Singular viscoelastic perturbation to soft lubrication

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 article, 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 nonlinear, 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.