Institute of Applied Mathematics Seminar: Saverio E. Spagnolie

The deformation and transport of elastic filaments in viscous fluids play central roles in many biological and technological processes. Compared with the well-studied case of sedimenting rigid rods, the introduction of filament compliance may cause a significant alteration in the long-time sedimentation orientation and filament geometry. In the weakly flexible regime, a multiple-scale asymptotic expansion is used to obtain expressions for filament translations, rotations and shapes which match excellently with full numerical simulations. In the highly flexible regime we show that a filament sedimenting along its long axis is susceptible to a buckling instability. Embedding the analytical results for a single filament into a mean-field theory, we show how flexibility affects a well established concentration instability in a sedimenting suspension. Related topics will make cameo appearances, from a zoology of dynamics of settling bodies near walls to a new traction boundary integral equation for viscous fluid-body interactions.