Contact mechanics of and Reynolds flow through saddle points: On the coalescence of contact patches and the leakage rate through near-critical constrictions

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 factors and the sign of $L_c-L$. The scaling factors lead to a Reynolds flow resistance which diverges as $(L_c-L)^\beta$ with $\beta = 3.45$. Contact merging and destruction near saddle points becomes discontinuous when either short-range adhesion or specific short-range repulsion are added to the hard-wall repulsion. These results imply that coalescence and break-up of contact patches can contribute to Coulomb friction and contact aging.Comment: 6 pages, 6 figures, submitted to Euro. Phys. Let

Towards time-dependent, non-equilibrium charge-transfer force fields: Contact electrification and history-dependent dissociation limits

Force fields uniquely assign interatomic forces for a given set of atomic coordinates. The underlying assumption is that electrons are in their quantum-mechanical ground state or in thermal equilibrium. However, there is an abundance of cases where this is unjustified because the system is only locally in equilibrium. In particular, the fractional charges of atoms, clusters, or solids tend to not only depend on atomic positions but also on how the system reached its state. For example, the charge of an isolated solid -- and thus the forces between atoms in that solid -- usually depends on the counterbody with which it has last formed contact. Similarly, the charge of an atom, resulting from the dissociation of a molecule, can differ for different solvents in which the dissociation took place. In this paper we demonstrate that such charge-transfer history effects can be accounted for by assigning discrete oxidation states to atoms. With our method, an atom can donate an integer charge to another, nearby atom to change its oxidation state as in a redox reaction. In addition to integer charges, atoms can exchange "partial charges" which are determined with the split charge equilibration method.Comment: 11 pages, 7 figure

Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids

The Prandtl model is certainly the simplest and most generic microscopic model describing solid friction. It consists of a single, thermalized atom attached to a spring, which is dragged past a sinusoidal potential representing the surface energy corrugation of a counterface. While it was primarily introduced to rationalize how Coulomb’s friction law can arise from small-scale instabilities, Prandtl argued that his model also describes the shear thinning of liquids. Given its success regarding the interpretation of atomic-force-microscopy experiments, surprisingly little attention has been paid to the question how the Prandtl model relates to fluid rheology. Analyzing its Langevin and Brownian dynamics, we show that the Prandtl model produces friction–velocity relationships, which, converted to a dependence of effective (excess) viscosity on shear rate η(γ˙), is strikingly similar to the Carreau–Yasuda (CY) relation, which is obeyed by many non-Newtonian liquids. The two dimensionless parameters in the CY relation are found to span a broad range of values. When thermal energy is small compared to the corrugation of the sinusoidal potential, the leading-order γ˙ 2 corrections to the equilibrium viscosity only matter in the initial part of the cross-over from Stokes friction to the regime, where η obeys approximately a sublinear power law of 1/γ

Are There Limits to Superlubricity of Graphene in Hard, Rough Contacts?

Yes, there are. They result from the splitting of a large correlated contact into many small patches. When the lubricant consists of thin solid sheets, like graphene, the patches are expected to act independently from each other. Crude estimates for the friction forces between hard, stiff solids with randomly rough surfaces are given, which apply to surfaces with Hurst roughness exponents H > 0.5. The estimates are obtained by combining realistic contact-patch-size distributions with friction-load relations deduced for isolated contact patches. The analysis reveals that load is carried predominantly by large patches, while most frictional forces stem from small contact patches. Low friction is favored when the root-mean-square height gradients are small, while a large roll-off wavelength and thus large root-mean-square roughness is predicted to lead to small friction. Moreover, friction is found to increase sublinearly with load in a nominally flat, structurally lubric contact

Elastic Contacts of Randomly Rough Indenters with Thin Sheets, Membranes Under Tension, Half Spaces, and Beyond

We consider the adhesion-less contact between a two-dimensional, randomly rough, rigid indenter, and various linearly elastic counterfaces, which can be said to differ in their spatial dimension D. They include thin sheets, which are either free or under equi-biaxial tension, and semi-infinite elastomers, which are either isotropic or graded. Our Green’s function molecular dynamics simulation identifies an approximately linear relation between the relative contact area ar and pressure p at small p only above a critical dimension. The pressure dependence of the mean gap ug obeys identical trends in each studied case: quasi-logarithmic at small p and exponentially decaying at large p. Using a correction factor with a smooth dependence on D, all obtained ug(p) relations can be reproduced accurately over several decades in pressure with Persson’s theory, even when it fails to properly predict the interfacial stress distribution function

Editorial: In Memory of Mark Robbins

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