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Rubber wear results from the removal of small (micrometer-sized) rubber particles through crack propagation. In this study, we investigate the wear behavior of Styrene-Butadiene Rubber (SBR) and Natural Rubber (NR) sliding on two different concrete surfaces under dry and wet conditions. Experiments were conducted at low sliding speeds ($\approx 1 \ {\rm mm/s}$) to minimize frictional heating and hydrodynamic effects. For two SBR compounds, we observe significantly higher wear rates in water compared to the dry state, with enhancement factors of $1.5-2.5$ for a low-glass-transition-temperature SBR compound ($T_{\rm g} = -50^\circ {\rm C}$) and approximately $4$ for a higher-glass-transition compound ($T_{\rm g} = -7^\circ {\rm C}$). In contrast, the NR compound showed no wear in water at low nominal contact pressures ($\sigma_0 \approx 0.12$, $0.16$, and $0.25 \ {\rm MPa}$), while at higher pressures ($\sigma_0 \approx 0.36$ and $0.49 \ {\rm MPa}$), the wear rates in dry and wet states were similar. The experimental results are analyzed using a recently developed rubber wear theory. The findings provide insights into the mechanisms of rubber wear under varying environmental and mechanical conditions, highlighting the influence of material properties, interfacial effects, and applied pressures on wear behavior.

We study the wear rate (mass loss per unit sliding distance) of a tire tread rubber compound sliding on concrete paver surfaces under dry and wet conditions, at different nominal contact pressures of $\sigma_0 = 0.12$, $0.29$, and $0.43 \ {\rm MPa}$, and sliding velocities ranging from $v= 1 \ {\rm \mu m/s}$ to $1 \ {\rm cm/s}$. We find that the wear rate is proportional to the normal force and remains independent of the sliding speed. Sliding in water and soapy water results in significantly lower wear rates compared to dry conditions. The experimental data are analyzed using a theory that predicts wear rates and wear particle size distributions consistent with the experimental observations.

I study the influence of temperature and the crack-tip velocity of the bond breaking at the crack tip in rubber-like materials. The bond breaking is considered as a stress-aided thermally activated process and result in an effective crack propagation energy which increases strongly with decreasing temperature or increasing crack-tip speed. This effect is particular important for adhesive (interfacial) crack propagation but less important for cohesive crack propagation owing to the much larger bond-breaking energies in the latter case. For adhesive cracks the theory results are consistent with adhesion measurements for silicone (PDMS) rubber in contact with silica glass surfaces. For cohesive cracks the theory agree well with experimental results PDMS films chemically bound to silinized glass.

Analytical contact mechanics theories depend on surface roughness through the surface roughness power spectrum. In the present study, we evaluated the usability of various experimental methods for studying surface roughness. Our findings indicated that height data obtained from optical methods often lack accuracy and should not be utilized for calculating surface roughness power spectra. Conversely, engineering stylus instruments and atomic force microscopy (AFM) typically yield reliable results that are consistent across the overlapping roughness length scale region. For surfaces with isotropic roughness, the two-dimensional (2D) power spectrum can be derived from the one-dimensional (1D) power spectrum using several approaches, which we explored in this paper.

We have studied the fluctuation (noise) in the position of sliding blocks under constant driving forces on different substrate surfaces. The experimental data are complemented by simulations using a simple spring-block model where the asperity contact regions are modeled by miniblocks connected to the big block by viscoelastic springs. The miniblocks experience forces that fluctuate randomly with the lateral position, simulating the interaction between asperities on the block and the substrate. The theoretical model provides displacement power spectra that agree well with the experimental results.

Crack propagation in viscoelastic solids like rubber is of great practical importance. Shrimali and Lopez-Pamies have proposed a new interesting approach for the crack propagation in viscoelastic solids. We give comments on the validity of the theory and point out some effects not included in the theory., Comment: 4 pages, 2 figures

When a body is exposed to external forces large local stresses may occur at the surface because of surface roughness. Surface stress concentration is important for many applications and in particular for fatigue due to pulsating external forces. For randomly rough surfaces I calculate the probability distribution of surface stress in response to a uniform external tensile stress with the displacement vector field parallel to the rough surface. I present numerical simulation results for the stress distribution $\sigma (x,y)$ and show that in a typical case, the maximum local tensile stress may be $\sim 10$ times bigger than the applied stress. I discuss the role of the stress concentration on plastic deformation and surface crack generation and propagation., Comment: 18 pages,15 figures

We study the heat transfer in weakly interacting particle systems in vacuum. The particles have surface roughness with self-affine fractal properties, as expected for mineral particles produced by fracture, e.g., by crunching brittle materials in a mortar. We show that the propagating electromagnetic (EM) waves and the evanescent EM-waves, which occur outside of all solids, give the dominant heat transfer for large and small particles, respectively, while the phononic contribution from the area of real contact is negligible. As an application we discuss the heat transfer in rubble pile asteroids.

