Dependence of kinetic friction on velocity: Master equation approach

TL;DR

This paper presents a master equation model to analyze how kinetic friction varies with velocity, considering thermal activation and contact aging effects, applicable across multiple scales.

Contribution

It introduces a comprehensive master equation framework that simultaneously accounts for thermal fluctuations and contact aging to predict velocity-dependent kinetic friction.

Findings

Friction increases monotonically with velocity due to thermal activation.

Aging effects can decrease friction with increasing velocity.

The model provides a complete velocity and temperature dependence of kinetic friction.

Abstract

We investigate the velocity dependence of kinetic friction with a model which makes minimal assumptions on the actual mechanism of friction so that it can be applied at many scales provided the system involves multi-contact friction. Using a recently developed master equation approach we investigate the influence of two concurrent processes. First, at a nonzero temperature thermal fluctuations allow an activated breaking of contacts which are still below the threshold. As a result, the friction force monotonically increases with velocity. Second, the aging of contacts leads to a decrease of the friction force with velocity. Aging effects include two aspects: the delay in contact formation and aging of a contact itself, i.e., the change of its characteristics with the duration of stationary contact. All these processes are considered simultaneously with the master equation approach, giving a complete dependence of the kinetic friction force on the driving velocity and system temperature, provided the interface parameters are known.