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 $W$ 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.
Highlights
Surface roughening due to randomness is ubiquitous in nature, and a problem spanning many disciplines, e.g., in the propagation of wetting fronts in porous media, in the growth of bacterial colonies, and in atomic deposition during the manufacture of computer chips (Kardar et al 1986)
One can see that the transient characteristics of the spectra are strongly influenced by the slip length, which is controlled in the molecular dynamics (MD) indirectly by the solid-liquid interaction potential (Appendix C provides details on how this parameter, and the effective film thickness, are extracted from independent MD simulations for use in the Langevin model, see the caption of figure 2 for values)
We have investigated the dynamic capillary waves of both planar and annular liquid films at the nanoscale
Summary
Surface roughening due to randomness is ubiquitous in nature, and a problem spanning many disciplines, e.g., in the propagation of wetting fronts in porous media, in the growth of bacterial colonies, and in atomic deposition during the manufacture of computer chips (Kardar et al 1986). The motivation of this work is to understand the time-dependent nature of capillary wave spectra, S(q, t), i.e. the surface roughening process (i) for different types of film (e.g. planar or annular), (ii) with different physics (e.g. with or without liquid slip at the substrate), and (iii) without the limitations of the lubrication approach. The subject is both of fundamental interest and practical value: creating a single theoretical framework under which the time evolution of thermal capillary waves on films can be studied; and allowing prediction of.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
