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

TL;DR

Introducing a flexible filament in a low Reynolds number flow can induce chaos and irreversibility, enhancing mixing, with distinct dynamical phases depending on filament stiffness.

Contribution

This study reveals how a single flexible filament can break flow reversibility and induce chaos in Stokes flow, a novel insight into microscale fluid dynamics.

Findings

Flexible filament induces chaos in low Reynolds flow.

Flow reversibility is broken by filament elasticity.

Multiple dynamical phases depending on filament stiffness.

Abstract

The flow of Newtonian fluid at low Reynolds number is, in general, regular and time-reversible due to absence of nonlinear effects. For example, if the fluid is sheared by its boundary motion that is subsequently reversed, then all the fluid elements return to their initial positions. Consequently, mixing in microchannels happens solely due to molecular diffusion and is very slow. Here, we show, numerically, that the introduction of a single, freely-floating, flexible filament in a time-periodic linear shear flow can break reversibility and give rise to chaos due to elastic nonlinearities, if the bending rigidity of the filament is within a carefully chosen range. Within this range, not only the shape of the filament is spatiotemporally chaotic, but also the flow is an efficient mixer. Overall, we find five dynamical phases: the shape of a stiff filament is time-invariant -- either straight or buckled; it undergoes a period-two bifurcation as the filament is made softer; becomes spatiotemporally chaotic for even softer filaments but, surprisingly, the chaos is suppressed if bending rigidity is decreased further.