Stick-slip Instability Research Articles

Texture-Induced Modulations of Friction Force: The Fingerprint Effect

Modulations of the friction force in dry solid friction are usually attributed to macroscopic stick-slip instabilities. Here we show that a distinct, quasistatic mechanism can also lead to nearly periodic force oscillations during sliding contact between an elastomer patterned with parallel grooves, and abraded glass slides. The dominant oscillation frequency is set by the ratio between the sliding velocity and the grooves period. A model is derived which quantitatively captures the dependence of the force modulations amplitude with the normal load, the grooves period, and the slides roughness characteristics. The model's main ingredient is the nonlinearity of the friction law. Since such nonlinearity is ubiquitous for soft solids, this "fingerprint effect" should be relevant to a large class of frictional configurations and have important consequences in human digital touch.

Syndeformational antigorite dehydration produces stable fault slip

We conducted deformation experiments in which temperature was increased above the thermal stability of antigorite to directly test the dehydration embrittlement hypothesis and its potential link to intermediate-depth earthquakes. The experiments were designed to maximize the possibility for instability: pore pressure was undrained, pre-dehydration stress was high, and deformation was localized prior to initiation of reaction. However, stick-slip instabilities (or unstable fault behavior) did not develop. Rather, we find that weakening occurs stably at a rate that depends on the ratio of the temperature ramp rate to the strain rate (), resulting in laboratory slow slip or stress relaxation events.

On the microphysical foundations of rate-and-state friction

The rate-and-state formulation of friction is well established as a phenomenological yet quantitative description of friction dynamics, in particular the onset of stick-slip instabilities arising from an oscillatory bifurcation. We first discuss the physical origins of two theories for the derivation of friction coefficients used in rate-and-state models, both derived from thermally activated rate processes. Secondly, we propose a general expression for the state evolution law in the form of a first order kinetics which describes the relaxation to a velocity dependent equilibrium interfacial state ϕ ss ( v ) over a velocity dependent dynamic rejuvenation time-scale t ϕ ( v ) . We show that the unknown relation ϕ ss ( v ) , defined as the ratio of t ϕ to a constant interfacial stationary healing time-scale t ⁎ ⁎ , can be estimated directly from the experimental measurements of the steady-state friction coefficient and the critical stiffness for the onset of stick-slip behaviour of a spring-block system. Using a specific experimental dataset, we finally illustrate that this method provides the experimental measurements of the apparent memory length L a ( v ) = v t ⁎ ⁎ ϕ ss ( v ) and the constant characteristic relaxation time t ⁎ ⁎ from which a constant intrinsic memory length L = V ⁎ t ⁎ ⁎ can be defined once a slip rate of reference V ⁎ is chosen. As a result the complete state evolution law can be experimentally characterised.

A nonsmooth Newton solver for capturing exact Coulomb friction in fiber assemblies

We focus on the challenging problem of simulating thin elastic rods in contact, in the presence of friction. Most previous approaches in computer graphics rely on a linear complementarity formulation for handling contact in a stable way, and approximate Coulombs's friction law for making the problem tractable. In contrast, following the seminal work by Alart and Curnier in contact mechanics, we simultaneously model contact and exact Coulomb friction as a zero finding problem of a nonsmooth function. A semi-implicit time-stepping scheme is then employed to discretize the dynamics of rods constrained by frictional contact: this leads to a set of linear equations subject to an equality constraint involving a nondifferentiable function. To solve this one-step problem we introduce a simple and practical nonsmooth Newton algorithm which proves to be reasonably efficient and robust for systems that are not overconstrained. We show that our method is able to finely capture the subtle effects that occur when thin elastic rods with various geometries enter into contact, such as stick-slip instabilities in free configurations, entangling curls, resting contacts in braid-like structures, or the formation of tight knots under large constraints. Our method can be viewed as a first step towards the accurate modeling of dynamic fibrous materials.

Finite Element Analysis of Rate- and State-Dependent Frictional Contact Behavior

In the present study, the rate- and state-dependent friction model [Hashiguchi and Ozaki, 2008] is implemented in the dynamic finite element method. The typical rate- and state-dependent frictional contact problems, which are consisted by elastic and rigid bodies having simple shapes, are then analyzed by the present method. The validity of the present method for the microscopic sliding and stick-slip instability is examined under various dynamic characteristics of the system, such as contact load, elastic stiffness, driving velocity and frictional properties. It is shown that the present method can solve simultaneously not only rate- and state-dependent frictional behavior on the contact boundary but also coupling effects with internal deformations, whereas it cannot predicted by the conventional finite element analysis with the Coulomb’s friction law.

