Document Type
Article
Publication Date
7-1-2019
Publication Title
Journal of Non-Newtonian Fluid Mechanics
Abstract
Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers. We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocity are found from numerical simulations in an oscillating 4-roll mill geometry. The stress from these simulations is compared with the theoretical calculation of stress in the decoupled (given flow) 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.
Keywords
Micro-organism locomotion, Oscillating extension, Viscoelasticity
Volume
269
First Page
47
Last Page
56
DOI
10.1016/j.jnnfm.2019.06.005
ISSN
03770257
Recommended Citation
Thomases, Becca and Guy, Robert D., "Polymer Stress Growth in Viscoelastic Fluids in Oscillating Extensional Flows with Applications to Micro-Organism Locomotion" (2019). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/160
Comments
Peer reviewed accepted manuscript.