  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.
