Sedimentation of a sphere near a rigid plane in an Oldroyd-B fluid

In this presentation, we will provide an introduction to Non-Newtonian fluid mechanics, with a particular focus on the Oldroyd-B model, a constitutive model used to characterize the behavior of viscoelastic fluids. Our primary investigation centers around the sedimentation of a sphere perpendicular to a rigid plane in an Oldroyd-B fluid. To tackle this problem, we employ lubrication approximations to derive analytical expressions for both resistive forces and sedimentation rates. Our emphasis will be on scenarios where the viscoelastic effects are weak, corresponding to small Deborah numbers.