Morphological Instability of Solid-on-Liquid Thin Film Structures

Subject to a compressive membrane force, a solid film on a liquid layer may form wrinkles. When the solid film is very thin, surface stresses contribute to the membrane force. When the liquid layer is very thin, the two interfaces bounding the liquid interact with each other through forces of various physical origins. We formulate the free energy of the solid-on-liquid structure, and carry out a linear perturbation analysis. A dimensionless parameter is identified to quantify the relative importance of fiexural rigidity, membrane force, and interfacial force. Depending on the nature of the interfacial force, several intriguing behaviors are possible; for example, the solid film may remain flat under a compressive membrane force, or form wrinkles under a tensile membrane force.