Numerical analysis of stick-slip instability by a rate-dependent elastoplastic formulation for friction

In various fields of engineering, it is important to clarify friction-induced vibration, such as stick-slip motion, for a wide range of scales from microscopic elements to continental plates. In the present study, we apply a rate- and state-dependent friction model [30] (Hashiguchi and Ozaki, 2008), which can rationally describe the reciprocal transition between the static friction and the kinetic friction by a unified formulation, to the simulation of stick-slip instability for a one-degree-of-freedom spring–mass system under various conditions. It is verified that the various basic experimental findings on stick-slip motion can be pertinently described by the present approach. Moreover, the effect of the dynamic characteristics of the system, such as the mass, stiffness and driving velocity, is discussed, and parameters prescribing the rate of reciprocal transition of static–kinetic frictions and the preliminary microscopic sliding on the instability of the stick-slip motion are also discussed.

Stick-slip instabilities and shear strain localization in amorphous materials

We study the impact of strain localization on the stability of frictional slipping in dense amorphous materials. We model the material using shear transformation zone (STZ) theory, a continuum approximation for plastic deformation in amorphous solids. In the STZ model, the internal state is quantified by an effective disorder temperature, and the effective temperature dynamics capture the spontaneous localization of strain. We study the effect of strain localization on stick-slip instabilities by coupling the STZ model to a noninertial spring slider system. We perform a linear stability analysis to generate a phase diagram that connects the small scale physics of strain localization to the macroscopic stability of sliding. Our calculations determine the values of spring stiffness and driving velocity where steady sliding becomes unstable and we confirm our results through numerical integration. We investigate both homogeneous deformation, where no shear band forms, and localized deformation, where a narrow shear band spontaneously forms and accommodates all of the deformation. Our results show that at a given velocity, strain localization leads to unstable frictional sliding at a much larger spring stiffness compared to homogeneous deformation, and that localized deformation cannot be approximated by a homogeneous model with a narrower material. We also find that strain localization provides a physical mechanism for irregular stick-slip cycles in certain parameter ranges. Our results quantitatively connect the internal physics of deformation in amorphous materials to the larger scale frictional dynamics of stick-slip.

Rheo-PIV analysis of the slip flow of a metallocene linear low-density polyethylene melt

The continuous extrusion of a metallocene linear low-density polyethylene through a transparent capillary die with and without slip was analyzed in this work by rheometrical measurements and particle image velocimetry (PIV). For this reason, a comparison was made between the rheological behaviors of the pure polymer and blended with a small amount of fluoropolymer polymer processing additive. Very good agreement was found between rheometrical and PIV measurements. The pure polymer exhibited stick-slip instabilities with nonhomogeneous slip at the die wall, whereas the blend showed stable flow. The slip velocity was measured directly from the velocity profiles and was negligible for the pure polymer before the stick-slip but increased monotonously as a function of the shear stress for the blend. The flow curves and the slip velocity as a function of the shear stress deviated from a power law and were well fitted by continuous “kink” functions. Comparison of PIV data with rheometrical ones permitted a direct proof of the basic assumption of the Mooney theory. Finally, the analysis of the velocity profiles showed that there is a maximum in the contribution of slip to the average fluid velocity, which is interpreted as the impossibility for the velocity profile to become plug like in the presence of shear thinning.

Cusp-catastrophe interpretation of the stick-slip behaviour of rough surfaces

The stick-slip instability is a typical manifestation of the nonlinearity of the frictional response of rough surfaces. As recently demonstrated by several researchers, the problem of contact loss is also inherently connected to the stick-slip instability and it has been detected both in elastically soft materials, such as rubber or gelatine, and in elastic stiff materials, such as for earthquake faults. Treating the problem of tangential contact in the framework of micromechanical contact models, the effect of the phenomenon of contact loss on the micro-slip behavior of rough surfaces is herein investigated. To this aim, the stick and slip components of the total applied tangential force and of the total real contact area are properly determined as functions of the total applied tangential force. A comparison with the behavior of smooth surfaces, such as spheres, cylinders and flat surfaces, is presented. Then, simulating the problem of tangential loading followed by a reduction of the applied normal force, it will be shown that the phenomenon of contact loss gives rise to energy release due to snap-back instability in the diagram relating the tangential force to the sliding displacement. This result provides for the very first time an explanation to the phenomenon of stick-slip according to the Catastrophe Theory, in close analogy with the cusp-catastrophe instability of Mode I crack propagation in cohesive solids.

