Quasi-steady sedimentation of a sphere in an Oldroyd-B fluid

We investigate the quasi-steady sedimentation of a sphere perpendicular

to a rigid plane in an Oldroyd-B fluid at low Deborah numbers. Utilizing

lubrication approximations, we derive analytical expressions for

resistive forces and pressures. Additionally, we introduce alternative

methods using a reciprocal theorem to improve perturbation corrections

for forces and consider different local geometries near the sphere's

lowest point to study their impact on viscoelasticity. Our results are

validated against numerical simulations using Basilisk.