Hydrodynamic interactions between pairs of sedimenting semi-flexible Brownian fibers

The sedimentation of semiflexible fibers is a central process in the production of a range of important materials such as paper and fiber-reinforced composites. Predicting the dynamics of such fibers when both Brownian motion and hydrodynamic interactions are relevant, which would be a powerful tool to support the design of these materials, is nonetheless numerically challenging. Here, we utilize a computational framework that incorporates fiber elasticity, thermal fluctuations, and hydrodynamic interactions represented as Rotne–Prager–Yamakawa kernels and perform a parametric study of the simplest system in which hydrodynamic interactions are relevant, that is, pairs of fibers starting from one of two initial configurations. We also provide analytical predictions for the initial velocity and rotation of rigid fibers in the Oseen approximation. We systematically studied the systems in which bending, thermal fluctuations, and hydrodynamic interactions are included for the sedimenting semi-flexible fibers. Our goal was to determine when one of thermal fluctuations or hydrodynamics dominates over the other, or when both must be considered together, to inform the understanding and design of such systems. The short- and long-time dynamics of the fibers are thoroughly characterized, with good agreement with the analytical calculations for the initial behavior, and the observed trends are interpreted in terms of the underlying physical mechanisms. We finish with a discussion of the use of Rotne–Prager–Yamakawa kernels over alternative frameworks such as bead models and suggest potential directions for future work.