Scaling of the critical slip distance in granular layers

TL;DR

This paper explores how the critical slip distance in granular layers scales with system parameters, revealing proportionality to layer thickness and pressure, and proposing a bulk relaxation law independent of surface geometry.

Contribution

It introduces a new scaling law for the critical slip distance based on relaxation time, independent of surface details, and connects it to system size and pressure effects.

Findings

Critical slip distance is proportional to sliding velocity.

Relaxation time scales with layer thickness and inversely with square root of pressure.

Critical slip distance scales with system size depending on experimental setup.

Abstract

We investigate the nature of friction in granular layers by means of numerical simulation focusing on the critical slip distance, over which the system relaxes to a new stationary state. Analyzing a transient process in which the sliding velocity is instantaneously changed, we find that the critical slip distance is proportional to the sliding velocity. We thus define the relaxation time, which is independent of the sliding velocity. It is found that the relaxation time is proportional to the layer thickness and inversely proportional to the square root of the pressure. An evolution law for the relaxation process is proposed, which does not contain any length constants describing the surface geometry but the relaxation time of the bulk granular matter. As a result, the critical slip distance is scaled with a typical length scale of a system. It is proportional to the layer thickness in an instantaneous velocity change experiment, whereas it is scaled with the total slip distance in a spring-block system on granular layers.