Follower Forces in Pre-Stressed Fixed-Fixed Rods to Mimic Oscillatory Beating of Active Filaments

TL;DR

This paper models elastic rods under follower forces to mimic biological filament oscillations, analyzing how pre-stress and fluid drag influence beating frequencies and critical forces.

Contribution

It introduces a comprehensive elastic rod model to study oscillatory behavior under different fluid drag conditions, highlighting the effects of pre-stress and drag type on stability and frequency.

Findings

Critical follower force depends on initial slack.

Emergent frequencies are influenced by pre-stress and drag type.

Critical force weakly depends on drag nature.

Abstract

Flagella and cilia are examples of actively oscillating, whiplike biological filaments that are crucial to processes as diverse as locomotion, mucus clearance, embryogenesis and cell motility. Elastic driven rod-like filaments subjected to compressive follower forces provide a way to mimic oscillatory beating in synthetic settings. In the continuum limit, this spatiotemporal response is an emergent phenomenon resulting from the interplay between the structural elastic instability of the slender rods subjected to the non-conservative follower forces, geometric constraints that control the onset of this instability, and viscous dissipation due to fluid drag by ambient media. In this paper, we use an elastic rod model to characterize beating frequencies, the critical follower forces and the non-linear rod shapes, for prestressed, clamped rods subject to two types of fluid drag forces, namely, linear Stokes drag and non-linear Morrison drag. We find that the critical follower force depends strongly on the initial slack and weakly on the nature of the drag force. The emergent frequencies however, depend strongly on both the extent of pre-stress as well as the nature of the fluid drag.