Wrinkle patterns of an elastic loop coupled with a transient gap flow

Thin elastic materials subjected to a compressive force can undergo wrinkling which results in a regular surface pattern characterized by specific length scales. One can manipulate the wavelength of wrinkle patterns by tuning material properties, while controlling the applied compressive force during dynamic buckling provides an alternative way. To genuinely control the pattern of a wrinkling surface, an experimental approach based on hydrodynamic coupling between transient loading and wrinkling is attempted. Here, we consider wrinkling on an elastic loop in a gap flow, which is induced by expanding a fluid-filled gap between a bottom substrate and a moving plate. Vortices formed across the elastic loop contribute to pressure difference between the inner and outer surfaces of the loop, and cause in-plane compression along its perimeter. Various modes of wrinkling emerge on the elastic loop depending on the time scale of the plate motion, such that shorter wavelength appears with the smaller time scale. Our results suggest the possibility of temporally controlling wrinkle patterns by dynamic hydrodynamic loading.