Existence of steady freefall of rigid bodies in a second order fluid with applications to particle sedimentation

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 full second order fluid equations with arbitrary material parameters α₁ + α₂. We show existence of steady state solutions for small Weissenberg numbers and zero Reynolds numbers and apply our equations to study the steady state orientations of symmetric bodies sedimenting in viscoelastic fluids.