Ice breakloose friction

We discuss the origin of the breakloose (or static) friction force when an ice block is slid on a hard randomly rough substrate surface. If the substrate has roughness with small enough amplitude (of order a 1 nm or less), the breakloose force may be due to interfacial slip and is determined by the elastic energy per unit area, Uel/A0, stored at the interface after the block has been displaced a short distance from its original position. The theory assumes complete contact between the solids at the interface and that there is no elastic deformation energy at the interface in the original state before the application of the tangential force. The breakloose force depends on the surface roughness power spectrum of the substrate and is found to be in good agreement with experimental observations. We show that as the temperature decreases, there is a transition from interfacial sliding (mode II crack propagation, where the crack propagation energy GII = Uel/A0) to opening crack propagation (mode I crack propagation with GI the energy per unit area to break the ice-substrate bonds in the normal direction).

Sliding friction on ice

We study the friction when rectangular blocks made from rubber, polyethylene, and silica glass are sliding on ice surfaces at different temperatures ranging from -40 to 0 °C, and sliding speeds ranging from 3 μm/s to 1 cm s-1. We consider a winter tire rubber compound both in the form of a compact block and as a foam with ∼10% void volume. We find that both rubber compounds exhibit a similar friction on ice for all studied temperatures. As in a previous study at low temperatures and low sliding speeds, we propose that an important contribution to the friction force is due to slip between the ice surface and ice fragments attached to the rubber surface. At temperatures around 0 °C (or for high enough sliding speeds), a thin pre-melted water film will occur at the rubber-ice interface, and the contribution to the friction from shearing the area of real contact is small. In this case, the dominant contribution to the friction force is due to viscoelastic deformations of the rubber by the ice asperities. The sliding friction for polyethylene (PE) and silica glass (SG) blocks on ice differs strongly from that of rubber. The friction coefficient for PE is ∼0.04-0.15 and is relatively weakly velocity dependent except close to the ice melting temperature where the friction coefficient increases toward low sliding speeds. Silica glass exhibits a similarly low friction as PE for T > -10 °C but very large friction coefficients (of order unity) at low temperatures. For both PE and SG, unless the ice track is very smooth, the friction force depends on the position x along the sliding track. This is due to bumps on the ice surface, which are sheared off by the elastically stiff PE and SG blocks, resulting in a plowing-type of contribution to the friction force. This results in friction coefficients, which locally can be very large ∼1, and visual inspection of the ice surface after the sliding acts show ice wear particles (white powder) in regions where ice bumps occur. Similar effects can be expected for rubber blocks below the rubber glass transition temperature, and the rubber is in the (elastically stiff) glassy state.

Side-leakage of face mask

Face masks are used to trap particles (or fluid drops) in a porous material (filter) in order to avoid or reduce the transfer of particles between the human lungs (or mouth and nose) and the external environment. The air exchange between the lungs and the environment is assumed to occur through the face mask filter. However, if the resistance to air flow through the filter is high some air (and accompanied particles) will leak through the filter-skin interface. In this paper I will present a model study of the side-leakage problem.

A simple model for viscoelastic crack propagation

 When a crack propagates in a viscoelastic solid, energy dissipation can occur very far from the crack tip where the stress field may be very different from the [Formula: see text] singular form expected close to the crack tip. Most theories of crack propagation focus on the near crack tip region. Remarkable, here I show that a simple theory which does not account for the nature of the stress field in the near crack tip region results in a crack propagation energy in semiquantitative agreement with a theory based on the stress field in the near crack tip region. I consider both opening and closing crack propagation and show that for closing crack propagation in viscoelastic solids, some energy dissipation processes must occur in the crack tip process zone. The theory is illustrated by new experimental results for the adhesive interaction between a silica glass ball and a silicone rubber surface.

Cylinder-flat-surface contact mechanics during sliding

Using molecular dynamics we study the dependency of the contact mechanics on the sliding speed when an elastic block (cylinder) with a cos(q_{0}x) surface height profile is sliding in adhesive contact on a rigid flat substrate. The atoms on the block interact with the substrate atoms by Lennard-Jones potentials, and we consider both commensurate and (nearly) incommensurate contacts. For the incommensurate system the friction force fluctuates between positive and negative values, with an amplitude proportional to the sliding speed, but with the average close to zero. For the commensurate system the (time-averaged) friction force is much larger and nearly velocity independent. For both types of systems the width of the contact region is velocity independent even when, for the commensurate case, the frictional shear stress increases from zero (before sliding) to ≈0.1MPa during sliding. This frictional shear stress, and the elastic modulus used, are typical for polydimethylsiloxane rubber sliding on a glass surface, and we conclude that the reduction in the contact area observed in some experiments when increasing the tangential force must be due to effects not included in our model study, such as viscoelasticity or elastic nonlinearity.

