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The well-known thermal capillary wave theory, which describes the capillaryspectrum of the free surface of a liquid film, does not reveal the transientdynamics of surface waves, e.g., the process through which a smooth surfacebecomes rough. Here, a Langevin model is proposed that can capture thesedynamics, goes beyond the long-wave paradigm which can be inaccurate at thenanoscale, and is validated using molecular dynamics simulations for nanoscalefilms on both planar and cylindrical substrates. We show that a scalingrelation exists for surface roughening of a planar film and the scalingexponents belong to a specific universality class. The capillary spectra ofplanar films are found to advance towards a static spectrum, with the roughnessof the surface $W$ increasing as a power law of time $W\sim t^{1/8}$ beforesaturation. However, the spectra of an annular film (with outer radius $h_0$)are unbounded for dimensionless wavenumber $qh_0<1$ due to the Rayleigh-Plateauinstability.

Thermal Capillary Wave Growth and Surface Roughening of Nanoscale Liquid Films