Dynamic Driving of Small Shallow Events during Strong Motion

Abstract High-pass filtering (>20 Hz) of acceleration records from the 1999 Chi-Chi, Taiwan, and 2004 Parkfield, California, earthquakes reveals a series of bursts that occur only during strong shaking. Initially interpreted as originating from asperity failure on the Chelungpu fault, bursts observed during the Chi-Chi earthquake were subsequently determined to be a local effect within about 1 km of the seismic stations. Similar bursts were observed at the U.S. Geological Survey Parkfield seismic array during the Parkfield earthquake and were constrained to originate less than 20 m from the instruments. Such small shallow events cannot result from the triggered release of stored elastic energy because rate-and-state friction rules out stick-slip instability on such small, shallow patches. Our hypothesis is that the bursts are not triggered but are driven by simultaneous shear and tensile stresses near the surface during the strong motion. At 2 Hz, SV - to P -wave mode conversion at the free surface produces tensile stresses to depths of 70 m. Where standard triggering releases stored elastic energy and adds to the incident wave field, this new driving mechanism takes energy out of the 2 Hz strong motion and reradiates it at high frequencies. It is thus an attenuation mechanism that we estimate can contribute 3% to the net attenuation in the very shallow crust.

Stability of the annular Poiseuille flow of a Newtonian liquid with slip along the walls

The annular Poiseuille flow a Newtonian fluid is studied assuming that slip occurs along the walls. Different slip models relating the wall shear stress to the slip velocity are employed. In the case of non-monotonic slip models with a maximum followed by a minimum, there exist linearly unstable steady-state solutions with one or both the slip velocities along the inner and outer cylinders of the annulus corresponding to the (unstable) negative-slope branch of the slip equation. The resulting flow curve is non-monotonic with one or even two narrow unstable branches corresponding to the stick–slip instability regime. The sizes of these two unstable regimes are reduced as the radii ratio is reduced. It is demonstrated that the second unstable branch may not be observed at all due to the presence of stable steady-states. These results provide a partial explanation for the absence of the stick–slip instability in annular extrusion experiments.

On the seismic cycle seen as a relaxation oscillation

An earthquake is commonly described as a stick-slip frictional instability occurring along preexisting crustal faults. The seismic cycle of earthquake recurrence is characterized by long periods of quasi-static evolution, which precede sudden slip events accompanied by elastic wave radiation: the earthquake. This succession of processes over two well-distinguished time-scales recalls the behavior of nonlinear relaxation oscillations. We explore this connection by studying, in the framework of rate-and-state friction, the sliding of two identical slabs of elastic solid driven in opposite directions with a constant relative velocity. Our first innovation is to establish that the motion of a spring–block system is an asymptotic mechanical analogue of the frictional sliding of a single interface from which elastic waves radiate. Due to wave reflection at the boundaries, the equivalent mass of the block M = k(h/c s )2/12 is not independent of the equivalent spring stiffness k, where h/2 denotes the slab thickness and c s is the shear wave speed. Considering a non-monotonic friction law, we show that the relaxation oscillation regime is reached when the characteristic time-scale of frictionless oscillations is much greater than the characteristic time of frictional memory effects: (M/k)1/2 ≫ L/V *. We combine a composite approximation of the stick-slip cycle and numerical studies to show that the interfacial relaxation oscillations result from the subtle interplay of the non-monotonic properties of the friction law driving the long stress build-up of the quasi-static phase, and the inertial control of the fast slip phase originating from the wave propagation. We discuss the geophysical consequences for earthquake mechanics, and connections between the rate-and-state and Coulomb models of friction.

