No abstract

When an elastomer approaches or retracts from an adhesive indenter, the elastomer’s surface can suddenly become unstable and reshape itself quasi-discontinuously, e.g., when small-scale asperities jump into or snap out of contact. Such dynamics lead to a hysteresis between approach and retraction. In this study, we quantify numerically and analytically the ensuing unavoidable energy loss for rigid indenters with flat, Hertzian and randomly rough profiles. The range of adhesion turns out to be central, in particular during the rarely modeled approach to contact. For example, negligible traction on approach but quite noticeable adhesion for nominal plane contacts hinges on the use of short-range adhesion. Central attention is paid to the design of cohesive-zone models for the efficient simulation of dynamical processes. Our study includes a Griffith’s type analysis for the energy lost during fracture and regeneration of a flat interface. It reveals that the leading-order corrections of the energy loss are due to the finite-range adhesion scale at best, with the third root of the linear mesh size, while leading-order errors in the pull-off force disappear linearly.

The relative contact area between an initially flat, adhesion-and frictionless, linearly elastic body and a variety of rough, rigid counterbodies is studied using Green's function molecular dynamics. The indenter's height profiles range from ideal random roughness through roughness with a moderate amount of correlation to periodically repeated, single-asperity indenters having perfect phase coherence. At small reduced pressures, p * ≡ p/(E * ḡ) ≪ 1, sufficiently large systems are consistent with a linear a c = κ p * relation. Here p is the pressure, E * is the contact modulus,ḡ the root-mean-square height gradient, and κ a unitless proportionality coefficient. However, the parameterḡ must be evaluated over the real contact area for the linear relation to hold if the random roughness is correlated or the interfacial dimension reduced. No single unitless structural parameter-including the Nayak parameter-correlates in a significant fashion with κ.

Contact problems as they occur in tribology and colloid science are often solved with the assumption of hard-wall and hard-disk repulsion between locally smooth surfaces. This approximation is certainly meaningful at sufficiently coarse scales. However, at small scales, thermal fluctuations can become relevant. In this study, we address the question how they render non-overlap constraints into finite-range repulsion. To this end, we derive a closed-form analytical expression for the potential of mean force between a hard wall and a thermally fluctuating, linearly elastic counterface. Theoretical results are validated with numerical simulations based on the Green's function molecular dynamics technique, which is generalized to include thermal noise while allowing for hard-wall interactions. Applications consist of the validation of our method for flat surfaces and the generalization of the Hertzian contact to finite temperature. In both cases, similar force-distance relationships are produced with effective potentials as with fully thermostatted simulations. Analytical expressions are identified that allow the thermal corrections to the Hertzian load-displacement relation to be accurately estimated. While these corrections are not necessarily small, they turn out surprisingly insensitive to the applied load.

Considerable efforts had been devoted to investigating numerically the droplet impact dynamics on a superhydrophobic surface. Whereas most of these numerical simulations were restricted to the two-dimension (2-D) axisymmetric coordinate system with the one-dimension (1-D) substrate surface. In this work, a three-dimension (3-D) computational fluid dynamics (CFD) model, which intergrew a 2-D random rough surface, was proposed to investigate the droplet impact dynamics, and the multi-phase flow issue was solved by the Navier-Stokes equations. It is remarkable that the 3-D CFD model revealed several significant dynamic details that were not easily captured in a 2-D axisymmetric coordinate system or practical experiments. For instance, the 3-D CFD model provided a unique perspective to understand the varying dynamic behaviors of impinged droplet in terms of the velocity streamline and dynamic viscosity analyses. Herein, the dynamic viscosity diagram revealed that the sprawl droplet on the 2-D random rough surface was classified as Cassie state, while as Wenzel state for smooth surface, which also explained the better bouncing behaviors of droplet from the random rough surface. Accordingly, we suggested a visual way to evaluate the solid-liquid contact area surrounded by the triple-phase contact line. The effects of finger protrusion and central cavity growth from the sprawl droplet on the vortex generation were further analyzed on the ground of the velocity amplitude distribution and streamline data. The present work can provide early guidance to inquire into the impact dynamics of droplets on the random rough surface.