Optimal Strokes of Low Reynolds Number Linked-Sphere Swimmers

TL;DR

This paper analyzes the optimal swimming strokes of linked-sphere micro-swimmers in low Reynolds number fluids, revealing that fewer shape deformation modes can lead to higher efficiency, challenging the assumption that more degrees of freedom always improve propulsion.

Contribution

It introduces a method to determine optimal gaits for linked-sphere swimmers using asymptotic analysis and the Euler-Lagrange equation, highlighting efficiency trade-offs with shape complexity.

Findings

Mixed deformation modes outperform single-mode strategies.

Efficiency decreases as the number of spheres increases.

Optimal gaits depend on minimal shape deformation degrees.

Abstract

Optimal gait design is important for micro-organisms and micro-robots that propel themselves in a fluid environment in the absence of external force or torque. The simplest models of shape changes are those that comprise a series of linked-spheres that can change their separation and their sizes. We examine the dynamics of three existing linked-sphere types of modeling swimmers in low Reynolds number Newtonian fluids using asymptotic analysis, and obtain their optimal swimming strokes by solving the Euler-Lagrange equation using the shooting method. The numerical results reveal that (1) with the minimal 2 degrees of freedom in shape deformations, the model swimmer adopting the mixed shape deformation modes strategy is more efficient than those with a single-mode of shape deformation modes, and (2) the swimming efficiency mostly decreases as the number of spheres increases, indicating that more degrees of freedom in shape deformations might not be a good strategy in optimal gait design in low Reynolds number locomotion.