LMP Seminar: How extensible bodies swim: bending-compression coupling at low Reynolds number

Undulatory slender objects are instrumental in the hydrodynamics of swimming at low Reynolds number, from eukaryotic flagella and cilia to artificial microrobots, because they enable nonreciprocal deformation cycles, which are famously necessary for locomotion at this scale. In most theoretical locomotion models, these slender bodies are assumed to be inextensible, and this is a reasonable approximation. Yet, several microorganisms and artificial microrobots display large compression and extension. The role of this degree of freedom in microswimming is somewhat overlooked. Hence, in this talk, I will present recent results that explore the role of compression in low-Reynolds-number locomotion. I will theoretically study the coupling between bending and compression shape modes, using a geometrical formulation of microswimmer hydrodynamics to deal with the non-commutative effects between translation and rotation. Interesting results on bending-compression coupling can be inferred by introducing a minimal model in the spirit of the Purcell swimmer, and by considering small-amplitude expansions. In particular, within the framework of resistive force theory, we show that compression-bending coupling notably allows net locomotion even under isotropic drag, while this is impossible for inextensible swimmers. If time permits, I will then give an outlook on elastohydrodynamics of compressible slender bodies, based on numerical simulation using a N-segment formulation, with applications to modelling the behaviour of Lacrymaria olor. This talk is based on joint work with Kenta Ishimoto (Kyoto University) and Johann Herault (IMT Atlantique).