 They found that hierarchical structure was not only necessary for a high contact angle but essential for the stability of the water-solid and water-air interfaces (the composite interface).Due to an external perturbation, a standing capillary wave can form at the liquid–air interface.If the amplitude of the capillary wave is greater than the height of the asperity, the liquid can touch the valley between the asperities; and if the angle under which the liquid comes in contact with the solid is greater than h0, it is energetically profitable for the liquid to fill the valley.