Two-dimensional flagellar synchronization in viscoelastic fluids

TL;DR

This paper analytically demonstrates that in viscoelastic fluids, symmetric swimmers can synchronize their flagella more rapidly and stably than in Newtonian fluids, due to polymeric stresses removing previous asymmetry constraints.

Contribution

It introduces a two-dimensional model showing that viscoelasticity enables symmetric flagellar synchronization, unlike in Newtonian fluids where asymmetry is required.

Findings

Synchronization occurs faster in viscoelastic fluids.

Symmetric swimmers can synchronize without asymmetry.

Stable in-phase conformation minimizes energy dissipation.

Abstract

Experimental studies have demonstrated that spermatozoa synchronize their flagella when swimming in close proximity. In a Newtonian fluid, it was shown theoretically that such synchronization arises passively due to hydrodynamic forces between the two swimmers if their waveforms exhibit a front-back geometrical asymmetry. Motivated by the fact that most biological fluids possess a polymeric microstructure, we address here synchronization in a viscoelastic fluid analytically. Using a two-dimensional infinite sheet model we show that the presence of polymeric stresses removes the geometrical asymmetry constraint, and therefore even symmetric swimmers synchronize. Such synchronization occurs on asymptotically faster time scales than in a Newtonian fluid, and the swimmers are seen to be driven into a stable in-phase conformation minimizing the energy dissipated in the surrounding fluid.