Buckling transitions of an elastic filament in a viscous stagnation point flow

The interplay of viscous and elastic stresses is relevant to a number of flow problems involving slender elastic fibers. These range from the swimming of microorganisms to the transport of pulp fibers in processing flow as well as from nanotube and nanocarpet applications to semi-flexible polymer behavior. In some applications, slender fibers are attached to walls where they experience externally applied flows. In this paper, we focus on the model problem of a wall mounted filament in a (compressive) extensional flow and characterize the flow-induced bending and buckling of the fiber. Using a combination of stability analysis and numerical simulations (with the latter based on a discretized beam model), we show that, for a critical value of the ratio between viscous and elastic forces, the filament is susceptible to bending and buckling instabilities at supercritical bifurcation points.