We present a molecular dynamics study of the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. The numerical calculations mainly focus on the contact area and the interfacial separation from small contact (low load) to full contact (high load). For small load the contact area varies linearly with the load and the interfacial separation depends logarithmically on the load. For high load the contact area approaches the nominal contact area (i.e., complete contact), and the interfacial separation approaches zero. The numerical results have been compared with analytical theory and experimental results. They are in good agreement with each other. The present findings may be very important for soft solids, e.g., rubber, or for very smooth surfaces, where complete contact can be reached at moderate high loads without plastic deformation of the solids.
We report a molecular dynamics study of the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. We study the contact area and the interfacial separation from small contact (low load) to full contact (high load). For small load the contact area varies linearly with the load and the interfacial separation depends logarithmically on the load. For high load the contact area approaches to the nominal contact area (i.e., complete contact), and the interfacial separation approaches to zero. The present results may be very important for soft solids, e.…
We study the adhesive contact between elastic solids with randomly rough, self affine fractal surfaces. We present molecular dynamics (MD) simulation results for the interfacial stress distribution and the wall-wall separation. We compare the MD results for the relative contact area and the average interfacial separation, with the prediction of the contact mechanics theory of Persson. We find good agreement between theory and the simulation results. We apply the theory to the system studied by Benz et al. involving polymer in contact with polymer, but in this case the adhesion gives only a sma…
I study the contact between a rigid solid with a randomly rough surface and an elastic block with a flat surface. I derive a relation between the (average) interfacial separation $u$ and the applied normal squeezing pressure $p$. I show that for non-adhesive inte raction and small applied pressure, p is proportional to exp (-u/u_0), in good agreement with recent experimental observation.
In this supplementary materials section, we provide (i) additional information on the numerical simulations of the main work, (ii) the derivation of all prefactors in the analytical theory, and (iii) unpublished experiments of the contact stiffness of a polymer pressed against a rough substrate.
In forced wetting, a rapidly moving surface drags with it a thin layer of trailing fluid as it is plunged into a second fluid bath. Using high-speed interferometry, we find characteristic structure in the thickness of this layer with multiple thin flat triangular structures separated by much thicker regions. These features, depending on liquid viscosity and penetration velocity, are robust and occur in both wetting and de-wetting geometries. Their presence clearly shows the inadequacy of theoretical analysis that ignores the instability in the transverse direction.
The total elastic stiffness of two contacting bodies with a microscopically rough interface has an interfacial contribution K that is entirely attributable to surface roughness. A quantitative understanding of K is important because it can dominate the total mechanical response and because it is proportional to the interfacial contributions to electrical and thermal conductivity in continuum theory. Numerical simulations of the dependence of K on the applied squeezing pressure p are presented for nominally flat elastic solids with a range of surface roughnesses. Over a wide range of p, K rises…
Smoothed particle hydrodynamics study of friction of the coarse-grained $α$-Al2O3/$α$-Al2O3 and $α$-Fe2O3/$α$-Fe2O3 contacts in behavior of the spring interfacial potential
We study the distribution of interfacial separations P(u) at the contact region between two elastic solids with randomly rough surfaces. An analytical expression is derived for P(u) using Persson's theory of contact mechanics, and is compared to numerical solutions obtained using (a) a half-space method based on the Boussinesq equation, (b) a Green's function molecular dynamics technique and (c) smart-block classical molecular dynamics. Overall, we find good agreement between all the different approaches.
Dynamic wetting plays an important role in the physics of multiphase flow, and has significant influence on many industrial and geotechnical applications. In this work, a modified smoothed particle hydrodynamics (SPH) model is employed to simulate surface tension, contact angle, and dynamic wetting effects. The wetting and dewetting phenomena are simulated in a capillary tube, where the liquid particles are raised or withdrawn by a shifting substrate. The SPH model is modified by introducing a newly-developed viscous force formulation at liquid-solid interface to reproduce the rate-dependent b…
A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by folding; its shape and energy have been computed exactly before self contact. Here, we address the mechanics of large folds, i.e. folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers and capillary rafts, we discuss how t…
A liquid drop moves on a solid surface if it is subjected to a gradient of wettability or temperature. However, the pinning defects on the surface manifested in terms of a wetting hysteresis, or first-order nonlinear friction, limit the motion in the sense that a critical size has to be exceeded for a drop to move. The effect of hysteresis can, however, be mitigated by an external vibration that can be either structured or stochastic, thereby creating a directed motion of the drop. Many of the well-known features of rectification, amplification, and switching that are generic to electronics ca…
We present single contact friction experiments between a glassy polymer and smooth silica substrates grafted with alkylsilane layers of different coverage densities and morphologies. This allows us to adjust the polymer/substrate interaction strength. We find that, when going from weak to strong interaction, the response of the interfacial junction where shear localizes evolves from that of a highly viscous threshold fluid to that of a plastically deformed glassy solid. This we analyse as resulting from an interaction-induced ``interfacial glass transition'' helped by pressure.
