  The macroscopic properties of polymeric fluids are inherited from the
material properties of the fibers embedded in the solvent. The behavior of such
passive fibers in flow has been of interest in a wide range of systems,
including cellular mechanics, nutrient aquisition by diatom chains in the
ocean, and industrial applications such as paper manufacturing. The rotational
dynamics and shape evolution of fibers in shear depends upon the slenderness of
the fiber and the non-dimensional "elasto-viscous" number that measures the
ratio of the fluid's viscous forces to the fiber's elastic forces. For a small
elasto-viscous number, the nearly-rigid fiber rotates in the shear, but when
the elasto-viscous number reaches a threshhold, buckling occurs. For even
larger elasto-viscous numbers, there is a transition to a "snaking behavior"
where the fiber remains aligned with the shear axis, but its ends curl in, in
opposite directions. These experimentally-observed behaviors have recently been
characterized computationally using slender-body theory and immersed boundary
computations. However, classical experiments with nylon fibers and recent
experiments with actin filaments have demonstrated that for even larger
elasto-viscous numbers, multiple buckling sites and coiling can occur. Using a
regularized Stokeslet framework coupled with a kernel independent fast
multipole method, we present simulations that capture these complex fiber
dynamics.
