The fluctuation properties of fluid interfaces bounded by rough surfaces are investigated within a linear generalization of the Derjaguin approximation. In the thick-film regime, the interface roughness amplitude is lower in magnitude from that obtained in the Derjaguin approximation. Nevertheless, for large healing lengths ζ the power-law asymptotic behavior ${\sigma }_w\sim {\zeta }^{-2},$ which is observed in the Derjaguin approximation, is still preserved. Moreover, the rms local interface slope ρ is shown to attain small values for film thicknesses larger than the substrate roughness amplitude and to follow an asymptotic power-law behavior $\rho \sim {\zeta }^{-2}$ for large ζ.

• Received 28 March 1997

DOI:https://doi.org/10.1103/PhysRevB.56.6478