Self-sustained rolling of a thermally responsive rod on a hot surface

Abstract

Recent experiments have reported an intriguing phenomenon of self-sustained rolling of a polymer rod on a flat and hot surface (Baumann et al., 2018; Ahn et al., 2018; Bazir et al., 2020). Although it has been postulated that the rod rolling is driven by its inhomogeneous thermal expansion, a quantitative thermo-mechanics model of the phenomenon, capable of explaining all the experimental observations, is not yet available. In this article, we have constructed a thermo-mechanics model of a rod rolling on a hot surface. In the model, we calculate the thermally induced deformation and stress field in the rod during its steady rolling, further enabling the prediction of its rolling speed at different conditions. Our model has also successfully predicted bistable state of the rod, which agrees well with the experimental observations.