A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number

TL;DR

This paper introduces a comprehensive Lagrange multiplier framework for simulating low Reynolds number fiber dynamics using Bead Models, enabling flexible modeling of fiber deformation, filament actuation, and swimmer propulsion.

Contribution

It presents a novel, versatile formalism for fiber simulation that efficiently incorporates kinematic constraints and introduces the Gears contact model to improve numerical stability.

Findings

The framework accurately models fiber deformation and rotation in shear flow.

The Gears Model effectively prevents numerical issues caused by artificial forces.

The method is versatile for simulating active filament propulsion.

Abstract

This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models.