We study numerically local models for the mechanical contact between two solids with rough surfaces. When the solids softly touch either through adhesion or by a small normal load $L$, contact only forms at isolated patches and fluids can pass through the interface. When the load surpasses a threshold value, $L_c$, adjacent patches coalesce at a critical constriction, i.e., near points where the interfacial separation between the undeformed surfaces forms a saddle point. This process is continuous without adhesion and the interfacial separation near percolation is fully defined by scaling fact…
We present a contact mechanics problem, which we consider to be representative for contacts between nominally flat surfaces. The main ingredients of the mathematically fully defined contact problem are: Self-affine roughness, linear elasticity, the small-slope approximation, and short-range adhesion between the frictionless surfaces. Surface energies, elastic contact modulus and computer-generated surface topographies are provided at www.lms.uni-saarland.de/contact-mechanics-challenge. To minimize the undesirable but frequent problem of unit conversion errors, we provide some benchmark results…
By extending the theoretical framework derived in our previous study [Y. Imaizumi et al., J. Chem. Phys. 153, 034701 (2020)], we successfully calculated the solid-liquid (SL) and solid-vapor (SV) interfacial tensions of a simple Lennard-Jones fluid around solid cylinders with nanometer-scale diameters from single equilibrium molecular dynamics (MD) systems, in which a solid cylinder was vertically immersed into a liquid pool. The SL and SV interfacial tensions $γ_\mathrm{SL} - γ_\mathrm{S0}$ and $γ_\mathrm{SV} - γ_\mathrm{S0}$ relative to that for bare solid surface $γ_\mathrm{S0}$, respective…
We present a model based on the lattice Boltzmann equation that is suitable for the simulation of dynamic wetting. The model is capable of exhibiting fundamental interfacial phenomena such as weak adsorption of fluid on the solid substrate and the presence of a thin surface film within which a disjoining pressure acts. Dynamics in this surface film, tightly coupled with hydrodynamics in the fluid bulk, determine macroscopic properties of primary interest: the hydrodynamic slip; the equilibrium contact angle; and the static and dynamic hysteresis of the contact angles. The pseudo- potentials em…
The adhesive contact between elastic solids with randomly rough, self affine fractal surfaces is studied by molecular dynamics (MD) simulations. The interfacial binding energy obtained from the simulations of nominally flat and curved surfaces is compared with the predictions of the contact mechanics theory by Persson. Theoretical and simulation results agree rather well, and most of the differences observed can be attributed to finite size effects and to the long-range nature of the interaction between the atoms in the block and the substrate in the MD model, as compared to the analytical the…
The interaction of interfacial water with graphitic carbon at the atomic scale is studied as a function of the hydrophobicity of epitaxial graphene. High resolution X-ray reflectivity shows that the graphene-water contact angle is controlled by the average graphene thickness, due to the fraction of the film surface expressed as the epitaxial buffer layer whose contact angle (contact angle θ_c = 73°) is substantially smaller than that of multilayer graphene (θ_c = 93°). Classical and ab initio molecular dynamics simulations show that the reduced contact angle of the buffer layer is due to both …
We introduce an accurate and efficient method for characterizing surface wetting and interfacial properties, such as the contact angle made by a liquid droplet on a solid surface, and the vapor-liquid surface tension of a fluid. The method makes use of molecular simulations in conjunction with the indirect umbrella sampling technique to systematically wet the surface and estimate the corresponding free energy. To illustrate the method, we study the wetting of a family of Lennard-Jones surfaces by water. We estimate contact angles for surfaces with a wide range of attractions for water by using…
Recent experiments and simulations have demonstrated that particle-covered interfaces can exist in stable non-spherical shapes as a result of the steric jamming of the interfacially trapped particles, which confers the interface with solid-like properties. We provide an experimental and theoretical characterization of the mechanical properties of these armored objects, with attention given to the two-dimensional granular state of the interface. Small inhomogeneous stresses produce a plastic response while homogeneous stresses produce a weak elastic response. Shear-driven particle-scale rearran…
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.
