Experimental and numerical study of the dynamics of sedimenting pairs of semi-flexible fibers close to attractive `aligned' relative configuration

Abstract

Dynamics of two short semi-flexible fibers settling under gravity in a viscous fluid are investigated at Reynolds numbers Re << 1. We focus on fibers initially relatively close to each other, and we check if later they approach an aligned horizontal configuration, previously identified numerically (Bukowicki and Ekiel-Jezewska, Soft Matter 46 (2019) 9379) as attractive for symmetric initial conditions of moderately elastic filaments. In our experiments, two semi-flexible ball chains sediment in a highly viscous silicone oil. They are initially straight and close to a parallel horizontal relative configuration. Their motion and shape deformation are recorded using two synchronized cameras. For most of the trials, ball chains stay together, with damped oscillations around the symmetric aligned configuration. For a few initial conditions, the ball chains move away horizontally or vertically. To study the behavior over a longer time, we perform numerical simulations, modeling moderately elastic filaments as chains of identical beads, with the centers of consecutive beads connected by springs and with the fibers&#39; elastic resistance to bending. Different initial positions and orientations are considered. Their dynamics are determined by the multipole expansion of the Stokes equations, implemented in the precise Hydromultipole numerical code. For short times, we observe the similar dynamics of semi-flexible ball chains and moderately elastic filaments. We provide examples of long-time numerical simulations illustrating that elastic filaments close to each other can move away horizontally or vertically, but after a long time, come back and perform damped oscillations while approaching the aligned configuration with almost touching filament ends. We confirm the attractive nature of the aligned configuration of very close semi-flexible sedimenting fibers, even if they are far away from each other.