Elastic filaments in viscous flows

Refreshments will be served from 2:30 - 2:45

To be held at Irving K Barber room 261 and on Zoom: https://ubc.zoom.us/j/68285564037?pwd=R2ZpLy9uc2pUYldHT3laK3orakg0dz09
Meeting ID: 682 8556 4037
Passcode: 636252

Hydrodynamic interactions between elastic filaments and external flows play a fundamental role in various natural processes, including the locomotion of flagellated and ciliated organisms. In this talk, we explore key problems involving elastic filaments immersed in a viscous fluid and subjected to a prescribed force or external flow.

We begin by analyzing a simple model of an elastic slender filament subject to a uniform force (e.g., gravity). We show that multiple branches of steady-state solutions exist, describing filaments with different conformations and terminal speeds. To gain further insight, we consider the limit of highly flexible filaments and derive closed-form asymptotic formulae for the bifurcation diagram and filament shape. Our approximations show good agreement with previous experiments and full numerical simulations of the problem.

Next, we analyze a tethered filament subject to an external flow. We show that the filament aligns with the flow, except for a small region near the tether point, causing the drag on the filament to scale nonlinearly with the flow strength. Using asymptotic techniques, we derive simple approximations for the drag and filament shape.