Adhesion paradox: Why adhesion is usually not observed for macroscopic solids

The adhesion paradox refers to the observation that for most solid objects no adhesion can be detected when they are separated from a state of molecular contact. The adhesion paradox results from surface roughness, and we present experimental and theoretical results that show that adhesion in most cases is "killed" by the longest-wavelength roughness. In addition, adhesion experiments between a human finger and a clean glass plate were carried out, and for a dry finger no macroscopic adhesion occurred. We suggest that the observed decrease in the contact area with increasing shear force results from nonadhesive finger-glass contact mechanics, involving large deformations of complex layered material.

Electric field effect in heat transfer in 2D devices

We calculate heat transfer between a 2D sheet (e.g. graphene) and a dielectric in presence of a gate voltage. The gate potential induces surface charge densities on the sheet and dielectric, which results in electric field, which is coupled to the surface displacements and, as a consequence, resulting an additional contributions to the radiative heat transfer. The electrostatic and van der Waals interactions between the surface displacement result in the phonon heat transfer, which we calculate taking into account the nonlocality of these interactions. Numerical calculations are presented for heat transfer between graphene and a SiO₂ substrate.

Interfacial fluid flow for systems with anisotropic roughness

I discuss fluid flow at the interface between solids with anisotropic roughness. I show that the Bruggeman effective medium theory and the critical junction theory give nearly the same results for the fluid flow conductivity. This shows that, in most cases, the surface roughness observed at high magnification is irrelevant for fluid flow problems such as the leakage of static seals, and fluid squeeze-out. The effective medium theory predicts that the fluid flow conductivity vanishes at the relative contact area A/A₀ = 0.5 independent of the anisotropy. However, the effective medium theory does not solve the elastic contact mechanics problem but is based on a purely geometric argument. Thus, for anisotropic roughness the contact area may percolate at different values of A/A₀ depending on the direction. We discuss how this may be taken into account in the effective medium and critical junction theories.

Lubricated sliding friction: Role of interfacial fluid slip and surface roughness

We derive approximate mean field equations for the fluid flow between elastic solids with randomly rough surfaces including interfacial fluid slip and shear thinning. We present numerical results for the fluid flow and friction factors for realistic systems, in particular, we consider the case of an elastic cylinder with random surface roughness in relative sliding contact with a flat rigid (low-energy) counter-surface. We present experimental data for the sliding friction between rubber stoppers and glass barrels lubricated with baked-on silicone oil. We find that the frictional shear stress acting in the rubber asperity contact regions is nearly velocity independent for velocities in the 10-1000μm/s range, and very small [Formula: see text] MPa, while for bare glass in silicone oil [Formula: see text] is much larger and velocity dependent.

Physics of suction cups

We have developed a theory of air leakage at interfaces between two elastic solids with application to suction cups in contact with randomly rough surfaces. We present an equation for the airflow in narrow constrictions which interpolates between the diffusive and ballistic (Knudsen) air-flow limits. To test the theory, we performed experiments using two different suction cups, made from soft polyvinylchloride (PVC), in contact with sandblasted polymethylmethacrylate (PMMA) plates. We found that the measured time to detach (lifetime) of the suction cups was in good agreement with theory, except for surfaces with a root-mean-square (rms) roughness below ≈1 μm, where diffusion of plasticizer from the PVC to the PMMA surface caused blockage of critical constrictions. The suction cup volume, stiffness, and elastic modulus have a huge influence on the air leakage and hence the failure time of the cups. Based on our research we propose an improved biomimetic design of suction cups that could show improved failure times with varying degrees of roughness under dry and wet environments.

