Floating elastic membrane in rotation : shape of interface and wrinkling instability

When rotated at constant speed, the surface of a liquid takes the well known shape of a parabola. If the surface of the liquid is covered with a thin elastic membrane, the force balance is modified, which changes the obtained shape. We study the influence of the elastic properties of the membrane on this shape, and compare with experiments. We also report the apparition of a buckling instability at the edges of the floating membrane : radial creases appear and grow closer to the center as rotation speed is increased.