In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double parabola potential, we reformulate the derivation of the interfacial model using a rigorous boundary integral approach. This is done for three scenarios: a single fluid phase in contact with a nonplanar substrate (i.e., wall); a free interface separating coexisting fluid phases (say, liquid and gas); and finally a liquid-gas interface in contact with a nonplanar confining wall, as is…
Due to the slow dynamics of the wetting ridge, it is challenging to predict the wetting morphology of liquid drops on thin lubricant coated surfaces. It is hypothesized that when a drop sinks on a lubricated surface, quasi-static wetting morphology can be numerically computed only from the knowledge of interfacial energies, lubricant thickness, and drop volume. We used Surface Evolver software for the numerical computation of the interface profiles for a four-phase system. For the experiments, we used drops of 80 wt% formamide on silicone oil coated substrates with varying lubricant thickness,…
Using molecular-dynamics simulation, we have calculated the interfacial free energy, γ, between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction η= ρσ^3/6, where ρand σare the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that γfor a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculati…
We analyze theoretically the effect of friction on quartz crystal microbalance (QCM) measurements that probe soft (viscoelastic) films and biomolecular layers adsorbed from aqueous solutions. While water provides a natural environment for biomolecules, an interface with unknown rheological properties forms between the adsorbed soft molecular layer and the quartz substrate in the latter case. We investigate therefore the dynamics of soft films adsorbed onto a solid quartz surface within a continuum mechanics approach using both the Maxwell and the Voight/Kelvin models of viscoelasticity and the…
The description of elastic, nonadhesive contacts between solids with self-affine surface roughness seems to necessitate knowledge of a large number of parameters. However, few parameters suffice to determine many important interfacial properties as we show by combining dimensional analysis with numerical simulations. This insight is used to deduce the pressure dependence of the relative contact area and the mean interfacial separation $Δ\bar{u}$ and to present the results in a compact form. Given a proper unit choice for pressure $p$, i.e., effective modulus $E^*$ times the root-mean-square gr…
Adhesion between two bodies is a key parameter in wear processes. At the macroscale, strong adhesive bonds are known to lead to high wear rates, as observed in clean metal-on-metal contact. Reducing the strength of the interfacial adhesion is then desirable, and techniques such as lubrication and surface passivation are employed to this end. Still, little is known about the influence of adhesion on the microscopic processes of wear. In particular, the effects of interfacial adhesion on the wear particle size and on the surface roughness evolution are not clear, and are therefore addressed here…
We present theoretical arguments, based on linear elasticity and thermodynamics, to show that interfacial tangential stresses in sliding adhesive contacts does not affet at all the adhesive behavior of the system, which then follows the classical JKR solution. Our finding explains the experimental observation of Vorvolakos and Chaudhury in 2003, who found that the contact area of a PDMS sphere remains constant during sliding and is in agreement with the JKR solution, at least up to velocity of 1mm/s, and of Carpick et al. Carpick, who observed that the friction force between a platinum-coated …
We present a numerical model for the prediction of the rough contact mechanics of a viscoelastic block, with graded rheology, in steady sliding contact with a randomly rough rigid surface. In particular, we derive the effective surface response of a stepwise or continuously-graded block in the Fourier domain, which is then embedded in a Fourier-based residuals molecular dynamic formulation of the contact mechanics. Finally we discuss on the role of small-scale wavelengths on rubber friction and contact area, and we demonstrate that the rough contact mechanics exhibits effective interface prope…
A flat sheet programmed with a planar pattern of spontaneous shape change will morph into a curved surface. Such metric mechanics is seen in growing biological sheets, and may be engineered in actuating soft matter sheets such as phase-changing liquid crystal elastomers (LCEs), swelling gels and inflating baromorphs. Here, we show how to combine multiple patterns in a sheet by stitching regions of different shape changes together piecewise along interfaces. This approach allows simple patterns to be used as building blocks, and enables the design of multi-material or active/passive sheets. We …
The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without ad…
Contact freezing is a mode of atmospheric ice nucleation in which a collision between a dry ice nucleating particle (INP) and a water droplet results in considerably faster heterogeneous nucleation. The molecular mechanism of such enhancement is, however, still a mystery. While earlier studies had attributed it to collision-induced transient perturbations, recent experiments point to the pivotal role of nanoscale proximity of the INP and the free interface. By simulating heterogeneous nucleation of ice within INP-supported nanofilms of two model water-like tetrahedral liquids, we demonstrate t…
Free surfaces of liquids exhibit thermally excited (capillary) surface waves. We show that the surface roughness which results from capillary waves when a glassy material is cooled below the glass transition temperature can have a large influence on the contact mechanics between the solids. The theory suggest a new explanation for puzzling experimental results [L. Bureau, T. Baumberger and C. Caroli, arXiv:cond-mat/0510232] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. It also lend support for a recently developed…
