Highly elastic loops settling under gravity in a viscous fluid

The gravitational settling of highly elastic non-Brownian loops in a viscous fluid at the Reynolds number much smaller than unity is investigated numerically. A loop is modelled as an almost inextensible bead-spring chain with small bending stiffness. Its dynamics are determined by the high-precision Hydromultipole numerical codes, which apply a multipole method corrected for lubrication. Starting from both planar and non-planar initial conditions, different attracting dynamical modes are observed for different values of the loop’s flexibility, which is represented by the elasto-gravitation number B – a ratio of the gravitational and bending forces.

Here, we characterise the observed modes. In addition to the vertical, tilted, frozen rotating, tank-treading, swinging, and flapping modes identified earlier by Gruziel-Słomka et al. (Soft Matt. 15, 7262, 2019), two additional modes – rocking and gyrating-rocking-tank-treading – are presented. We focus on the evaluation and comparison of the characteristic time scales & velocities for all the modes, and the numerical analysis of the transitions (bifurcations) to a different mode at specific critical values of the elasto-gravitation number (Melikhov, Ekiel-Jezewska, J. Fluid Mech. 1013, A13, 2025).