Rolling friction of elastomers: role of strain softening

We study the temperature and velocity dependency of rolling friction. Steel and PMMA cylinders are rolled on sheets of nitrile butadiene rubber (NBR), with and without filler, and fluoroelastomer (FKM) with filler. Measurements of the rolling friction are performed for temperatures between -40 °C and 20 °C, and for velocities between 5 μm s^-1 and 0.5 cm s^-1. For the unfilled NBR, a smooth rolling friction master curve is obtained using the bulk viscoelastic frequency-temperature shift factor a_T. For the filled rubber compounds, a small deviation from the bulk viscoelastic shift factor is observed at low temperatures. The experimental data are analyzed using an analytical theory of rolling friction. For the filled compounds, good agreement with theory is obtained when strain softening is included, which increases the rolling friction by a factor ∼2 for the filled FKM and ∼3 for the filled NBR compounds. For the unfilled NBR, the maximum of the rolling friction occurs at higher sliding speeds than predicted by the theory. We discuss the role of the adhesive (crack-opening) contribution to the rolling friction, and the role of frozen-in elastic deformations as the rubber is cooled down below the rubber glass transition temperature.

Electroadhesion with application to touchscreens

There is growing interest in touchscreens displaying tactile feedback due to their tremendous potential in consumer electronics. In these systems, the friction between the user's fingerpad and the surface of the touchscreen is modulated to display tactile effects. One of the promising techniques used in this regard is electrostatic actuation. If, for example, an alternating voltage is applied to the conductive layer of a surface capacitive touchscreen, an attractive electrostatic force is generated between the finger and the surface, which results in an increase in frictional forces acting on the finger moving on the surface. By altering the amplitude, frequency, and waveform of this signal, a rich set of tactile effects can be generated on the touchscreen. Despite the ease of implementation and its powerful effect on our tactile sensation, the contact mechanics leading to an increase in friction due to electroadhesion has not been fully understood yet. In this paper, we present experimental results for how the friction between a finger and a touchscreen depends on the electrostatic attraction and the applied normal pressure. The dependency of the finger-touchscreen interaction on the applied voltage and on several other parameters is also investigated using a mean field theory based on multiscale contact mechanics. We present detailed theoretical analysis of how the area of real contact and the friction force depend on contact parameters, and show that it is possible to further augment the friction force, and hence the tactile feedback displayed to the user by carefully choosing those parameters.

Surface topography and water contact angle of sandblasted and thermally annealed glass surfaces

Surface roughness has a huge influence on most tribology properties. Sandblasting is a standard way to produce surface roughness in a controlled and reproducible way. Sometimes the sandblasted surfaces are annealed to reduce the roughness and reduce the sharpness of the roughness. We study the nature of the surface roughness of sandblasted silica glass surfaces and how it is modified by annealing at different temperatures. The surface roughness decreases with increasing annealing temperature due to viscous flow of the glass driven by the surface tension. However, the skewness and kurtosis remain nearly unchanged. Optical pictures of the annealed glass surfaces exhibit cell-like structures (cell diameter ≈20-40 μm), which we interpret as micro-cracks. The concentration of micro-cracks increases with increasing annealing temperature. The micro-cracks result in a (advancing) water contact angle which decreases with increasing annealing temperature, which is opposite to what is expected from the theory if no micro-cracks would occur.

Ice friction: Glacier sliding on hard randomly rough bed surface

I present a theory for ice friction for ice sliding on a hard randomly rough surface which includes ice melting-freezing (regelation), viscoelastic energy dissipation, and cavitation. The theory is an extension of earlier work by Weertman, Lliboutry, Nye, and Kamb. I present numerical results for surfaces with realistic surface roughness power spectra. I consider both airfilled and (pressurized) waterfilled cavities. The calculated frictional shear stresses are consistent with experimental observations for temperate glaciers.

Adhesion and friction between glass and rubber in the dry state and in water: role of contact hydrophobicity

We study the contact mechanics between 3 different tire tread compounds and a smooth glass surface in water. We study both adhesion and sliding friction at low-sliding speeds. For 2 of the compounds the rubber-glass contact in water is hydrophobic and we observe adhesion, and slip-stick sliding friction dynamics. For one compound the contact is hydrophilic, resulting in vanishing adhesion, and steady-state (or smooth) sliding dynamics. We also show the importance of dynamical scrape, both on the macroscopic level and at the asperity level, which reduces the water film thickness between the solids during slip. The experiments show that the fluid is removed much faster from the rubber-glass asperity contact regions for a hydrophobic contact than for a hydrophilic contact. We also study friction on sandblasted glass in water. In this case all the compounds behave similarly and we conclude that no dewetting occur in the asperity contact regions. We propose that this is due to the increased surface roughness which reduces the rubber-glass binding energy.

