Gwennou Coupier (LIPhy, Grenoble). Buckling instability and swimming of elastic spherical shells.

Under pressure, a hollow elastic sphere becomes unstable and collapses. It reinflates back when the pressure is decreased. The shape hysteresis associated to this deformation cycle makes this simple object a good candidate for becoming a microswimmer, that is, a swimmer able to move at low Reynolds number.

We first explored this possibility through a macroscopic experiment in fluids of varying viscosities so as to explore different flow regimes [1]. We showed that not only the shape sequence hysteresis leads to swimming but the asymetry in the deformation velocity makes the fast buckling phase an efficient mechanism for propulsion that implies inertial effects and subtle coupling between shape post-buckling oscillations and fluid flow patterns.

We also explore dnumerically the forcing of the deformation by waves of frequency close to that intrinsic to the shell dynamics.  This forced oscillator exhibits chaotic behaviour, similar to that observed in Duffing oscil- lators. The map of resulting swimming motions as a function of acoustic wave frequency and amplitude will be described and discussed. These results open the way towards active control of spherical shell becoming fast, inertial microswimmers.

[1] A. Djellouli, P. Marmottant, H. Djeridi, C. Quilliet and G. Coupier, Phys. Rev. Lett. 119, 224501 (2017).