Most asteroids with a diameter larger than $\sim 300 \ {\rm m}$ are rubble piles i.e. consisting of more than one solid object. All asteroids are rotating but almost all asteroids larger than $\sim 300 \ {\rm m}$ rotate with a period longer than $2.3 \ {\rm hours}$, which is the critical period where the centrifugal force equals the gravitational force. This indicates that there are nearly no adhesive interaction forces between the asteroid fragments. We show that this is due to the surface roughness of the asteroid particles which reduces the van der Waals interaction between the particles by a factor of $100$ for micrometer sized particles and even more for larger particles. We show that surface roughness results in an interaction force which is independent of the size of the particles, in contrast to the linear size dependency expected for particles with smooth surfaces. Thus, two stone fragments of size $100 \ {\rm nm}$ attract each other with the same non-gravitational force as two fragments of size $10 \ {\rm m}$., Comment: 24 pages, 30 figures

We study the leakage of fluids (liquids or gases) in syringes with glass barrel, steel plunger and rubber O-ring stopper. The leakrate depends on the interfacial surface roughness and on the viscoelastic properties of the rubber. Random surface roughness is produced by sandblasting the rubber O-rings. We present a very simple theory for gas flow which takes into account both the diffusive and ballistic flow. The theory shows that the interfacial fluid flow (leakage) channels are so narrow that the gas flow is mainly ballistic (the so called Knudsen limit). We compare the leakrate obtained using air and helium. For barrels filled with water we observe no leakage even if leakage occurs for gases. We interpret this as resulting from capillary (Laplace pressure or surface energy) effects., Comment: 18 pages, 28 figures

We study the leakage of air in syringes with Teflon coated rubber stopper and glass barrel. The leakrate depends on the interfacial surface roughness, the viscoelastic properties of the rubber and on the elastoplastic properties of the Teflon coating. The measured leakage rates are compared to the predictions of a simple theory for gas flow, which takes into account both the diffusive and ballistic air flow, and the elastoplastic multiscale contact mechanics which determines the probability distribution of interfacial separations. The theory shows that the interfacial air flow (leakage) channels are so narrow that the gas flow is mainly ballistic (the so called Knudsen limit). The implications for container closure integrity is discussed., Comment: 7 pages, 9 figures

We show that the Persson-Brener theory of crack propagation in viscoelastic solids gives a viscoelastic fracture energy factor $G/G_0 = 1+f$ which is nearly the same as the viscoelastic factor obtained using the cohesive-zone model. We also discuss finite-size effects and comment on the use of crack propagation theories for "solids" with a viscoelastic modulus that vanishes at zero frequency., Comment: 5 pages, 5 figures

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 facemask 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., Comment: 9 pages, 15 figures

We study the influence of the surface energy and contamination films on rubber adhesion and sliding friction. We find that there is a transfer of molecules from the rubber to the substrate which reduces the work of adhesion and makes the rubber friction insensitive to the substrate surface energy. We show that there is no simple relation between adhesion and friction: adhesion is due to (vertical) detachment processes at the edge of the contact regions (opening crack propagation), while friction in many cases is determined mainly by (tangential) stick-slip instabilities of nanosized regions, within the whole sliding contact. Thus while the pull-off force in fluids may be strongly reduced (due to a reduction of the work of adhesion), the sliding friction may be only slightly affected as the area of real contact may be dry, and the frictional shear stress in the contact area nearly unaffected by the fluid., Comment: 13 pages, 21 figures

When a crack propagate in a viscoelastic solid energy dissipation can occur very far from the crack tip where the stress field may be very different from the $r^{-1/2}$ 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 result in a crack propagation energy in semi-quantitative 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 thecrack tip process zone., Comment: 9 pages, 12 figures. arXiv admin note: text overlap with arXiv:2009.04936

