Dynamical modes of highly elastic loops settling under gravity in a viscous fluid

TL;DR

This study numerically investigates the complex dynamical modes of highly elastic loops settling under gravity in a viscous fluid, revealing a new mode and analyzing transitions between modes based on the elasto-gravitation number.

Contribution

It introduces a more precise numerical method to identify and characterize a new dynamical mode of elastic loops and analyzes mode transitions and coexistence.

Findings

Discovery of a new settling mode for elastic loops.

Identification of bifurcation points at critical elasto-gravitation numbers.

Comparison of different dynamical modes and their timescales.

Abstract

The settling of highly elastic non-Brownian closed fibres (called loops) under gravity in a viscous fluid is investigated numerically. The loops are represented using a bead-spring model with harmonic bending potential and finitely extensible nonlinear elastic (FENE) stretching potential. Numerical solutions to the Stokes equations are obtained with the use of HYDROMULTIPOLE numerical codes, which are based on the multipole method corrected for lubrication to calculate hydrodynamic interactions between spherical particles with high precision. Depending on the elasto-gravitation number B, a ratio of gravitation to bending forces, the loop approaches different attracting dynamical modes, as described by Gruziel-Slomka et al. (Soft Matter, vol. 15, 2019, pp. 7262-7274) with the use of the Rotne-Prager mobility of the elastic loop made of beads. Here, using a more precise method, we find and characterise a new mode, analyse typical timescales, velocities, and orientations of all the modes, compare them, and investigate their coexistence. We analyse the transitions (bifurcations) to a different mode at certain critical values of the elasto-gravitation number B.