Instability and self-propulsion of flexible autophoretic filaments

Over the past decade, autophoretic colloids have emerged as a prototypical system for studying self-propelled motion at microscopic scales, with promising applications in microfluidics, micro-machinery, and therapeutics. Their motion in a viscous fluid hinges on their ability to induce surface slip flows that are spatially asymmetric, from self-generated solute gradients. Here, we demonstrate theoretically that a straight elastic filament with homogeneous surface chemical properties -- which is otherwise immotile -- can spontaneously achieve self-propulsion by experiencing a buckling instability that serves as the symmetry-breaking mechanism. Using efficient numerical simulations, we characterize the nonlinear dynamics of the elastic filament and show that, over time, it attains distinct swimming modes such as a steadily translating "U" shape and a metastable rotating "S" shape when semi-flexible, and an oscillatory state when highly flexible. Our findings provide physical insight into future experiments and the design of reconfigurable synthetic active colloids.