Lubricated motion in an elastic tube

The motion of objects through elastic constrictions is relevant to various problems in physiology and biology. We describe a model experiment where a rigid sphere is displaced through a narrower elastic tube. Lubricating the contact with a fluid significantly reduces friction on the wall of the tube. The friction force increases as the sliding velocity to the power 1/3 and depends on the fluid viscosity, mechanical properties of the tube and geometric mismatch. We derive a scaling law and a minimal numerical model to account for our experimental data.