An important category of microscale fluid–structure interactions concerns how flexible fibres deform and interact with flows. Many experimental and numerical studies have focused on the shape dynamics of fibres in linear shear flows. Here, instead, we consider a fully three-dimensional background flow with non-constant vorticity and study the shape evolution of fibres in a zero-Reynolds-number analogue of a Burgers vortex. This flow is created by the superposition of regularised singularities of the Stokes equations. Using a Kirchhoff rod model with regularised Stokeslet segments that track both curvature and torsion evolution along the fibre, we observe novel three-dimensional deformations. The shape dynamics depends on two non-dimensional parameters: an elastoviscous number and the ratio of vortex core diameter to fibre length. We focus on the special case of fibre excursions when the fibre is placed in the horizontal plane of symmetry, centred at the vortex core. We reveal robust orbits where fibres spin about the z axis as they deform, but ultimately straighten out and reach a vertical equilibrium state. Our model demonstrates that the fibre flexibility influences the time it takes to complete this orbit, with flexible fibres reaching equilibrium sooner than their stiffer counterparts. In addition, we demonstrate that fibres placed asymmetrically within this fully three-dimensional background flow exhibit a wide array of shape evolutions, including helical buckling.
Islam et al. (Mon,) studied this question.