Thermal capillary wave growth and surface roughening of nanoscale liquid films

Abstract

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 this 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 increasing as a power law of time W ∼ t1/8 before saturation. However, the spectra of an annular film (with outer radius h0) are unbounded for dimensionless wavenumber qh0 < 1 due to the Rayleigh-Plateau instability.