Drifting via bending: Sensing extrinsic curvature for propulsion

Stresses arising from curvature mismatches can result in propulsive net forces and torques. Frustrated elastic objects have been observed to move along gradients in intrinsic curvature [1] and, on fluid membranes, meniscus-climbing insects generate curvature mismatches via capillary disturbances [2]. Inspired by such systems, we consider a simple elastic object consisting of two inextensible filaments with non-zero bending moduli. The filaments are attached at their midpoints and the angle between them is our control parameter. When confined to move on a curved surface, the local alignment of such an object depends on the principal directions while its drift senses gradients in the principal curvatures. We observe two possible local alignment states that are hysteretic in the control parameter. Furthermore, the two alignment states differ in the extrinsic curvature gradients they perceive, allowing for switchable coasting behavior and a programmable family of fixed points on a curved surface. This propulsion mechanism can be employed on fluid and biological membranes where extrinsic curvature is the dominant geometric property.

[1] H. Aharoni, J. M. Kolinski, M. Moshe, I. Meirzada, and E. Sharon, Internal stresses lead to net forces and torques on extended elastic bodies, Phys. Rev. Lett. 117, 124101 (2016).

[2] Hu, D., Bush, J. Meniscus-climbing insects. Nature 437, 733–736 (2005).