework, incorporates known important interactions such as retrograde flow of actin, myosin contractility, force dependent assembly and disassembly of focal adhesions coupled with cell-s…
Stick-slip, manifest as intermittent tangential motion between two solids, is a well-known friction instability that occurs in a number of natural and engineering systems. In the context of adhesive polymer interfaces, this phenomenon has often been solely associated with Schallamach waves, which are termed slow waves due to their low propagation speeds. We study the dynamics of a model polymer interface using coupled force measurements and high speed \emph{in situ} imaging, to explore the occurrence of stick-slip linked to other slow wave phenomena. Two new waves---slip pulse and separation p…
A decade ago, Budakian and Putterman (Phys. Rev. Lett., {\bf 85}, 1000 (2000)) ascribed friction to the formation of bonds arising from contact charging when a gold tip of a surface force apparatus was dragged on polymethylmethacrylate surface. We propose a stick-slip model that captures the observed correlation between stick-slip events and charge transfer, and the lack of dependence of the scale factor connecting the force jumps and charge transfer on normal load. Here, stick-slip dynamics arises as a competition between the visco-elastic and plastic deformation time scales and that due to t…
We study the effect of atomic scale surface-lubricant interactions on nanoscale boundary-lubricated friction, by considering two example surfaces - hydrophilic mica and hydrophobic graphene - confining thin layers of water in molecular dynamics simulations. We observe stick-slip dynamics for thin water films confined by mica sheets, involving periodic breaking-reforming transitions of atomic scale capillary water bridges formed around the potassium ions of mica. However, only smooth sliding without stick-slip events is observed for water confined by graphene, as well as for thicker water layer…
We revisit the Hébraud-Lequeux (HL) model for the rheology of jammed materials and argue that a possibly important time scale is missing from HL's initial specification. We show that our generalization of the HL model undergoes interesting oscillating instabilities for a wide range of parameters, which lead to intermittent, stick-slip flows under constant shear rate. The instability we find is akin to the synchronization transition of coupled elements that arises in many different contexts (neurons, fireflies, financial bankruptcies, etc.). We hope that our scenario could shed light on the com…
We experimentally study the frictional behavior of a two-dimensional slider pulled slowly over a granular substrate comprised of photoelastic disks. The slider is vibrated at frequencies ranging from 0 to 30 Hz in a direction parallel to sliding. The applied vibrations have constant peak acceleration, which results in constant average friction levels. Surprisingly, we find that stick-slip behavior, where stress slowly builds up and is released in intermittent slips, is enhanced as the frequency of vibration is increased. Our results suggest that increasing the frequency of vibration may help t…
Constitutive equations are proposed for dense materials, based on the identification of two types of free-volume activated rearrangements associated to shear and compaction. Two situations are studied: the case of an amorphous solid in a stress-strain test, and the case of a lubricant in tribology test. Varying parameters, strain softening, shear thinning, and stick-slip motion can be observed.
We present a comprehensive study of water drops sliding down chemically heterogeneous surfaces formed by a periodic pattern of alternating hydrophobic and hydrophilic stripes. Drops are found to undergo a stick-slip motion whose average speed is an order of magnitude smaller than that measured on a homogeneous surface having the same static contact angle. This motion is the result of the periodic deformations of the drop interface when crossing the stripes. Numerical simulations confirm this view and are used to elucidate the principles underlying the experimental observations.
We consider the response of an adsorbed polymer that is pulled by an AFM within a simple geometric framework. We separately consider the cases of i) fixed polymer-surface contact point, ii) sticky case where the polymer is peeled off from the substrate, and iii) slippery case where the polymer glides over the surface. The resultant behavior depends on the value of the surface friction coefficient and the adsorption strength. Our resultant force profiles in principle allow to extract both from non-equilibrium force-spectroscopic data.
