Helical locomotion in dilute suspensions

Abstract

Motivated by the aim of understanding the effect of media heterogeneity on the swimming dynamics of flagellated bacteria, we study the rotation and swimming of rigid helices in dilute suspensions experimentally and theoretically. We first measure the torque experienced by, and thrust force generated by, helices rotating without translating in suspensions of neutrally buoyant particles with varying concentrations and sizes. Using the ratio of thrust to drag forces $\xi$ as an empirical proxy for propulsion efficiency, our experiments indicate that $\xi$ increases with the concentration of particles in the fluid, with the enhancement depending strongly on the geometric parameters of the helix. To rationalize these experimental results, we then develop a dilute theoretical approach that accounts for the additional hydrodynamic stress generated by freely suspended spheres around the helical tail. We predict similar enhancements in the drag coefficient ratio and propulsion at a given angular speed in a suspension and study its dependence on the helix geometry and the spatial distribution of the suspended spheres. These results are further reinforced by experiments on freely swimming artificial swimmers, which propel faster in dilute suspensions, with speed increases over $60 \%$ for optimal geometries. Our findings quantify how biological swimmers might benefit from the presence of suspended particles, and could inform the design of artificial self-propelled devices for biomedical applications.