Size scaling of static friction

TL;DR

This paper develops a scaling law predicting how static friction decreases with contact area in soft lubricants, supported by molecular dynamics simulations, indicating the potential for smooth large-scale sliding.

Contribution

It introduces a new scaling law for static friction in soft lubricants, enabling prediction of large-area behavior from small-scale simulations.

Findings

Static friction decreases as a power law with contact area.

Simulations verify the proposed scaling law.

Large contact areas may lead to smooth sliding due to vanishing static friction.

Abstract

Sliding friction across a thin soft lubricant film typically occurs by stick-slip, the lubricant fully solidifying at stick, yielding and flowing at slip. The static friction force per unit area preceding slip is known from molecular dynamics (MD) simulations to decrease with increasing contact area. That makes the large-size fate of stick-slip unclear and unknown; its possible vanishing is important as it would herald smooth sliding with a dramatic drop of kinetic friction at large size. Here we formulate a scaling law of the static friction force, which for a soft lubricant is predicted to decrease as f_m + \Delta f /A^gamma for increasing contact area A, with gamma>0. Our main finding is that the value of f_m, controlling the survival of stick-slip at large size, can be evaluated by simulations of comparably small size. MD simulations of soft lubricant sliding are presented, which verify this theory.