Adhesion between rubber and glass in dry and lubricated condition

We study the adhesion between differently processed glass and filled bromobutyl rubber in dry conditions, in water, and in silicone oil. The boundary line between contact and non-contact in adhesion experiments can be considered as a mode I crack, and we show that viscoelastic energy dissipation, close to the opening (or closing) crack tip and surface roughness, strongly affects the work of adhesion. We observe strong adhesion hysteresis and, in contrast to the Johnson-Kendall-Roberts theory prediction for elastic solids, this results in a pull-off force (and work of adhesion) which depends on the loading force and contact time. In particular, for the system immersed in water and silicone oil, we register very weak adhesive bonding. For glass ball with baked-on silicone oil, the pull-off force is nearly independent of the contact time, but this is not observed for the unprocessed glass surface.

Rubber friction: The contribution from the area of real contact

There are two contributions to the friction force when a rubber block is sliding on a hard and rough substrate surface, namely, a contribution F_ad = τ_f A from the area of real contact A and a viscoelastic contribution F_visc from the pulsating forces exerted by the substrate asperities on the rubber block. Here we present experimental results obtained at different sliding speeds and temperatures, and we show that the temperature dependency of the shear stress τ_f, for temperatures above the rubber glass transition temperature T_g, is weaker than that of the bulk viscoelastic modulus. The physical origin of τ_f for T > T_g is discussed, and we propose that its temperature dependency is determined by the rubber molecule segment mobility at the sliding interface, which is higher than in the bulk because of increased free-volume effect due to the short-wavelength surface roughness. This is consistent with the often observed reduction in the glass transition temperature in nanometer-thick surface layers of glassy polymers. For temperatures T < T_g, the shear stress τ_f is nearly velocity independent and of similar magnitude as observed for glassy polymers such as PMMA or polyethylene. In this case, the rubber undergoes plastic deformations in the asperity contact regions and the contact area is determined by the rubber penetration hardness. For this case, we propose that the frictional shear stress is due to slip at the interface between the rubber and a transfer film adsorbed on the concrete surface.

Contact mechanics for polydimethylsiloxane: from liquid to solid

Adhesion between a glass ball and a polydimethylsiloxane (PDMS) sample is dependent on the PDMS cross-link density, and the transformation of the material from the uncrosslinked liquid state to the fully crosslinked solid state is investigated in this study. The physical picture reflected a gradual transition from capillary forces driven contact mechanics to the classical Johnson-Kendall-Roberts (JKR)-type contact mechanics. PDMS was produced by mixing the base fluid and a cross-linker at a ratio of 10 : 1 and allowed to slowly cross-link at room temperature with simultaneous measurement of the ball-PDMS interaction force. The PDMS sample was in the liquid state during the first ≈16 hours, and in this case the ball-PDMS interaction was purely adhesive, i.e., no repulsive interaction was observed. Later at the PDMS gel-point the cross-linked PDMS clusters percolate, converting the fluid into a soft (fluid-filled) poroelastic solid. In the transition period, PDMS appears similar to pressure-sensitive adhesives. There we observe so-called "stringing" and permanent deformation of the material impacted by the ball. At room temperature, it takes more than ∼100 hours for PDMS to fully cross-link that can be confirmed by the comparison with the earlier-studied reference PDMS produced at elevated temperatures.

Rubber contact mechanics: adhesion, friction and leakage of seals

We study the adhesion, friction and leak rate of seals for four different elastomers: Acrylonitrile Butadiene Rubber (NBR), Ethylene Propylene Diene (EPDM), Polyepichlorohydrin (GECO) and Polydimethylsiloxane (PDMS). Adhesion between smooth clean glass balls and all the elastomers is studied both in the dry state and in water. In water, adhesion is observed for the NBR and PDMS elastomers, but not for the EPDM and GECO elastomers, which we attribute to the differences in surface energy and dewetting. The leakage of water is studied with rubber square-ring seals squeezed against sandblasted glass surfaces. Here we observe a strongly non-linear dependence of the leak rate on the water pressure ΔP for the elastomers exhibiting adhesion in water, while the leak rate depends nearly linearly on ΔP for the other elastomers. We attribute the non-linearity to some adhesion-related phenomena, such as dewetting or the (time-dependent) formation of gas bubbles, which blocks fluid flow channels. Finally, rubber friction is studied at low sliding speeds using smooth glass and sandblasted glass as substrates, both in the dry state and in water. The measured friction coefficients are compared to theory, and the origin of the frictional shear stress acting in the area of real contact is discussed. The NBR rubber, which exhibits the strongest adhesion both in the dry state and in water, also shows the highest friction both in the dry state and in water.

