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

Contacts With Negative Work of “Adhesion” and Superlubricity

Van der Waals forces between solids in vacuum are always attractive and are considered as the main source of adhesion. However, in the presence of an intermediate medium, they can also be repelling (Dzyaloshinskii et al., 1961) which means that the “work of adhesion” becomes negative. Similarly to the case of adhesion, the interaction range of these forces can be either comparable (or larger) than the minimum characteristic length scale of the contact problem or it can be negligible compared with all characteristic length scales. We call this latter case the “JKR-approximation,” as the JKR theory of adhesion (Johnson et al., 1971) is also valid in this limit. The repelling interaction can also be due to the presence (and squeezing out) of a thin fluid layer between solids as considered in Müser (2014). In the papers Popov and Hess (2018) and Heß and Popov (2019), it was shown that the contact of two oppositely charged surfaces at a constant voltage is equivalent to the adhesive contact with an effective van der Waals interaction. Similarly, the contact of the bodies with the same charge would be equivalent to repelling van der Waals forces with a negative work of adhesion. Further kinds of repelling forces may be solvation, structural, and hydration forces (Israelachvili, 2011). In the following, we speak about van der Waals forces, but they are thought as representative for a larger class of long range repelling forces. We argue that in the JKR approximation, the Hertz' solution of the contact problem with a repelling van der Waals interaction, remains practically unchanged. However, the contact area falls apart into the area of “weak (van der Waals) interaction” and “strong (rigid wall) interaction.” It is speculated that if the normal force is smaller than a critical value at which the core region of strong interaction disappears, a macroscopic superlubricity state of the contact may be observed.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

Contact of Single Asperities with Varying Adhesion: Comparing Continuum Mechanics to Atomistic Simulations

Atomistic simulations are used to test the equations of continuum contact mechanics in nanometer scale contacts. Nominally spherical tips, made by bending crystals or cutting crystalline or amorphous solids, are pressed into a flat, elastic substrate. The normal displacement, contact radius, stress distribution, friction and lateral stiffness are examined as a function of load and adhesion. The atomic scale roughness present on any tip made of discrete atoms is shown to have profound effects on the results. Contact areas, local stresses, and the work of adhesion change by factors of two to four, and the friction and lateral stiffness vary by orders of magnitude. The microscopic factors responsible for these changes are discussed. The results are also used to test methods for analyzing experimental data with continuum theory to determine information, such as contact area, that can not be measured directly in nanometer scale contacts. Even when the data appear to be fit by continuum theory, extracted quantities can differ substantially from their true values

Cancer-associated epithelial cell adhesion molecule (EpCAM; CD326) enables epidermal Langerhans cell motility and migration in vivo

After activation, Langerhans cells (LC), a distinct subpopulation of epidermis-resident dendritic cells, migrate from skin to lymph nodes where they regulate the magnitude and quality of immune responses initiated by epicutaneously applied antigens. Modulation of LC-keratinocyte adhesion is likely to be central to regulation of LC migration. LC express high levels of epithelial cell adhesion molecule (EpCAM; CD326), a cell-surface protein that is characteristic of some epithelia and many carcinomas and that has been implicated in intercellular adhesion and metastasis. To gain insight into EpCAM function in a physiologic context in vivo, we generated conditional knockout mice with EpCAM-deficient LC and characterized them. Epidermis from these mice contained increased numbers of LC with normal levels of MHC and costimulatory molecules and T-cell-stimulatory activity in vitro. Migration of EpCAM-deficient LC from skin explants was inhibited, but chemotaxis of dissociated LC was not. Correspondingly, the ability of contact allergen-stimulated, EpCAM-deficient LC to exit epidermis in vivo was delayed, and strikingly fewer hapten-bearing LC subsequently accumulated in lymph nodes. Attenuated migration of EpCAM-deficient LC resulted in enhanced contact hypersensitivity responses as previously described in LC-deficient mice. Intravital microscopy revealed reduced translocation and dendrite motility in EpCAM-deficient LC in vivo in contact allergen-treated mice. These results conclusively link EpCAM expression to LC motility/migration and LC migration to immune regulation. EpCAM appears to promote LC migration from epidermis by decreasing LC-keratinocyte adhesion and may modulate intercellular adhesion and cell movement within in epithelia during development and carcinogenesis in an analogous fashion

