Elastic fibres in shear flow: rotating and non-rotating states

Solid particles immersed in a low-Reynolds-number shear flow generally tend to rotate. It is, however, possible to construct rigid particles that adopt a constant orientation relative to the flow while drifting across the streamlines. A recent study by Roggeveen & Stone (2022 J. Fluid Mech . 939, A23), analysed the existence and stability of such orientations for ‘boomerang’-shaped rigid fibres formed by two straight arms of different lengths. Given that slender fibres are easily deformed by the fluid traction, we extend their study to the case of elastic fibres, allowing for arbitrary stress-free initial shapes. We establish the conditions under which such fibres adopt a constant shape and orientation while drifting steadily across the streamlines. Numerical simulations show that, in other parameter regimes, the fibres perform Jeffery-like rotations while undergoing large-amplitude deformations. In such regimes, the fibres are advected by the flow but have a zero net drift across the streamlines, implying that a shear flow might be used to separate dilute suspensions of such fibres based on their shapes and/or elasticity. We explore the transition between steady (non-rotating) and Jeffery-like (rotating) states and show that the transition between these regimes arises through a degenerate