Simple contact mechanics model of the vertebrate cartilage

We study a simple contact mechanics model of the vertebrate cartilage, which includes (bulk) osmotic effects. The surface roughness power spectrum of a pig cartilage is obtained from the measured surface topography. Using the Reynolds equations with fluid flow factors, calculated using the Persson contact mechanics theory and the Bruggeman effective medium theory, we show how the area of contact and the average interfacial separation change with time. We found that in most cases the contact area percolates, resulting in islands of confined fluid which carry most of the external load. Most importantly, we find that the pressure in the area of real contact is nearly independent of the external load, and well below 1 MPa. This allows the surfaces in the area of "real contact", to be separated (at nanometer range separation distance) by osmotic repulsion, resulting in a very small (breakloose) friction force observed even after a long time of stationary contact.

The effect of surface roughness and viscoelasticity on rubber adhesion

Adhesion between silica glass or acrylic balls and silicone elastomers and various industrial rubbers is investigated. The work of adhesion during pull-off is found to strongly vary depending on the system, which we attribute to the two opposite effects: (1) viscoelastic energy dissipation close to an opening crack tip and (2) surface roughness. Introducing surface roughness on the glass ball is found to increase the work of adhesion for soft elastomers, while for the stiffer elastomers it results in a strong reduction in the work of adhesion. For the soft silicone elastomers a strong increase in the work of adhesion with increasing pull-off velocity is observed, which may result from the non-adiabatic processes associated with molecular chain pull-out. In general, the work of adhesion is decreased after repeated contacts due to the transfer of molecules from the elastomers to the glass ball. Thus, extracting the free chains (oligomers) from the silicone elastomers is shown to make the work of adhesion independent of the number of contacts. The viscoelastic properties (linear and nonlinear) of all of the rubber compounds are measured, and the velocity dependent crack opening propagation energy at the interface is calculated. Silicone elastomers show a good agreement between the measured work of adhesion and the predicted results, but carbon black filled hydrogenated nitrile butadiene rubber compounds reveal that strain softening at the crack tip may play an important role in determining the work of adhesion. Additionally, adhesion measurement under submerged conditions in distilled water and water + soap solutions are also performed: a strong reduction in the work of adhesion is measured for the silicone elastomers submerged in water, and a complete elimination of adhesion is found for the water + soap solution attributed to an osmotic repulsion between the negatively charged surface of the glass and the elastomer.

The effect of surface nano-corrugation on the squeeze-out of molecular thin hydrocarbon films between curved surfaces with long range elasticity

The properties of linear alkane lubricants confined between two approaching solids are investigated by a model that accounts for the roughness, curvature and elastic properties of the solid surfaces. We consider linear alkanes of different chain lengths from [Formula: see text] to [Formula: see text], confined between corrugated solid walls. The pressure necessary to squeeze out the lubricant increases rapidly with the alkane chain length, but is always much lower than in the case of smooth surfaces. The longest alkanes form domains of ordered chains and the squeeze-out appears to nucleate in the more disordered regions between these domains. The short alkanes stay fluid-like during the entire squeeze out process which result in a very small squeeze-out pressure which is almost constant during the squeeze-out of the last monolayer of the fluid. In all cases we observe lubricant trapped in the valley of the surface roughness, which cannot be removed independent of the magnitude of the squeezing pressures.

Soft matter dynamics: Accelerated fluid squeeze-out during slip

Using a Leonardo da Vinci experimental setup (constant driving force), we study the dependency of lubricated rubber friction on the time of stationary contact and on the sliding distance. We slide rectangular rubber blocks on smooth polymer surfaces lubricated by glycerol or by a grease. We observe a remarkable effect: during stationary contact the lubricant is only very slowly removed from the rubber-polymer interface, while during slip it is very rapidly removed resulting (for the grease lubricated surface) in complete stop of motion after a short time period, corresponding to a slip distance typically of order only a few times the length of the rubber block in the sliding direction. For an elastically stiff material, poly(methyl methacrylate), we observe the opposite effect: the sliding speed increases with time (acceleration), and the lubricant film thickness appears to increase. We propose an explanation for the observed effect based on transient elastohydrodynamics, which may be relevant also for other soft contacts.

