Beating patterns of filaments in viscoelastic fluids

TL;DR

This paper investigates how viscoelastic fluids influence the motion and beating patterns of elastic filaments, such as sperm flagella, revealing modifications in hydrodynamic forces and resulting in observed distal-end concentrated beating patterns.

Contribution

It provides a detailed analysis of the effects of viscoelasticity on filament dynamics, including both passive and active models, and explains experimentally observed flagellar beating patterns.

Findings

Viscoelasticity alters hydrodynamic forces on filaments.

High viscosity leads to distal-end concentrated beating.

Theoretical results match observed sperm flagella patterns.

Abstract

Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end, and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high viscosity of purely viscous or viscoelastic solutions can lead to the experimentally observed beating patterns of sperm flagella, in which motion is concentrated at the distal end of the flagella.