Swimming in viscoplastic fluids

Abstract

Locomotion at small scales in the absence of inertia is a classical and enduring research topic. Here, recent developments in the theory of such locomotion through a viscoplastic ambient fluid are reviewed and explored. The specific focus here applies to motion of cylindrical filamentary bodies that are long and thin, for which an asymptotic slender-body theory can be exploited. Details of this theory are summarised and then applied to describe different swimming waveforms: undulation, peristalsis, and helical motion. It is shown that, in general, strong force anisotropy close to the limit of axial cylindrical motion has a significant effect on locomotion in viscoplastic media, allowing for highly efficient motion in which the swimmer is able to ‘cut’ through the material following very closely the path of its own axis. Some qualitative comparison with experiments is presented, and future extensions and research directions are reviewed.

Deformation fields around cylinders moving at different angles to their axis through a yield stress fluid, showing (a) a low yield stress and (b) a high yield stress