Very thin solid-on-liquid structures: the interplay of flexural rigidity, membrane force, and interfacial force

Abstract

This paper studies a solid film lying on a liquid layer, which in turn lies on a solid substrate. It is well known that, subject to a compressive membrane force, the solid film wrinkles, dragging the liquid underneath to flow. When the solid film is very thin, the ratio between the number of atoms at the surface and that in the bulk becomes significant, so that surface stress contributes 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 system, and carry out a linear perturbation analysis. A dimensionless parameter is identified to quantify the relative importance of flexural rigidity, membrane force, and interfacial force on stability of the structure. 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. We estimate the dimensionless parameter for interfacial forces of several specific origins, including photon dispersion, electrical double layer, and electron confinement. Emphasis is placed on identifying the thickness ranges of the solid film and of the liquid layer within which these forces are important.