Chaos and irreversibility of a flexible filament in periodically--driven Stokes flow

We use direct numerical simulations to solve for a filament (with bending modulus B, length L), suspended in a fluid (dynamic viscosity η), obeying Stokesian dynamics in a linear flow, γ˙=Ssin(ωt).The dynamical behavior is determined by the elasto-viscous number, μ≡(8πηSL4)/B and σ=ω/S. For a fixed σ, for small enough μ, the filament remains straight; as μ increases we observe respectively buckling, breakdown of time-reversibility and appearance of two-period and eventually chaotic spatiotemporal solutions. To analyze the dynamics of this non-autonomous system we consider the map obtained by integrating the dynamical equations over exactly one period. We find that this map has multiple fixed points and periodic orbits for large enough μ. For μ and σ within a certain range we find evidence of mixing of passive tracers.