A Review of the Method of Dimensionality Reduction in Contact Mechanics: Applications for Structural Damping, Wear and Adhesion

In the method of dimensionality reduction (MDR), contacts of three-dimensional bodies are mapped to the contact problem with a one-dimensional elastic or viscoelastic foundation. This is valid for the normal contact, the tangential contact and the normal contact of viscoelastic bodies. For the above classes of contact problems, several examples are considered and discussed in detail. This includes: (a) Fretting wear for arbitrary histories of loading (for simultaneous oscillations both in normal and horizontal directions); (b) Frictional damping under the influence of oscillations in normal and tangential direction as well as normal and torsional loading; (c) Adhesion of bodies of arbitrary axis-symmetric shape with extension to the adhesive contact of elastomers

Humidity effects on adhesion of nickel-zinc ferrite in elastic contact with magnetic tape and itself

The effects of humidity on the adhesion of Ni-Zn ferrite and magnetic tape in elastic contact with a Ni-Zn ferrite hemispherical pin in moist nitrogen were studied. Adhesion was independent of normal load in dry, humid, and saturated nitrogen. Ferrites adhere to ferrites in a saturated atmosphere primarily from the surface tension effects of a thin film of water adsorbed on the ferrite surfaces. The surface tension of the water film calculated from the adhesion results was 48 times 0.00001 to 56 times 0.00001 N/cm; the accepted value for water is 72.7 x 0.00001 N/cm. The adhesion of ferrite-ferrite contacts increased gradually with increases in relative humidity to 80 percent, but rose rapidly above 80 percent. The adhesion at saturation was 30 times or more greater than that below 80 percent relative humidity. Although the adhesion of magnetic tape - ferrite contacts remained low below 40 percent relative humidity and the effect of humidity was small, the adhesion increased considerably with increasing relative humidity above 40 percent. The changes in adhesion of elastic contacts were reversible on humidifying and dehumidifying

Geometry of lipid vesicle adhesion

The adhesion of a lipid membrane vesicle to a fixed substrate is examined from a geometrical point of view. This vesicle is described by the Helfrich hamiltonian quadratic in mean curvature; it interacts by contact with the substrate, with an interaction energy proportional to the area of contact. We identify the constraints on the geometry at the boundary of the shared surface. The result is interpreted in terms of the balance of the force normal to this boundary. No assumptions are made either on the symmetry of the vesicle or on that of the substrate. The strong bonding limit as well as the effect of curvature asymmetry on the boundary are discussed.Comment: 7 pages, some major changes in sections III and IV, version published in Physical Review

Continuum contact models for coupled adhesion and friction

We develop two new continuum contact models for coupled adhesion and friction, and discuss them in the context of existing models proposed in the literature. Our new models are able to describe sliding friction even under tensile normal forces, which seems reasonable for certain adhesion mechanisms. In contrast, existing continuum models for combined adhesion and friction typically include sliding friction only if local contact stresses are compressive. Although such models work well for structures with sufficiently strong local compression, they fail to capture sliding friction for soft and compliant systems (like adhesive pads), for which the resistance to bending is low. This can be overcome with our new models. For further motivation, we additionally present experimental results for the onset of sliding of a smooth glass plate on a smooth elastomer cap under low normal loads. As shown, the findings from these experiments agree well with the results from our models. In this paper we focus on the motivation and derivation of our continuum contact models, and provide a corresponding literature survey. Their implementation in a nonlinear finite element framework as well as the algorithmic treatment of adhesion and friction will be discussed in future work

Effective shear displacement on lateral adhesion force of a liquid bridge between separated plates

Adhesion force is among the most influencing factors in micro- and nano-mechanics. A liquid bridge between two bodies gives rise to the adhesion force, which usually acts as additional normal load. However, the adhesion force acts also in lateral. We measured the lateral adhesion force of a sheared liquid bridge between parallel plates. In addition, movement of contact lines is tracked by using an image processing technique, which allowed us to introduce an effective shear displacement. The lateral adhesion force has a linear relation with the effective shear displacement. It shows good agreement between experimental result and the analytical approach regarding changes of interfacial energy with simple rectangular shape of the liquid bridge. We further revealed that there is no contact line in pinned state even in the case with the very beginning of the sheared process. In this regard, however, the contact line on rougher surface is awkward in its movement. Therefore, the liquid bridge between two rougher surfaces has higher effective shear displacement, and it results in the higher lateral adhesion force