Universal features of the shape of elastic fibres in shear flow. (5th March 2021)

• Record Type: Journal Article
• Authors: Żuk, Paweł J.; Słowicka, Agnieszka M.; Ekiel-Jeżewska, Maria L.; Stone, Howard A.
• Is Part Of: Journal of fluid mechanics. Volume 914(2021)
• Publication Date: 2021-03-05
• Subjects: Stokesian dynamics, -- particle/fluid flow, -- slender-body theory; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.1048
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: Abstract : We present a numerical study of the dynamics of an elastic fibre in a shear flow at low Reynolds number, and seek to understand several aspects of the fibre's motion using the equations for slender-body theory coupled to the elastica. The numerical simulations are performed in the bead-spring framework including hydrodynamic interactions in two theoretical schemes: the generalized Rotne–Prager–Yamakawa model and a multipole expansion corrected for lubrication forces. In general, the two schemes yield similar results, including for the dominant scaling features of the shape that we identify. In particular, we focus on the evolution of an initially straight fibre oriented in the flow direction and show that the time scales of fibre bending, curling and rotation, which depend on its length and stiffness, determine the overall motion and evolution of the shapes. We document several characteristic time scales and curvatures representative of the shape that vary as power laws of the bending stiffness and fibre length. The numerical results are further supported by an interpretation using an elastica model.