Orientational dynamics of sedimenting prolate spheroidal particles in a viscoelastic fluid

We investigate the orientational dynamics of a prolate spheroid sedimenting in an inertia-less viscoelastic fluid using a combination of theory and numerical simulations. While a fore-aft, axisymmetric particle sedimenting in a quiescent Newtonian fluid with negligible inertia maintains its initial orientation, fluid viscoelasticity causes the particle to rotate toward a stable equilibrium orientation. Previous studies have suggested that the stable equilibrium for a prolate particle is longside-on, regardless of the particle's aspect ratio, initial orientation, or the rheology of the polymer solution. In this work, we demonstrate that the longside-on orientation is not the only possible orientation for a sedimenting prolate particle. In the limit of small Deborah number, $De$, our theory predicts a transition from longside-on to broadside-on orientation for aspect ratios $\kappa$ beyond $\kappa = 123$ for an Oldroyd-B fluid. Numerical simulations enable us to examine the effects of other properties. Increasing $De$ lowers the transition $\kappa$ so that broadside orientation can be observed for aspect ratios as low as $\kappa=20$. The polymer concentration and maximum extensibility are also found to have profound qualitative effects on the particle dynamics. The detailed physical mechanism behind the reversal in the sign of the viscoelastic rotation rate is presented, with findings indicating that polymer-induced solvent stress is the primary cause of the change in stable orientation.