Surfing locomotion of elastic sheets driven by curvature mismatch

The locomotion of flexible membranes on top of curved surfaces appears in different contexts and scales, from cells to tissue and to cm-scale organisms. We present an experimental and theoretical study of curvature-driven locomotion, using gel ribbons that surf on a curved fluid-fluid interface via autonomous periodic modulation of their curvature. We derive a mechanical model in which forces and torques emerge from the curvature mismatch between the ribbon and the substrate. Analytic and numerical solutions of the equations of motion successfully predict the experimentally measured velocity profiles. We conclude by highlighting the relevance of this curvature-driven mode of locomotion to other mechanical, as well as biological systems.