Fluid contact angle on solid surfaces: Role of multiscale surface roughness

We present a simple analytical model and an exact numerical study which explain the role of roughness on different length scales for the fluid contact angle on rough solid surfaces. We show that there is no simple relation between the distribution of surface slopes and the fluid contact angle. In particular, surfaces with the same distribution of slopes may exhibit very different contact angles depending on the range of length-scales over which the surfaces have roughness.

Theory of adhesion: role of surface roughness

We discuss how surface roughness influences the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length scales. We consider two limiting cases relevant for (a) elastically hard solids with weak (or long ranged) adhesive interaction (DMT-limit) and (b) elastically soft solids with strong (or short ranged) adhesive interaction (JKR-limit). For the former cases we study the nature of the adhesion using different adhesive force laws (F ∼ u(-n), n = 1.5-4, where u is the wall-wall separation). In general, adhesion may switch from DMT-like at short length scales to JKR-like at large (macroscopic) length scale. We compare the theory predictions to results of exact numerical simulations and find good agreement between theory and simulation results.

General theory of frictional heating with application to rubber friction

The energy dissipation in the contact regions between solids in sliding contact can result in high local temperatures which may strongly effect friction and wear. This is the case for rubber sliding on road surfaces at speeds above 1 mm s(-1). We derive equations which describe the frictional heating for solids with arbitrary thermal properties. The theory is applied to rubber friction on road surfaces and we take into account that the frictional energy is partly produced inside the rubber due to the internal friction of rubber and in a thin (nanometer) interfacial layer at the rubber-road contact region. The heat transfer between the rubber and the road surface is described by a heat transfer coefficient which depends on the sliding speed. Numerical results are presented and compared to experimental data. We find that frictional heating results in a kinetic friction force which depends on the orientation of the sliding block, thus violating one of the two basic Leonardo da Vinci 'laws' of friction.

Friction and universal contact area law for randomly rough viscoelastic contacts

We present accurate numerical results for the friction force and the contact area for a viscoelastic solid (rubber) in sliding contact with hard, randomly rough substrates. The rough surfaces are self-affine fractal with roughness over several decades in length scales. We calculate the contribution to the friction from the pulsating deformations induced by the substrate asperities. We also calculate how the area of real contact, A(v, p), depends on the sliding speed v and on the nominal contact pressure p, and we show how the contact area for any sliding speed can be obtained from a universal master curve A(p). The numerical results are found to be in good agreement with the predictions of an analytical contact mechanics theory.

Role of hydrophobicity on interfacial fluid flow: theory and some applications

The fluid flow through a seal interface depends on the percolating non-contact channels morphology, size and length, and on the interfacial surface energies. In particular, hydrophobic interfaces may expel fluids and decrease the fluid flow of seals, while increasing the sliding friction. We present results of interfacial fluid flow experiments on a hydrostatic column device which demonstrate how interfacial hydrophobicity can block fluid flow at interfaces and reduce the leak rate of seals. The presented results may help to understand the role of interfacial hydrophobicity in many practical applications, some of which we discuss briefly in this paper, e.g., rubber wiper blades on hydrophobic (usually wax-coated) glass, the locomotion of insects on surfaces in water, and syringes.

Static or breakloose friction for lubricated contacts: the role of surface roughness and dewetting

We present experimental data for the static or breakloose friction for lubricated elastomer contacts, as a function of the time of stationary contact. Due to fluid squeeze-out from the asperity contact regions, the breakloose friction force increases continuously with the time of stationary contact. We consider three different cases: (a) PDMS rubber balls against flat smooth glass surfaces, (b) PDMS cylinder ribs against different substrates (glass, smooth and rough PMMA and an inert polymer) and (c) application to syringes. Due to differences in the surface roughness and contact pressures the three systems exhibit very different time dependences of the breakloose friction. In case (a) for rough surfaces the dry contact area A is a small fraction of the nominal contact area A0, and the fluid squeeze-out is fast. In case (b) the dry contact area is close to the nominal contact area, A/A0 ≈ 1, and fluid squeeze-out is very slow due to percolation of the contact area. In this case, remarkably, different fluids with very different viscosities, ranging from 0.005 Pa s (water–glycerol mixture) to 1.48 Pa s (glycerol), give very similar breakloose friction forces as a function of the time of stationary contact. In case (c) the contact pressure and the surface roughness are larger than in case (b), and the squeeze-out is very slow so that even after a very long time the area of real contact is below the percolation threshold. For all cases (a)–(c), the increase in the breakloose friction is mainly due to the increase in the area of real contact with increasing time, because of the fluid squeeze-out and dewetting.