We review a theory of crack propagation in viscoelastic solids. We consider both cracks in infinite systems and in finite sized systems. As applications of the theory we consider two adhesion problems, namely pressure sensitive adhesives and the ball-flat adhesion problem. We also study crack propagation in the pig skin dermis, which is of medical relevance, and rubber wear in the context of tires., Comment: 21 pages, 41 figures

We study the nominal (ensemble averaged) contact pressure $p(x)$ acting on a cylinder squeezed in contact with an elastic half-space with random surface roughness. The contact pressure is Hertzian-like for $\alpha < 0.01$ and Gaussian-like for $\alpha > 10$, where the dimensionless parameter $\alpha = h_{\rm rms}/\delta$ is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact)., Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:2007.13576

Metallic seals are crucial machine elements in many important applications, e.g., in ultrahigh vacuum systems. Due to the high elastic modulus of metals, and the surface roughness which exists on all solid surfaces, if no plastic deformation would occur one expects in most cases large fluid flow channels between the contacting metallic bodies, and large fluid leakage. However, in most applications plastic deformation occurs, at least at the asperity level, which allows the surfaces to approach each other to such an extent that fluid leakage often can be neglected. In this study, we present an experimental set-up for studying the fluid leakage in metallic seals. We study the water leakage between a steel sphere and a steel body (seat) with a conical surface. The experimental results are found to be in good quantitative agreement with a (fitting-parameter-free) theoretical model. The theory predicts that the plastic deformations reduce the leak-rate by a factor $\approx 8$, Comment: 10 pages, 10 figures

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 which shows that adhesion in most cases is "killed" by the longest wavelength roughness. 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 non-adhesive finger-glass contact mechanics, involving large deformations of a complex layered material., Comment: 6 Pages, 9 figures. arXiv admin note: text overlap with arXiv:2002.02226

Using molecular dynamics (MD) we study the dependency of the contact mechanics on the sliding speed when an elastic block (cylinder) with a ${\rm cos} (q_0 x)$ 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 (LJ) 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 type 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 $\approx 0.1 \ {\rm MPa}$ during sliding. This frictional shear stress, and the elastic modulus used, are typical for Polydimethylsiloxan (PDMS) 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, Comment: 6 pages , 7 figures

We present experimental and theoretical results for the surface topography of a plastically deformed metallic (aluminum) block. When a hard spherical body (here a steel-, silica glass- or silicon nitride ball) with a smooth surface is indented in a metal block with a nominally flat, but still rough, surface, a spherical-cup-like indentation result due to plastic flow. The surface roughness in the indented region is, however, not entirely flattened. The long wavelength (macroasperity) content of the roughness result from the roughness on the original (aluminum) surface, but now plastically deformed. The roughness at short length scale, in the plastically deformed macroasperity contact regions, result from the roughness on the hard ball, and from inhomogeneous plastic flow. We model the contact mechanics using the boundary element method, combined with a simple numerical procedure to take into account the plastic flow. The theory can semi-quantitatively describe the modification of the roughness by the plastic flow. Since the fluid leakage of metallic seals in most cases is determined by the long wavelength roughness, we predict that the leakage can be estimated based on the elastoplastic contact mechanics model employed here. The plastic deformations of surfaces of some glassy polymers is very different from what we observed for aluminum, which we attribute to strong work-hardening and to inhomogeneous plastic flow for the polymers. Thus the numerical procedure to account for the plastic flow proposed here cannot be applied to glassy polymers in general., Comment: 10 pages, 18 figures

We study the role of electronegativity in sliding friction for five different two dimensional (2D) monolayer systems using density functional theory (DFT) with van der Waals (vdW) corrections. We show that the friction between the commensurate 2D layered systems depends strongly on the electronegativity difference of the involved atoms. All the 2D layered structures exhibit almost the same magnitude of friction force when sliding along the nonpolar path, independent of the material and the surface structures. In contrast, for sliding friction along the polar path, the friction force obeys a universal linear scaling law as a function of the electronegativity difference of its constituent atoms. Further analyses demonstrate that atomic dipoles in the 2D monolayers induced by the electronegativity difference enhance the corrugation of charge distribution and increase the sliding barrier accordingly. Our studies reveal that electronegativity plays an important role in friction of low dimensional systems, and will provide a strategy for designing nanoscale devices further., Comment: manuscript 13 pages, 5 figures. Supporting Information 1 table and 1 figure