Laboratory investigation of the frictional behavior of granular volcanic material

We report on detailed laboratory experiments designed to illustrate the frictional behavior of granular volcanic debris. The materials include pyroclastic flow debris from Soufrière Hills Volcano, Montserrat, and from Stromboli Volcano, Italy, and lahar deposits from Mount St. Helens. Experiments were conducted in a servo-controlled, double-direct shear apparatus under conditions of displacement-control and with monitored temperature and humidity. The effects of loading velocity, normal stress, grain-size range, and saturation state were examined for normal stresses from 0.75 to 8 MPa. The Soufrière Hills debris was sampled in the field using a 2 mm sieve. Samples from Stromboli and MSH represent the original bulk material. The influence of grain-size and size distribution were examined in detail for the Soufrière Hills material for 1) two narrow size ranges (3–4 ϕ, 0.063–0.125 mm; and 0–1 ϕ, 0.5–1 mm), 2) a wide size range (3–0 ϕ, 0.125–1 mm), and 3) the natural size distribution in the range 0–1 mm. These four data sets show remarkably uniform properties: coefficients of residual internal friction varied from 0.62 to 0.64 and coefficients of peak internal friction varied from 0.66 to 0.69, with zero cohesion in each case. For the natural grain-size distribution, we find a small but clear increase in residual sliding friction with increasing slip velocity in the range 10 to 900 μm/s, i.e. velocity strengthening frictional behavior. For Soufrière Hills pyroclastic material the coefficient of internal friction changes very little when water saturated. The frictional characteristics were remarkably similar for the three volcanoes. For the natural grain-size distributions, the coefficient of residual internal friction ranged from 0.61 to 0.63 and peak internal friction values ranged from 0.65 to 0.66. Pre-loaded and over-compacted materials sheared at reduced normal stress gave peak coefficients as high as 0.80. Our results imply that granular volcanic debris should often fail via stable creep, but may exhibit stick-slip instability under some conditions.

Stick-Slip: Wet Versus Dry

A rubber lens (polydimethylsiloxane) is pressed against silanated or bare glass plates (Johnson-Kendall-Roberts (JKR) contact). As the plate slides with a velocity U, we measure the friction on the lens using a “macro Atomic Force Microscope (AFM)”, where the cantilever is a thin rectangular glass rod and the tip is the rubber lens. We observe the contact area via optical interferometry. In air for “hard” lenses (Young's modulus E ≈ 1 MPa), we find smooth sliding on a model substrate, and a transition to stick-slip on a hysteretic substrate above a threshold velocity, V M . For soft lenses (E ≈ 0.1 MPa), we observe Schallamach waves and stick-slip depending on normal force and the plate's velocity, U. When immersed in a liquid (silicone oils, water-glycerol mixtures), the contact remains dry at low velocities, but is invaded by a liquid film above a critical velocity, U c . For hard lenses we observe smooth sliding and high friction below U c , and low friction above U c . For soft lenses, we find wet Schallamach waves for U < V M and stick-slip instabilities at large velocities. In the stick-slip regime, the contact is wet in the slip phase, and dewets in the stick phase. We measure the period of the stick-slip cycle as a function of the liquid viscosity. We interpret the stick-slip process by the formation and rupture of adhesive bonds (between the rubber polymer chains and active sites on the glass). Using a recent model, we can explain most of the data for the stick-slip period and slip threshold velocity.

Silanols cured by borates as lubricants in extrusion of LLDPE. Impact of elasticity of the lubricant on sliding friction

Addition of a viscoelastic material based on silanols cured by boron oxide was used to delay sharkskin and stick–slip instabilities in extrusion of linear low-density polyethylene (LLDPE). Delay of flow instabilities to rates of extrusion 25–35 times higher than without additive and about 40% less extrusion pressure at the same throughput are achieved by the use of this material as an additive (∼0.1%) to LLDPE or as a coating of the extrusion die. Mechanical properties of the lubricant were changed by small variations of composition to investigate the impact of elasticity on lubrication and sharkskin delay. Both lubrication and sharkskin delay were considerably improved when more elastic lubricants were used while the chemical composition of the lubricants was nearly the same. Filling the lubricants with powders of metal oxides or especially particulates having plate-like particles (kaolin, mica, BN) helped to delay the flow instabilities further to even higher throughputs. Together with experimental results, we present a tentative explanation for the importance of elasticity of polymer processing aids in the delay of sharkskin and the stabilization of slip.

