Mathematical modelling of droplets and bubbles on surfaces

In this thesis we focus on calculating the shape of small bubbles and droplets near surfaces, in regimes where intermolecular forces are significant. In the first part of this thesis we focus on vapour nanobubbles where we use classical density functional theory (DFT) to determine the interfacial free energy (the binding potential) of simple model fluids in contact with a planar surface. This is done by calculating sequences of constrained density profiles for varying amounts of vapour adsorbed between the wall and the bulk liquid. This allows us to determine multi-scale properties of fluids at interfaces, and thereby determine the structure and the thermodynamics of vapour adsorption at solvophobic interfaces and how these depend on the microscopic properties of the fluid. We then use the binding potentials obtained as an input to the interfacial Hamiltonian (IH) model and study the properties of vapour nanobubbles at equilibrium.