Relaxation of Thermal Capillary Waves for Nanoscale Liquid Films on Anisotropic-slip Substrates

TL;DR

This study investigates how anisotropic slip on substrates affects the relaxation of thermal capillary waves in nanoscale liquid films, using molecular dynamics simulations and a Langevin model to reveal wave-direction dependent dynamics.

Contribution

It introduces a tensorial slip coefficient in the Langevin model to describe anisotropic slip effects, aligning well with MD simulation results.

Findings

Larger slip lengths accelerate wave correlation decay.

Wave correlations depend on wave direction on anisotropic-slip substrates.

The Langevin model accurately predicts MD simulation outcomes.

Abstract

The relaxation dynamics of thermal capillary waves for nanoscale liquid films on anisotropic-slip substrates are investigated, using both molecular dynamics (MD) simulations and a Langevin model. The anisotropy of slip on substrates is achieved using a specific lattice plane of a face-centred cubic lattice. This surface's anisotropy breaks the simple scalar proportionality between slip velocity and wall shear stress and requires the introduction of a slip-coefficient tensor. The Langevin equation can describe both the growth of capillary wave spectra and the relaxation of capillary wave correlations, with the former providing a time scale for the surface to reach thermal equilibrium. Temporal correlations of interfacial Fourier modes, measured at thermal equilibrium in MD, demonstrate that (i) larger slip lengths lead to a faster decay in wave correlations, and (ii) unlike on isotropic-slip substrates, the time correlations of waves on anisotropic-slip substrates are wave-direction dependent. These findings emerge naturally from the proposed Langevin equation, which becomes wave-direction dependent, agrees well with MD results, and allows to produce experimentally-verifiable predictions.