Department of Mathematics
Polymer stress growth in viscoelastic fluids in oscillating extensional
flows with applications to micro-organism locomotion
- Author(s): Thomases, Becca
- Guy, Robert D
- et al.
Viscoelastic stress growth at oscillating extensional points is calculated in the Stokes-Oldroyd-B model of a viscoelastic fluid. The analysis identifies a Deborah number dependent Weissenberg number transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. For the case of given flow independent of the stress, the polymer stress is computed analytically at an oscillating extensional stagnation point. Fully coupled simulations in a oscillating 4-roll mill geometry are compared with the theoretical calculation of stress in the decoupled case, and similar stress behavior is observed. The flow around tips of a time-reversible flexing filament in a viscoelastic fluid is shown to exhibit an oscillating extension along particle trajectories, and the stress response exhibits similar transitions. However in the high amplitude, high De regime the stress feedback on the flow leads to non time-reversible particle trajectories that experience asymmetric stretching and compression, and the stress grows more significantly in this regime. These results help explain past observations of large stress concentration for large amplitude swimmers and non-monotonic dependence on De of swimming speeds.