Swimming speeds of filaments in nonlinearly viscoelastic fluids

TL;DR

This study investigates how nonlinear viscoelastic fluids affect microorganism swimming speeds, revealing that such fluids diminish velocities and can violate classical constraints like Purcell's scallop theorem.

Contribution

It provides an analytical framework for understanding microorganism propulsion in nonlinear viscoelastic fluids, highlighting conditions where classical swimming constraints are broken.

Findings

Swimming velocities are reduced by nonlinear viscoelastic effects.

Reciprocal motions with different forward and backward stroke rates can produce net translation.

Classical constraints like Purcell's scallop theorem are violated in nonlinear fluids.

Abstract

Many microorganisms swim through gels and non-Newtonian fluids in their natural environments. In this paper, we focus on microorganisms which use flagella for propulsion. We address how swimming velocities are affected in nonlinearly viscoelastic fluids by examining the problem of an infinitely long cylinder with arbitrary beating motion in the Oldroyd-B fluid. We solve for the swimming velocity in the limit in which deflections of the cylinder from its straight configuration are small relative to the radius of the cylinder and the wavelength of the deflections; furthermore, the radius of the cylinder is small compared to the wavelength of deflections. We find that swimming velocities are diminished by nonlinear viscoelastic effects. We apply these results to examine what types of swimming motions can produce net translation in a nonlinear fluid, comparing to the Newtonian case, for which Purcell's "scallop" theorem describes how time-reversibility constrains which swimming motions are effective. We find that the leading order violation of the scallop theorem occurs for reciprocal motions in which the backward and forward strokes occur at different rates.