  The interaction of flexible structures with viscoelastic flows can result in
very rich dynamics. In this paper, we present the results of the interactions
between the flow of a viscoelastic polymer solution and a cantilevered beam in
a confined microfluidic geometry. Cantilevered beams with varying length and
flexibility were studied. With increasing flow rate and Weissenberg number, the
flow transitioned from a fore-aft symmetric flow to a stable detached vortex
upstream of the beam, to a time-dependent unstable vortex shedding. The
shedding of the unstable vortex upstream of the beam imposed a time-dependent
drag force on the cantilevered beam resulting in flow-induced beam
oscillations. The oscillations of the flexible beam were classified into two
distinct regimes: a regime with a clear single vortex shedding from upstream of
the beam resulting in a sinusoidal beam oscillation pattern with the frequency
of oscillation increasing monotonically with Weissenberg number, and a regime
at high Weissenberg numbers characterized by 3D chaotic flow instabilities
where the frequency of oscillations plateaued. The critical onset of the flow
transitions, the mechanism of vortex shedding and the dynamics of the
cantilevered beam response are presented in detail here as a function of beam
flexibility and flow viscoelasticity.