We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs, when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state …
Reversibility is of paramount importance in the correct representation of surface peeling in various physical settings, ranging from motility in nature, to gripping devices in robotic applications, and even to sliding of tectonic plates. Modeling the detachment-reattachment sequence, known as stick-slip, imposes several challenges in a continuum framework. Here we exploit customized reversible cohesive elements in a hybrid finite element model that can handle occurrence of snap-through instabilities. The simulations capture various peeling phenomena that emerge in experimental observations, wh…
We study the forces and torques experienced by pill-shaped Janus particles of different aspect ratios where half of the surface obeys the no-slip boundary condition and the other half obeys the Navier slip condition of varying slip lengths. Using a recently developed boundary integral formulation whereby the traditional singular behaviour of this approach is removed analytically, we quantify the strength of the forces and torques experienced by such particles in a uniform flow field in the Stokes regime. Depending on the aspect ratio and the slip length, the force transverse to the flow direct…
Intermittent motion, called stick--slip, is a friction instability that commonly occurs during relative sliding of two elastic solids. In adhesive polymer contacts, where elasticity and interface adhesion are strongly coupled, stick--slip results from the propagation of slow detachment waves at the interface. Using \emph{in situ} imaging experiments at an adhesive contact, we show the occurrence of two distinct detachment waves moving parallel (Schallamach wave) and anti-parallel (separation wave) to the applied remote sliding. Both waves cause slip in the same direction and travel at speeds m…
Despite extensive studies on either smooth granular-fluid flow or the solid-like deformation at the slow limit, the change between these two extremes remains largely unexplored. By systematically investigating the fluctuations of tightly packed grains under steady shearing, we identify a transition zone with prominent stick-slip avalanches. We establish a state diagram, and propose a new dimensionless shear rate based on the speed dependence of inter-particle friction and particle size. With fluid-immersed particles confined in a fixed volume and forced to "flow" at viscous numbers $J$ decades…
We discuss the results of simulations of an intruder pulled through a two-dimensional granular system by a spring, using a model designed to lend insight into the experimental findings described by Kozlowski et al. [Phys. Rev. E, 100, 032905 (2019)]. In that previous study the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick-slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions …
We report results of 3D Discrete Element Method (DEM) simulations aiming at investigating the role of the boundary vibration in inducing frictional weakening in sheared granular layers. We study the role of different vibration amplitudes applied at various shear stress levels, for a granular layer in the stick-slip regime and in the steady-sliding regime. Results are reported in terms of friction drops and kinetic energy release associated with frictional weakening events. We find that larger vibration amplitude induces larger frictional weakening events. The results show evidence of a thresho…
We consider a system of granular particles, modeled by two dimensional frictional elastic disks, that is exposed to externally applied time-dependent shear stress in a planar Couette geometry. We concentrate on the external forcing that produces intermittent dynamics of stick-slip type. In this regime, the top wall remains almost at rest until the applied stress becomes sufficiently large, and then it slips. We focus on the evolution of the system as it approaches a slip event. Our main finding is that there are two distinct groups of measures describing system behavior before a slip event. Th…
The surfaces of many planetary bodies, including asteroids and small moons, are covered with dust to pebble-sized regolith held weakly to the surface by gravity and contact forces. Understanding the reaction of regolith to an external perturbation will allow for instruments, including sensors and anchoring mechanisms for use on such surfaces, to implement optimized design principles. We analyze the behavior of a flexible probe inserted into loose regolith simulant as a function of probe speed and ambient gravitational acceleration to explore the relevant dynamics. The EMPANADA experiment (Ejec…
We set up an original apparatus to measure the grain grain friction stress inside a granular medium composed of sodo-silicate-glass beads surrounded by a water vapor atmosphere.We analyze here the influence of the physico chemistry of water on our glass beads and its consequences on our shear experiment. We found two scales in the analysis of the shear stress signal. On the microscopic scale of one bead, the experimental results show a dependence on the size of beads, on the shear rate and on humidity for the resulting stick slip signal. On the macroscopic scale of the whole assembly of beads,…
We phenomenologically investigate stick-slip motion of sheared granular layers. Our phenomenology is constructed in the context of nucleation-and-growth of the fluidized area which is triggered by collapsing of stress chains. Based on this picture, we give a simple friction model by introducing the degree of the fluidization. It is found that the present model can successfully reproduce major features of the experimental results reported by Nasuno {\it et al.} (Phys. Rev. E {\bf 58}, 2161 (1998)) with quantitatively good agreement.
