Helical swimming in Stokes flow using a novel boundary-element method

TL;DR

This paper introduces a computationally efficient boundary-element method leveraging helical symmetry to simulate Stokes flows around rotating helical flagella, validated against experiments and theoretical models.

Contribution

The paper presents a novel boundary-element approach that reduces computational complexity for helical flows by exploiting symmetry, with validation against experiments and existing theories.

Findings

Reduced computational cost while maintaining resolution.

Good agreement with experimental measurements.

Reliable convergence with proper singularity treatment.

Abstract

We apply the boundary-element method to Stokes flows with helical symmetry, such as the flow driven by an immersed rotating helical flagellum. We show that the two-dimensional boundary integral method can be reduced to one dimension using the helical symmetry. The computational cost is thus much reduced while spatial resolution is maintained. We review the robustness of this method by comparing the simulation results with the experimental measurement of the motility of model helical flagella of various ratios of pitch to radius, along with predictions from resistive-force theory and slender-body theory. We also show that the modified boundary integral method provides reliable convergence if the singularities in the kernel of the integral are treated appropriately.