Microstructures developed by coseismic and aseismic faulting in near-surface sediments, San Andreas fault, California

Research Article| July 01, 2007 Microstructures developed by coseismic and aseismic faulting in near-surface sediments, San Andreas fault, California Susan M. Cashman; Susan M. Cashman 1Department of Geology, Humboldt State University, Arcata, California 95521, USA Search for other works by this author on: GSW Google Scholar John N. Baldwin; John N. Baldwin 2William Lettis and Associates Inc., 1777 Botelho Drive, Suite 262, Walnut Creek, California 94596, USA Search for other works by this author on: GSW Google Scholar Katharine V. Cashman; Katharine V. Cashman 3Department of Geological Sciences, 1272 University of Oregon, Eugene, Oregon 97403, USA Search for other works by this author on: GSW Google Scholar Karl Swanson; Karl Swanson 4Lawrence and Associates, 2001 Market Street, Room 523, Redding, California 96001, USA Search for other works by this author on: GSW Google Scholar Ryan Crawford Ryan Crawford 5Department of Geology, Humboldt State University, Arcata, California 95521, USA Search for other works by this author on: GSW Google Scholar Author and Article Information Susan M. Cashman 1Department of Geology, Humboldt State University, Arcata, California 95521, USA John N. Baldwin 2William Lettis and Associates Inc., 1777 Botelho Drive, Suite 262, Walnut Creek, California 94596, USA Katharine V. Cashman 3Department of Geological Sciences, 1272 University of Oregon, Eugene, Oregon 97403, USA Karl Swanson 4Lawrence and Associates, 2001 Market Street, Room 523, Redding, California 96001, USA Ryan Crawford 5Department of Geology, Humboldt State University, Arcata, California 95521, USA Publisher: Geological Society of America Received: 30 Nov 2006 Revision Received: 18 Feb 2007 Accepted: 21 Feb 2007 First Online: 09 Mar 2017 Online ISSN: 1943-2682 Print ISSN: 0091-7613 Geological Society of America Geology (2007) 35 (7): 611–614. https://doi.org/10.1130/G23545A.1 Article history Received: 30 Nov 2006 Revision Received: 18 Feb 2007 Accepted: 21 Feb 2007 First Online: 09 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Susan M. Cashman, John N. Baldwin, Katharine V. Cashman, Karl Swanson, Ryan Crawford; Microstructures developed by coseismic and aseismic faulting in near-surface sediments, San Andreas fault, California. Geology 2007;; 35 (7): 611–614. doi: https://doi.org/10.1130/G23545A.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Evaluation of microstructures in unlithified near-surface sediments provides promising results for differentiating between earthquake rupture-related (coseismic) and creep-related (aseismic) structures formed by the San Andreas fault. Paleoseismic trenches excavated at two sites, Flook Ranch on the creeping section, and Alder Creek on the 1906 rupture trace, show contrasting fault-zone structures and microstructures in near-surface, late Holocene sand. At Alder Creek, the 1–2-m-wide fault zone consists of both faults and 2–10-mm-thick deformation bands. Deformation bands have preferred grain orientations ∼30° counterclockwise from the fault (viewed in the slip-parallel direction), broken and disaggregated grains, smaller than average grain size, and lower porosity than control samples. In contrast, at Flook Ranch, two 4–6-m-wide fault zones consist of multiple faults but lack deformation bands. Silty sand in the fault zone at Flook Ranch has preferred grain orientations ∼10° clockwise from the fault, lacks broken grains, and has comparable grain size but lower porosity than control samples. These microstructures record different deformation mechanisms in near-surface sediment: cataclasis at Alder Creek, and distributed deformation at Flook Ranch. Deformation bands on the 1906 rupture trace of the San Andreas fault at Alder Creek demonstrate that these structures, with their grain rotation, grain breakage, and localized porosity variations, can form coseismically in unlithified sediment. The grain bridge model accounts for fundamental microstructural characteristics of Alder Creek deformation bands, and it provides a connection between these microstructures and laboratory studies of stick-slip instability. Deformation bands are easily recognizable in field and trench exposures and may be a useful indicator of coseismic slip. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Novel processing aid based on modified Silly Putty®

AbstractA viscoelastic material based on low‐molecular‐weight silanols cured by boric acid, i.e., having a composition similar to that of the well‐known Silly Putty®, was used to delay sharkskin and stick–slip instabilities in the extrusion of linear low‐density polyethylene (LLDPE). The use of sodium hydroxide and phosphoric acid in the composition helped to improve adhesion of the material to metal and to extend its efficiency above 200°C. Adding powders of metal oxides, e.g., borax, silica, and especially silicates, further helped to delay the flow instabilities. A delay of the sharkskin instability to 25–35 times higher extrusion rates was achieved, and about 45% less pressure was observed in a screw extruder at the same throughput when this material was used as an additive to LLDPE (∼0.1%) or as a coating of the extrusion die. Tentative explanations of the sharkskin origin and for the delay of the instability are proposed. J. VINYL. ADDIT. TECHNOL., 12:131–142, 2006. © 2006 Society of Plastics Engineers

