Effect of fluid elasticity on the emergence of oscillations in an active elastic filament

TL;DR

This study investigates how fluid elasticity influences the emergence and characteristics of oscillations in an elastic filament driven by a follower force, revealing that elasticity increases the force needed for oscillations and raises their frequency.

Contribution

It provides a mechanistic understanding of how viscoelastic fluid properties affect filament oscillations, combining linear analysis, numerical simulations, and experimental data comparison.

Findings

Higher force needed to induce oscillations in viscoelastic fluids

Oscillation frequency increases with fluid relaxation time

Model aligns with experimental data on bi-flagellated algae

Abstract

Many microorganisms propel through complex media by deformations of their flagella. The beat is thought to emerge from interactions between forces of the surrounding fluid, passive elastic response from deformations of the flagellum, and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there is limited data on how systematic changes in elasticity alters the beat. This work analyzes a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip in a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. Compared to a Newtonian fluid, it takes more force to induce the instability in viscoelastic fluids, and the frequency of the oscillation is higher. The linear analysis predicts that the frequency increases with the fluid relaxation time. Using numerical simulations, the model predictions are compared with experimental data on frequency changes in bi-flagellated alga Chlamydomonas reinhardtii. The model shows the same trends in response to changes in both fluid viscosity and Deborah number, and thus provides a mechanistic understanding of the experimental observations.