Sliding friction across a thin soft lubricant film typically occurs by stick-slip, the lubricant fully solidifying at stick, yielding and flowing at slip. The static friction force per unit area preceding slip is known from molecular dynamics (MD) simulations to decrease with increasing contact area. That makes the large-size fate of stick-slip unclear and unknown; its possible vanishing is important as it would herald smooth sliding with a dramatic drop of kinetic friction at large size. Here we formulate a scaling law of the static friction force, which for a soft lubricant is predicted to d…
Complex liquids flow is known to be drastically affected by the roughness condition at the interfaces. We combined stresses measurements and observations of the flow during the motion of different rough surfaces in dry liquid foams. We visually show that three distinct friction regimes exists: slippage, stick-slip motion, and anchored soap films. Our stress measurements are validated for slippage and anchored regimes based on existing models, and we propose a leverage rule to describe the stresses during the stick-slip regime. We find that the occurrence of the stick-slip or anchored regimes i…
Based on (overdamped) Stokesian dynamics simulations and video microscopy experiments, we study the non equilibrium dynamics of a sheared colloidal cluster, which is confined to a two-dimensional disk. The experimental system is composed of a mixture of paramagnetic and non magnetic polystyrene particles, which are held in the disk by time shared optical tweezers. The paramagnetic particles are located at the center of the disk and are actuated by an external, rotating magnetic field that induces a magnetic torque. We identify two different steady states by monitoring the mean angular velociti…
We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail the behavior of friction at interfaces between wacroscopic hard rough solids, whose main dynamical features are well described by the Rice-Ruina rate and state dependent constitutive law. We show that it results from two combined effects : (i) the threshold rheology of nanometer-thick junctions jammed under confinement into a soft glassy structure (ii) geometric aging, i.e. slow growth of the real arrea of contact via asperity creep int…
Dense granular systems subjected to an imposed shear stress undergo stick-slip dynamics with systematic patterns of dilation-compaction. During each stick phase, as the frictional strength builds up, the granular system dilates to accommodate shear strain, developing stronger force networks. During each slip event, when the stored energy is released, particles experience large rearrangements and the granular network can significantly change. Here, we use numerical simulations of 3D, sheared frictional packings to show that the mean betweenness centrality -- a property of network of interpartic…
A two dimensional amorphous material is modeled as an assembly of mesoscopic elemental pieces coupled together to form an elastically coherent structure. Plasticity is introduced as the existence of different minima in the energy landscape of the elemental constituents. Upon the application of an external strain rate, the material shears through the appearance of elemental slip events with quadrupolar symmetry. When the energy landscape of the elemental constituents is kept fixed, the slip events distribute uniformly throughout the sample, producing on average a uniform deformation. However, w…
We propose that several mechanisms contribute to friction in a polymer melt adsorbed at a structured surface. The first one is the well known disentanglement of bulk polymer chains from the surface layer. However, if the surface is ideal at the atomic scale, the adsorbed parts of polymer chains can move along the equipotential lines of the surface potential. This gives rise to a strong slippage of the melt. For high shear rates chains partially desorb. However, the friction force on adsorbed chains increases, resulting in quasi-stick boundary conditions. We propose that the adsorbed layers can…
We theoretically investigate general properties of driven (sheared) colloidal suspensions in confinement, based on methods of classical density functional theory. In the absence of an exact closed (Smoluchowski-) equation for the one-particle density under shear, we formulate a set of general conditions for approximations, and show that a simple closure fulfills them. The exact microscopic stress tensor is identified. Exemplifying the situation near a wall (oriented parallel to the direction of shear), we note that the microscopic shear stress is not necessarily homogeneous. Formulating a seco…
Super-hydrophobic array of grooves containing trapped gas (stripes), have the potential to greatly reduce drag and enhance mixing phenomena in microfluidic devices. Recent work has focused on idealized cases of stick-perfect slip stripes, with limited guidance. Here, we analyze the experimentally relevant situation of a pressure-driven flow past striped slip-stick surfaces with arbitrary local slip at the gas sectors. We derive analytical formulas for maximal (longitudinal) and minimal (transverse) directional effective slip lengths that can be used for any surface slip fraction (validated by …
The local and global dynamics of a sheared granular medium are studied in a model experiment as a function of several macroscopic parameters. We observe that by changing the shear rate or the loading stiffness, the system crackles, with intermittent slip avalanches, or exhibits periodic motion. By analyzing the global force, induced while shearing, we capture the transition from the crackling to the periodic regime and associated scaling laws. We deduce a novel dynamic phase diagram as a function of the shear rate and the system's stiffness. Using photo-elasticimetry, we also capture the grain…
We study the flow of a pressure-driven foam through a straight channel using numerical simulations, and examine the effects of a tuneable attractive potential between bubbles. This potential, which accounts for the effects of disjoining pressure in the liquid films between separating bubbles, is shown here to introduce jamming and stick-slip flow in a straight channel. We report on the behaviour of these new regimes by varying the strength of the attractive potential. It is seen that there is a force threshold below which the flow jams, and on increasing the driving force, a cross over from in…
High-frequency ultrasonic pulses at 36 MHz are used to measure velocity profiles in a complex fluid sheared in the Couette geometry. Our technique is based on time-domain cross-correlation of ultrasonic speckle signals backscattered by the moving medium. Post-processing of acoustic data allows us to record a velocity profile in 0.02--2 s with a spatial resolution of 40 $μ$m over 1 mm. After a careful calibration using a Newtonian suspension, the technique is applied to a sheared lyotropic lamellar phase seeded with polystyrene spheres of diameter 3--10 $μ$m. Time-averaged velocity profiles rev…
We present an experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity : steady sliding at high velocity (> Vc = 100-125 μm/s), caracterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a ``healing instability'' occuring when the local sliding velocity reaches the macroscopic transition velocity Vc. At driving velocities close below Vc, the system exhibits complex spatio-temporal behavior.
