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

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.

26 pages

References in corpus (16)

• Theory of High-Force DNA Stretching and Overstretching
• The sedimentation of flexible filaments
• Hydrodynamic induced deformation and orientation of a microscopic elastic filament
• A review of shaped colloidal particles in fluids: Anisotropy and chirality
• Sedimentation of pairs of hydrodynamically interacting semiflexible filaments
• Conformations, hydrodynamic interactions, and instabilities of sedimenting semiflexible filaments
• Periodic motion of sedimenting flexible knots
• Kepler orbits of settling discs
• Hydrodynamic Interactions between Two Forced Objects of Arbitrary Shape: I Effect on Alignment
• Hydrodynamic orienting of asymmetric microobjects under gravity
• Hydrodynamic Interactions between Two Forced Objects of Arbitrary Shape: II Relative Translation
• Helical Ribbons: Simple Chiral Sedimentation
• Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion
• U-shaped disks in Stokes flow: Chiral sedimentation of a non-chiral particle
• Stability of sedimenting flexible loops
• Sedimentation Dynamics of Bodies with Two Planes of Symmetry