Steady fall of bodies of arbitrary shape in a second-order fluid at zero Reynolds number

We study the slow motion of rigid bodies of arbitrary shape sedimenting in a quiescent viscoelastic liquid under the action of gravity. The liquid is modeled by the second-order fluid equations. We show existence of steady state solutions for small Weissenberg numbers. The case of pure translational motions is analyzed for specific geometric symmetries of the body and this allows us to show that the sedimentation behavior can be dramatically different between Newtonian and viscoelastic liquids.