  We consider a cylinder immersed in viscous fluid moving near a flat substrate
covered by an incompressible viscoelastic fluid layer, and study the effect of
the fluid viscoelasticity on the lift force exerted on the cylinder. The lift
force is zero when the viscoelastic layer is not deformed, but becomes non-zero
when it is deformed. We calculate the lift force by considering both the
tangential stress and the normal stress applied at the surface of the
viscoelastic layer. Our analysis indicates that as the layer changes from the
elastic limit to the viscous limit, the lift force decreases with the decrease
of the Deborah number (De). For small De, the effect of the layer elasticity is
taken over by the surface tension and the lift force can become negative. We
also show that the tangential stress and the interface slip velocity (the
surface velocity relative to the substrate), which have been ignored in the
previous analysis, give important contributions to the lift force. Especially
for thin elastic layer, they give dominant contributions to the lift force.
