Thermal capillary wave growth and surface roughening of nanoscale liquid films

Y Zhang and JE Sprittles and DA Lockerby, JOURNAL OF FLUID MECHANICS, 915, A135 (2021).

DOI: 10.1017/jfm.2021.164

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 similar to 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.

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