Thermal Capillary Wave Growth and Surface Roughening of Nanoscale Liquid Films

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