Dynamics of flexible filaments in oscillatory shear flows

Understanding the transport and conformational dynamics of flexible microfibers in time-dependent flows is of key importance for the characterization of complex biological phenomena and the control of polymer-based material properties during processing. Here, we combine experiments in microfluidic channels and computational modeling to study the dynamics of elastic, Brownian, actin filaments submitted to oscillatory forcing. Unlike time-invariant shear flows, in which the emergence of morphological transitions is essentially governed by a single parameter, the elastoviscous number, that compares viscous to elastic restoring forces, the addition of an independent timescale in the problem makes way for a variety of unexplored behaviors. We show that the dynamics now strongly depends on a new dimensionless number ρ, comparing the maximum shear rate to the oscillation period, and θ₀, the filament orientation at the beginning of each period. Of particular interest is the possibility of suppression of buckling instabilities for combined values of ρ and θ₀, even in very strong flows. We explain this remarkable behavior through a weakly nonlinear Landau theory of buckling, in which we treat the filaments as inextensible elastic rods whose hydrodynamics are described by local slender-body theory.