Lubrication of soft viscoelastic solids

TL;DR

This paper investigates how viscoelastic properties of soft materials influence lubrication, deriving scaling laws that reveal a decrease in lift force compared to elastic systems, with implications for engineering and biological applications.

Contribution

It introduces a method for analyzing viscoelastic lubrication and explores three rheological models, highlighting the impact of viscoelasticity on lubrication performance.

Findings

Lift force decreases with viscoelasticity compared to elastic materials

Scaling laws relate lift force to sliding velocity and rheology

Viscoelastic effects become significant when loading timescales match rheological timescales

Abstract

Lubrication flows appear in many applications in engineering, biophysics, and in nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubrication fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin-Voigt-, Standard Linear-, and Power Law-rheology. It is shown how the solid viscoelasticity affects the lubrication process when the timescale of loading becomes comparable to the rheological timescale. We derive asymptotic relations between lift force and sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.