Morphological Instability of Solid-on-Liquid Thin Film Structures
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Morphological Instability of Solid-on-Liquid Thin Film Structures Rui Huang1 and Z. Suo2 1 Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX 78712 2 Department of Mechanical and Aerospace Engineering and Princeton Materials Institute, Princeton University, Princeton, NJ 08544 ABSTRACT 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 flexural 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. INTRODUCTION A thin liquid layer, lying on a solid substrate by itself, can rupture to form islands and dry spots [1-4]. The instability is driven by long-range attractive interactions between the two interfaces that bound the liquid layer. The surface energy of the liquid can stabilize perturbations of short wavelengths, but not those of long wavelengths. As a result, perturbations of long wavelengths grow and the liquid layer is unstable. If the liquid layer is covered by a thin solid film, as shown in Fig. 1, several differences are expected. The flexural rigidity of the solid film provides resistance against instability. If the solid film is subject to a residual stress, tension stabilizes the film, and compression destabilizes it. The long-range interactions between the interfaces can be attractive or repulsive, destabilizing or stabilizing the system. Yet another difference is about surface energy. As first pointed out by Gibbs [5], for a solid-liquid interface, the change of surface energy depends on the elastic strain. Unlike the surface energy density at an air-liquid interface, which is a positive constant and always tends to stabilize the liquid layer, the surface stress at a solid-liquid interface can be Solid film
λ = 2π/k
Wrinkled solid film
h H
(a)
Liquid layer
Liquid layer
Rigid substrate
Rigid substrate (b)
Figure 1: Illustration of a solid-on-liquid thin film structure: (a) flat and reference state; (b) wrinkled state.
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either positive or negative [6-9], and thus can either stabilize or destabilize the solid-on-liquid (SOL) structure. Recently, we and others have studied the stability of a SOL structure by considering the elastic deformation of the solid and the viscous flow of the liquid, but ignoring the effects of surface stresses and interfacial forces [10-13]. The analysis is valid as long as both the solid film and the liquid layer are sufficiently thick.
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