Pattern Formation in a Substrate–Contactor System with Two Interacting Incompressible Elastic Films

The surface stability of two interacting (for example, by van der Waals forces) incompressible thin films, one bonded to a substrate and the other to a contactor, is studied extending the work of Shenoy and Sharma, Physical Review Letters 18, 119–122 (2001). The analysis indicates that the wavelength of the instability depends strongly on the shear moduli and thicknesses of the films but not on the nature and magnitude of the interaction. When the films have equal shear moduli, the wavelength of the instability has an intermediate value between the wavelengths of the instabilities had each of the films been interacting with rigid contactors. On the other hand, if the films have different shear moduli but equal thicknesses, then the wavelength of the instability is identical to that had the films been interacting with rigid contactors. In the more general case when the two films have different shear moduli and thicknesses, the nature of the critical wavelength is more complex. When ratio of the shear moduli of the contacting film to that of the film bonded to the substrate exceeds 5.32, the wavelength of the of the instability jumps from the value close to that determined by the thickness of the film bonded to the substrate to that of the contacting film, as the thickness of the contacting film is increased.