Helical locomotion in a porous medium

Abstract

Microorganisms and artificial microswimmers often need to swim through environments that are more complex than purely viscous liquids in their natural habitats or operational environments, such as gel-like mucus, wet soil, and aquifers. The question of how the properties of these complex environments affect locomotion has attracted considerable recent attention. In this paper, we present a theoretical model to examine how the additional resistance due to the network of stationary obstacles in a porous medium affects helical locomotion. Here, we focus on helical locomotion for its ubiquity as a propulsion mechanism adopted by many swimming bacteria and artificial microswimmers. We show that the additional resistance can have qualitatively different effects on various scenarios of helical locomotion: (1) a helical propeller driven by an external torque, (2) a free swimming bacterium consisting of a helical flagellum and a head, and (3) a cargo-carrying helical propeller driven by an external torque. Our results elucidate the subtle and significant differences between torqued helical propulsion versus force-free and torque-free swimming in a porous medium. We also remark on the limitations as well as potential connections of our results with experimental measurements of bacterial swimming speeds in polymeric solutions.