Dynamics of flexible filaments in oscillatory shear flows.

The fluid-structure interactions between flexible fibers and viscous flows play an essential role in various biological phenomena, medical problems, and industrial processes. Of particular interest is the case of particles freely transported in time-dependent flows. This work elucidates the dynamics and morphologies of actin filaments under oscillatory shear flows by combining microfluidic experiments, numerical simulations, and theoretical modeling. Our work reveals that, in contrast to steady shear flows, in which small orientational fluctuations from a flow-aligned state initiate tumbling and deformations, the periodic flow reversal allows the filament to explore many different configurations at the beginning of each cycle. Investigation of filament motion during half time periods of oscillation highlights the critical role of the initial filament orientation on the emergent dynamics. This strong coupling between orientation and deformation results in new deformation regimes and novel higher-order buckling modes absent in steady shear flows. The primary outcome of our analysis is the possibility of suppression of buckling instabilities for certain combinations of the oscillation frequency and initial filament orientation, even in very strong flows. We explain this unusual behavior through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible Brownian Euler-Bernoulli rods whose hydrodynamics are described by local slender-body theory.