Rotational dynamics of a superhelix towed in a Stokes fluid

TL;DR

This study investigates the rotational behavior of superhelical structures in viscous fluids, revealing how the interplay of two helices influences rotation, with experimental and computational results aligning closely and surpassing classical theories.

Contribution

It provides a comprehensive analysis combining experiments, analytics, and simulations to understand superhelix dynamics, highlighting the dominance shift between helices at different amplitudes.

Findings

Rotation direction depends on the competition between the two helices.

Agreement between experiments and Regularized Stokeslets computations is excellent.

Classical resistive force theory predictions are less accurate than the new methods.

Abstract

Motivated by the intriguing motility of spirochetes (helically-shaped bacteria that screw through viscous fluids due to the action of internal periplasmic flagella), we examine the fundamental fluid dynamics of superhelices translating and rotating in a Stokes fluid. A superhelical structure may be thought of as a helix whose axial centerline is not straight, but also a helix. We examine the particular case where these two superimposed helices have different handedness, and employ a combination of experimental, analytic, and computational methods to determine the rotational velocity of superhelical bodies being towed through a very viscous fluid. We find that the direction and rate of the rotation of the body is a result of competition between the two superimposed helices; for small axial helix amplitude, the body dynamics is controlled by the short-pitched helix, while there is a cross-over at larger amplitude to control by the axial helix. We find far better, and excellent, agreement of our experimental results with numerical computations based upon the method of Regularized Stokeslets than upon the predictions of classical resistive force theory.