The interfacial mechanics of soft elastic networks play a central role in biological and technological contexts. Yet, effects of solid capillarity have remained controversial, primarily due to the strain-dependent surface energy. Here we derive the equations that govern the selection of contact angles of liquid drops on elastic surfaces from variational principles. It is found that the substrate's elasticity imposes a nontrivial condition that relates pinning, hysteresis and contact line mobility to the so-called Shuttleworth effect. We experimentally validate our theory for droplets on a sili…
We present exact 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 univers…
We generalize the Persson contact mechanics and rubber friction theory to the case where both surfaces have surface roughness. The solids can be rigid, elastic or viscoelastic, and can be homogeneous or layered. We calculate the contact area, the viscoelastic contribution to the friction force, and the average interfacial separation as a function of the sliding speed and the nominal contact pressure. We illustrate the theory with numerical results for a rubber block sliding on a road surface. We find that with increasing sliding speed, the influence of the roughness on the rubber block decreas…
Different computational techniques in combination with molecular dynamics computer simulation are used to to determine the wall-liquid and the wall-crystal interfacial free energies of a modified Lennard-Jones (LJ) system in contact with a solid wall. Two different kinds of solid walls are considered: a flat structureless wall and a structured wall consisting of an ideal crystal with the particles rigidly attached to fcc lattice sites. Interfacial free energies are determined by a thermodynamic integration scheme, the anisotropy of the pressure tensor, the non-equilibrium work method based on …
Rolling of a small sphere on a solid support is governed by a non-linear friction that is akin to the Coulombic dry fiction. No motion occurs when the external field is weaker than the frictional resistance. However, with the intervention of an external noise, a viscous friction like property emerges; thus the sphere rolls with an uniform drift velocity that is proportional to the applied field. As the sphere rolls, it rocks forward and backward resulting in substantial fluctuation of displacement opposite to the net drift. The ratio of the integrated probabilities of the negative to positive …
Field-theoretical approach to estimate mean gap and gap distribution in randomly rough surface contact mechanics
Yangzhou University（扬州大学）；Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Hefei University of Technology（合肥工业大学）
An increase of static friction during stationary contacts of two solids due to interfacial chemical bonding has been reported in multiple experiments. However, the physics underlying such frictional aging is still not fully understood because it involves multiple physical and chemical effects coupled with each other, making direct interpretation of experimental results difficult. Here, we develop a multiphysics chemical aging model that combines contact mechanics, mechanochemistry, and interfacial chemical reaction kinetics. Our model predicts that aging is proportional to normal loads in a lo…
The surface or contact potential at the water liquid-vapor interface is discussed in relation to determinations of absolute ion hydration free energies and distributions of ions near the interface. It is shown that, rather than the surface potential itself, the net electrostatic potential at the center of an uncharged solute can aid both in relating differences between tabulations of hydration free energies and in explaining differing classical and quantum surface potential estimates. Quantum mechanical results are consistent with conclusions from classical simulations that there is a net driv…
Smectite clay minerals have an outsize impact on the response of clay-rich media to common stimuli, such as water imbibition and ion exchange, motivating extensive effort to understand microscopic behaviors resulting from these processes such as swelling and exfoliation. Nonetheless, there is no general consensus about the microscopic forces that govern smectite properties, which are model systems for understanding colloidal and interfacial phenomena more generally. We find that the complex free energy surface arising from the interplay of at least four intermolecular forces and their nonlinea…
Role of transfer films and interfacial cracking in metallic sliding wear
State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences（中国科学院兰州化学物理研究所固体润滑国家重点实验室）；Peter Grünberg Institute (PGI-1), Forschungszentrum Jülich（于利希研究中心彼得·格林贝格研究所（PGI-1））；MultiscaleConsulting（多尺度咨询公司）
Multiscale contact mechanics for elastoplastic contacts
Luleå University of Technology（吕勒奥理工大学）；Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences（中国科学院兰州化学物理研究所）；Peter Grünberg Institute (PGI-1), Forschungszentrum Jülich（于利希研究中心彼得·格林伯格研究所（PGI-1））；MultiscaleConsulting（多尺度咨询公司）
The wetting of solid surfaces can be manoeuvred by altering the energy balance at the interfacial region. While electric field acts favourably to spread a droplet on a rigid surface, this tendency may be significantly suppressed over soft surfaces, considering a part of the interfacial energy being utilized to deform the solid elastically by capillary forces. Here, we bring out a unique mechanism by virtue of which addition of nano-particles to the droplet brings in a favourable recovery of the electro-spreading characteristics of a soft surface, by realizing an alteration in the effective die…
We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width $l$ and the macroscopic diffusive length $l_D= (Mη)^{1/2}$, where $η$ is the fluid viscosity and $M$ the mobility governing intermolecular diffusion. For small $l_D/l$ we find a diffuse interface regime in which the slip length scales as $ξ\sim(l_Dl)^{1/2}$. For larger $l_D/l>1$ we find a sharp interface regime in which the slip length …