Comment on "Friction between a viscoelastic body and a rigid surface with random self-affine roughness"

A Comment on the Letter by Q. Li, M. Popov, A. Dimaki, A. E. Filippov, S. Kürschner, and V. L. Popov, Phys. Rev. Lett. 111, 034301 (2013). The authors of the Letter offer a Reply.

Adhesion: role of bulk viscoelasticity and surface roughness

We study the adhesion between smooth polydimethylsiloxane (PDMS) rubber balls and smooth and rough poly(methyl methacrylate) (PMMA) surfaces, and between smooth silicon nitride balls and smooth PDMS surfaces. From the measured viscoelastic modulus of the PDMS rubber we calculate the viscoelastic contribution to the crack-opening propagation energy γeff(v,T) for a wide range of crack tip velocities v and for several temperatures T. The Johnson-Kendall-Roberts (JKR) contact mechanics theory is used to analyze the ball pull-off force data, and γeff(v,T) is obtained for smooth and rough surfaces. We conclude that γeff(v,T) has contributions of similar magnitude from both the bulk viscoelastic energy dissipation close to the crack tip, and from the bond-breaking process at the crack tip. The pull-off force on the rough surfaces is strongly reduced compared to that of the flat surface, which we attribute mainly to the decrease in the area of contact on the rough surfaces.

Rubber friction for tire tread compound on road surfaces

We have measured the surface topography and calculated the surface roughness power spectrum for an asphalt road surface. For the same surface we have measured the friction for a tire tread compound for velocities 10(-6) m s(-1) < v < 10(-3) m s(-1) at three different temperatures (at -8 °C, 20 °C and 48 °C). The friction data was shifted using the bulk viscoelasticity shift factor a(T) to form a master curve. We have measured the effective rubber viscoelastic modulus at large strain and calculated the rubber friction coefficient (and contact area) during stationary sliding and compared it to the measured friction coefficient. We find that for the low velocities and for the relatively smooth road surface we consider, the contribution to friction from the area of real contact is very important, and we interpret this contribution as being due to shearing of a very thin confined rubber smear film.

On the origin of why static or breakloose friction is larger than kinetic friction, and how to reduce it: the role of aging, elasticity and sequential interfacial slip

We discuss the origin of static friction and show how it can be reduced towards kinetic friction by the appropriate design of the sliding system. The basic idea is to use elastically soft solids and apply the external forces in such a way that different parts of the contacting interface start to slip at different times during the (tangential) loading process. In addition, the local slip must be large enough in order to result in a strong drop in the static friction force. We illustrate the theoretical predictions with the results of a simple model experiment.

Contact mechanics for layered materials with randomly rough surfaces

The contact mechanics model of Persson is applied to layered materials. We calculate the M function, which relates the surface stress to the surface displacement, for a layered material, where the top layer (thickness d) has different elastic properties than the semi-infinite solid below. Numerical results for the contact area as a function of the magnification are presented for several cases. As an application, we calculate the fluid leak rate for laminated rubber seals.

Effective viscosity of confined hydrocarbons

We present molecular dynamics friction calculations for confined hydrocarbon films with molecular lengths from 20 to 1400 carbon atoms. We find that the logarithm of the effective viscosity η(eff) for nanometer-thin films depends linearly on the logarithm of the shear rate: log η(eff)=C-nlog ̇γ, where n varies from 1 (solidlike friction) at very low temperatures to 0 (Newtonian liquid) at very high temperatures, following an inverse sigmoidal curve. Only the shortest chain molecules melt, whereas the longer ones only show a softening in the studied temperature interval 0<T<900 K. The results are important for the frictional properties of very thin (nanometer) films and to estimate their thermal durability.

