  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.
