Taylor's swimming sheet near a soft boundary

TL;DR

This paper extends Taylor's classic model of a swimming sheet to include the effects of a nearby soft boundary, revealing how boundary softness influences swimming velocity, energetics, and boundary deformation.

Contribution

It introduces a correction to Taylor's model accounting for soft boundary effects, analyzing velocity changes, energetics, and boundary deformation in this context.

Findings

Swimming velocity decreases near soft boundaries for transverse waves.

Swimming velocity increases near soft boundaries for longitudinal waves.

Soft boundary deformation synchronizes with wave passing, affecting power exerted.

Abstract

In 1951, G.I. Taylor modeled swimming microorganisms by hypothesizing an infinite sheet in 2D moving in a viscous medium due to a wave passing through it. This simple model not only captured the ability of microorganisms to swim due to the wavy motion of a flagella, but further development into the model captured the optimal nature of metachronal waves observed in ciliates. While the additional effects of nearby rigid boundaries and complex environments have been addressed, herein we explore the correction induced by a nearby soft boundary. Our simple model allows us to show that the magnitude of the swimming velocity gets modified near soft boundaries, and reduces for transverse waves while it increases for longitudinal waves. We further delve into the energetics of the process and the deformation of the corresponding soft boundary, highlighting the synchronization of the oscillations induced on the soft boundary with the waves passing through the sheet and the corresponding changes to the power exerted on the fluid.