Singular viscoelastic perturbation to soft lubrication

TL;DR

This paper develops a minimal viscoelastic model for soft lubrication, revealing how viscoelasticity uniquely influences the mobility of objects near elastic and polymeric surfaces, with implications for biological and complex systems.

Contribution

It introduces a singular perturbation approach to incorporate viscoelastic effects into soft lubrication models, advancing understanding of complex substrate interactions.

Findings

Viscoelasticity causes singular effects in soft lubrication dynamics.

Numerical solutions show altered colloidal mobility near viscoelastic surfaces.

The model predicts complex migration behaviors relevant to biological membranes.

Abstract

Soft lubrication has been shown to drastically affect the mobility of an object immersed in a viscous fluid in the vicinity of a purely elastic wall. In this theoretical study, we develop a minimal model incorporating viscoelasticity, carrying out a perturbation analysis in both the elastic deformation of the wall and its viscous damping. Our approach reveals the singular-perturbation nature of viscoelasticity to soft lubrication. Numerical resolution of the resulting non-linear, singular and coupled equations of motion reveals peculiar effects of viscoelasticity on confined colloidal mobility, opening the way towards the description of complex migration scenarios near realistic polymeric substrates and biological membranes.