  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.