Elastic contact mechanics: percolation of the contact area and fluid squeeze-out

The dynamics of fluid flow at the interface between elastic solids with rough surfaces depends sensitively on the area of real contact, in particular close to the percolation threshold, where an irregular network of narrow flow channels prevails. In this paper, numerical simulation and experimental results for the contact between elastic solids with isotropic and anisotropic surface roughness are compared with the predictions of a theory based on the Persson contact mechanics theory and the Bruggeman effective medium theory. The theory predictions are in good agreement with the experimental and numerical simulation results and the (small) deviation can be understood as a finite-size effect. The fluid squeeze-out at the interface between elastic solids with randomly rough surfaces is studied. We present results for such high contact pressures that the area of real contact percolates, giving rise to sealed-off domains with pressurized fluid at the interface. The theoretical predictions are compared to experimental data for a simple model system (a rubber block squeezed against a flat glass plate), and for prefilled syringes, where the rubber plunger stopper is lubricated by a high-viscosity silicon oil to ensure functionality of the delivery device. For the latter system we compare the breakloose (or static) friction, as a function of the time of stationary contact, to the theory prediction.

Rubber friction: comparison of theory with experiment

We have measured the friction force acting on a rubber block slid on a concrete surface. We used both unfilled and filled (with carbon black) styrene butadiene (SB) rubber and have varied the temperature from -10 °C to 100 °C and the sliding velocity from 1 μm/s to 1000 μm/s. We find that the experimental data at different temperatures can be shifted into a smooth master-curve, using the temperature-frequency shifting factors obtained from measurements of the bulk viscoelastic modulus. The experimental data has been analyzed using a theory which takes into account the contributions to the friction from both the substrate asperity-induced viscoelastic deformations of the rubber, and from shearing the area of real contact. For filled SB rubber the frictional shear stress σ(f) in the area of real contact results mainly from the energy dissipation at the opening crack on the exit side of the rubber-asperity contact regions. For unfilled rubber we instead attribute σ(f) to shearing of a thin rubber smear film, which is deposited on the concrete surface during run in. We observe very different rubber wear processes for filled and unfilled SB rubber, which is consistent with the different frictional processes. Thus, the wear of filled SB rubber results in micrometer-sized rubber particles which accumulate as dry dust, which is easily removed by blowing air on the concrete surface. This wear process seams to occur at a steady rate. For unfilled rubber a smear film forms on the concrete surface, which cannot be removed even using a high-pressure air stream. In this case the wear rate appears to slow down after some run in time period.

Lubricated sliding dynamics: flow factors and Stribeck curve

We study the fluid flow at the interface between elastic solids with randomly rough surfaces. We derive (approximate) analytical expressions for the fluid flow factors which enter in the equation describing the fluid flow, and for the frictional shear stress factors which enter in the equation for the frictional shear stress. Numerical results for a rubber cylinder with surface roughness sliding on a flat lubricated substrate, under "low" and "high" pressure conditions, are presented and discussed. Finally we discuss the role of the fluid-induced elastic deformations of the surface roughness profile.

Fluid squeeze-out between rough surfaces: comparison of theory with experiment

We study the time dependence of the (average) interfacial separation between an elastic solid with a flat surface and a rigid solid with a randomly rough surface, squeezed together in a fluid. We use an analytical theory describing the fluid flow factors, based on the Persson contact mechanics theory and the Bruggeman effective medium theory, to calculate the removal of the fluid from the contacting interface of the two solids. In order to test this approach, we have performed simple squeeze-out experiments. The experimental results are compared to the theoretical predictions.

Quantum friction

We investigate the van der Waals friction between graphene and an amorphous SiO(2) substrate. We find that due to this friction the electric current is saturated at a high electric field, in agreement with experiment. The saturation current depends weakly on the temperature, which we attribute to the quantum friction between the graphene carriers and the substrate optical phonons. We calculate also the frictional drag between two graphene sheets caused by van der Waals friction, and find that this drag can induce a voltage high enough to be easily measured experimentally.

Transverse and normal interfacial stiffness of solids with randomly rough surfaces

Using a theoretical approach and computer simulations, we calculate the normal stiffness K(perpendicular) and the transverse stiffness K(parallel) of the interface between two contacting isotropic solids with randomly rough surfaces and Poisson ratio ν. The theoretical predictions for K(perpendicular) agree well with the simulations. Moreover, the theoretical result for the ratio K(perpendicular)/K(parallel) is (2 - ν)/(2 - 2ν), as predicted by Mindlin for a single circular contact region. Finally, we compare the theory to experimental ultrasonic data.