I discuss fluid flow at the interface between solids with anisotropic roughness. I show that for randomly rough surfaces with anisotropic roughness, the contact area percolate at the same relative contact area as for isotropic roughness, and 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., Comment: 14 pages, 7 figures

Using molecular dynamics we study the dependence of the friction force on the sliding speed when an elastic slab (block) is sliding on a rigid substrate with a ${\rm sin} (q_0 x)$ surface height profile. The friction force is nearly velocity independent due to phonon emission at the closing and opening crack tips, where rapid atomic snap-in and -out events occur during sliding. The rapid events result from lattice trapping and are closely related to the velocity gap and hysteresis effects observed in model studies of crack propagation in solids. This indicates that the friction force is dominated by processes occurring at the edges of the contact area, which is confirmed by calculations showing that the friction force is independent of the normal force. The friction force increases drastically when the sliding velocity approaches the solid transverse sound velocity, as expected from the theory of cracks., Comment: 5 pages, 6 figures. arXiv admin note: text overlap with arXiv:2002.02226

Using molecular dynamics (MD) we study the dependency of the contact mechanics on the sliding speed when an elastically soft slab (block) is sliding on a rigid substrate with a ${\rm sin} (q_0 x)$ surface height profile. The atoms on the block interact with the substrate atoms by Lennard-Jones potentials. We consider contacts with and without adhesion. We found that the contact area and the friction force are nearly velocity independent for small velocities ($v < 0.25 \ {\rm m/s}$) in spite of the fact that the shear stress in the contact area is rather non-uniform. For the case of no adhesion the friction coefficient is very small. For the case of adhesion the friction coefficient is higher, and is mainly due to energy dissipation at the opening crack tip, where rapid atomic snap-off events occur during sliding. 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 non-adhesive finger-glass contact mechanics, involving large deformations of a complex layered material., Comment: 14 pages, 20 Figures

In their interesting study (Ref. [1]) Hu et al have shown that for a simple "harmonium" solid model the slip-induced motion of surface atoms is close to critically damped. This result is in fact well known from studies of vibrational damping of atoms and molecules at surfaces. However, for real practical cases the situation may be much more complex and the conclusions of Hu et al invalid., Comment: 2 pages, 1 figure

I show how flexoelectricity result in a fluctuating surface electric potential when elastic solids with random roughness are squeezed into contact. The flexoelectric potential may induce surface charge distributions and hence contribute to triboelectricity. Using the developed theory I analyze the Kelvin Force Microscopy data of Baytekin et al for the electric potential above a polydimethylsiloxane (PDMS) surface after it was peeled away from another PDMS surface, Comment: 6 pages and 4 figures

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 SiO$_2$ substrate., Comment: 10 pages, 2 figures

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 interpolate 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 detatch (lifetime) of suction cups were in good agreement with theory, except for surfaces with the root-mean-square (rms) roughness below $\approx 1 \ {\rm \mu m}$, where diffusion of plasticizer from the PVC to the PMMA surface caused blockage of critical constrictions. 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 in varying degree of roughness under dry and wet environments., Comment: 18 pages, 29 figures. arXiv admin note: substantial text overlap with arXiv:1905.09042

We present experimental results for the dependency of the pull-off time (failure time) on the pull-off force for suction cups in the air and in water. The results are analyzed using a theory we have developed for the contact between suction cups and randomly rough surfaces. The theory predicts the dependency of the pull-off time (failure time) on the pull-off force, and is tested with measurements performed on suction cups made from a soft polyvinyl chloride (PVC). As substrates we used sandblasted poly(methyl methacrylate) (PMMA). The theory is in good agreement with the experiments in air, except for surfaces with the root-mean-square (rms) roughness below $\approx 1 \ {\rm \mu m}$, where we observed lifetimes much longer than predicted by the theory. We show that this is due to out-diffusion of plasticizer from the soft PVC, which block the critical constrictions along the air flow channels. In water some deviation between theory and experiments is observed which may be due to capillary forces. We discuss the role of cavitation for the failure time of suction cups in water., Comment: 11 pages, 16 figures

Machine elements and mechanical components have often surfaces with anisotropic roughness, which may result from the machining processes, e.g. grinding, or from wear. Hence, it is important to understand how surface roughness anisotropy affects contact mechanics properties, such as friction and the interface separation, which is important for lubricated contacts. Here we extend and apply a multiscale mean-field model to the lubricated contact between a soft (e.g. rubber) elastic solid and a rigid countersurface. We consider surfaces with anisotropic surface roughness, and discuss how the fluid flow factors and friction factors depend on the roughness. We present an experimental study of the lubricated sliding contact between a nitrile butadiene rubber O-ring and steel surfaces with different types of isotropic and anisotropic surface roughness. The good quantitative comparison between the experimental results and the theory predictions suggests that the multiscale lubrication mechanisms are accurately captured by the theory.

