Low Reynolds number hydrodynamics of asymmetric, oscillating dumbbell pairs

TL;DR

This paper derives and analyzes simplified, stroke-averaged equations for the hydrodynamic interactions of asymmetric, oscillating dumbbell pairs at low Reynolds number, facilitating faster simulations and insights into collective swimmer behavior.

Contribution

It introduces a novel stroke-averaged model for asymmetric dumbbell interactions, enabling efficient simulation and analysis of collective swimming dynamics at low Reynolds number.

Findings

Stroke-averaged equations significantly speed up simulations.

Model helps explore effects of swimmer asymmetry on collective behavior.

Provides a foundation for deriving continuum models of swimmer suspensions.

Abstract

Active dumbbell suspensions constitute one of the simplest model system for collective swimming at low Reynolds number. Generalizing recent work, we derive and analyze stroke-averaged equations of motion that capture the effective hydrodynamic far-field interaction between two oscillating, asymmetric dumbbells in three space dimensions. Time-averaged equations of motion, as those presented in this paper, not only yield a considerable speed-up in numerical simulations, they may also serve as a starting point when deriving continuum equations for the macroscopic dynamics of multi-swimmer suspensions. The specific model discussed here appears to be particularly useful in this context, since it allows one to investigate how the collective macroscopic behavior is affected by changes in the microscopic symmetry of individual swimmers.