Microscopic wrinkles on supported surfactant monolayers.

We discuss mechanical buckling instabilities of a rigid film under compression interacting repulsively with a substrate through a thin fluid layer. The buckling occurs at a characteristic wavelength that increases as the one-fourth power of the bending stiffness, such as the gravitational instability studied previously by Milner However, the potential can affect the characteristic buckling wavelength strongly, as predicted by Huang and Suo. If the potential changes sufficiently sharply with thickness, this instability is continuous, with an amplitude varying as the square root of overpressure. We discuss three forms of interaction important for the case of Langmuir monolayers transferred to a substrate: Casimir-van der Waals interaction, screened charged double-layer interaction, and the Sharma potential. We verify these predictions numerically in the van der Waals case.