Rubber friction: role of the flash temperature

When a rubber block is sliding on a hard rough substrate, the substrate asperities willexert time-dependent deformations of the rubber surface resulting in viscoelastic energydissipation in the rubber, which gives a contribution to the sliding friction. Most surfaces ofsolids have roughness on many different length scales, and when calculating the frictionforce it is necessary to include the viscoelastic deformations on all length scales. The energydissipation will result in local heating of the rubber. Since the viscoelastic properties ofrubber-like materials are extremely strongly temperature dependent, it is necessary to includethe local temperature increase in the analysis. At very low sliding velocity the temperatureincrease is negligible because of heat diffusion, but already for velocities of order10−2 m s−1 the local heating may be very important. Here I study the influence of the localheating on the rubber friction, and I show that in a typical case the temperatureincrease results in a decrease in rubber friction with increasing sliding velocity forv>0.01 m s−1. This may result in stick–slip instabilities, and is of crucial importance in manypractical applications, e.g. for tyre–road friction and in particular for ABS brakingsystems.

Study of the stick-slip phenomenon of linear low-density polyethylene in a brass die by using electrical measurements

Extrusion through brass dies has been found to be useful to eliminate sharkskin and stick-slip instabilities in linear low-density polyethylene. However, the physicochemical interaction of polyethylene melts with brass dies is not well understood. In the present work, such an interaction is analyzed by using electrical measurements. Experiments were performed in a single screw extruder at a temperature of 190°C with a metallocene linear low-density polyethylene and a brass die. The interaction between the polymer melt and the die changed with time. Different flow curves were obtained as the extrusion time was increased to reach an invariant flow curve. An irreversible transition from slip to no-slip at the die wall under stable flow was observed, consistent with a change in the sign of the measured electric charge. The critical shear stress for the onset of the stick-slip also increased with the extrusion time. Electrical measurements reproduced the stick-slip dynamics with fidelity. Pressure oscillations were accompanied by in-phase variations of electrical charge during the stick-slip, from which a cohesive failure is suggested for slip in this flow regime. For long extrusion times, a new phenomenon was observed, which is the disappearance of pressure and electric charge oscillations, but in the presence of a nonmonotonic flow curve. It is suggested that the density of adsorbed chains at the wall increases with time because of contamination of the die wall, ending in a “dry brush” regime that suppresses pressure oscillations and produces a true plateau in the flow curve.

Unsteady bubble propagation in a flexible channel: predictions of a viscous stick-slip instability

We investigate the unsteady motion of a long bubble advancing under either prescribed pressure p(b) or prescribed volume flux q(b) into a fluid-filled flexible-walled channel at zero Reynolds number, an idealized model for the reopening of a liquid-lined lung airway. The channel walls are held under longitudinal tension and are supported by external springs; the bubble moves with speed U. Provided p(b) exceeds a critical pressure p(crit) the system exhibits two types of steady motion. At low speeds, the bubble acts like a piston, slowly pushing a column of fluid ahead of itself, and U decreases with increasing p(b). At high speeds, the bubble rapidly peels the channel walls apart and U increases with increasing p(b.) Using two independent time-dependent simulation techniques (a two-dimensional boundary-element method and a one-dimensional asymptotic approximation), we show that with prescribed p(b) > p(crit), peeling motion is stable and the steady pushing solution is unstable; for p(b) > p(crit) the system ultimately exhibits unsteady pushing behaviour for which U continually diminishes with time. When q(b) is prescribed, peeling motion (with large q(b)) is again stable, but pushing motion (with small q(b)) loses stability at long times to a novel instability leading to spontaneous relaxation oscillations of increasing amplitude and period, for which the bubble switches abruptly between slow unsteady pushing and rapid quasi-steady peeling. This stick-slip motion is characterized using a third-order lumped-parameter model which in turn is reduced to a nonlinear map. Implications for the inflation of occluded lung airways are discussed.