Reversible to chaotic transitions in the dynamics of fluctuating elastic filaments in oscillatory shear flow

We study the long-time dynamics of Brownian inextensible elastic filaments in a uniform oscillatory shear flow. We perform experiments using actin filaments in a microfluidic chamber as well as numerical simulations based on a fluctuating Euler-Bernoulli elastica model. Our analysis focuses on the regime of strong flows where buckling instabilities are prevalent, and highlight a strong dependence of the dynamics on the dimensionless period of oscillation ρ=γ_mT, where γ_m is the maximum shear rate. At low values of ρ, the period is too short for appreciable deformations to arise and the filament displays nearly reversible rigid-body dynamics. At larger values of ρ, a transition to a new regime is uncovered, with the emergence of quasi-reversible attracting states characterized by a straight conformation nearly aligned with the flow direction on each integer period, alternating with a random deformed conformation on the half-period. Two such attracting states in fact coexist with a phase shift of a half period, and analysis of our data shows that the system tends to lock itself onto one such state, but intermittently switches between them as a result of noise, giving the appearance of alternating stretches of quasi-reversibility and chaotic behavior.