A huge number of technological and biological systems involves the lubricated contact between rough surfaces of soft solids in relative accelerated motion. Examples include dynamical rubber seals and the human joints. In this study we consider an elastic cylinder with random surface roughness in accelerated sliding motion on a rigid, perfectly flat (no roughness) substrate in a fluid. We calculate the surface deformations, interface separation and the contributions to the friction force and the normal force from the area of real contact and from the fluid. The driving velocity profile as a function of time is assumed to be either a sine-function, or a linear multi-ramp function. We show how the squeeze-in and squeeze-out processes, occurring in accelerated sliding, quantitatively affect the Stribeck curve with respect to the steady sliding. Finally, the theory results are compared to experimental data.

We study the quantum Vavilov-Cherenkov (QVC) radiation and quantum friction occurring during motion of a small neutral particle parallel to a transparent dielectric plate with the refractive index $n$. This phenomenon occurs above the threshold velocity $v_c=c/n$. The particle acceleration and rate of heating are determined by the friction force and heating power in the rest reference frame of the particle. We calculate these quantities starting from the expressions for the friction force and the radiative energy transfer in the plate-plate configuration, assuming plate at the rest in the \textit{lab} frame rarefied. Close to the light velocity there is a big difference between the friction force and the radiation power in the rest frame of a particle and in the \textit{lab} reference frame. This difference is connected with the change of the rest mass of the particle due to absorption of radiation. Close to the threshold velocity the decrease of the kinetic energy of the particle is determined mainly by radiation power in in the \textit{lab} frame. However, close to the light velocity it is determined also by the heating power for the particle. We establish the connections between the quantities in the different reference frames. For a nanoparticle the QVC radiation intensity can be comparable to classical one. We discuss the possibility to detect QVC radiation., Comment: 7 pages, 2 figures. arXiv admin note: text overlap with arXiv:1511.06573

In rubber friction studies it is often observed that the kinetic friction coefficient {\mu} depends on the nominal contact pressure p. We discuss several possible origins of the pressure dependency of {\mu}: (a) saturation of the contact area (and friction force) due to high nominal squeezing pressure, (b) non-linear viscoelasticity, (c) non-randomness in the surface topography, in particular the influence of the skewness of the surface roughness profile, (d) adhesion, and (e) frictional heating. We show that in most cases the non-linearity in the {\mu}(p) relation is mainly due to process (e) (frictional heating), which softens the rubber, increases the area of contact, and (in most cases) reduces the viscoelastic contribution to the friction. In fact, since the temperature distribution in the rubber at time t depends on on the sliding history (i.e., on the earlier time t0 < t), the friction coefficient at time t will also depend on the sliding history, i.e. it is, strictly speaking, a time integral operator. The energy dissipation in the contact regions between solids in sliding contact can result in high local temperatures which may strongly affect the area of real contact and the friction force (and the wear-rate). This is the case for rubber sliding on road surfaces at speeds above 1 mm/s. In Ref. [14] we have derived equations which describe the frictional heating for solids with arbitrary thermal properties. In this paper the theory is applied to rubber friction on road surfaces. Numerical results are presented and compared to experimental data. We observe good agreement between the calculated and measured temperature increase., Comment: 14 pages, 21 figures

Using a fully relativistic theory we study the quantum Vavilov-Cherenkov radiation and quantum friction occurring during relative sliding of the two transparent dielectric plates with the refractive index $n$. These phenomena occur above the threshold velocity $v_c=2nc/(n^2+1)$. Close to the threshold velocity they are dominated by the contribution from $s$--polarized electromagnetic waves, which agrees with the approximate (relativistic) theory by Pendry (J. Mod. Opt. \textbf{45}, 2389 (1998)). However, in the ultra relativistic case ($v\rightarrow c$), the contributions from both polarisations are strongly enhanced in the comparison with the approximate theory, and a new contribution occurs from the mixing of the electromagnetic waves with the different polarization. The numerical results are supplemented by an analytical treatment close to the threshold velocity and the light velocity., Comment: 7 pages, 3 figures