UC San Diego

Elastic filaments subjected to hydrodynamic forcing are a common class of fluid-structure interaction problems. In biology, they are crucial to cytoskeletal motions of the cell, the locomotion of micro-organisms, and mucal transport. In engineering, they are often the source of non-Newtonian rheological properties and a variety of complex fluid behavior such as hydrodynamic instabilities and chaotic mixing. At the heart of many of these dynamics is the competition between an elastic backbone and viscous forces acting to deform it, tangled with the anisotropic shape of such filaments as well as slowly decaying hydrodynamic interactions in a Stokesian fluid. In this work, we use slender-body theory for low-Reynolds-number hydrodynamics to address theoretically and computationally a few such problems of physical and biological significance. We first describe the tumbling of polymers in shear flow and the suppression of thermal fluctuations in extensional flow. A theory for the stretch-coil transition of semiflexible polymers is also developed. We then turn to the transport properties of semiflexible filaments in a flow setup that mimics some of the dynamics of biological polymers in motility assays. Thermal fluctuations frequently trap polymers within vortical cells, and are shown to lead to subdiffusive transport at long times. The mechanism behind this anomalous feature and the subtle role of flexibility is emphasized. Then we focus on the sedimentation of flexible filaments. In the weakly flexible regime, a multiple-scale asymptotic expansion is used to obtain expressions for filament shapes and peculiar trajectories. In the highly flexible regime, we show that a filament sedimenting along its long axis is susceptible to a buckling instability. Our predictions are corroborated by detailed numerical simulations. Finally, we look at suspensions of sedimenting elastic fibers, emphasizing the role of filament shape, flexibility, and long-ranged hydrodynamic interactions. We develop a mean-field theory for such a suspension, and its stability to perturbations of fiber concentration is analytically explored. Detailed numerical simulations are also performed to verify these predictions and elucidate the microstructural mechanisms tied to the growth or suppression of this instability.