Binding potentials for vapour nanobubbles on surfaces using density functional theory

We calculate one-body density profiles of a simple model fluid in contact with a planar surface using density functional theory (DFT), in particular for the case where there is a vapour layer intruding between the wall and the bulk liquid. We apply the method of Hughes \emph{et al.}\ [J.\ Chem.\ Phys.\ {\bf 142}, 074702 (2015)] to calculate the density profiles for varying (specified) amounts of the vapour adsorbed at the wall. This is equivalent to varying the thickness $h$ of the vapour at the surface. From the resulting sequence of density profiles we calculate the thermodynamic grand potential as $h$ is varied and thereby determine the binding potential as a function of $h$. The binding potential obtained via this coarse-graining approach allows us to determine the disjoining pressure in the film and also to predict the shape of vapour nano-bubbles on the surface. Our microscopic DFT based approach captures information from length scales much smaller than some commonly used models in continuum mechanics.