  The effect of confining walls on the fluctuation of a nanoscale thin film's
free surface is studied using stochastic thin-film equations (STFEs). Two
canonical boundary conditions are employed to reveal the influence of the
confinement: (1) an imposed contact angle and (2) a pinned contact line. A
linear stability analysis provides the wave eigenmodes, after which
thermal-capillary-wave theory predicts the wave fluctuation amplitudes.
Molecular dynamics (MD) simulations are performed to test the predictions, and
a Langevin diffusion model is proposed to capture oscillations of the contact
lines observed in MD simulations. Good agreement between the theoretical
predictions and the MD simulation results is recovered, and it is discovered
that confinement can influence the entire film. Notably, a constraint on the
length scale of wave modes is found to affect fluctuation amplitudes from our
theoretical model, especially for 3D films. This opens up challenges and future
lines of inquiry.
