Bending modes and transition criteria for a flexible fiber in viscous flows

The present paper follows our previous work in which a coupling approach of smoothed particle hydrodynamics (SPH) and element bending group (EBG) was developed for modeling the interaction of viscous incompressible flows with flexible fibers. It was also shown that a flexible object may experience drag reduction because of its reconfiguration due to fluid force on it. However, the reconfiguration of deformable bodies does not always result in drag reduction as different deformation patterns can result in different drag scales. In the present work, we studied the bending modes of a flexible fiber in viscous flows using the presented SPH and EBG coupling approach. The flexible fiber is immersed in a fluid and is tethered at its center point, while the two ends of the fiber are free to move. We showed that the fiber undergoes four different bending modes: stable U-shape, slight swing, violent flapping, and stable closure modes. We found there is a transition criterion for the flexible fiber from slight swing, suddenly to violent flapping. We defined a bending number to characterize the bending dynamics of the interaction of flexible fiber with viscous fluid and revealed that this bending number is relevant to the non-dimensional fiber length. We also identified the critical bending number from slight swing mode to violent flapping mode.