Pertrurbation theory for dynamic behavior of a sphere settling in a viscoelastic fluid

We present a new perturbation theory for the motion of a rigid sphere settling in a viscoelastic Oldroyd-B fluid that can be generalized to other scenarios of viscoelastic fluid-structure interaction. In contrast to previous perturbation theories, the perturbative expansion variable is not the Weissenberg number, but instead it is a parameter measuring the feedback of the viscoelastic stress into the fluid momentum. This allows for accurate calculations at large Weissenberg numbers. Previous experiments, including our own, have documented that a sphere overshoots its terminal velocity on a transient timescale comparable to the fluid relaxation time. Our theory predicts this behavior as well as a non-trivial dependence of the drag on the Weissenberg number. I will also discuss experiments in which periodic forcing is applied to a body moving through a viscoelastic fluid, and the perturbation theory is used as a predictive tool.