Stokesian dynamics of sedimenting elastic rings

Abstract

We study numerically the dynamics of elastic microfilaments which form closed loops and settle under gravity in a viscous fluid. We observe diversity of periodic and stationary sedimentation modes, dependent on flexibility and initial configuration.

Stability of sedimenting flexible loops

“…(2020) linking extrachromosomal circular DNA properties with neuroblastoma, and partly inspired by previous numerical work using bead-spring hydrodynamic models (Gruziel-Słomka et al. 2019). Electrophoretic and ultracentrifugation measurements of mobility pose questions about what constitutes a flexible regime, correct values of drag coefficients and the stress distribution along the filament.…”

“…2018; Gruziel-Słomka et al. 2019) that high flexibility leads to a change in orientation (and sometimes shape) of sedimenting objects, affecting their sedimentation speed. Independently, in the case of linear filaments, Reichert & Stark (2005) observed that including elasticity can change the behaviour qualitatively when looking at bundling vs non-bundling flagella.…”

“…In bead-spring models, Gruziel-Słomka et al. (2019) observed the existence of an elasticity threshold beyond which flexible loops undergo significant changes in sedimentation dynamics. While stiff loops were seen to attain almost planar, oval shapes and sediment vertically or at an acute angle to gravity, depending on their stiffness, more flexible fibres exhibited a complex shape evolution.…”

“…This leads to equations in the form with a single dimensionless parameter , analogous to (the inverse of) that used by Gruziel-Słomka et al. (2019) for the bead-spring model. Here, is the mass per unit length of the fibre corrected for buoyancy, with and being the densities of the beam material and the fluid, respectively.…”

Sedimenting pairs of elastic microfilaments

“…Finally, it would be worthwhile to study hydrodynamic interactions of pairs of sedimenting elastic loops. 46,60…”