arXiv subjects
Publications and source records attributed to B. N. J. Persson.
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 $α< 0.01$ and Gaussian-like for $α> 10$, where the dimensionless parameter $α= h_{\rm rms}/δ$ is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact).
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.
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
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.
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.
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.
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.
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.
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
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.
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 $\approx 1 \ {\rm μm}$, 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.
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.
In rubber friction studies it is often observed that the kinetic friction coefficient μ depends on the nominal contact pressure p. We discuss several possible origins of the pressure dependency of μ: (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 μ(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.
We investigate the dependence of the thermal Casimir force between two graphene sheets on the drift velocity of the electrons in one graphene sheet. We show that the drift motion produces a measurable change of the thermal Casimir force due to the Doppler effect. The thermal Casimir force as well as the Casimir friction are strongly enhanced in the case of resonant photon tunneling when the energy of the emitted photon coincides with the energy of electron-hole pair excitations. In the case of resonant photon tunneling, even for temperatures above room temperature the Casimir friction is dominated by quantum friction due to quantum fluctuations. Quantum friction can be detected in frictional drag experiment between graphene sheets for high electric field.
We study the near-field radiative energy transfer between graphene and an amorphous SiO$_2$ substrate. In comparison with the existing theories of near-field radiative heat transfer our theory takes into account that the free carriers in graphene are moving relative to the substrate with a drift velocity $v$. In this case the heat flux is determined by both thermal and quantum fluctuations. We find that quantum fluctuations give an important contribution to the radiative energy transfer for low temperatures and high electric field (large drift velocities). For nonsuspended graphene the near-field radiative energy transfer gives a significant contribution to the heat transfer, in addition to the contribution from phononic coupling. For suspended graphene (large separation) the corresponding radiative energy transfer coefficient at nanoscale gap is $\sim$ 3 orders of magnitude larger than radiative heat transfer coefficient of the blackbody radiation limit.
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.