Flexible filaments buckle into helicoidal shapes in strong compressional flows

Abstract

The occurrence of coiled or helical morphologies is common in nature, from plant roots to DNA packaging into viral capsids, as well as in applications such as oil drilling processes. In many examples, chiral structures result from the buckling of a straight fiber either with intrinsic twist or to which end moments have been applied in addition to compression forces. Here, we elucidate a generic way to form regular helicoidal shapes from achiral straight filaments transported in viscous flows with free ends. Through a combination of experiments using fluorescently labeled actin filaments in microfluidic divergent flows and of two distinct sets of numerical simulations, we demonstrate the robustness of helix formation. A nonlinear stability analysis is performed and explains the emergence of such chiral structures from the nonlinear interaction of perpendicular planar buckling modes, an effect that solely requires a strong compressional flow, independent of the exact nature of the fiber or type of flow field. The fundamental mechanism for the uncovered morphological transition and characterization of the emerging conformations advance our understanding of several biological and industrial processes and can also be exploited for the controlled microfabrication of chiral objects.